Curriculum (France)

Mathematics — Grade 5

Imaginesis: printable math worksheets for this grade (France) — word problems with hints, answer keys and step-by-step solutions as PDF, also as a test in two to four groups (A–D).

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For a test or quiz: print in up to four groups (A–D) — same layout, different numbers and a different order of answer options in each group, one shared answer key.

5th grade mathematics according to the cycle 3 curriculum: numbers up to one billion, common divisors and multiples, fraction of a whole number, thousandths, decimal division, areas in cm², dm², and m², durations in seconds, and probability. Each concept is accompanied by exercise templates ready for printable worksheets.

What does a child learn in 5th grade mathematics?

In CM2, students work with nine-digit numbers, determine all divisors of a number and the common divisors or multiples of two numbers. They multiply a fraction by a whole number, go up to thousandths, perform mental calculations with decimal numbers (double, half, ×5, ×50), and set up decimal long division. They convert areas, calculate the area of squares and rectangles, know that a right angle measures 90°, measure durations in hours, minutes, and seconds, read pie charts, express probability as “a chances out of b”, and solve proportionality problems.

About the curriculum: the mathematics curriculum sets the learning objectives for each year of Cycle 2 (CP, CE1, CE2) and Cycle 3 (CM1, CM2, 6e), so that the end-of-year expectations are met. Each concept below therefore appears in the year specified by the curriculum itself. The complete list of objectives for this year, quoted verbatim, can be found in the section below.

Curriculum scope

CM2.NC (our numbering) · Teaching content · checked against the act

Numbers, calculation and problem solving

our translation · original wording (FR): Nombres, calcul et résolution de problèmes

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes
CM2.NC.1 (our numbering) · Teaching content · checked against the act

Know and use the relationships between place value units

our translation · original wording (FR): Connaître et utiliser les relations entre les unités de numération

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.1

Reading, writing, and comparing large numbers (we teach it in grade 3–6)
CM2.NC.2 (our numbering) · Teaching content · checked against the act

Know the written sequence and the spoken sequence of numbers up to 999 999 999

our translation · original wording (FR): Connaître la suite écrite et la suite orale des nombres jusqu’à 999 999 999

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.2

Reading, writing, and comparing large numbers (we teach it in grade 3–6)
CM2.NC.3 (our numbering) · Teaching content · checked against the act

Know and use various representations of a number and move from one to another

our translation · original wording (FR): Connaître et utiliser diverses représentations d’un nombre et passer de l’une à l’autre

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.3

Reading, writing, and comparing large numbers (we teach it in grade 3–6)
CM2.NC.4 (our numbering) · Teaching content · checked against the act

Know the value of digits according to their position in a number

our translation · original wording (FR): Connaître la valeur des chiffres en fonction de leur position dans un nombre

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.4

Reading, writing, and comparing large numbers (we teach it in grade 3–6)
CM2.NC.5 (our numbering) · Teaching content · checked against the act

Compare, bracket and place whole numbers between others using the symbols =, < and >

our translation · original wording (FR): Comparer, encadrer, intercaler des nombres entiers en utilisant les symboles =, < et >

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.5

Reading, writing, and comparing large numbers (we teach it in grade 3–6)
CM2.NC.6 (our numbering) · Teaching content · checked against the act

Order numbers in ascending or descending order

our translation · original wording (FR): Ordonner des nombres dans l’ordre croissant ou décroissant

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.6

Reading, writing, and comparing large numbers (we teach it in grade 3–6)
CM2.NC.7 (our numbering) · Teaching content · checked against the act

Placing numbers and locating points on a graduated half-line

our translation · original wording (FR): Placer des nombres et repérer des points sur une demi-droite graduée

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.7

Locating points on a number ray (we teach it in grade 1–5)
CM2.NC.8 (our numbering) · Teaching content · checked against the act

Determine whether a whole number less than or equal to 10 is a divisor of a given whole number, or whether a given whole number is a multiple of a whole number less than or equal to 10

our translation · original wording (FR): Déterminer si un nombre entier inférieur ou égal à 10 est un diviseur d’un nombre entier donné ou si un nombre entier donné est un multiple d’un nombre entier inférieur ou égal à 10

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.8

Finding the divisors and multiples of a number (we teach it in grade 3–10) · Using divisibility rules (we teach it in grade 4–7)
CM2.NC.9 (our numbering) · Teaching content · checked against the act

Determine divisors of a whole number less than or equal to 100

our translation · original wording (FR): Déterminer des diviseurs d’un nombre entier inférieur ou égal à 100

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.9

Finding the divisors and multiples of a number (we teach it in grade 3–10)
CM2.NC.10 (our numbering) · Teaching content · checked against the act

Determine all the divisors of an integer less than or equal to 30

our translation · original wording (FR): Déterminer tous les diviseurs d’un nombre entier inférieur ou égal à 30

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.10

Finding the divisors and multiples of a number (we teach it in grade 3–10)
CM2.NC.11 (our numbering) · Teaching content · checked against the act

Determine the common divisors of two integers less than or equal to 30

our translation · original wording (FR): Déterminer les diviseurs communs à deux nombres entiers inférieurs ou égaux à 30

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.11

Find the greatest common divisor (GCD) (we teach it in grade 5–9)
CM2.NC.12 (our numbering) · Teaching content · checked against the act

Determine common multiples of two whole numbers less than 15

our translation · original wording (FR): Déterminer des multiples communs à deux nombres entiers inférieurs à 15

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres entiers, objectif CM2.NC.12

Finding the least common multiple (LCM) (we teach it in grade 5)
CM2.NC.13 (our numbering) · Teaching content · checked against the act

Interpret, represent, write and read fractions

our translation · original wording (FR): Interpréter, représenter, écrire et lire des fractions

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.13

Understanding and calculating a fraction of a quantity (we teach it in grade 2–5)
CM2.NC.14 (our numbering) · Teaching content · checked against the act

Write a fraction greater than 1 as the sum of a whole number and a fraction less than 1

our translation · original wording (FR): Écrire une fraction supérieure à 1 comme la somme d’un entier et d’une fraction inférieure à 1

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.14

Converting from a Fraction to a Mixed Number (we teach it in grade 4–6)
CM2.NC.15 (our numbering) · Teaching content · checked against the act

Writing the sum of a whole number and a fraction less than 1 as a single fraction

our translation · original wording (FR): Écrire la somme d’un entier et d’une fraction inférieure à 1 comme une unique fraction

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.15

Converting from a Fraction to a Mixed Number (we teach it in grade 4–6)
CM2.NC.16 (our numbering) · Teaching content · checked against the act

Bracket a fraction between two consecutive whole numbers

our translation · original wording (FR): Encadrer une fraction entre deux nombres entiers consécutifs

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.16

Converting from a Fraction to a Mixed Number (we teach it in grade 4–6)
CM2.NC.17 (our numbering) · Teaching content · checked against the act

Locate a fraction, or the sum of a whole number and a fraction less than one, on a graduated number line

our translation · original wording (FR): Placer une fraction ou la somme d’un nombre entier et d’une fraction inférieure à un sur une demi-droite graduée

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.17

Reading a fraction on a number line (we teach it in grade 3–10)
CM2.NC.18 (our numbering) · Teaching content · checked against the act

Locate a point on a graduated half-line by a fraction or by the sum of a whole number and a fraction

our translation · original wording (FR): Repérer un point d’une demi-droite graduée par une fraction ou par la somme d’un nombre entier et d’une fraction

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.18

Reading a fraction on a number line (we teach it in grade 3–10)
CM2.NC.19 (our numbering) · Teaching content · checked against the act

Compare fractions

our translation · original wording (FR): Comparer des fractions

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.19

Comparing fractions with different denominators (we teach it in grade 4–10)
CM2.NC.20 (our numbering) · Teaching content · checked against the act

Adding and subtracting fractions

our translation · original wording (FR): Additionner et soustraire des fractions

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.20

Adding and subtracting fractions with the same denominator (we teach it in grade 2–5) · Adding and subtracting different fractions (we teach it in grade 5–10) · Putting fractions over a common denominator (we teach it in grade 4–6)
CM2.NC.21 (our numbering) · Teaching content · checked against the act

Calculate the product of an integer and a fraction

our translation · original wording (FR): Calculer le produit d’un entier et d’une fraction

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.21

Multiplying a fraction by a whole number (we teach it in grade 5–6)
CM2.NC.22 (our numbering) · Teaching content · checked against the act

Determine a fraction of a quantity or a magnitude

our translation · original wording (FR): Déterminer une fraction d’une quantité ou d’une grandeur

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les fractions, objectif CM2.NC.22

Calculating a fraction of a number (we teach it in grade 4–8)
CM2.NC.23 (our numbering) · Teaching content · checked against the act

Interpret, represent, write and read decimal fractions

our translation · original wording (FR): Interpréter, représenter, écrire et lire des fractions décimales

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.23

Writing a decimal number as a fraction (we teach it in grade 4–10) · Reading and writing decimal numbers (we teach it in grade 4–6)
CM2.NC.24 (our numbering) · Teaching content · checked against the act

Know and use the relationships between simple units, tenths, hundredths and thousandths

our translation · original wording (FR): Connaître et utiliser les relations entre unités simples, dixièmes, centièmes et millièmes

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.24

Reading and writing decimal numbers (we teach it in grade 4–6)
CM2.NC.25 (our numbering) · Teaching content · checked against the act

Place a decimal fraction on a graduated half-line and locate a point on a graduated half-line by a decimal fraction

our translation · original wording (FR): Placer une fraction décimale sur une demi-droite graduée et repérer un point d’une demi-droite graduée par une fraction décimale

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.25

Reading a decimal number on a number line (we teach it in grade 4–7)
CM2.NC.26 (our numbering) · Teaching content · checked against the act

Write a decimal fraction greater than 1 as the sum of a whole number and a decimal fraction less than 1

our translation · original wording (FR): Écrire une fraction décimale supérieure à 1 comme la somme d’un nombre entier et d’une fraction décimale inférieure à 1

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.26

Converting from a Fraction to a Mixed Number (we teach it in grade 4–6)
CM2.NC.27 (our numbering) · Teaching content · checked against the act

Write a decimal fraction greater than 1 as the sum of a whole number and decimal fractions having a numerator less than 10

our translation · original wording (FR): Écrire une fraction décimale supérieure à 1 comme la somme d’un nombre entier et de fractions décimales ayant un numérateur inférieur à 10

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.27

Reading and writing decimal numbers (we teach it in grade 4–6)
CM2.NC.28 (our numbering) · Teaching content · checked against the act

Compare, bracket and place decimal fractions between two given numbers using the symbols =, < and >

our translation · original wording (FR): Comparer, encadrer, intercaler des fractions décimales en utilisant les symboles =, < et >

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.28

Comparing decimal numbers (we teach it in grade 4–6)
CM2.NC.29 (our numbering) · Teaching content · checked against the act

Order decimal fractions in ascending or descending order

our translation · original wording (FR): Ordonner des fractions décimales dans l’ordre croissant ou décroissant

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.29

Comparing decimal numbers (we teach it in grade 4–6)
CM2.NC.30 (our numbering) · Teaching content · checked against the act

Converting between a fraction-form writing of a decimal fraction or a sum of decimal fractions and a decimal-point (comma) writing, and vice versa

our translation · original wording (FR): Passer d’une écriture sous forme d’une fraction décimale ou de la somme de fractions décimales à une écriture à virgule et réciproquement

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.30

Writing a decimal number as a fraction (we teach it in grade 4–10) · Writing a fraction in decimal form (we teach it in grade 4–10)
CM2.NC.31 (our numbering) · Teaching content · checked against the act

Interpret, represent, write and read decimal numbers (decimal notation)

our translation · original wording (FR): Interpréter, représenter, écrire et lire des nombres décimaux (écriture à virgule)

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.31

Reading and writing decimal numbers (we teach it in grade 4–6)
CM2.NC.32 (our numbering) · Teaching content · checked against the act

Place a decimal number written with a decimal comma on a graduated half-line, and identify a point on a graduated half-line by a number written with a decimal comma

our translation · original wording (FR): Placer un nombre décimal en écriture à virgule sur une demi-droite graduée et repérer un point d’une demi-droite graduée par un nombre en écriture à virgule

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.32

Reading a decimal number on a number line (we teach it in grade 4–7)
CM2.NC.33 (our numbering) · Teaching content · checked against the act

Knowing how to give the integer part and the rounding to the nearest whole number of a decimal number

our translation · original wording (FR): Savoir donner la partie entière et l’arrondi à l’entier d’un nombre décimal

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.33

Rounding a decimal number to the nearest tenth or hundredth (we teach it in grade 4–10)
CM2.NC.34 (our numbering) · Teaching content · checked against the act

Compare, bound, insert, order in ascending or descending order decimal numbers given in decimal notation using the symbols =, < and >

our translation · original wording (FR): Comparer, encadrer, intercaler, ordonner par ordre croissant ou décroissant des nombres décimaux donnés par leur écriture à virgule en utilisant les symboles =, < et >

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les nombres décimaux, objectif CM2.NC.34

Comparing decimal numbers (we teach it in grade 4–6)
CM2.NC.35 (our numbering) · Teaching content · checked against the act

Know common number facts with whole numbers

our translation · original wording (FR): Connaître des faits numériques usuels avec des entiers

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Mémoriser des faits numériques, objectif CM2.NC.35

Multiplication tables up to 100 (we teach it in grade 1–5) · Calculating cleverly with operations (we teach it in grade 3–5)
CM2.NC.36 (our numbering) · Teaching content · checked against the act

Know half of the odd numbers up to 15

our translation · original wording (FR): Connaître la moitié des nombres impairs jusqu’à 15

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Mémoriser des faits numériques, objectif CM2.NC.36

Long division with decimals (we teach it in grade 5–7)
CM2.NC.37 (our numbering) · Teaching content · checked against the act

Know some relationships between common fractions

our translation · original wording (FR): Connaître quelques relations entre des fractions usuelles

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Mémoriser des faits numériques, objectif CM2.NC.37

Write a fraction with a larger denominator (we teach it in grade 3–6) · Simplifying a fraction (we teach it in grade 5–10)
CM2.NC.38 (our numbering) · Teaching content · checked against the act

Know the decimal notation of common fractions

our translation · original wording (FR): Connaître l’écriture décimale de fractions usuelles

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Mémoriser des faits numériques, objectif CM2.NC.38

Writing a fraction in decimal form (we teach it in grade 4–10)
CM2.NC.39 (our numbering) · Teaching content · checked against the act

Adding or subtracting a whole number to or from a decimal number when there is no carrying or borrowing

our translation · original wording (FR): Ajouter ou soustraire un nombre entier à un nombre décimal lorsqu’il n’y a pas de retenue

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Utiliser ses connaissances en numération pour calculer mentalement, objectif CM2.NC.39

Adding and Subtracting Decimals (we teach it in grade 4–7)
CM2.NC.40 (our numbering) · Teaching content · checked against the act

Adding a whole number to a decimal number when there is a carry-over

our translation · original wording (FR): Ajouter un nombre entier à un nombre décimal lorsqu’il y a une retenue

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Utiliser ses connaissances en numération pour calculer mentalement, objectif CM2.NC.40

Adding and Subtracting Decimals (we teach it in grade 4–7)
CM2.NC.41 (our numbering) · Teaching content · checked against the act

Multiplier un nombre décimal par 10, 100 ou 1 000

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Utiliser ses connaissances en numération pour calculer mentalement, objectif CM2.NC.41

Multiplying and dividing a decimal by 10, 100, or 1,000 (we teach it in grade 4–6)
CM2.NC.42 (our numbering) · Teaching content · checked against the act

Dividing a decimal number by 10, 100 or 1,000

our translation · original wording (FR): Diviser un nombre décimal par 10, 100 ou 1 000

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Utiliser ses connaissances en numération pour calculer mentalement, objectif CM2.NC.42

Multiplying and dividing a decimal by 10, 100, or 1,000 (we teach it in grade 4–6)
CM2.NC.43 (our numbering) · Teaching content · checked against the act

Add two decimal numbers less than 10, written with at most one digit after the decimal point

our translation · original wording (FR): Ajouter deux nombres décimaux inférieurs à 10, s’écrivant avec au plus un chiffre après la virgule

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.43

Adding and Subtracting Decimals (we teach it in grade 4–7)
CM2.NC.44 (our numbering) · Teaching content · checked against the act

Add or subtract 8, 9, 18, 19, 28, 29, …, 98 or 99 to a number

our translation · original wording (FR): Ajouter ou soustraire 8, 9, 18, 19, 28, 29, …, 98 ou 99 à un nombre

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.44

Calculating cleverly with operations (we teach it in grade 3–5)
CM2.NC.45 (our numbering) · Teaching content · checked against the act

Multiply a whole number less than 10 of tens, hundreds or thousands by a whole number less than 10 of tens, hundreds or thousands

our translation · original wording (FR): Multiplier un nombre entier, inférieur à 10, de dizaines, de centaines ou de milliers par un nombre entier, inférieur à 10, de dizaines, de centaines ou de milliers

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.45

Multiplying a digit by a multiple of 10 (we teach it in grade 3–5) · Calculating cleverly with operations (we teach it in grade 3–5)
CM2.NC.46 (our numbering) · Teaching content · checked against the act

Use the distributive property of multiplication over addition in simple cases

our translation · original wording (FR): Utiliser la distributivité de la multiplication par rapport à l’addition dans des cas simples

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.46

Calculating cleverly with operations (we teach it in grade 3–5)
CM2.NC.47 (our numbering) · Teaching content · checked against the act

Calculate the double of a decimal number in simple cases

our translation · original wording (FR): Calculer le double d’un nombre décimal dans des cas simples

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.47

Multiplying decimal numbers (we teach it in grade 4–7)
CM2.NC.48 (our numbering) · Teaching content · checked against the act

Calculate half of a decimal number in simple cases

our translation · original wording (FR): Calculer la moitié d’un nombre décimal dans des cas simples

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.48

Long division with decimals (we teach it in grade 5–7)
CM2.NC.49 (our numbering) · Teaching content · checked against the act

Divide a whole number by 4 or by 8

our translation · original wording (FR): Diviser un nombre entier par 4 ou par 8

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.49

Calculating cleverly with operations (we teach it in grade 3–5)
CM2.NC.50 (our numbering) · Teaching content · checked against the act

Multiply a decimal number by 5

our translation · original wording (FR): Multiplier un nombre décimal par 5

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.50

Multiplying decimal numbers (we teach it in grade 4–7)
CM2.NC.51 (our numbering) · Teaching content · checked against the act

Multiply a decimal number by 50

our translation · original wording (FR): Multiplier un nombre décimal par 50

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Apprendre des procédures de calcul mental, objectif CM2.NC.51

Multiplying decimal numbers (we teach it in grade 4–7)
CM2.NC.52 (our numbering) · Teaching content · checked against the act

Estimate the result of an operation

our translation · original wording (FR): Estimer le résultat d’une opération

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les quatre opérations, objectif CM2.NC.52

Estimating the result of an addition (we teach it in grade 4–10)
CM2.NC.53 (our numbering) · Teaching content · checked against the act

Being able to carry out a calculation containing one or two pairs of brackets

our translation · original wording (FR): Savoir réaliser un calcul contenant une ou deux paires de parenthèses

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les quatre opérations, objectif CM2.NC.53

Calculating with one or two pairs of parentheses (we teach it in grade 4–8)
CM2.NC.54 (our numbering) · Teaching content · checked against the act

Set up and carry out the multiplication of a decimal number by a whole number

our translation · original wording (FR): Poser et effectuer la multiplication d’un nombre décimal par un nombre entier

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les quatre opérations, objectif CM2.NC.54

Multiplying decimal numbers (we teach it in grade 4–7)
CM2.NC.55 (our numbering) · Teaching content · checked against the act

Pose and carry out decimal divisions with a whole-number dividend and a one-digit divisor

our translation · original wording (FR): Poser et effectuer des divisions décimales avec un dividende entier et un diviseur à un chiffre

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les quatre opérations, objectif CM2.NC.55

Long division with decimals (we teach it in grade 5–7) · Long division by a single-digit number (we teach it in grade 4–5)
CM2.NC.56 (our numbering) · Teaching content · checked against the act

Set up and carry out decimal divisions with a decimal dividend and a one-digit divisor

our translation · original wording (FR): Poser et effectuer des divisions décimales avec un dividende décimal et un diviseur à un chiffre

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Les quatre opérations, objectif CM2.NC.56

Long division with decimals (we teach it in grade 5–7)
CM2.NC.57 (our numbering) · Teaching content · checked against the act

Solve additive problems in one or more steps

our translation · original wording (FR): Résoudre des problèmes additifs en une ou plusieurs étapes

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, La résolution de problèmes, objectif CM2.NC.57

Solving complex multi-step problems (we teach it in grade 1–6)
CM2.NC.58 (our numbering) · Teaching content · checked against the act

Solve one-step multiplicative problems of the "part-whole" type

our translation · original wording (FR): Résoudre des problèmes multiplicatifs de type « parties-tout » en une étape

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, La résolution de problèmes, objectif CM2.NC.58

Solving complex multi-step problems (we teach it in grade 1–6)
CM2.NC.59 (our numbering) · Teaching content · checked against the act

Solve mixed multi-step problems

our translation · original wording (FR): Résoudre des problèmes mixtes en plusieurs étapes

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, La résolution de problèmes, objectif CM2.NC.59

Solving complex multi-step problems (we teach it in grade 1–6)
CM2.NC.60 (our numbering) · Teaching content · checked against the act

Solve multiplicative comparison problems

our translation · original wording (FR): Résoudre des problèmes de comparaison multiplicative

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, La résolution de problèmes, objectif CM2.NC.60

Comparing numbers: difference or multiplication (we teach it in grade 3–10)
CM2.NC.61 (our numbering) · Teaching content · checked against the act

Solve counting problems

our translation · original wording (FR): Résoudre des problèmes de dénombrement

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, La résolution de problèmes, objectif CM2.NC.61

Counting all possible combinations (we teach it in grade 3–5)
CM2.NC.62 (our numbering) · Teaching content · checked against the act

Solve optimization problems

our translation · original wording (FR): Résoudre des problèmes d’optimisation

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, La résolution de problèmes, objectif CM2.NC.62

Solving complex multi-step problems (we teach it in grade 1–6)
CM2.NC.63 (our numbering) · Teaching content · checked against the act

Solve problems preparing for the use of algorithms

our translation · original wording (FR): Résoudre des problèmes préparant à l’utilisation d’algorithmes

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, La résolution de problèmes, objectif CM2.NC.63
CM2.NC.64 (our numbering) · Teaching content · checked against the act

Find the missing number in an equation with a gap

our translation · original wording (FR): Trouver le nombre manquant dans une égalité à trous

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Algèbre, objectif CM2.NC.64

Finding the missing number in an equality (we teach it in grade 1–5)
CM2.NC.65 (our numbering) · Teaching content · checked against the act

Solve algebraic problems

our translation · original wording (FR): Résoudre des problèmes algébriques

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Algèbre, objectif CM2.NC.65

Finding an unknown value in a problem (we teach it in grade 4–8)
CM2.NC.66 (our numbering) · Teaching content · checked against the act

Execute or produce a calculation programme

our translation · original wording (FR): Exécuter ou produire un programme de calcul

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Algèbre, objectif CM2.NC.66

Complete a table according to a calculation rule (we teach it in grade 4–8)
CM2.NC.67 (our numbering) · Teaching content · checked against the act

Identify and formulate a calculation rule to continue a sequence of numbers

our translation · original wording (FR): Identifier et formuler une règle de calcul pour poursuivre une suite de nombres

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Algèbre, objectif CM2.NC.67

Find the rule of a sequence and continue it (we teach it in grade 4–6)
CM2.NC.68 (our numbering) · Teaching content · checked against the act

Identify patterns and continue a growing sequence of patterns

our translation · original wording (FR): Identifier des régularités et poursuivre une suite de motifs évolutive

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Algèbre, objectif CM2.NC.68

Find the rule of a sequence and continue it (we teach it in grade 4–6)
CM2.NC.69 (our numbering) · Teaching content · checked against the act

Find the number of elements for a given step in a growing pattern sequence

our translation · original wording (FR): Trouver le nombre d’éléments pour une étape donnée dans une suite de motifs évolutive

Programme de mathématiques du cycle 3, CM2, Nombres, calcul et résolution de problèmes, Algèbre, objectif CM2.NC.69

Find the rule of a sequence and continue it (we teach it in grade 4–6)
CM2.GM (our numbering) · Teaching content · checked against the act

Measurement and quantities

our translation · original wording (FR): Grandeurs et mesures

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures
CM2.GM.1 (our numbering) · Teaching content · checked against the act

Compare the areas of different plane figures

our translation · original wording (FR): Comparer les aires de différentes figures planes

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les aires, objectif CM2.GM.1

Measuring areas by tiling with squares (we teach it in grade 4–5)
CM2.GM.2 (our numbering) · Teaching content · checked against the act

Determine areas

our translation · original wording (FR): Déterminer des aires

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les aires, objectif CM2.GM.2

Area of a rectangle and calculating a missing side (we teach it in grade 5–6) · Measuring areas by tiling with squares (we teach it in grade 4–5)
CM2.GM.3 (our numbering) · Teaching content · checked against the act

Know and use the units square centimetre, square decimetre and square metre to express areas

our translation · original wording (FR): Connaître et utiliser les unités centimètre carré, décimètre carré et mètre carré pour exprimer des aires

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les aires, objectif CM2.GM.3

Converting area and volume measurements (we teach it in grade 5–10)
CM2.GM.4 (our numbering) · Teaching content · checked against the act

Convert areas between different units

our translation · original wording (FR): Convertir des aires entre différentes unités

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les aires, objectif CM2.GM.4

Converting area and volume measurements (we teach it in grade 5–10)
CM2.GM.5 (our numbering) · Teaching content · checked against the act

Determine the area of a square or a rectangle

our translation · original wording (FR): Déterminer l’aire d’un carré ou d’un rectangle

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les aires, objectif CM2.GM.5

Area of a rectangle and calculating a missing side (we teach it in grade 5–6)
CM2.GM.6 (our numbering) · Teaching content · checked against the act

Use the specific vocabulary associated with angles

our translation · original wording (FR): Utiliser le lexique spécifique associé aux angles

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les angles, objectif CM2.GM.6

Identify acute, right, and obtuse angles (we teach it in grade 2–6)
CM2.GM.7 (our numbering) · Teaching content · checked against the act

Understand and use the notations for angles

our translation · original wording (FR): Comprendre et utiliser les notations des angles

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les angles, objectif CM2.GM.7

Identify acute, right, and obtuse angles (we teach it in grade 2–6)
CM2.GM.8 (our numbering) · Teaching content · checked against the act

Compare angles

our translation · original wording (FR): Comparer des angles

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les angles, objectif CM2.GM.8

Identify acute, right, and obtuse angles (we teach it in grade 2–6)
CM2.GM.9 (our numbering) · Teaching content · checked against the act

Construct an angle equal to the sum of two given angles or an angle that is a multiple of a given angle

our translation · original wording (FR): Construire un angle égal à la somme de deux angles donnés ou un angle multiple d’un angle donné

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les angles, objectif CM2.GM.9
CM2.GM.10 (our numbering) · Teaching content · checked against the act

Construct half of a given angle by folding

our translation · original wording (FR): Construire par pliage la moitié d’un angle donné

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les angles, objectif CM2.GM.10
CM2.GM.11 (our numbering) · Teaching content · checked against the act

Know that a right angle measures 90°

our translation · original wording (FR): Savoir qu’un angle droit mesure 90°

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Les angles, objectif CM2.GM.11

Identify acute, right, and obtuse angles (we teach it in grade 2–6)
CM2.GM.12 (our numbering) · Teaching content · checked against the act

Read the time on an analogue clock

our translation · original wording (FR): Lire l’heure sur une horloge à aiguilles

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Le repérage dans le temps et les durées, objectif CM2.GM.12

Reading the exact time on an analog clock (we teach it in grade 1–5)
CM2.GM.13 (our numbering) · Teaching content · checked against the act

Setting the hands of a clock to show a given time in hours, minutes and seconds

our translation · original wording (FR): Positionner les aiguilles d’une horloge correspondant à une heure donnée en heure, minute et seconde

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Le repérage dans le temps et les durées, objectif CM2.GM.13

Reading the exact time on an analog clock (we teach it in grade 1–5) · Calculating durations: hours, minutes, and seconds (we teach it in grade 3–6)
CM2.GM.14 (our numbering) · Teaching content · checked against the act

Compare and measure elapsed times between two instants shown on a clock (instants and durations are expressed in hours, minutes and seconds)

our translation · original wording (FR): Comparer et mesurer des durées écoulées entre deux instants affichés sur une horloge (instants et durées sont exprimés en heure, minute et seconde)

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Le repérage dans le temps et les durées, objectif CM2.GM.14

Calculating durations: hours, minutes, and seconds (we teach it in grade 3–6)
CM2.GM.15 (our numbering) · Teaching content · checked against the act

Solve one- or multi-step problems involving durations

our translation · original wording (FR): Résoudre des problèmes à une ou plusieurs étapes impliquant des durées

Programme de mathématiques du cycle 3, CM2, Grandeurs et mesures, Le repérage dans le temps et les durées, objectif CM2.GM.15

Calculating durations: hours, minutes, and seconds (we teach it in grade 3–6)
CM2.EG (our numbering) · Teaching content · checked against the act

Space and geometry

our translation · original wording (FR): Espace et géométrie

Programme de mathématiques du cycle 3, CM2, Espace et géométrie
CM2.EG.1 (our numbering) · Teaching content · checked against the act

Use the appropriate geometric vocabulary in the context of learning the corresponding concepts

our translation · original wording (FR): Utiliser le vocabulaire géométrique approprié dans le contexte d’apprentissage des notions correspondantes

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.1

Classifying triangles by their sides and angles (we teach it in grade 4–6) · Naming quadrilaterals according to their properties (we teach it in grade 3–7)
CM2.EG.2 (our numbering) · Teaching content · checked against the act

Use the common geometric tools: ruler, graduated ruler, set square and compass

our translation · original wording (FR): Utiliser les outils géométriques usuels : règle, règle graduée, équerre et compas

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.2
CM2.EG.3 (our numbering) · Teaching content · checked against the act

Know the usual notations and codes used in geometry

our translation · original wording (FR): Connaître les notations et les codes usuels utilisés en géométrie

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.3

Parallel and Perpendicular Segments on a Grid (we teach it in grade 2–5) · Identify acute, right, and obtuse angles (we teach it in grade 2–6)
CM2.EG.4 (our numbering) · Teaching content · checked against the act

Recognise and use the notion of perpendicularity

our translation · original wording (FR): Reconnaître et utiliser la notion de perpendicularité

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.4

Parallel and Perpendicular Segments on a Grid (we teach it in grade 2–5)
CM2.EG.5 (our numbering) · Teaching content · checked against the act

Recognise and use the concept of parallelism

our translation · original wording (FR): Reconnaître et utiliser la notion de parallélisme

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.5

Parallel and Perpendicular Segments on a Grid (we teach it in grade 2–5)
CM2.EG.6 (our numbering) · Teaching content · checked against the act

Describe and recognise a circle and a disc as a set of points characterised by their distance from a given point

our translation · original wording (FR): Décrire et reconnaître un cercle et un disque comme un ensemble de points caractérisés par leur distance à un point donné

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.6

Calculate the radius and diameter of a circle (we teach it in grade 4–6)
CM2.EG.7 (our numbering) · Teaching content · checked against the act

Recognise and name the following figures by relying on their definition: triangle, right-angled triangle, isosceles triangle, equilateral triangle, quadrilateral, square, rectangle, rhombus, trapezium, right-angled trapezium, pentagon and hexagon

our translation · original wording (FR): Reconnaître et nommer les figures suivantes en s’appuyant sur leur définition : triangle, triangle rectangle, triangle isocèle, triangle équilatéral, quadrilatère, carré, rectangle, losange, trapèze, trapèze rectangle, pentagone et hexagone

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.7

Classifying triangles by their sides and angles (we teach it in grade 4–6) · Naming quadrilaterals according to their properties (we teach it in grade 3–7)
CM2.EG.8 (our numbering) · Teaching content · checked against the act

Know the properties of parallelism of opposite sides, and of equal lengths and angles, for common figures: right triangle, isosceles triangle, equilateral triangle, square, rectangle, rhombus, trapezium and right trapezium

our translation · original wording (FR): Connaître les propriétés de parallélisme des côtés opposés, des égalités de longueurs et d’angles pour les figures usuelles : triangle rectangle, triangle isocèle, triangle équilatéral, carré, rectangle, losange, trapèze et trapèze rectangle

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.8

Naming quadrilaterals according to their properties (we teach it in grade 3–7) · Classifying triangles by their sides and angles (we teach it in grade 4–6)
CM2.EG.9 (our numbering) · Teaching content · checked against the act

Reproduce or construct a square, a rectangle, a triangle, a right-angled triangle or a circle, or assemblies of these figures, on any medium (squared, dotted or plain paper), using a graduated ruler, a set square or a compass.

our translation · original wording (FR): Reproduire ou construire un carré, un rectangle, un triangle, un triangle rectangle ou un cercle ou des assemblages de ces figures sur tout support (papier quadrillé, pointé ou uni), avec une règle graduée, une équerre ou un compas.

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.9
CM2.EG.10 (our numbering) · Teaching content · checked against the act

Construct a geometric figure composed of segments, lines, common polygons and circles

our translation · original wording (FR): Construire une figure géométrique composée de segments, de droites, de polygones usuels et de cercles

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.10
CM2.EG.11 (our numbering) · Teaching content · checked against the act

Develop a construction program

our translation · original wording (FR): Élaborer un programme de construction

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.11
CM2.EG.12 (our numbering) · Teaching content · checked against the act

Construct, on squared paper, the figure symmetrical to a given figure with respect to a vertical, horizontal or diagonal line of the grid

our translation · original wording (FR): Construire, sur papier quadrillé, la figure symétrique d’une figure donnée par rapport à une droite verticale, horizontale ou une diagonale du quadrillage

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, La géométrie plane, objectif CM2.EG.12

Reflection of a point across a line (we teach it in grade 3–6)
CM2.EG.13 (our numbering) · Teaching content · checked against the act

Name a cube, a sphere, a cuboid, a cone, a pyramid, a cylinder or a right prism

our translation · original wording (FR): Nommer un cube, une boule, un pavé, un cône, une pyramide, un cylindre ou un prisme droit

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Les solides, objectif CM2.EG.13

Recognizing and naming common solids (we teach it in grade 4–8)
CM2.EG.14 (our numbering) · Teaching content · checked against the act

Describe a cube, a cuboid, a pyramid or a right prism by referring to properties and using appropriate vocabulary

our translation · original wording (FR): Décrire un cube, un pavé, une pyramide ou un prisme droit en faisant référence à des propriétés et en utilisant le vocabulaire approprié

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Les solides, objectif CM2.EG.14

Prisms and pyramids: faces, vertices and edges (we teach it in grade 4–5)
CM2.EG.15 (our numbering) · Teaching content · checked against the act

Recognise a net of a cube

our translation · original wording (FR): Reconnaître un patron d’un cube

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Les solides, objectif CM2.EG.15

Recognizing a net of a cube (we teach it in grade 4–7)
CM2.EG.16 (our numbering) · Teaching content · checked against the act

Construct a net of a cube

our translation · original wording (FR): Construire un patron d’un cube

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Les solides, objectif CM2.EG.16

Recognizing a net of a cube (we teach it in grade 4–7)
CM2.EG.17 (our numbering) · Teaching content · checked against the act

Recognize a net of a rectangular prism

our translation · original wording (FR): Reconnaître un patron d’un pavé

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Les solides, objectif CM2.EG.17

Recognizing a net of a cube (we teach it in grade 4–7)
CM2.EG.18 (our numbering) · Teaching content · checked against the act

Know and use the vocabulary related to movements

our translation · original wording (FR): Connaître et utiliser le vocabulaire lié aux déplacements

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Déplacements dans l’espace, objectif CM2.EG.18
CM2.EG.19 (our numbering) · Teaching content · checked against the act

Understand, use and produce a sequence of instructions that describe a movement using precise spatial vocabulary

our translation · original wording (FR): Comprendre, utiliser et produire une suite d’instructions qui décrivent un déplacement en utilisant un vocabulaire spatial précis

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Déplacements dans l’espace, objectif CM2.EG.19
CM2.EG.20 (our numbering) · Teaching content · checked against the act

Solve problems involving assemblies of cubes

our translation · original wording (FR): Résoudre des problèmes portant sur des assemblages de cubes

Programme de mathématiques du cycle 3, CM2, Espace et géométrie, Déplacements dans l’espace, objectif CM2.EG.20
CM2.OGD (our numbering) · Teaching content · checked against the act

Organisation and management of data

our translation · original wording (FR): Organisation et gestion de données

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données
CM2.OGD.1 (our numbering) · Teaching content · checked against the act

Collect data and produce a table, a bar chart or a set of points on a coordinate plane to present the collected data

our translation · original wording (FR): Recueillir des données et produire un tableau, un diagramme en barres ou un ensemble de points dans un repère pour présenter des données recueillies

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, objectif CM2.OGD.1

Organizing data in a table (we teach it in grade 1–6)
CM2.OGD.2 (our numbering) · Teaching content · checked against the act

Read and interpret data from a table, a bar chart, a pie chart or a line graph

our translation · original wording (FR): Lire et interpréter les données d’un tableau, d’un diagramme en barres, d’un diagramme circulaire ou d’une courbe

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, objectif CM2.OGD.2

Comparing data in a bar chart (we teach it in grade 4–11)
CM2.OGD.3 (our numbering) · Teaching content · checked against the act

Solve one- or two-step problems using data from a table, a bar chart, a pie chart or a line graph

our translation · original wording (FR): Résoudre des problèmes en une ou deux étapes en utilisant les données d’un tableau, d’un diagramme en barres, d’un diagramme circulaire ou d’une courbe

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, objectif CM2.OGD.3

Comparing data in a bar chart (we teach it in grade 4–11)
CM2.OGD.4 (our numbering) · Teaching content · checked against the act

Identify all possible outcomes in a simple random experiment

our translation · original wording (FR): Identifier toutes les issues possibles lors d’une expérience aléatoire simple

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, Les probabilités, objectif CM2.OGD.4

Counting all possible combinations (we teach it in grade 3–5)
CM2.OGD.5 (our numbering) · Teaching content · checked against the act

Identify all the outcomes that realise an event in a simple random experiment

our translation · original wording (FR): Identifier toutes les issues réalisant un évènement dans une expérience aléatoire simple

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, Les probabilités, objectif CM2.OGD.5

Counting all possible combinations (we teach it in grade 3–5)
CM2.OGD.6 (our numbering) · Teaching content · checked against the act

In a situation of equiprobability, in a simple random experiment, express the probability of an event in the form “a chances out of b”

our translation · original wording (FR): Dans une situation d’équiprobabilité, lors d’une expérience aléatoire simple, exprimer la probabilité d’un évènement sous la forme « a chances sur b »

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, Les probabilités, objectif CM2.OGD.6

Expressing a probability as "chances in" (we teach it in grade 5–10)
CM2.OGD.7 (our numbering) · Teaching content · checked against the act

Compare probabilities in simple cases

our translation · original wording (FR): Comparer des probabilités dans des cas simples

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, Les probabilités, objectif CM2.OGD.7

Comparing chances in simple situations (we teach it in grade 4–5)
CM2.OGD.8 (our numbering) · Teaching content · checked against the act

Understand the notion of independence when repeating the same random experiment

our translation · original wording (FR): Comprendre la notion d’indépendance lors de la répétition de la même expérience aléatoire

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, Les probabilités, objectif CM2.OGD.8
CM2.OGD.9 (our numbering) · Teaching content · checked against the act

In situations of equal likelihood, list all possible outcomes of a two-stage random experiment in a table or a tree diagram in order to determine probabilities

our translation · original wording (FR): Dans des situations d’équiprobabilité, recenser toutes les issues possibles d’une expérience aléatoire en deux étapes dans un tableau ou dans un arbre afin de déterminer des probabilités

Programme de mathématiques du cycle 3, CM2, Organisation et gestion de données, Les probabilités, objectif CM2.OGD.9

Counting all possible combinations (we teach it in grade 3–5)
CM2.P (our numbering) · Teaching content · checked against the act

Proportionality

our translation · original wording (FR): La proportionnalité

Programme de mathématiques du cycle 3, CM2, La proportionnalité
CM2.P.1 (our numbering) · Teaching content · checked against the act

Identify a situation of proportionality

our translation · original wording (FR): Identifier une situation de proportionnalité

Programme de mathématiques du cycle 3, CM2, La proportionnalité, objectif CM2.P.1

Calculate the value for a single object (we teach it in grade 4–7)
CM2.P.2 (our numbering) · Teaching content · checked against the act

Be able to solve a proportionality problem

our translation · original wording (FR): Savoir résoudre un problème de proportionnalité

Programme de mathématiques du cycle 3, CM2, La proportionnalité, objectif CM2.P.2

Finding a missing value in a proportion (we teach it in grade 4–8) · Calculate the value for a single object (we teach it in grade 4–7)

Skills step by step

Measuring areas by tiling with squares

The student learns to determine and compare the area of figures by covering them with unit squares, notably in square centimetres.

Curriculum point CM1.GM.20 (our numbering) Compare the areas of different plane figures (our translation)
Curriculum point CM1.GM.21 (our numbering) Determine areas (our translation)
Curriculum point CM1.GM.22 (our numbering) Know and use square centimetres to express areas (our translation)
Curriculum point CM2.GM.1 (our numbering) Compare the areas of different plane figures (our translation)
Curriculum point CM2.GM.2 (our numbering) Determine areas (our translation)

In grade 5 (CM2), to determine or compare the area of plane figures, pupils learn to measure a surface using a regular tiling made of unit squares or square centimetres. They practise quantifying the space occupied by counting the tiles of a rectangle or of a surface formed by several rectangles, but also relating this total to the side lengths in order to find a missing length.

A common confusion among pupils is mixing up perimeter and area by counting around the outline of figures rather than the number of interior tiles. Errors also appear when the reference unit changes, for example if a given tile covers two squares of the grid, or when an incomplete surface must be estimated without recounting the same squares twice.

In written work, pupils work with gridded representations through very concrete instructions:

count how many tiles cover a figure, or determine how many are missing to complete it;
compare two surfaces to calculate by how many tiles one area is larger than another;
draw a rectangle of a given area, or calculate the length of a side from the total area.

Create a worksheet for this skill Multiple-choice test

Task types: Area on a grid: how many squares cover the shape? (grade 2–3) · Rectangle area: how many squares cover it? (grade 3–4) · Area and one side: how long is the other (grade 3–4) · Area by tiling: choose the correct answer (grade 3–4) · Area by tiling: true or false (grade 3–4) · Area with tiles: how many two-square tiles? (grade 2–4) · Area: correct someone else's answer (grade 2–4) · Draw a rectangle with the given area (grade 2–4) · Area of a shape made of two rectangles (grade 3–4) · Area of two shapes: how much bigger is one? (grade 3–4) · Area with tiles: how many tiles are still missing? (grade 3–4)

Finding the missing number in an equality

In CM2 (the last year of primary school), pupils learn to find the missing number in an addition or a subtraction in order to restore the balance of an equality.

Curriculum point CM1.NC.60 (our numbering) Find the missing number in an equation with a gap (our translation)
Curriculum point CM2.NC.64 (our numbering) Find the missing number in an equation with a gap (our translation)
Curriculum point CP.NC.15 (our numbering) Understand and use the symbols "+", "-" and "=". (our translation)
Curriculum point CP.NC.23 (our numbering) Finding the complement of a number to the next ten. (our translation)

In CM2 (the final year of primary school), pupils consolidate their understanding of the relationship between addition and subtraction by learning to find the missing number in an equation with a blank. It is no longer only a matter of calculating a result placed after the "=" sign, but of working with calculations where the unknown, represented by a box, can be at the beginning, in the middle, or within a sum of three numbers.

The most common mistake is to apply the displayed operation mechanically without analysing the structure of the equality. For example, faced with a subtraction where the box stands for the starting number, pupils often subtract the result from the known term instead of adding them, confusing the search for the whole with the search for a part.

In practice, exercises appear as equations to be completed directly, but also in visual form, such as a balance in equilibrium from which the mass of a hidden block must be deduced. Activities also ask pupils to determine how much to add to make two quantities equal, to find what number has been taken away from a term, or to fill in two boxes one after the other.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Break apart a number within 10 (grade 1) · Break apart a number within 10: choose the result (grade 1) · Break apart a number within 10: true or false (grade 1) · Equation with a box: choose the missing number (grade 3) · Missing addend (box equation) (grade 3) · Put the sign between the sum and the number (grade 2–4) · A balanced scale: how much does the hidden block weigh (grade 2–3) · Box in subtraction: what number was taken from? (grade 2–3) · Equal sides: how many more to add (grade 2–4) · Equation with a box: missing first addend (grade 2–3) · Equation with a box: true or false (grade 2–3) · Equation with a box: a sum of three numbers (grade 3) · Equation with a box: fill in both boxes (grade 2–3)

Multiplication tables up to 100

In CM2 (the final year of primary school in France), pupils instantly recall the multiplication tables up to 100 and find a missing factor in either direction to solve problems.

Curriculum point CE1.NC.23 (our numbering) Understand and use the symbol "×". (our translation)
Curriculum point CE1.NC.27 (our numbering) Know the multiplication tables in both directions. (our translation)
Curriculum point CE1.NC.28 (our numbering) Know common multiplication facts. (our translation)
Curriculum point CE1.NC.35 (our numbering) Calculate the product of a number between 11 and 19 and a number less than 10 by decomposing the larger of the two factors into the sum of two numbers (distributivity property of multiplication over addition). (our translation)
Curriculum point CE1.NC.39 (our numbering) Solve one-step multiplicative problems. (our translation)
Curriculum point CE2.NC.21 (our numbering) Know the multiplication tables in both directions. (our translation)
Curriculum point CE2.NC.22 (our numbering) Know common multiplication facts. (our translation)
Curriculum point CM1.NC.35 (our numbering) Know common number facts relating to whole numbers (our translation)
Curriculum point CM2.NC.35 (our numbering) Know common number facts with whole numbers (our translation)
Curriculum point CP.NC.17 (our numbering) Understand the meaning of multiplication. (our translation)

In Grade 5 (CM2), the student masters basic number facts and knows their multiplication tables up to 100 in both directions. They can directly give the result of a product (for example 8 × 7 = 56) or find a missing factor without having to rewrite the whole series.

Hesitation appears mainly when working backwards to find the missing multiplier (finding the missing number in 6 × ... = 42) or through confusion between close results. In problem-solving situations, the common error is to use an extra value given in the statement instead of identifying the equal groups to multiply.

The exercises offered allow these calculations to be automated through different situations:

finding a missing product or factor in an equation;
checking a multiplication to spot and correct an error;
comparing two operations to determine which product is larger and calculate the difference;
counting points arranged in a table or solving a problem that includes a piece of unnecessary data.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Missing factor: choose the number (grade 3) · Times tables: choose the result (grade 3) · Multiplication as addition: how many times it was taken (grade 2–3) · Multiplication table (to 100) (grade 3) · Multiplication: equal groups altogether (grade 2–3) · Multiplication: how many dots in the array (grade 2–3) · Missing factor (multiplication table) (grade 3) · Multiplication with one number too many (grade 3) · Multiplication: check and find the mistake (grade 3) · Multiplication: which is larger and by how much? (grade 3)

Counting all possible combinations

In CM2 (the final year of primary school), students learn to systematically list and count all possible combinations or outcomes, using a table, a tree diagram, or a multiplication.

Curriculum point CE2.NC.34 (our numbering) Solve problems involving Cartesian products. (our translation)
Curriculum point CM1.NC.58 (our numbering) Solve counting problems (our translation)
Curriculum point CM1.OGD.5 (our numbering) Identify all possible outcomes in a simple random experiment (our translation)
Curriculum point CM2.NC.61 (our numbering) Solve counting problems (our translation)
Curriculum point CM2.OGD.4 (our numbering) Identify all possible outcomes in a simple random experiment (our translation)
Curriculum point CM2.OGD.5 (our numbering) Identify all the outcomes that realise an event in a simple random experiment (our translation)
Curriculum point CM2.OGD.9 (our numbering) In situations of equal likelihood, list all possible outcomes of a two-stage random experiment in a table or a tree diagram in order to determine probabilities (our translation)

In CM2, pupils learn to count systematically all the possible outcomes of a random situation or experiment in two steps. To leave nothing to chance, they organise their work by drawing up an ordered list, a two-way table or a tree diagram of choices. They thus discover how to combine two or three kinds of objects by linking each element of the first group with every element of the other groups.

The most common mistake is to proceed haphazardly, writing down solutions as they come to mind. The child then easily forgets some combinations, counts the same pair several times, or simply adds the number of objects instead of multiplying the possibilities together.

In practice, the activities involve writing out all the possible combinations of outfits or meals (with two or three categories of items), calculating the number of pairs remaining if one item disappears, or determining how many elements make up a set when the total number of pairs is already known.

Create a worksheet for this skill Multiple-choice test

Task types: Combinations: how many different sets can you make? (grade 2–4) · How many different pairs: choose the correct answer (grade 2–4) · How many different pairs: true or false (grade 2–4) · List all the combinations (grade 2–4) · Combinations: how many more pairs after adding one? (grade 3–4) · Combinations: how many pairs are left after one breaks? (grade 3–4) · Combinations: how many sets from three kinds? (grade 3–4) · Known number of pairs: how many in the other set (grade 3–4)

Complete a table according to a calculation rule

The student learns to apply or identify a calculation rule to complete a table of numbers, by following a specific program.

Curriculum point 5e.PF.10 (our numbering) Read and interpret a table of values. (our translation)
Curriculum point 5e.PF.13 (our numbering) Translate the dependency relationship between two quantities into a table of values, based on a formula. (our translation)
Curriculum point 5e.PF.5 (our numbering) Represent a situation of proportionality using a table or a graph. (our translation)
Curriculum point 5e.PF.8 (our numbering) Introduce the expression "en fonction de" in concrete or mathematical contexts. (our translation)
Curriculum point 5e.PF.9 (our numbering) Produce a table of values. (our translation)
Curriculum point 5e.PI.5 (our numbering) Predict the value of a computational expression before executing it. (our translation)
Curriculum point 6e.PI.2 (our numbering) Produce and execute a sequence of instructions (our translation)
Curriculum point CM1.NC.63 (our numbering) Execute a calculation program (our translation)
Curriculum point CM2.NC.66 (our numbering) Execute or produce a calculation programme (our translation)

In grade 5 (CM2), students learn to carry out or produce a calculation program presented as a correspondence table or as a machine that transforms numbers. By following a precise instruction (such as a multiplication rule or a systematic subtraction), they calculate the result corresponding to each starting value, or analyze the completed columns to work out the common rule.

The most frequent error occurs when they have to find the starting number from the final result: the student tends to reapply the direct operation instead of its inverse (for example, subtracting instead of adding). Another common mistake is to validate a rule after testing only one row, without checking that it works for the whole table.

In practice, practice worksheets offer very concrete situations:

applying the instruction to fill in the empty boxes (Choisis ce qui sort de la machine or Une table qui enlève);
finding the initial value by working the path backwards (Quel nombre est entré dans la machine);
deducing the hidden operation or spotting an anomaly in the results (Table de correspondance : trouve la règle and Corrige l'erreur dans le tableau).

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Function table: calculation program · Function table: fill in using the multiplying rule (grade 2–4) · Rule table (subtraction): fill in the results (grade 2–4) · Function table: find the rule (grade 2–4) · Machine rule: choose the number (grade 2–4) · Rule table: choose what comes out of the machine (grade 2–4) · Rule table: correct the mistake (grade 3–4) · Rule table: which number went in (grade 2–4)

Prisms and pyramids: faces, vertices and edges

Your child learns to identify and count the faces, edges and vertices of right prisms and pyramids from a drawing or from their characteristics.

Curriculum point CM1.EG.15 (our numbering) Describe a cube, a cuboid, a pyramid and a right prism by referring to properties and using appropriate vocabulary (our translation)
Curriculum point CM1.EG.16 (our numbering) Know the number and nature of the faces of a cube or a cuboid (our translation)
Curriculum point CM1.EG.17 (our numbering) Know the nature of the faces of a pyramid (our translation)
Curriculum point CM1.EG.18 (our numbering) Know the nature of the faces of a right prism (our translation)
Curriculum point CM2.EG.14 (our numbering) Describe a cube, a cuboid, a pyramid or a right prism by referring to properties and using appropriate vocabulary (our translation)

In CM2 (the final year of primary school), pupils consolidate their knowledge of solids by precisely describing right prisms and pyramids, in addition to the cube and the cuboid. They use rigorous geometric vocabulary to characterise each figure: identifying the nature of its faces (triangles, rectangles or other polygons), and determining its total number of faces, vertices and edges.

The most frequent error appears when reading a figure drawn flat in perspective. Pupils tend to forget the edges and faces hidden from view, which are shown as dotted lines, or to omit the base of the pyramid by counting only its triangular lateral faces. The confusion between the word sommet (a point) and the word arête (a segment) also remains common.

In written work, exercises ask pupils to analyse an illustrated figure in order to count or highlight its components (as in Arêtes d'un solide sur un dessin or Sommets d'un solide sur un dessin). Other activities lead the child to reason without direct visual support, or from a given solid, by answering targeted questions: Combien d'arêtes a le prisme ? or Combien de faces a la pyramide ?

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Prism: choose the number of vertices · Prism: how many vertices? · Pyramid: how many faces? · Edges of a solid from a picture · Faces of a solid from a picture · Prism: choose the number of edges · Prism: how many edges? · Prism: the base from the number of edges · Pyramid: choose the number of edges · Pyramid: how many edges? · Pyramid: the base from the number of edges · Vertices of a solid from a picture

Comparing chances in simple situations

In grade 5 (CM2), pupils learn to compare the chances of simple events and to recognise situations where several outcomes have the same probability of occurring.

Curriculum point CM1.OGD.7 (our numbering) Compare outcomes of random experiments or events according to their probability of occurrence (our translation)
Curriculum point CM1.OGD.8 (our numbering) Understand that the fact that there are two possible outcomes does not mean that each has a one-in-two chance of occurring (our translation)
Curriculum point CM1.OGD.9 (our numbering) Recognise situations of equiprobability (our translation)
Curriculum point CM2.OGD.7 (our numbering) Compare probabilities in simple cases (our translation)

In CM2 (age 10–11), students practise comparing probabilities in familiar chance situations. Starting from a finite set of objects, they observe the different possible outcomes to determine which result is more or less likely to occur, or to recognise a situation of equiprobability (when two events have an equal chance of happening).

A common mistake is to confuse a higher probability with absolute certainty, believing that the majority colour will necessarily come up in the next draw. Students also tend to overlook cases of equality by trying at all costs to find a winner, or to judge an event impossible simply because it is represented by only one element.

Exercises rely on highly visual supports, such as draws of coloured marbles from a bag. The concrete activities invite the child to:

Determine what is more likely or choose which chance is greater between two colours of marbles.
Analyse a character's reasoning to indicate whether they have correctly compared the chances or to correct their mistake.
Complete the contents of a bag to make a draw more advantageous, less probable, or perfectly fair.

Create a worksheet for this skill Multiple-choice test

Task types: A bag of marbles: which is more likely (grade 2–4) · Chance: correct the comparison (grade 2–4) · Chance: is the comparison correct? (grade 2–4) · Chance: what are you most likely to draw? (grade 2–4) · Chance: which is bigger? Choose (grade 2–4) · Fill the bag: bigger, smaller or equal chance (grade 2–4)

Reading the exact time on an analog clock

In CM2 (the final year of primary school in France), your child learns to read the exact time on an analogue clock and to set the hands to a given time in hours, minutes and seconds.

Curriculum point CE1.GM.19 (our numbering) Read the time on an analogue clock (when the time is given in whole hours, in hours and half hours, or in hours and quarter hours). (our translation)
Curriculum point CE1.GM.20 (our numbering) Set the hands of a clock to show a given time in whole hours, in hours and half hours, or in hours and quarter hours. (our translation)
Curriculum point CE1.GM.21 (our numbering) Know, use and distinguish the hours of the morning and those of the afternoon. (our translation)
Curriculum point CE2.GM.23 (our numbering) Read the time on an analogue clock. (our translation)
Curriculum point CE2.GM.24 (our numbering) Setting the hands of a clock to show a given time in whole hours or in hours and minutes. (our translation)
Curriculum point CM1.GM.26 (our numbering) Read the time on an analogue clock (our translation)
Curriculum point CM1.GM.27 (our numbering) Setting the hands of a clock to show a given time in hours and minutes (our translation)
Curriculum point CM2.GM.12 (our numbering) Read the time on an analogue clock (our translation)
Curriculum point CM2.GM.13 (our numbering) Setting the hands of a clock to show a given time in hours, minutes and seconds (our translation)
Curriculum point CP.GM.15 (our numbering) Read a given time in whole hours on an analogue clock with hands. (our translation)
Curriculum point CP.GM.16 (our numbering) Set the hands of a clock to show a given time (only whole hours less than or equal to twelve). (our translation)
Curriculum point CP.GM.17 (our numbering) Associate a time with a moment of the day. (our translation)

In CM2 (the final year of primary school), pupils consolidate their mastery of the analogue clock face. They learn to read the time accurately and to position the hands for a given time in hours, minutes and seconds, clearly distinguishing the role of the hour hand, the minute hand and the second hand.

The most common mistake occurs when the minute hand approaches the next hour (for example at 6 : 55): since the hour hand is already almost on the 7, the child tends to read 7 : 55. Similarly, when it comes to working out the time remaining to complete the hour, pupils sometimes forget that an hour has 60 minutes, not 100.

In practice, exercises ask pupils to state the exact time shown on a clock face, to spot an incorrect reading in a true or false exercise, or to correct a given error. Other activities invite pupils to compare several clocks to determine the earliest time, or to calculate the number of minutes until the next full hour.

Create a worksheet for this skill Multiple-choice test

Task types: Reading a clock: true or false (grade 2–3) · Reading a clock: which time is on the dial (grade 2–3) · Reading the clock (grade 3) · Clock: correct the mistake in reading (grade 2–3) · Clock: how many minutes to the full hour? (grade 3) · Clock: which shows the earlier time? (grade 3)

Organizing data in a table

Your child learns to organise data in a table, to calculate or find totals, and to use pictograms where one symbol stands for several units.

Curriculum point 6e.OGD.3 (our numbering) Construct a simple table to present data (observations, characteristics) (our translation)
Curriculum point CE1.OGD.1 (our numbering) Produce a table or a bar chart to present collected data. (our translation)
Curriculum point CE2.OGD.1 (our numbering) Produce a table or a bar chart to present collected data. (our translation)
Curriculum point CE2.OGD.2 (our numbering) Read and interpret the data in a two-way table or a bar chart. (our translation)
Curriculum point CM1.OGD.1 (our numbering) Collect data and produce a table, a bar chart or a set of points on a coordinate grid to present them (our translation)
Curriculum point CM2.OGD.1 (our numbering) Collect data and produce a table, a bar chart or a set of points on a coordinate plane to present the collected data (our translation)
Curriculum point CP.OGD.1 (our numbering) Collect data and present this data in the form of a table or a bar chart. (our translation)
Curriculum point CP.OGD.2 (our numbering) Construct and complete a two-way table. (our translation)

In Grade 5 (CM2), pupils learn to organise numerical information so that it can be presented clearly. They know how to fill in a table, calculate sums by row or by column to obtain a total, and carry out the reverse operation: finding a missing value when the overall total is already given. They also work with visual representations such as pictograms, where one image stands for a fixed quantity greater than one.

The most common mistake with pictograms is forgetting the scale and counting each drawing as a single unit, for example counting 4 instead of 40 when the symbol is worth 10. In numerical tables, confusion often arises when calculating a missing row, the pupil adding the total to the other data instead of subtracting the known values.

The exercises offered put these skills directly into practice:

calculate the sum of the items in a record (How many in total in the table or Table total: choose the correct answer);
check a result with true or false;
find an empty cell using a subtraction (The missing row when the total is known);
count quantities from a numerical key (Pictogram: one drawing stands for several).

Create a worksheet for this skill Multiple-choice test

Task types: Table: how many altogether? (grade 2–4) · Tally chart – total: find the mistake (grade 1–3) · Tally chart – two rows together: find the mistake (grade 1–2) · Tally chart: count the marks (K – grade 1) · Tally chart: how many more (grade 1–3) · Tally chart: how many more: choose the result (grade 1–3) · Tally chart: read a row (grade 1–3) · Tally chart: the biggest row (grade 1–2) · Tally chart: the biggest row: choose the result (grade 1–2) · Tally chart: total (grade 1–3) · Tally chart: total: true or false (grade 1–3) · Tally chart: two rows together (grade 1–2) · Tally chart: two rows together: true or false (grade 1–2) · Tally chart – most minus least: find the mistake (grade 2–4) · Tally chart: four rows altogether (grade 2–4) · Tally chart: four rows altogether: choose the result (grade 2–4) · Tally chart: how many marks to add (grade 1–2) · Tally chart: most minus least (grade 2–4) · Tally chart: most minus least: true or false (grade 2–4) · Tally chart: the hidden row (grade 2–3) · Tally chart: the hidden row: choose the result (grade 2–3) · Pictogram: one picture stands for several (grade 2–4) · The missing row when the total is known (grade 2–4) · Total from a table: choose the correct answer (grade 2–4) · Total from a table: true or false (grade 2–4)

Converting area and volume measurements

Your child learns to convert area measurements between cm², dm², m², ares or hectares, and to move to a smaller unit of volume.

Curriculum point 2de.AUT.7 (our numbering) Carry out unit conversions: lengths, areas, volumes, capacities, durations, speeds, masses. (our translation)
Curriculum point 5e.EG.27 (our numbering) Solve problems involving conversions of units of length and units of area. (our translation)
Curriculum point 5e.EG.6 (our numbering) Know and convert common units (volume and capacity). (our translation)
Curriculum point 6e.GM.6 (our numbering) Carry out area conversions (our translation)
Curriculum point CM2.GM.3 (our numbering) Know and use the units square centimetre, square decimetre and square metre to express areas (our translation)
Curriculum point CM2.GM.4 (our numbering) Convert areas between different units (our translation)

In the CM2 class (final year of primary school), pupils learn to handle and convert area measurements, mainly using the square centimetre (cm²), the square decimetre (dm²) and the square metre (m²). They also discover the common land units, the are and the hectare, while beginning the first conversions to a smaller unit of volume.

The classic pitfall is treating areas as simple lengths. Pupils often forget that there is a ratio of 100 between each consecutive unit of area (1 m² = 100 dm²). In a conversion table, they tend to reserve only one column per unit instead of two, which leads them to multiply or divide by 10 instead of 100.

In written work, the exercises ask for targeted unit changes using precise instructions:

Convert to a larger or smaller unit of area;
Convert the ares into square metres or the hectares into ares;
Convert to a smaller unit of volume.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Convert to a larger unit of area · Convert to a smaller unit of area · Convert to a smaller unit of volume · Units of area: choose the conversion · Units of area: find the mistake · Units of area: true or false · Units of area: compare the quantities

Solving a simple equation with one unknown

Your child is learning to find the value of an unknown number represented by a letter, particularly by completing multiplicative equations.

Curriculum point 5e.NC.43 (our numbering) Give the letter the status of an unknown. (our translation)
Curriculum point 5e.NC.45 (our numbering) Solve equations of the type a𝑥 = c or 𝑥 + b = c using arithmetic methods based on inverse operations. (our translation)
Curriculum point 6e.NC.27 (our numbering) Complete multiplicative equations with blanks (our translation)
Curriculum point CM1.NC.61 (our numbering) Determine the value of an unknown number by using a symbol or a letter to represent it (our translation)

In CM2 (the final year of primary school), pupils learn to determine the value of an unknown number represented by a letter or a symbol. They rely on their understanding of operations to find the missing term, particularly when completing multiplicative missing-number equations.

The most common mistake is to carry out the visible operation directly instead of using the inverse operation. Faced with a multiplicative equation, a pupil may be tempted to multiply the two numbers present, or to subtract at random, instead of using sharing or division to find the missing factor.

In the practice worksheets, under the instruction Solve the equation, the child is faced with a simple equation containing an unknown and must write the appropriate operation to find the exact result.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Equation a · x = b: find the mistake · Equation a · x = b: is the number a solution? · Equation a × x = b · Equation x + a = b · Equation x ÷ a = b · Equation x − a = b · Equation x − a = b: choose the solution · Equation x + a = b: change on both sides

Adding and subtracting different fractions

The student learns to add and subtract fractions with different denominators in order to calculate a result or solve a problem.

Curriculum point 2de.AUT.2 (our numbering) Perform operations and comparisons between simple fractions. (our translation)
Curriculum point 5e.NC.26 (our numbering) Add and subtract fractions with any denominators. (our translation)
Curriculum point 5e.NC.27 (our numbering) Solve problems with addition and subtraction of fractions. (our translation)
Curriculum point 6e.NC.35 (our numbering) Add and subtract fractions (our translation)
Curriculum point CM2.NC.20 (our numbering) Adding and subtracting fractions (our translation)

In grade 5 (CM2), students learn to add and subtract fractions that do not have the same denominator. To carry out these calculations, they use common multiples to rewrite the fractions and obtain an identical denominator before operating.

The most common error is to add or subtract the numerators together and the denominators together directly (for example, writing 1/2 + 1/4 = 2/6). The child then applies the whole-number reflex, forgetting that only parts of the same size can be combined.

In practice, the exercises alternate between written calculations with Add fractions with different denominators and Subtract fractions with different denominators, and concrete contexts with the problem model How many in all? Fractions with different denominators.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Fractions with unlike denominators: find the mistake · Fractions with unlike denominators: true or false · Subtracting unlike fractions: find the mistake · Subtracting unlike fractions: true or false · Add fractions with unlike denominators · Adding unlike fractions: word problem · Fractions with unlike denominators: choose the sum · Fractions with unlike denominators: numerator after renaming · Subtract fractions with unlike denominators · Subtracting unlike fractions: choose the result · Subtracting unlike fractions: the numerator

Adding and Subtracting Decimals

In CM2 (the final year of primary school in France), your child learns to set up and calculate additions and subtractions with decimal numbers, and to perform these calculations mentally or with quantities such as masses.

Curriculum point 5e.NC.1 (our numbering) Add, subtract, multiply and divide to solve problems and check the plausibility of one's result. (our translation)
Curriculum point 6e.NC.14 (our numbering) Adding and subtracting decimal numbers (our translation)
Curriculum point CM1.NC.38 (our numbering) Add or subtract a whole number less than 10 of units, tens, hundreds, tenths or hundredths to or from a decimal number, when there is no carrying (our translation)
Curriculum point CM1.NC.49 (our numbering) Set out in columns and carry out additions and subtractions of decimal numbers (our translation)
Curriculum point CM2.NC.39 (our numbering) Adding or subtracting a whole number to or from a decimal number when there is no carrying or borrowing (our translation)
Curriculum point CM2.NC.40 (our numbering) Adding a whole number to a decimal number when there is a carry-over (our translation)
Curriculum point CM2.NC.43 (our numbering) Add two decimal numbers less than 10, written with at most one digit after the decimal point (our translation)

In Year 6 (CM2), pupils consolidate column addition and subtraction with decimal numbers. In mental calculation, they learn to add or subtract a whole number to or from a decimal number (with or without carrying), as well as to add two decimals less than 10 that have at most one digit after the decimal point.

The most common mistake is to align the numbers on the right, as with whole numbers, rather than aligning the decimal points. A pupil then risks adding tenths to hundredths or units, which distorts the place value of the digits and the placement of the decimal point in the result.

In practice, exercises ask pupils to set out and solve additions or subtractions of decimal numbers, but also to use these operations in measurement contexts, for example by adding masses written in decimal form.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Add decimals · Decimals – addition: find the mistake · Decimals – subtraction: find the mistake · Decimals: addition — choose the result · Decimals: addition — true or false · Decimals: subtraction — choose the result · Decimals: subtraction — true or false · Subtract decimals · Add masses written as decimals · Decimals: the missing addend · Decimals: the missing number to subtract

Multiplying and dividing a decimal by 10, 100, or 1,000

Your child is learning to multiply and divide decimal numbers by 10, 100 or 1,000, as well as to multiply by 0.1, 0.01 and 0.001, by sliding the digits' places.

Curriculum point 6e.NC.15 (our numbering) Multiply a whole number or a decimal number by 0.1, by 0.01, and by 0.001 (our translation)
Curriculum point 6e.NC.16 (our numbering) Know the link with division by 10, 100 and 1,000 (our translation)
Curriculum point CM1.NC.39 (our numbering) Multiplier un nombre entier par 10, 100 ou 1 000
Curriculum point CM1.NC.40 (our numbering) Multiplying a decimal number by 10 (our translation)
Curriculum point CM1.NC.41 (our numbering) Divide a decimal number by 10 (our translation)
Curriculum point CM2.NC.41 (our numbering) Multiplier un nombre décimal par 10, 100 ou 1 000
Curriculum point CM2.NC.42 (our numbering) Dividing a decimal number by 10, 100 or 1,000 (our translation)

In Year 5 (CM2), students consolidate calculation with decimal numbers by multiplying and dividing decimals by 10, 100 or 1,000. They also tackle multiplication by 0.1, 0.01 and 0.001, explicitly linking it to division. The key is to understand the change in place value of each digit in decimal notation: multiplying by 100 gives each digit a value one hundred times greater, while dividing by 10 makes it ten times smaller.

The classic mistake is to apply the reflex learned with whole numbers by adding a zero at the end, which leads to writing 3.4 × 10 = 3.40 instead of 34. Confusions about direction are also common: shifting the decimal point to the right instead of the left for a division, or hesitating when zeros must be added to mark empty places, as in 0.5 ÷ 10 = 0.05.

On practice worksheets, this work takes the form of mental or written calculation exercises across three types of activities:

Multiply by 10, 100, 1000 to move the decimal point to the right (for example 7.25 × 100);
Divide by 10, 100, 1000 to reduce orders of magnitude (for example 83.4 ÷ 10);
Multiply by 0.1, 0.01, 0.001 to apply the same procedure as division and gain greater flexibility in calculation.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Divide by 10, 100 or 1000 · Dividing by 10, 100, 1000: choose the result · Multiply by 0.1, 0.01 or 0.001 · Multiply by 10, 100 or 1000 · Multiplying by 10, 100, 1000: choose the result · Multiplying by 10, 100, 1000: what was it multiplied by?

Converting units of length from mm to km

Your child is learning to convert from one unit of length to another, from the millimetre to the kilometre, and to express a measurement in a single unit.

Curriculum point 5e.EG.27 (our numbering) Solve problems involving conversions of units of length and units of area. (our translation)
Curriculum point 6e.GM.5 (our numbering) Solve problems involving lengths (our translation)
Curriculum point CE2.GM.2 (our numbering) Know the relationships between units of length. (our translation)
Curriculum point CM1.GM.1 (our numbering) Know and use the units of length from millimetre to kilometre and their associated symbols (our translation)
Curriculum point CM1.GM.2 (our numbering) Know the relationships between units of length (our translation)
Curriculum point CM1.GM.4 (our numbering) Compare lengths (our translation)

In Year 5 (CM2), pupils work with units of length from the millimetre (mm) up to the kilometre (km). They use the relationships between these units (such as the fact that one metre equals 100 centimetres, or that one kilometre is 1,000 metres) to convert measurements from one unit to another as a problem requires.

Difficulties often arise when converting to a larger unit: pupils sometimes confuse the direction of the conversion and multiply instead of dividing. Another classic mistake is forgetting intermediate units in compound conversions, for example writing 2 m 5 cm = 25 cm instead of 205 cm, because the zero for the decimetres has been left out.

In practice, exercises involve direct instructions:

Convert to a smaller unit of length (for example, changing metres into millimetres).
Convert to a larger unit of length (for example, converting metres into kilometres).
Write the length in a single unit (to turn a mixed measurement, such as metres and centimetres, into one single target unit).

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: A length in one unit: find the mistake · A length in one unit: true or false · Convert to a larger unit of length · Convert to a smaller unit of length · Units of length: choose the converted value · Units of length: compare · Write a length in one unit · Adding lengths given in two units

Area of a rectangle and calculating a missing side

In grade 5 (CM2), students learn to calculate the area of a rectangle in cm², dm², or m², and to find the length of a missing side from the total area.

Curriculum point 6e.GM.7 (our numbering) Know the formula for the area of a square or a rectangle (our translation)
Curriculum point 6e.GM.8 (our numbering) Calculate the area of a square or a rectangle (our translation)
Curriculum point CM2.GM.2 (our numbering) Determine areas (our translation)
Curriculum point CM2.GM.5 (our numbering) Determine the area of a square or a rectangle (our translation)

In Grade 5 (CM2), students learn to find the area of a rectangle by multiplying its length by its width, expressing the result in appropriate units (cm², dm² or m²). They also reach an important milestone by doing the reverse calculation: when given the total area and the measurement of one side, they use division to find the missing dimension.

The most common difficulty lies in confusing area with perimeter. Faced with a figure, some students continue to add the sides instead of multiplying them, or try to find a missing side by subtracting instead of dividing.

On worksheets, this skill appears in different practice situations:

Direct calculations with Area of a rectangle to memorize and apply the formula.
Real-life problems with The area of a rectangle in everyday life, where students must estimate the surface of an object or a real space.
Problem-solving situations with Missing side of a rectangle, which require dividing the given area by the known length to find the width.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Area of a rectangle · Area of a rectangle in everyday life · Area of a rectangle: extra data · Area of a rectangle: find the mistake · Area of a rectangle: true or false · Area of a square: side from area · Missing side of a rectangle from its area · Missing side of a rectangle: choose the side · Area of a rectangle: compare two areas · Area of a rectangle: shape with a corner cut out · Area of a rectangle: sides k times longer

Expressing a probability as "chances in"

In CM2 (the last year of French primary school), your child learns to express the probability of a simple event as "a chances out of b" in a situation where every outcome has the same chance of occurring.

Curriculum point 2de.AUT.27 (our numbering) Knowing that a probability is a number between 0 and 1. (our translation)
Curriculum point 2de.AUT.28 (our numbering) Know how to calculate the probability of the complementary event. (our translation)
Curriculum point 2de.AUT.29 (our numbering) Calculate the probability of an event as the sum of the probabilities of the outcomes that make it up. (our translation)
Curriculum point 2de.AUT.30 (our numbering) Use the relation P(A) = Card(A)/Card(Ω) in the case of equiprobability. (our translation)
Curriculum point 5e.OGD.7 (our numbering) Aborder les questions relatives au hasard à partir de problèmes simples. (our translation)
Curriculum point 5e.OGD.8 (our numbering) Use the vocabulary of probability in concrete contexts: random experiment, outcome, event. (our translation)
Curriculum point 5e.OGD.9 (our numbering) Assign probabilities in simple cases (equiprobability). (our translation)
Curriculum point 6e.OGD.5 (our numbering) Knowing that the probability of an event is a number between 0 and 1 (our translation)
Curriculum point 6e.OGD.6 (our numbering) Calculate probabilities in simple equiprobability situations (our translation)
Curriculum point CM2.OGD.6 (our numbering) In a situation of equiprobability, in a simple random experiment, express the probability of an event in the form “a chances out of b” (our translation)

In CM2, during a simple random experiment, pupils learn to express the chances of an outcome in the form "a chances out of b". In this first step of cycle 3, the aim is to identify the favourable cases and relate them to the total number of possibilities, before later addressing probability in 6th grade as a number between 0 and 1.

The most common mistake consists of comparing the favourable cases to the unfavourable cases rather than to the total number of outcomes. For example, faced with a box containing 2 red balls and 3 blue balls, a child often instinctively says "2 chances out of 3" of drawing a red one, forgetting to add all the balls together to find 2 chances out of 5.

In class, the work relies on simple hands-on activities:

Rolling a die with six faces to determine the chances of getting a specific number or a particular result;
Drawing a numbered card from a deck to count the corresponding cases;
Drawing a ball from an opaque box containing items of different colours.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Drawing a ball from a box (grade 7–8) · Rolling a die (grade 7–8) · Chances in two bags: compare (grade 7–8) · Drawing a numbered card (grade 7–8) · Probability of the complement (grade 7–8) · Probability: choose the result (grade 7–8) · Probability: find the mistake (grade 7–8) · Probability: true or false (grade 7–8) · Probability: how many balls of that colour (grade 7–8) · Drawing without looking: what is the probability? (grade 7–8)

Comparing numbers: difference or multiplication

In grade 5 (CM2), pupils learn to compare two quantities by distinguishing the difference ("how much more") from the multiplicative ratio ("how many times more").

Curriculum point 2de.AUT.1 (our numbering) Compare two numbers directly or by calculation: • of their difference; • if they are strictly positive, of their quotient. (our translation)
Curriculum point 2de.NC.18 (our numbering) Additive comparison (by difference), multiplicative comparison (by ratio, for two strictly positive numbers). (our translation)
Curriculum point 2de.NC.26 (our numbering) Compare two quantities using their difference, or their ratio in the case of positive quantities. Interpret, depending on the context, this comparison in terms of additive or multiplicative variation. (our translation)
Curriculum point CE2.NC.33 (our numbering) Solve one-step multiplicative comparison problems. (our translation)
Curriculum point CM1.NC.56 (our numbering) Solve multiplicative comparison problems (our translation)
Curriculum point CM2.NC.60 (our numbering) Solve multiplicative comparison problems (our translation)

In CM2, the pupil consolidates problem-solving involving multiplicative comparison. Faced with two quantities, they are now able to choose the right type of comparison: calculating a difference by subtraction, or determining a ratio by looking for a multiplicative factor or a quotient.

The common mistake is confusing these two approaches. When a problem asks for a comparison, many children automatically fall back on subtraction. For example, they answer that an object costs "15 euros more" when they were asked to observe that it costs "4 times as much".

On the worksheets, the work is organised around targeted activities:

How much bigger?: the pupil calculates the numerical difference between two values.
How many times bigger? and How many times more?: they identify the coefficient that links the two numbers using a multiplication or a division.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: A number k times as large · Comparison by difference: how much greater · Comparison by ratio: how many times as large · Comparison by ratio: how many times as many (word problem) · How many times as large: choose the answer · How much greater one number is: choose the answer

Calculating durations: hours, minutes, and seconds

Your child is learning to convert durations into seconds and to calculate the time elapsed between two given moments in hours, minutes and seconds.

Curriculum point 6e.GM.12 (our numbering) Carry out calculations with times and durations (our translation)
Curriculum point 6e.GM.13 (our numbering) Solve problems involving schedules and durations (our translation)
Curriculum point 6e.GM.14 (our numbering) Convert durations (our translation)
Curriculum point CE2.GM.26 (our numbering) Solve one- or two-step problems involving durations. (our translation)
Curriculum point CM1.GM.28 (our numbering) Compare and measure elapsed durations between two times shown on a clock (times and durations are expressed in hours and minutes) (our translation)
Curriculum point CM1.GM.29 (our numbering) Solve one- and two-step problems involving durations (our translation)
Curriculum point CM2.GM.13 (our numbering) Setting the hands of a clock to show a given time in hours, minutes and seconds (our translation)
Curriculum point CM2.GM.14 (our numbering) Compare and measure elapsed times between two instants shown on a clock (instants and durations are expressed in hours, minutes and seconds) (our translation)
Curriculum point CM2.GM.15 (our numbering) Solve one- or multi-step problems involving durations (our translation)

In CM2 (the final year of primary school), the pupil takes another step forward by handling time precisely, down to the second. They learn to read and position the hands of a clock, to measure the time elapsed between two precise moments, and to convert time measurements, in particular minutes and seconds into whole seconds.

The classic pitfall lies in the automatic use of decimal numeration (in base 10 or 100). Many children try to set up an ordinary subtraction between two times, forgetting that an hour has 60 minutes and that a minute has 60 seconds. For example, to go from 10 h 45 to 11 h 15, they may be tempted to calculate 11.15 − 10.45 and get 70 minutes instead of the actual 30 minutes.

In practice, the work is based on three types of concrete exercises:

Minutes and seconds into seconds: convert a mixed duration by multiplying the number of minutes by 60 before adding the remaining seconds;
How many minutes have passed?: determine the interval between two readings on an analog clock face;
How long did it last?: solve duration problems by crossing a full hour to find the result in hours, minutes and seconds.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Minutes and seconds to seconds · Durations: compare · Elapsed time word problem: how long did it last · Elapsed time: choose how many minutes passed · Minutes and seconds: find the mistake · Minutes and seconds: true or false · Time on a clock: how many minutes passed

Find the rule of a sequence and continue it

Your child learns to identify the calculation rule of a number sequence, whether it involves adding a regular step or multiplying, in order to determine the following numbers.

Curriculum point 6e.NC.43 (our numbering) Identify the structure of a growing pattern by recognising a regularity and identifying a structure (our translation)
Curriculum point CM1.NC.64 (our numbering) Identify and formulate a calculation rule to continue a number sequence (our translation)
Curriculum point CM1.NC.65 (our numbering) Identify patterns and extend a growing pattern (our translation)
Curriculum point CM2.NC.67 (our numbering) Identify and formulate a calculation rule to continue a sequence of numbers (our translation)
Curriculum point CM2.NC.68 (our numbering) Identify patterns and continue a growing sequence of patterns (our translation)
Curriculum point CM2.NC.69 (our numbering) Find the number of elements for a given step in a growing pattern sequence (our translation)

In CM2, your child practises observing an ordered sequence of numbers in order to understand its logic. They state precisely the operating rule that allows them to move from one term to the next, mainly by repeatedly adding a constant step or by multiplying, so that they can continue the sequence and write the following numbers.

The most common mistake is to deduce a rule from the first two numbers only, without checking whether it applies to the rest of the series. Faced with the start of the sequence 2, 4, 8, a distracted pupil often applies the initial difference of 2, thinking it is an addition, instead of identifying the multiplication by 2 that governs the whole chain.

In class, the work is organised around progressive exercises: Sequence: always add the same step to consolidate repeated addition, Sequence: always multiply by the same number to master multiplicative jumps, and finally Find the rule and continue the sequence, where the pupil must analyse the differences by themselves before calculating the missing terms.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Pattern with a constant step: choose the term · Pattern with a constant step: find the mistake · Pattern with a constant step: true or false · Pattern: add the same step · Pattern: multiply by the same number · Pattern with a constant step: the first term · Pattern with a constant step: which term is it · Spot the rule and continue the pattern · Visual pattern: how many squares in figure n

Adding and subtracting fractions with the same denominator

Your child is learning to add and subtract fractions with the same denominator by working on the numerators while keeping the common denominator.

Curriculum point CE1.NC.21 (our numbering) Add and subtract fractions with the same denominator. (our translation)
Curriculum point CE2.NC.14 (our numbering) Add and subtract fractions. (our translation)
Curriculum point CM1.NC.21 (our numbering) Add and subtract fractions (our translation)
Curriculum point CM2.NC.20 (our numbering) Adding and subtracting fractions (our translation)

In CM2 (the final year of primary school), students learn to perform operations on fractions that share the same denominator. They apply addition or subtraction directly to the numerators to find the new number of parts, without changing the denominator, which defines the unit of division.

The most common mistake is to also add or subtract the numbers on the bottom. For example, faced with a calculation like 2/5 + 1/5, the child may write 3/10. They apply the reflex of calculating with whole numbers in both the numerator and the denominator, forgetting that the denominator indicates the fixed size of the part.

In written work, exercises appear as calculations written in line, to be solved directly:

Add fractions with the same denominator: the student calculates the sum of two fractions, for example 3/7 + 2/7.
Subtract fractions with the same denominator: the student calculates the difference between two fractions with the same denominator, for example 5/9 - 2/9.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Add fractions with like denominators · Fractions with like denominators: choose the sum · Fractions with like denominators: find the mistake · Fractions with like denominators: the missing numerator · Fractions with like denominators: true or false · Fractions: how much is missing to make a whole? · Subtract fractions with like denominators · Subtracting fractions: choose the difference · Subtracting fractions: find the mistake · Subtracting fractions: take away from a whole · Subtracting fractions: the missing numerator · Subtracting fractions: true or false · Fractions with like denominators: a sum greater than 1 · Fractions with like denominators: compare the sums · Subtracting fractions: compare the differences · Fractions: how many pairs make a whole?

Converting from a Fraction to a Mixed Number

In CM2 (the final year of primary school in France), your child learns to convert a fraction greater than 1 into the sum of a whole number and a fraction less than 1, and vice versa.

Curriculum point 6e.NC.34 (our numbering) Ordering a list of numbers written as fractions or mixed numbers (our translation)
Curriculum point 6e.NC.6 (our numbering) Associate and use different representations of a decimal number: decimal notation, fraction, mixed number, percentage (our translation)
Curriculum point CM1.NC.15 (our numbering) Knowing how to write a fraction greater than 1 as the sum of a whole number and a fraction less than 1 (our translation)
Curriculum point CM1.NC.16 (our numbering) Knowing how to write the sum of a whole number and a fraction less than 1 as a single fraction (our translation)
Curriculum point CM1.NC.17 (our numbering) Knowing how to bracket a fraction between two consecutive whole numbers (our translation)
Curriculum point CM1.NC.26 (our numbering) Writing a decimal fraction greater than 1 as the sum of a whole number and a decimal fraction less than 1 (our translation)
Curriculum point CM2.NC.14 (our numbering) Write a fraction greater than 1 as the sum of a whole number and a fraction less than 1 (our translation)
Curriculum point CM2.NC.15 (our numbering) Writing the sum of a whole number and a fraction less than 1 as a single fraction (our translation)
Curriculum point CM2.NC.16 (our numbering) Bracket a fraction between two consecutive whole numbers (our translation)
Curriculum point CM2.NC.26 (our numbering) Write a decimal fraction greater than 1 as the sum of a whole number and a decimal fraction less than 1 (our translation)

In Grade 5 (CM2), students learn to connect a fraction greater than 1 with its decomposition into a whole number together with a fraction less than 1. They thus learn to extract the whole units contained in a fraction and, conversely, to combine a whole number and a fractional part into a single fraction.

A common error occurs when returning to a single fraction: the child often tends to add the whole number and the numerator directly, without taking the parts of the unit into account (for example, writing that 2 + 1/3 equals 3/3 instead of 7/3). When decomposing, the other usual pitfall is forgetting to extract all possible whole units, leaving a remaining fraction that is still greater than 1.

Practice exercises come in two complementary instructions:

Write the fraction as a mixed number: the student determines the number of whole units and the remaining fraction less than 1;
Write the mixed number as a fraction: the student converts the whole number into equal parts to rebuild a single fraction.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Improper fraction: how many wholes? · Mixed number: choose the improper fraction · Mixed number: choose the whole part · Mixed number: the missing numerator · Write a mixed number as a fraction · Write an improper fraction as a mixed number

Rounding a decimal number to the nearest tenth or hundredth

Your child is learning to give the rounded value of a decimal number to the nearest tenth or hundredth.

Curriculum point 2de.NC.9 (our numbering) Set 𝔻 of decimal numbers. Decimal bounding of a real number to within 10⁻ⁿ. (our translation)
Curriculum point 6e.NC.11 (our numbering) Give the value of a decimal number rounded to the unit, the tenth or the hundredth (our translation)
Curriculum point CM1.NC.33 (our numbering) Knowing how to give the integer part and the rounding to the nearest whole number of a decimal number (our translation)
Curriculum point CM2.NC.33 (our numbering) Knowing how to give the integer part and the rounding to the nearest whole number of a decimal number (our translation)

In grade 5 (CM2), students consolidate their understanding of decimal numbers. After learning to find the integer part and to round to the nearest whole number, they practise tightening this approximation by determining the value of a number rounded to the nearest tenth or hundredth.

The most common mistake is confusing rounding with simple truncation: faced with a number such as 4.28, the child often instinctively cuts off the extra digits to write 4.2. They then forget to look at the following digit (here the 8) to decide whether to keep the tenths digit or move up to the next tenth (4.3).

In practice, training relies on two targeted types of exercises: Rounding to the tenth and Rounding to the hundredth. Starting from decimal numbers with two or three decimal places (up to thousandths), the student identifies the required place value, analyses the digit that follows it, and writes the correct approximate value.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Round to the nearest hundredth · Round to the nearest tenth · Rounding to tenths: choose the result · Rounding to tenths: find the mistake · Rounding to tenths: true or false

Finding the least common multiple (LCM)

The student learns to identify the common multiples of two whole numbers less than 15 and to determine their least common multiple (LCM).

Curriculum point CM2.NC.12 (our numbering) Determine common multiples of two whole numbers less than 15 (our translation)

In CM2 (Grade 5), your child learns to list and compare the multiples of two whole numbers that are strictly less than 15. Using multiplication tables, they write the first multiples of each number to spot the ones they have in common, then identify the smallest of them that is not zero.

The most common mistake is to multiply the two starting numbers together, thinking this will directly give the smallest possible answer. For example, given 4 and 6, a pupil often calculates 4 × 6 = 24, without seeing that 12 appears earlier in both lists of multiples.

The exercises take the form of guided calculations (as in the worksheet Calcule le PPCM de deux nombres) or small real-life problems about periodicity (such as Quand à nouveau ensemble ?), where the aim is to work out when two regular events will happen at the same moment.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: LCM: choose the least common multiple · LCM: find the mistake · LCM: true or false · Find the least common multiple · LCM word problem: when together again · GCF and LCM: find the other number (grade 6–7)

Multiplying decimal numbers

In Year 5 (CM2), pupils learn how to set out the multiplication of a decimal number by a whole number and practise calculating simple products of decimal numbers.

Curriculum point 5e.NC.1 (our numbering) Add, subtract, multiply and divide to solve problems and check the plausibility of one's result. (our translation)
Curriculum point 6e.NC.17 (our numbering) Understand the meaning of multiplication of two decimal numbers (our translation)
Curriculum point 6e.NC.18 (our numbering) Calculate the product of two decimal numbers (our translation)
Curriculum point 6e.NC.20 (our numbering) Solve problems involving multiplications of decimal numbers (our translation)
Curriculum point CM1.NC.51 (our numbering) Pose and carry out multiplications of a decimal number by a whole number less than 10 (our translation)
Curriculum point CM2.NC.47 (our numbering) Calculate the double of a decimal number in simple cases (our translation)
Curriculum point CM2.NC.50 (our numbering) Multiply a decimal number by 5 (our translation)
Curriculum point CM2.NC.51 (our numbering) Multiply a decimal number by 50 (our translation)
Curriculum point CM2.NC.54 (our numbering) Set up and carry out the multiplication of a decimal number by a whole number (our translation)

In grade 5 (CM2), pupils mainly learn to set up and carry out the multiplication of a decimal number by a whole number. In mental calculation, they consolidate precise reflexes: finding the double of a simple decimal, or quickly multiplying by 5 and by 50. Multiplying two decimal numbers together begins to be introduced in suitable situations, before being fully mastered in 6th grade.

The most common error concerns the handling of the decimal point. Used to addition, some pupils try to needlessly align decimal points as soon as the calculation is set out in columns. Others correctly multiply the digits but forget to count the total number of digits after the decimal point in order to place the decimal point in the final result.

In class, the work takes the form of concrete measurement problems, such as the exercise Multiply a length by a number of pieces, or guided computational practice exercises using the template Multiply decimal numbers.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Multiplying decimals: choose the result · Multiplying decimals: find the mistake · Multiplying decimals: true or false · Multiply a length by a number of pieces · Multiply decimals · Multiplying decimals: is the product larger?

Using divisibility rules

The student learns to quickly determine whether an integer is divisible by 2, 3, 4, 5, 9, or 10 without having to perform the division.

Curriculum point 5e.NC.10 (our numbering) Know the divisibility rules for 3 and 9. (our translation)
Curriculum point CM1.NC.11 (our numbering) Being able to recognise multiples of 2, 5 and 10 from their written numerals (our translation)
Curriculum point CM2.NC.8 (our numbering) Determine whether a whole number less than or equal to 10 is a divisor of a given whole number, or whether a given whole number is a multiple of a whole number less than or equal to 10 (our translation)

In grade 5 (CM2), your child learns to determine whether a whole number less than or equal to 10 (in particular 2, 3, 4, 5, 9 and 10) is a divisor of a given whole number. Thanks to divisibility rules based on the written digits, they can tell whether a number is a multiple of these reference numbers without complex written calculation.

The classic mistake is mixing up the different rules. For 3 or 9, pupils often have the reflex of looking only at the last digit, as they do for 2, 5 or 10. A child may thus wrongly claim that 43 is divisible by 3 because it ends in 3, forgetting that here you must add all the digits of the number.

In written work, the practice revolves around two types of exercises:

Apply a divisibility rule: sort or tick numbers according to whether they are divisible by 2, 3, 4, 5, 9 or 10;
Find the missing digit for divisibility: complete a number with a gap (for example 5_2) with the appropriate digit so that the requested rule is respected.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Divisibility rules: by 2, 5 and 10 · Divisibility rules: check divisibility · Divisibility rules: by 6, 12, 15, 18 · Divisibility rules: missing digit · Remainder when dividing by 9, without dividing

Find the greatest common divisor (GCD)

Your child learns to identify the common divisors of two numbers up to 30 and to find the greatest of them in order to solve fair-sharing problems.

Curriculum point CM2.NC.11 (our numbering) Determine the common divisors of two integers less than or equal to 30 (our translation)

In CM2 (the last year of primary school), pupils learn to list all the divisors of two whole numbers less than or equal to 30 in order to spot the ones they have in common. They then determine the largest of these, called the GCD (greatest common divisor). For example, faced with the numbers 18 and 24, they find their shared divisors (1, 2, 3 and 6) and identify 6 as the greatest common divisor.

The classic mistake is to confuse divisors with multiples, or to forget pairs of divisors during the search (such as 1 and the number itself). Pupils also often tend to stop at the first common divisor they find, such as 2 for two even numbers, without checking whether a larger one exists.

In written work, the practice is organised around two types of task:

direct practice exercises where the instruction asks to calculate the GCD of two given numbers;
concrete problems of sharing into identical groups, where, for example, pupils must share out marbles or cards equally without any remainder.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: GCF: choose the greatest common factor · GCF: find the mistake · GCF: true or false · Find the greatest common factor · GCF word problem: share into identical packs · GCF: factor out of a sum (grade 6–7)

Finding a missing value in a proportion

The student learns to calculate a missing value from already known proportional quantities by using simple multiplicative relationships.

Curriculum point 5e.PF.15 (our numbering) Characterise proportionality graphically. (our translation)
Curriculum point 5e.PF.3 (our numbering) Identify situations of proportionality in concrete contexts (prices, recipes, distances, scales). (our translation)
Curriculum point 5e.PF.6 (our numbering) Recognise a proportional situation from a table or a graph. (our translation)
Curriculum point 5e.PF.7 (our numbering) Recognise graphically that a scatter plot is or is not associated with a situation of proportionality between discrete data. (our translation)
Curriculum point 6e.P.1 (our numbering) Know the definition of proportionality between two quantities and relate it to everyday expressions (our translation)
Curriculum point 6e.P.2 (our numbering) Identify whether a situation falls under the "model" of proportionality (our translation)
Curriculum point 6e.P.3 (our numbering) Solve a proportionality problem by choosing an appropriate procedure: linearity property for multiplication or addition, return to the unit (our translation)
Curriculum point 6e.P.4 (our numbering) Represent a proportional situation using a table or symbolic notation (our translation)
Curriculum point CM1.P.2 (our numbering) Being able to solve a proportionality problem (our translation)
Curriculum point CM2.P.2 (our numbering) Be able to solve a proportionality problem (our translation)

In grade 5 (CM2), students learn to determine an unknown quantity linked to data already given in a proportional situation. To find the sought value, they use suitable procedures such as multiplying or dividing by a simple whole number (for example doubling, tripling or taking half), as well as finding the value for a single unit.

The classic obstacle lies in the additive trap. Faced with two quantities that both increase, the child often has the reflex of adding the same difference to both measures instead of identifying a multiplicative coefficient, thus applying an additive scheme that is unsuitable for proportionality.

On the practice worksheets, the work relies on two types of concrete exercises:

Complete the proportion, where one completes an equality or the terms of a numerical relationship;
From one known quantity to another, where the student transposes a starting measure (a batch, a price or a weight) to a new requested quantity.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Proportion: choose the missing term · Proportion: find the mistake · Proportion: missing value · Proportion: true or false · Proportion word problem: scale to another number of items · Proportion: the missing third term · Direct proportion: complete the table (grade 6–7)

Perimeter of a polygon and missing side

The student learns to calculate the perimeter of a polygon and to find the length of a missing side when the total perimeter is known.

Curriculum point 2de.AUT.21 (our numbering) Calculate perimeters (polygon and circle), areas (rectangle, triangle and disc) and volumes (cuboid, prism, cylinder, pyramid, cone and sphere). (our translation)
Curriculum point 6e.GM.4 (our numbering) Calculate the perimeters of composite figures (our translation)
Curriculum point 6e.GM.5 (our numbering) Solve problems involving lengths (our translation)
Curriculum point CM1.GM.7 (our numbering) Knowing what the perimeter of a plane figure is (our translation)
Curriculum point CM1.GM.8 (our numbering) Determine the perimeter of a polygon using a graduated ruler (our translation)
Curriculum point CM1.GM.9 (our numbering) Solve problems involving the lengths of the sides of a polygon and its perimeter (our translation)

In CM2 (the final year of primary school), pupils consolidate the notion of perimeter by determining the total length of the outline of various polygons. They apply the addition of the lengths of all the sides to obtain the result. In problem-solving situations, they can reverse the process: starting from the known total perimeter and the lengths of the other segments, they use subtraction to determine the exact measure of the missing side.

The most frequent error occurs when a side is forgotten in figures with many segments. When looking for a missing dimension, some pupils simply subtract the first measurement they see from the total perimeter, forgetting to first add up all the other known sides before performing the final subtraction.

In practice, the worksheets offer two types of concrete activities based on labelled geometric figures:

With the Perimeter of a polygon model, the child reads the dimensions marked on each side of the figure and calculates their sum.
With the Missing side from the perimeter model, the overall perimeter is given in the statement and the pupil must find the measure of the segment marked with a question mark.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Perimeter of a polygon · Missing side from the perimeter · Missing side from the perimeter: choose the side · Perimeter of a polygon: choose the result · Perimeter of a rectangle step by step · Perimeter of a rectangle: extra data · Perimeter of a regular polygon: find the side · Perimeters of a rectangle and a square: compare · Perimeter of a polygon: word problem (fence)

Calculate the radius and diameter of a circle

Your child learns to relate the radius and diameter of a circle by calculating double or half of the given length.

Curriculum point 6e.EG.3 (our numbering) Know the definitions of a circle, a disc, a radius, a diameter, a chord (our translation)
Curriculum point 6e.EG.4 (our numbering) Understand the definition of a circle and that of a disc as sets of points (our translation)
Curriculum point 6e.EG.5 (our numbering) Solve problems involving distances from a point (our translation)
Curriculum point 6e.GM.1 (our numbering) Know that the perimeter of a disc is proportional to its diameter (our translation)
Curriculum point CM1.EG.4 (our numbering) Describe and recognise a circle and a disc as a set of points characterised by their distance from a given point (our translation)
Curriculum point CM2.EG.6 (our numbering) Describe and recognise a circle and a disc as a set of points characterised by their distance from a given point (our translation)

In grade 5 (CM2), the student consolidates their understanding of the circle as a set of points located at equal distance from a center. They learn to connect the fundamental measurements of this figure: the diameter measures twice the radius, and the radius represents half of the diameter.

The most frequent error comes from a confusion between the two notions. The child sometimes multiplies the measurement by two when they are already given the diameter and are looking for the radius, or they divide by two instead of multiplying. It also happens that they confuse the diameter with any simple line drawn inside the circle without passing through the center.

Practice exercises target this numerical conversion directly through two task models:

Diameter from the radius: the student calculates the length of the diameter by multiplying the given radius by 2 (for example, a radius of 6 cm gives a diameter of 12 cm).
Radius from the diameter: the student finds the distance from the center to the edge by dividing the diameter by 2 (for example, finding that a diameter of 15 cm corresponds to a radius of 7.5 cm).

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Diameter from the radius · Radius and diameter: find the mistake · Radius and diameter: true or false · Radius from diameter: choose the result · Radius from the diameter

Adding and subtracting amounts in euros

Your child learns to set up and carry out additions and subtractions with euro amounts to solve shopping situations.

Curriculum point CE2.GM.21 (our numbering) Add amounts of money in euros by setting out and carrying out the calculations. (our translation)
Curriculum point CE2.GM.22 (our numbering) Write and carry out subtractions of amounts in euros. (our translation)

At this stage, the student knows how to set up and calculate additions and subtractions with euro amounts. They use these operations to determine the total value of several expenses or to calculate the difference between a given sum and a price.

The main difficulty often lies in aligning the digits when working in columns, especially when combining whole euros and cents. If the currency units and decimal points are not rigorously aligned vertically, the carrying of digits shifts and distorts the final result.

In practice, the exercises ask students to set up and solve these operations to evaluate the amount of a grouped purchase or to calculate the exact change to return on a payment.

Reading, writing, and comparing large numbers

In CM2 (the final year of primary school in France), your child learns to read, write and compare whole numbers up to 999,999,999 while understanding the value of each digit.

Curriculum point 6e.NC.1 (our numbering) 6e.NC.3 (our numbering) CE2.NC.1 (our numbering) CE2.NC.2 (our numbering) CE2.NC.3 (our numbering) CE2.NC.4 (our numbering) CE2.NC.5 (our numbering) CE2.NC.6 (our numbering) CE2.NC.7 (our numbering) CE2.NC.8 (our numbering) CE2.NC.9 (our numbering) CM1.NC.3 (our numbering) CM1.NC.4 (our numbering) CM1.NC.5 (our numbering) CM1.NC.6 (our numbering) CM1.NC.7 (our numbering) CM1.NC.8 (our numbering) CM1.NC.9 (our numbering) CM2.NC.1 (our numbering) CM2.NC.2 (our numbering) CM2.NC.3 (our numbering) CM2.NC.4 (our numbering) CM2.NC.5 (our numbering) CM2.NC.6 (our numbering) Know and use the value of digits according to their position in the writing of a number (our translation)
Curriculum point Know large whole numbers (our translation)
Curriculum point Count collections. (our translation)
Curriculum point Build collections of a given cardinal number. (our translation)
Curriculum point Know and use the relationships between the units of numeration. (our translation)
Curriculum point Know the written and oral sequence of numbers up to ten thousand. (our translation)
Curriculum point Know and use various representations of a number and move from one to another. (our translation)
Curriculum point Know the value of digits according to their position in a number. (our translation)
Curriculum point Compare, bound and order whole numbers using the symbols (=, <, >). (our translation)
Curriculum point Order numbers in ascending or descending order. (our translation)
Curriculum point Understand and know how to use the expressions "equal to", "greater than", "less than", "between … and …". (our translation)
Curriculum point Know and use the relationships between the units of numeration (our translation)
Curriculum point Know the written sequence and the spoken sequence of numbers up to 999,999 (our translation)
Curriculum point Know the value of digits according to their position in a number (our translation)
Curriculum point Know and use various representations of a number and move from one to another (our translation)
Curriculum point Understand and know how to use the expressions "equal to", "greater than", "less than", "between … and …" (our translation)
Curriculum point Compare, bound, insert whole numbers using the symbols =, < and > (our translation)
Curriculum point Order numbers in ascending or descending order (our translation)
Curriculum point Know and use the relationships between place value units (our translation)
Curriculum point Know the written sequence and the spoken sequence of numbers up to 999 999 999 (our translation)
Curriculum point Know and use various representations of a number and move from one to another (our translation)
Curriculum point Know the value of digits according to their position in a number (our translation)
Curriculum point Compare, bracket and place whole numbers between others using the symbols =, < and > (our translation)
Curriculum point Order numbers in ascending or descending order (our translation)

In CM2 (Year 6), pupils consolidate their mastery of place-value notation for whole numbers up to 999,999,999. They learn to read and write these large numbers, to convert between digit form, written-word form and expanded form, and to order or compare them correctly using the symbols =, < and >.

A common difficulty arises when comparing two numbers with different numbers of digits: some pupils look only at the leftmost digit without first counting the total number of digits. Another classic confusion concerns place value, for example by confusing the value of a digit (the ten-thousands digit) with the total number of units it represents.

Through concrete activities, the child practises two types of exercises:

Compare large numbers: they place the correct comparison sign between two whole numbers of several millions, or arrange them in increasing or decreasing order.
How many times greater? Place value: they use the relationships between units of numeration to determine the value of a digit according to its position, or understand that a hundred-thousand is ten times greater than a ten-thousand.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Expanded form: the missing part · Multi-digit numbers: compare · Place value: choose how many times greater · Place value: how many times as large · Value of a digit: choose the answer · Building a number from its places (zeros inside)

Calculating cleverly with operations

In CM2 (the fifth year of primary school in France), your child learns to simplify calculations by breaking numbers down or rearranging additions and multiplications.

Curriculum point CE2.NC.26 (our numbering) Multiply a whole number by 4 or by 8. (our translation)
Curriculum point CE2.NC.28 (our numbering) Calculate the product of a number between 11 and 99 by a number less than 10 by decomposing the larger of the two factors into the sum of two numbers (distributivity property of multiplication over addition). (our translation)
Curriculum point CM1.NC.35 (our numbering) Know common number facts relating to whole numbers (our translation)
Curriculum point CM1.NC.42 (our numbering) Add or subtract 8, 9, 18, 19, 28, 29, 38 or 39, to a number (our translation)
Curriculum point CM1.NC.44 (our numbering) Multiply a whole number by 4 or by 8 (our translation)
Curriculum point CM1.NC.45 (our numbering) Multiply a whole number by 5 (our translation)
Curriculum point CM1.NC.46 (our numbering) Use the distributivity of multiplication over addition in simple cases (our translation)
Curriculum point CM2.NC.35 (our numbering) Know common number facts with whole numbers (our translation)
Curriculum point CM2.NC.44 (our numbering) Add or subtract 8, 9, 18, 19, 28, 29, …, 98 or 99 to a number (our translation)
Curriculum point CM2.NC.45 (our numbering) Multiply a whole number less than 10 of tens, hundreds or thousands by a whole number less than 10 of tens, hundreds or thousands (our translation)
Curriculum point CM2.NC.46 (our numbering) Use the distributive property of multiplication over addition in simple cases (our translation)
Curriculum point CM2.NC.49 (our numbering) Divide a whole number by 4 or by 8 (our translation)

In Year 5 (CM2), pupils learn to choose the quickest route to calculate mentally without writing out the operation. In particular, they learn to quickly add or subtract numbers close to a multiple of ten, such as 8, 9, 19, or numbers up to 98 and 99. They also apply the distributive property in simple situations and learn to multiply whole numbers less than 10 by tens, hundreds, or thousands.

The most common error appears when adjusting the result. To add 19 or 29, the pupil correctly thinks of adding 20 or 30, but often forgets to subtract 1 at the end, or else adds it by mistake. Similarly, when breaking down a multiplication, the classic oversight is to multiply only the tens while forgetting to also multiply the units.

The exercises offered under the headings Additionne astucieusement and Multiplie astucieusement train children to spot these number shortcuts. They practise breaking down one term to rely on round numbers, or distributing a product to find the exact result with ease.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Add the smart way · Multiply the smart way · Smart addition: whole hundreds: choose the answer · Clever multiplication: find the mistake · Clever multiplication: true or false · Mental maths: multiplying by a number close to 100

Finding an unknown value in a problem

Your child learns to set up and solve an equation to find a mystery number or a starting quantity from a word problem.

Curriculum point 5e.NC.44 (our numbering) Model problems involving missing-number operations by equations of the form a𝑥 = c or 𝑥 + b = c . (our translation)
Curriculum point 6e.NC.42 (our numbering) Use pre-algebraic models to solve algebraic problems (our translation)
Curriculum point CM1.NC.62 (our numbering) Solve algebraic problems (our translation)
Curriculum point CM2.NC.65 (our numbering) Solve algebraic problems (our translation)

In CM2 (the last year of primary school), pupils begin learning to solve simple algebraic problems. Faced with a word problem, they learn to identify what is being asked and to translate the steps of the story into a diagram or an equation with a blank in order to calculate the missing value.

The most common mistake is to apply the operations from the text directly to the final result instead of reversing the process. For example, if the problem states that 15 objects were added to reach a total, the child often instinctively adds 15 again to the final number, instead of subtracting to get back to the starting situation.

On practice worksheets, this work takes the form of concrete situations drawn from two models :

What number was it? The pupil must find a starting number after a series of successive calculations.
How many were there at the beginning? The child traces back through a story involving gains or losses to find the exact quantity present at the start.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Equation from context: which number was it · Equation with an unknown: choose the answer · Equation with an unknown: find the mistake · Equation with an unknown: true or false · Equation for the starting amount: word problem

Naming quadrilaterals according to their properties

The student learns to identify and name special quadrilaterals by relying on their right angles, their parallel sides, and their equal side lengths.

Curriculum point 5e.EG.20 (our numbering) Define the parallelogram. (our translation)
Curriculum point 5e.EG.23 (our numbering) Use a characteristic property of the diagonals or the sides to construct them or to identify the nature of the quadrilateral. (our translation)
Curriculum point 5e.EG.24 (our numbering) Define the special parallelograms (rectangle, rhombus, square). (our translation)
Curriculum point CE2.EG.8 (our numbering) Recognise, name and describe the square, the rectangle, the triangle, the right-angled triangle and the rhombus. (our translation)
Curriculum point CE2.EG.9 (our numbering) Know the properties of angles and the equalities of length for squares, rectangles and rhombuses. (our translation)
Curriculum point CM1.EG.1 (our numbering) Use appropriate geometric vocabulary in the context of learning the corresponding concepts (our translation)
Curriculum point CM1.EG.7 (our numbering) Recognise and name the following figures by referring to their definition: triangle, right-angled triangle, isosceles triangle, equilateral triangle, quadrilateral, square, rectangle and rhombus (our translation)
Curriculum point CM1.EG.8 (our numbering) Know the properties of parallelism of opposite sides and of equalities of lengths and angles for common figures: right triangle, isosceles triangle, equilateral triangle, square, rectangle and rhombus (our translation)
Curriculum point CM2.EG.1 (our numbering) Use the appropriate geometric vocabulary in the context of learning the corresponding concepts (our translation)
Curriculum point CM2.EG.7 (our numbering) Recognise and name the following figures by relying on their definition: triangle, right-angled triangle, isosceles triangle, equilateral triangle, quadrilateral, square, rectangle, rhombus, trapezium, right-angled trapezium, pentagon and hexagon (our translation)
Curriculum point CM2.EG.8 (our numbering) Know the properties of parallelism of opposite sides, and of equal lengths and angles, for common figures: right triangle, isosceles triangle, equilateral triangle, square, rectangle, rhombus, trapezium and right trapezium (our translation)

In grade 5 (CM2), the student no longer relies merely on the visual appearance of a figure to recognize it. They identify and precisely name the different quadrilaterals (square, rectangle, rhombus, trapezoid and right trapezoid), justifying their choice by their geometric definitions: the parallelism of opposite sides, the presence of right angles, or the equality of side lengths.

A classic difficulty arises as soon as a figure changes orientation: a square tilted on its corner is often mistaken for a simple rhombus, or a rhombus is not recognized when it is not in its usual position. In addition, students sometimes struggle to grasp the nesting of definitions, forgetting, for example, that a square has four right angles and therefore perfectly satisfies the definition of a rectangle.

In practice exercises, the student answers concrete questions such as "What is the name of this quadrilateral?" based on a coded drawing, or solves logic questions such as "Is a square also a rectangle?" while explaining the common geometric properties.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Pairs of parallel sides: true or false · Quadrilaterals: how many pairs of parallel sides? · What is this quadrilateral called? · Quadrilaterals: is a square also a rectangle

Classifying triangles by their sides and angles

Your child learns to identify and name special triangles (isosceles, equilateral, right-angled) by observing their equal sides and right angles.

Curriculum point 6e.EG.15 (our numbering) Know and use the angle properties of special triangles: right-angled triangle, isosceles triangle, equilateral triangle (our translation)
Curriculum point CM1.EG.1 (our numbering) Use appropriate geometric vocabulary in the context of learning the corresponding concepts (our translation)
Curriculum point CM1.EG.7 (our numbering) Recognise and name the following figures by referring to their definition: triangle, right-angled triangle, isosceles triangle, equilateral triangle, quadrilateral, square, rectangle and rhombus (our translation)
Curriculum point CM1.EG.8 (our numbering) Know the properties of parallelism of opposite sides and of equalities of lengths and angles for common figures: right triangle, isosceles triangle, equilateral triangle, square, rectangle and rhombus (our translation)
Curriculum point CM2.EG.1 (our numbering) Use the appropriate geometric vocabulary in the context of learning the corresponding concepts (our translation)
Curriculum point CM2.EG.7 (our numbering) Recognise and name the following figures by relying on their definition: triangle, right-angled triangle, isosceles triangle, equilateral triangle, quadrilateral, square, rectangle, rhombus, trapezium, right-angled trapezium, pentagon and hexagon (our translation)
Curriculum point CM2.EG.8 (our numbering) Know the properties of parallelism of opposite sides, and of equal lengths and angles, for common figures: right triangle, isosceles triangle, equilateral triangle, square, rectangle, rhombus, trapezium and right trapezium (our translation)

In CM2, pupils rely on geometric definitions to recognise and name shapes precisely: the right triangle (which has a right angle), the isosceles triangle (which has two sides of equal length and two equal angles) and the equilateral triangle (whose three sides and three angles are all equal).

The most common mistake is to judge a shape by its orientation or its general appearance rather than by its actual properties. A child may thus confuse an isosceles triangle with an equilateral triangle as soon as the triangle is tilted, or fail to spot a right angle when it is not placed on a horizontal base.

In the worksheets, the work is organised around two concrete approaches: Type of triangle by angles and Type of triangle by sides. The pupil observes figures showing measurements or geometric markings, then applies the corresponding definition to classify each triangle in the correct category.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Kind of triangle by its sides · Kind of triangle by its angles · Types of triangles: true or false · Types of triangles: which names include others

Calculating with one or two pairs of parentheses

In CM2, the student learns to organize their calculation steps to solve expressions containing one or two pairs of parentheses.

Curriculum point 5e.NC.21 (our numbering) Know and justify the situations in which parentheses are essential to the meaning of expressions. (our translation)
Curriculum point 5e.NC.32 (our numbering) Calculate the numerical value of expressions containing simple powers, additions, subtractions and products. (our translation)
Curriculum point 5e.NC.4 (our numbering) Chaining operations. (our translation)
Curriculum point 5e.NC.7 (our numbering) Know and use the order of operations. (our translation)
Curriculum point CM1.NC.48 (our numbering) Know how to perform a calculation containing brackets (our translation)
Curriculum point CM2.NC.53 (our numbering) Being able to carry out a calculation containing one or two pairs of brackets (our translation)

In CM2 (fifth grade), the student takes a new step by learning to perform calculations involving one or two pairs of parentheses. They know that parentheses indicate the priority calculations and that they must necessarily solve them first before moving on to the other operations.

The most common error consists of reading and calculating the expression from left to right in a linear way, ignoring the order imposed by the parentheses. When a line of calculation contains two distinct pairs, the child also tends to forget to reduce one of the two blocks before performing the final operation that links them.

In the practice worksheets based on the exercise Calcule l'expression avec parenthèses, the student is faced with equations to complete. They practice identifying the priority blocks, writing the intermediate steps, and determining the final result.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Evaluate an expression with brackets · Order of operations with brackets step by step · Order of operations with brackets: choose the result · Order of operations with brackets: find the mistake · Order of operations with brackets: true or false · Two expressions with brackets: compare

Estimating the result of an addition

In CM2 (the final year of French primary school), pupils learn to estimate the order of magnitude of a sum in order to anticipate or check whether a calculation is plausible.

Curriculum point 2de.AUT.5 (our numbering) Estimate an order of magnitude. (our translation)
Curriculum point 6e.NC.19 (our numbering) Check results using orders of magnitude (our translation)
Curriculum point CM1.NC.47 (our numbering) Estimate the result of an operation (our translation)
Curriculum point CM2.NC.52 (our numbering) Estimate the result of an operation (our translation)

In grade 5 (CM2), students learn to estimate the result of an operation by relying on orders of magnitude. For an addition, this means mentally replacing each term with a nearby, simpler number (rounded to the nearest ten, hundred or thousand) in order to quickly obtain an approximate value of the sum.

The classic difficulty is wanting to calculate the exact sum before giving a rounded result, which defeats the purpose of the method. Students may also make place-value errors with large numbers, for example by forgetting a zero during the estimate, which gives an order of magnitude ten times too small or too large.

Through exercises such as Estime une somme, students practise replacing the terms of an addition with approximate values in order to choose or write a consistent estimate, thereby developing the habit of self-checking their future written calculations.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Estimate a sum · Estimating a sum: choose the estimate · Estimating: choose the rounding to hundreds

Solving complex multi-step problems

The student learns to organize several calculation steps and to manage stock constraints in order to solve concrete everyday problems.

Curriculum point 6e.NC.20 (our numbering) Solve problems involving multiplications of decimal numbers (our translation)
Curriculum point 6e.NC.22 (our numbering) Solve problems involving decimal divisions (our translation)
Curriculum point 6e.NC.24 (our numbering) Solve problems involving Euclidean divisions (our translation)
Curriculum point 6e.NC.37 (our numbering) Solve problems involving fractions (our translation)
Curriculum point CE1.NC.38 (our numbering) Solve two-step additive problems. (our translation)
Curriculum point CE1.NC.40 (our numbering) Solve two-step mixed problems (one additive step and one multiplicative step). (our translation)
Curriculum point CE2.NC.30 (our numbering) Solve two-step additive problems. (our translation)
Curriculum point CE2.NC.32 (our numbering) Solve mixed problems in two or three steps. (our translation)
Curriculum point CM1.NC.53 (our numbering) Solve one-step additive problems of the "part-whole" and "comparison" types (our translation)
Curriculum point CM1.NC.54 (our numbering) Solve additive problems in two or three steps (our translation)
Curriculum point CM1.NC.55 (our numbering) Solve multiplicative part-whole problems in one step (our translation)
Curriculum point CM1.NC.57 (our numbering) Solve mixed problems in two or three steps (our translation)
Curriculum point CM1.NC.59 (our numbering) Solve optimization problems (our translation)
Curriculum point CM2.NC.57 (our numbering) Solve additive problems in one or more steps (our translation)
Curriculum point CM2.NC.58 (our numbering) Solve one-step multiplicative problems of the "part-whole" type (our translation)
Curriculum point CM2.NC.59 (our numbering) Solve mixed multi-step problems (our translation)
Curriculum point CM2.NC.62 (our numbering) Solve optimization problems (our translation)
Curriculum point CP.NC.30 (our numbering) Solve two-step additive problems (number field less than or equal to 30). (our translation)

In CM2 (the final year of primary school), the pupil can chain several successive calculation steps by combining different operations (addition, subtraction, multiplication or division). They also solve search and optimisation problems by using numerical data to find a final result or to determine a maximum possible quantity.

The main difficulty often lies in planning the approach. Faced with a long problem statement, the child tends to start calculating immediately with the first numbers they read, without defining an intermediate question. In resource-management situations, they frequently forget to identify the most limiting constraint, which leads them to overestimate the final result.

The exercises offered illustrate these skills through two types of situations:

The multi-step problem (combining), where the pupil must first calculate subtotals (for example, the earnings or spending of different people) before being able to determine the overall total or a remainder.
The exercise how many objects at most with the stock, where it is a matter of adjusting a production or an assembly according to limited supplies of different items, by finding which part runs out first.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Stock and sets: choose the number of sets · Stock and sets: the most sets you can make · Two-step word problem (combine) (grade 3) · Word problem, three days: choose the result (grade 3) · Word problem, three days: true or false (grade 3)

Comparing fractions with different denominators

In CM2 (the final year of primary school in France), your child learns to compare two fractions that do not have the same denominator, in order to determine which one is larger or whether they are equal.

Curriculum point 2de.AUT.2 (our numbering) Perform operations and comparisons between simple fractions. (our translation)
Curriculum point 5e.NC.25 (our numbering) Compare fractions. (our translation)
Curriculum point 6e.NC.33 (our numbering) Compare and bracket fractions (our translation)
Curriculum point 6e.NC.34 (our numbering) Ordering a list of numbers written as fractions or mixed numbers (our translation)
Curriculum point CM1.NC.20 (our numbering) Comparing fractions (our translation)
Curriculum point CM2.NC.19 (our numbering) Compare fractions (our translation)

In CM2 (the final year of primary school), pupils reach a key milestone by learning to compare fractions that share neither the same numerator nor the same denominator. It is no longer only a matter of noticing how many parts are taken from the same whole, but of assessing the real value of each fractional notation in order to determine which is greater or to identify equivalences.

The most common mistake is to treat the numerator and the denominator as two independent whole numbers. The pupil may then think that 3/8 is greater than 1/2 because 3 is bigger than 1 and 8 is bigger than 2, without realising the overall ratio that each quantity represents.

Through the exercises in the worksheet Compare fractions with different denominators, the child practises concretely placing the signs <, > or = between two fractions, for example by rewriting one of the fractions or by relying on simple reference points such as the whole (1).

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Equivalent fractions: choose the missing numerator · Equivalent fractions: find the mistake · Equivalent fractions: the missing numerator · Equivalent fractions: true or false · Fractions with the same numerator: compare · Fractions: compare with one half · Fractions with unlike denominators: compare

Write a fraction with a larger denominator

In CM2 (the final year of primary school), your child learns to find a fraction equivalent to a common fraction by multiplying the numerator and the denominator by the same whole number.

Curriculum point 6e.NC.32 (our numbering) Establish equalities of fractions (our translation)
Curriculum point CE2.NC.11 (our numbering) Know how to establish equalities of fractions less than or equal to 1. (our translation)
Curriculum point CM1.NC.36 (our numbering) Know some relationships between common fractions (our translation)
Curriculum point CM2.NC.37 (our numbering) Know some relationships between common fractions (our translation)

In CM2 (the final year of primary school), pupils rely on the relationships between common fractions (halves, thirds, quarters, fifths or tenths). They learn to transform a fraction into another one that represents exactly the same quantity but is divided into a greater number of parts, by multiplying the numerator and the denominator by the same factor.

The most classic mistake is to multiply only the bottom of the fraction and forget the top, or to add a number instead of multiplying (for example, believing that 1/2 becomes 2/3 by adding 1 to the numerator and to the denominator). The child then loses the equivalence with the original value.

Through activities such as the exercise Find the equal fraction, the pupil is asked to complete equalities with a gap (such as finding the missing numerator in 3/4 = .../12) or to identify the correct fraction among several proposed options.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Expanding fractions: choose the multiplier · Expanding fractions: find the mistake · Expanding fractions: the missing denominator · Expanding fractions: true or false · Expanding fractions: what was it multiplied by? · Find the equivalent fraction

Simplifying a fraction

The student learns to simplify a fraction to find a simpler equal fraction, by using common divisors and the relationships between common fractions.

Curriculum point 2de.NC.4 (our numbering) Present fractions in their simplest (irreducible) form. (our translation)
Curriculum point 6e.NC.32 (our numbering) Establish equalities of fractions (our translation)
Curriculum point CM2.NC.37 (our numbering) Know some relationships between common fractions (our translation)

In CM2 (the final year of primary school), children learn to establish equivalences between fractions by relying on common divisors and their knowledge of common fractions (such as halves, thirds, or quarters). They discover that a fraction can be written in a simpler form by dividing its numerator and its denominator by the same whole number, without changing the value it represents.

The most frequent error is to divide only one of the two terms (the numerator or the denominator), or to subtract the same number instead of dividing. Pupils also often stop after a first step without noticing that a common divisor could still reduce the fraction further.

In the exercise Simplify the fraction, a starting fraction is given. The pupil must look for a common divisor of the two numbers in order to write the most reduced equivalent fraction possible, for example by turning 4/8 into 1/2 or 6/9 into 2/3.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Simplify the fraction · Simplifying fractions: choose the missing denominator · Simplifying fractions: choose the new numerator · Simplifying fractions: the missing denominator · Simplifying fractions: what was it divided by?

Multiplying a fraction by a whole number

The student learns to calculate the product of a whole number by a fraction in order to determine a fraction of a whole number.

Curriculum point 6e.NC.36 (our numbering) Multiplying a fraction by a whole number (our translation)
Curriculum point CM2.NC.21 (our numbering) Calculate the product of an integer and a fraction (our translation)

In grade 5 (CM2), students learn to calculate the product of a whole number and a fraction. This skill allows them to make sense of multiplying a fraction by a whole number (for example 3 × 2/5) and to concretely calculate the fraction of a quantity.

The most common error is to multiply both the numerator and the denominator by the whole number (for example, calculating 3 × 2/5 = 6/15). The child must understand that the whole number multiplies only the numerator: the number of parts changes, but the size of each part stays the same.

In exercises of the type Multiply a fraction by a whole number, students practice performing these calculations directly to obtain the result as a fraction or a whole number.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Multiplying a fraction by a whole: repeated addition · Fraction times a whole number: the missing numerator · Multiply a fraction by a whole number · Multiplying a fraction by a whole number: choose the result · Multiplying a fraction by a whole number: find the mistake · Multiplying a fraction by a whole number: true or false

Identify acute, right, and obtuse angles

In CM2, students learn to compare an angle with the right angle of 90° in order to determine precisely whether it is an acute, right, or obtuse angle.

Curriculum point 6e.EG.11 (our numbering) Construct an angle of a given measure (our translation)
Curriculum point 6e.EG.9 (our numbering) Know and use angles, together with the associated vocabulary and notation: right angle, straight angle, full angle, zero angle, acute angle, obtuse angle, vertically opposite angles, adjacent angles, supplementary angles (our translation)
Curriculum point CE1.EG.10 (our numbering) Use a ruler to check alignments and a set square to check that an angle is a right angle. (our translation)
Curriculum point CE1.EG.12 (our numbering) Know and use the code for right angles. (our translation)
Curriculum point CE2.EG.11 (our numbering) Know and use the notation for a right angle and the notation showing that segments have the same length. (our translation)
Curriculum point CM1.EG.3 (our numbering) Know the common codes used in geometry (our translation)
Curriculum point CM1.GM.23 (our numbering) Use the specific vocabulary associated with angles (our translation)
Curriculum point CM1.GM.24 (our numbering) Understand and use the notations of angles (our translation)
Curriculum point CM1.GM.25 (our numbering) Compare angles (our translation)
Curriculum point CM2.EG.3 (our numbering) Know the usual notations and codes used in geometry (our translation)
Curriculum point CM2.GM.11 (our numbering) Know that a right angle measures 90° (our translation)
Curriculum point CM2.GM.6 (our numbering) Use the specific vocabulary associated with angles (our translation)
Curriculum point CM2.GM.7 (our numbering) Understand and use the notations for angles (our translation)
Curriculum point CM2.GM.8 (our numbering) Compare angles (our translation)

In Year 6 (CM2), pupils rely on the fundamental benchmark of the right angle, which measures 90°, to compare and classify openings. They consolidate the associated geometric vocabulary: they identify an acute angle (narrower than a right angle) and an obtuse angle (wider than a right angle).

The most common error is confusing the length of the drawn lines with the measure of the angle. An acute angle drawn with very long segments often seems "bigger" to the pupil than an obtuse angle drawn with short segments. A tilted orientation can also distort the visual estimate of the opening.

Through activities such as the exercise Recognise the type of angle, the pupil observes angles presented in various positions and must name the corresponding category, using a template or a set square if necessary to check the comparison with 90°.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Classify the angle · Complementary angles: find the other angle · Supplementary angles: choose the other angle · Supplementary angles: find the other angle · Vertical angles: choose the measure · A half turn of a clock hand (grade 2–3) · A half turn of a clock hand: true or false (grade 2–3) · A quarter turn anticlockwise (grade 2–3) · A quarter turn clockwise (grade 2–3) · A quarter turn clockwise: choose the result (grade 2–3) · A three-quarter turn clockwise (grade 2–3)

Calculating a fraction of a number

Your child is learning to calculate a fraction of a whole number or of a concrete quantity.

Curriculum point 6e.NC.31 (our numbering) Use multiplication to apply a fraction to a whole number (our translation)
Curriculum point 6e.NC.37 (our numbering) Solve problems involving fractions (our translation)
Curriculum point CM1.NC.22 (our numbering) Determining a fraction of a quantity or of a magnitude (our translation)
Curriculum point CM2.NC.22 (our numbering) Determine a fraction of a quantity or a magnitude (our translation)

In CM2 (the last year of primary school), pupils learn to find a fraction of a quantity or a whole number. They understand how to share the total quantity into equal parts according to the denominator, then how to multiply the result obtained by the numerator to find the required value.

The most common mistake is to reverse the roles of the numbers: the child divides by the numerator instead of the denominator, or stops after the first division, forgetting to multiply by the number of parts remaining.

With the exercise Calcule la fraction d’un nombre, practice takes the form of simple direct applications, such as calculating two thirds of 18 or three fifths of 40.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Fraction of a number step by step · Fraction of a number: calculate · Fraction of a number: choose the result · Fraction of an amount on a bar model · The whole from a part on a bar model · Find a fraction of a number · Fraction of a number: choose the whole · Fraction of a number: compare two parts · Fraction of a number: find the whole from a part · Fraction of a number: what is left after taking a part

Putting fractions over a common denominator

Your child is learning to convert fractions so they share a common denominator, which makes it possible to compare, add, or subtract them.

Curriculum point 6e.NC.35 (our numbering) Add and subtract fractions (our translation)
Curriculum point CM1.NC.20 (our numbering) Comparing fractions (our translation)
Curriculum point CM2.NC.20 (our numbering) Adding and subtracting fractions (our translation)

In grade 5 (CM2), to compare, add, or subtract simple fractions, students must learn to express them with the same division of the whole. The child relies on finding common multiples to transform one of the fractions (or both) into an equivalent fraction without changing its value.

The most frequent mistake is to multiply only the denominator and forget to multiply the numerator by the same number. Another classic pitfall during a calculation is adding the denominators directly instead of first looking for a shared denominator.

Through the exercise Find the common denominator, the student practices identifying the number that works for two given fractions (for example, converting thirds into sixths so they can be paired with sixths). They rewrite the fractions over this common base, an essential step before setting up an addition or subtraction.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Common denominator: choose the numerator · Common denominator: find the least one · Common denominator: choose the least one

Writing a decimal number as a fraction

In CM2, pupils learn to convert a decimal number into a decimal fraction, relying on tenths, hundredths and thousandths.

Curriculum point 2de.AUT.4 (our numbering) Convert between different representations of a number (decimal, fraction, percentage). (our translation)
Curriculum point 6e.NC.6 (our numbering) Associate and use different representations of a decimal number: decimal notation, fraction, mixed number, percentage (our translation)
Curriculum point CM1.NC.23 (our numbering) Interpret, represent, write and read decimal fractions (our translation)
Curriculum point CM1.NC.30 (our numbering) Convert between a representation as a decimal fraction or a sum of decimal fractions and a decimal-point notation, and vice versa (our translation)
Curriculum point CM2.NC.23 (our numbering) Interpret, represent, write and read decimal fractions (our translation)
Curriculum point CM2.NC.30 (our numbering) Converting between a fraction-form writing of a decimal fraction or a sum of decimal fractions and a decimal-point (comma) writing, and vice versa (our translation)

In CM2, the pupil strengthens the link between decimal notation and decimal fractions. They learn to convert decimal numbers that include tenths, hundredths and now thousandths. For example, they know that 0.3 corresponds to 3/10, that 2.35 becomes 235/100, and that 0.007 is written 7/1,000.

The most common error is choosing a wrong denominator by ignoring the number of digits after the decimal point. Many pupils tend to put everything over 10 (writing, for example, 25/10 for 0.25). The presence of zeros after the decimal point is also a frequent trap: a pupil may be tempted to write 5/10 for 0.05, overlooking the zero in the tenths place.

In the exercises given under the heading "Write the decimal number as a fraction", the pupil is given a decimal number and must directly give its equivalent fractional form (with a denominator equal to 10, 100 or 1,000).

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Decimal to fraction: choose the fraction · Decimal to fraction: find the mistake · Decimal to fraction: true or false · Write a decimal as a fraction

Writing a fraction in decimal form

In Year 6 (CM2), pupils learn to convert decimal or common fractions into decimal numbers.

Curriculum point 2de.AUT.4 (our numbering) Convert between different representations of a number (decimal, fraction, percentage). (our translation)
Curriculum point 6e.NC.30 (our numbering) Know that the fraction a/b can represent a whole number, a non-whole decimal number or a non-decimal number (our translation)
Curriculum point CM1.NC.30 (our numbering) Convert between a representation as a decimal fraction or a sum of decimal fractions and a decimal-point notation, and vice versa (our translation)
Curriculum point CM1.NC.37 (our numbering) Know the decimal notation of common fractions (our translation)
Curriculum point CM2.NC.30 (our numbering) Converting between a fraction-form writing of a decimal fraction or a sum of decimal fractions and a decimal-point (comma) writing, and vice versa (our translation)
Curriculum point CM2.NC.38 (our numbering) Know the decimal notation of common fractions (our translation)

In grade 5 (CM2), children learn to convert a decimal fraction (in tenths, hundredths or thousandths) as well as common fractions (such as 1/2 or 1/4) into the form of a decimal number. They make a direct link between fractional notation and the place value of each digit, establishing for example that 25/100 is written 0.25 or that 1/2 corresponds to 0.5.

The most common error consists of placing the numerator directly after the decimal point: a pupil might write 0.3 for 3/100 instead of 0.03, forgetting the zero in the tenths place, or write 1.2 for 1/2 instead of looking for the decimal value of the sharing.

In written work, the practice is based on explicit instructions such as: "Write the fraction as a decimal number". The child practises matching each given fraction with its exact decimal form.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Fraction to decimal: choose the decimal · Fraction to decimal: find the mistake · Fraction to decimal: true or false · Write a fraction as a decimal

Comparing decimal numbers

The student learns to compare two decimal numbers using the symbols =, < and >, first by looking at their whole-number parts and then at their decimal digits.

Curriculum point 6e.NC.10 (our numbering) Order a list of decimal numbers (our translation)
Curriculum point 6e.NC.13 (our numbering) Frame a decimal number between two decimal numbers, insert a decimal number between two decimal numbers (our translation)
Curriculum point 6e.NC.4 (our numbering) Recognise a decimal number (our translation)
Curriculum point 6e.NC.9 (our numbering) Compare two decimal numbers (our translation)
Curriculum point CM1.NC.28 (our numbering) Compare, bracket and insert decimal fractions using the symbols =, < and > (our translation)
Curriculum point CM1.NC.29 (our numbering) Order decimal fractions in ascending or descending order (our translation)
Curriculum point CM1.NC.34 (our numbering) Compare, bracket, insert between, and order, in ascending or descending order, decimal numbers given in their decimal notation, using the symbols =, < and > (our translation)
Curriculum point CM2.NC.28 (our numbering) Compare, bracket and place decimal fractions between two given numbers using the symbols =, < and > (our translation)
Curriculum point CM2.NC.29 (our numbering) Order decimal fractions in ascending or descending order (our translation)
Curriculum point CM2.NC.34 (our numbering) Compare, bound, insert, order in ascending or descending order decimal numbers given in decimal notation using the symbols =, < and > (our translation)

In CM2, the student can compare two decimal numbers written with a decimal point, extending to thousandths, using the symbols =, < and >. They learn to analyze the whole-number part first, then, when those are equal, to successively compare the digit of the tenths, the hundredths and the thousandths.

The most common error consists of treating the decimal part as an independent whole number: the child claims, for example, that 3.18 is greater than 3.4 because 18 is greater than 4. They rely on the length of the written form instead of considering the place value of each digit after the decimal point.

Through the practice worksheets based on the model Compare decimal numbers, the student is invited to complete direct comparisons by writing the appropriate symbol between two numbers, for example to decide between 12.35 and 12.4.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Comparing decimals: choose the greatest · Comparing decimals: true or false · Decimals: compare · Decimals: order from smallest

Long division with decimals

Your child is learning to set up and carry out decimal divisions with a one-digit divisor, for a whole or decimal dividend.

Curriculum point 5e.NC.1 (our numbering) Add, subtract, multiply and divide to solve problems and check the plausibility of one's result. (our translation)
Curriculum point 5e.NC.3 (our numbering) Dividing by a decimal number. (our translation)
Curriculum point 6e.NC.21 (our numbering) Dividing a decimal number by a non-zero whole number less than 10 (our translation)
Curriculum point 6e.NC.22 (our numbering) Solve problems involving decimal divisions (our translation)
Curriculum point CM2.NC.36 (our numbering) Know half of the odd numbers up to 15 (our translation)
Curriculum point CM2.NC.48 (our numbering) Calculate half of a decimal number in simple cases (our translation)
Curriculum point CM2.NC.55 (our numbering) Pose and carry out decimal divisions with a whole-number dividend and a one-digit divisor (our translation)
Curriculum point CM2.NC.56 (our numbering) Set up and carry out decimal divisions with a decimal dividend and a one-digit divisor (our translation)

In grade 5 (CM2), students learn to set up and carry out decimal divisions when the divisor has only a single digit. The dividend may be a whole number that is shared beyond the units, or directly a decimal number. At the same time, they consolidate mental arithmetic by learning, in particular, to find half of odd numbers up to 15 and of simple decimals.

The most common mistake concerns forgetting the decimal point in the quotient. Many students carry out the successive subtractions without difficulty, but forget to write the decimal point in the result at the precise moment they bring down the tenths digit. They then obtain a quotient that is ten or a hundred times too large, without noticing the real order of magnitude of the result.

In the exercise Divise des nombres décimaux, the child is asked to set up the operation in columns. They first divide the whole-number part by the single-digit divisor, place the decimal point in the result as soon as they cross the one in the dividend, then continue the successive shares to calculate the decimal value.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Dividing decimals: by a whole number · Dividing decimals: choose the result · Dividing decimals: find the mistake · Dividing decimals: move the point in both numbers · Dividing decimals: true or false · Divide decimals · Dividing decimals: is the quotient larger?

Finding the divisors and multiples of a number

In grade 5 (CM2), students learn to recognize multiples and to systematically list all the divisors of whole numbers up to 30.

Curriculum point 2de.NC.3 (our numbering) Model and solve problems involving the notions of multiple, divisor, even number and odd number. (our translation)
Curriculum point 5e.NC.9 (our numbering) Use the concepts of multiples and divisors. (our translation)
Curriculum point CE2.NC.17 (our numbering) Understand and use the words "factor", "product" and "multiple". (our translation)
Curriculum point CM1.NC.12 (our numbering) Being able to determine whether a given whole number is a multiple of a whole number less than or equal to 10 (our translation)
Curriculum point CM1.NC.13 (our numbering) Being able to determine whether a whole number less than or equal to 10 is a divisor of a given whole number (our translation)
Curriculum point CM2.NC.10 (our numbering) Determine all the divisors of an integer less than or equal to 30 (our translation)
Curriculum point CM2.NC.8 (our numbering) Determine whether a whole number less than or equal to 10 is a divisor of a given whole number, or whether a given whole number is a multiple of a whole number less than or equal to 10 (our translation)
Curriculum point CM2.NC.9 (our numbering) Determine divisors of a whole number less than or equal to 100 (our translation)

In CM2 (the final year of primary school), your child is consolidating the use of multiplication tables to study relationships between numbers. They can determine whether a whole number less than or equal to 10 is a divisor of a given number (or whether that number is a multiple of it). They practise finding divisors for whole numbers up to 100, and learn to find all the divisors of whole numbers less than or equal to 30.

The most common mistake is forgetting divisors along the way: students often omit 1 and the number itself, or skip an intermediate pair (such as forgetting 3 and 8 for the number 24). Confusion between the terms multiple and divisor also remains common, with some students claiming, for example, that 6 is a multiple of 18.

In practice, this shows up in exercises titled "Write all the divisors of a number". Faced with a number such as 18, 20 or 24, the student looks for all the possible decompositions as products in order to produce the complete ordered list of its divisors (for example 1, 2, 4, 5, 10 and 20 for the number 20).

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Factors of a number: choose how many · List all factors of a number · Factors: how many are there? · Factors: smallest number with k factors (grade 6–7) · Smallest number with k divisors: find the mistake (grade 6–7) · Smallest number with k divisors: true or false (grade 6–7)

Multiplying a digit by a multiple of 10

The student learns to quickly calculate the product of a number less than 10 by a multiple of ten, such as 4 × 30 or 7 × 60, by relying on their multiplication tables.

Curriculum point CE2.NC.23 (our numbering) Multiply a whole number by 10 or 100. (our translation)
Curriculum point CE2.NC.27 (our numbering) Multiplier un nombre inférieur à 10 par un nombre entier de dizaines.Multiply a number less than 10 by a whole number of tens. (our translation)
Curriculum point CM1.NC.39 (our numbering) Multiplier un nombre entier par 10, 100 ou 1 000
Curriculum point CM1.NC.43 (our numbering) Multiply a whole number less than 10 by a whole number of tens or hundreds (our translation)
Curriculum point CM2.NC.45 (our numbering) Multiply a whole number less than 10 of tens, hundreds or thousands by a whole number less than 10 of tens, hundreds or thousands (our translation)

In Grade 5 (CM2), students consolidate their mental calculation by multiplying a whole number less than 10 by a whole number of tens (20, 30, 40, etc.). To find the result, they break the operation down by relying on times tables: for example, to calculate 6 × 40, they first calculate 6 × 4 tens to get 24 tens, that is 240.

The most common error occurs when the product of the first two digits already ends in a zero, as in 5 × 40. Students often write 20, thinking that the final zero of 40 has already been taken into account, instead of obtaining 20 tens, that is 200. Another common confusion consists of adding the zero rather than multiplying by ten.

In practice, exercises from the Multiplying by a multiple of ten model appear as direct calculations in a line, such as 8 × 50 = … or 30 × 7 = …, to be solved without setting out the operation in order to automate the reasoning.

Create a worksheet for this skill Multiple-choice test

Task types: Multiplying by tens: choose the result (grade 3) · Multiply by a multiple of ten (grade 3) · Multiplying by tens: true or false (grade 3)

Understanding and calculating a fraction of a quantity

In Year 6 (CM2), pupils learn to read, write and interpret fractions in order to determine a precise share of a collection or of a whole number.

Curriculum point CE1.NC.16 (our numbering) Know how to interpret, represent, write and read the fractions 1/2, 1/3, 1/4, 1/5, 1/6, 1/8 and 1/10. (our translation)
Curriculum point CE1.NC.17 (our numbering) Know how to interpret, represent, write and read fractions less than or equal to 1. (our translation)
Curriculum point CE1.NC.18 (our numbering) To know and use the words “denominator” and “numerator”. (our translation)
Curriculum point CM1.NC.14 (our numbering) Know how to interpret, represent, write and read fractions (our translation)
Curriculum point CM2.NC.13 (our numbering) Interpret, represent, write and read fractions (our translation)

In CM2 (the final year of primary school), students consolidate their use of the terms numerator and denominator to read, write, and interpret fractions of the form a/b. At this level, a fraction is no longer just a geometric partitioning: it is also used to designate a precise quantity taken from a whole number or from a group of objects.

A common difficulty is confusing the role of each term in the fraction. Faced with a quantity to be shared, some students divide by the numerator instead of sharing according to the denominator, or forget to multiply the part obtained by the number of parts requested.

In practice, exercises focus on the fraction of a collection: a/b of the whole. For example, faced with a set of 24 objects from which they must find 3/4, the student first divides the whole into 4 equal parts (obtaining 6 objects per part), then takes 3 of these parts to find the final result of 18 objects.

Create a worksheet for this skill Multiple-choice test

Task types: Fraction of a set: choose how many items (grade 3) · Fraction of a set: a/b of the whole (grade 3) · One part of a set: choose the number (grade 3)

Locating points on a number ray

The student learns to place numbers and locate points on a graduated half-line by relying on regular jumps, notably by tens.

Curriculum point CE1.NC.10 (our numbering) Knowing how to place numbers on a graduated half-line. (our translation)
Curriculum point CE2.NC.10 (our numbering) Knowing how to place numbers on a graduated half-line. (our translation)
Curriculum point CM1.NC.10 (our numbering) Know how to place numbers and locate points on a graduated half-line (our translation)
Curriculum point CM2.NC.7 (our numbering) Placing numbers and locating points on a graduated half-line (our translation)
Curriculum point CP.NC.8 (our numbering) Knowing how to place numbers on a graduated half-line, counting one by one. (our translation)

In grade 5 (CM2), your child learns to place numbers and to locate precise points on a graduated number line. They strengthen their understanding of the regularity of the markings by learning to jump by constant steps, such as moving forward or backward by tens along the line.

The most common mistake is counting the tick marks one by one without identifying the actual value of the interval. The student then risks confusing the label of a mark with the value of the number, or counting the bars instead of measuring the gaps between them.

Through exercises on jumping by tens on the number line, the child practises concretely following jumps of 10 to find the exact position of a value or to name the number associated with a precise point on the line.

Create a worksheet for this skill Multiple-choice test

Task types: Jump by tens on the number line (grade 2) · Jump by tens: choose the number (grade 2) · Jump by tens: true or false (grade 2)

Calculate the value for a single object

Your child learns to determine the value of a single unit from a total quantity in order to solve proportionality problems.

Curriculum point 5e.PF.4 (our numbering) Use a coefficient of proportionality in concrete contexts (unit price, average speed, scale, etc.). (our translation)
Curriculum point 6e.P.1 (our numbering) Know the definition of proportionality between two quantities and relate it to everyday expressions (our translation)
Curriculum point 6e.P.2 (our numbering) Identify whether a situation falls under the "model" of proportionality (our translation)
Curriculum point 6e.P.3 (our numbering) Solve a proportionality problem by choosing an appropriate procedure: linearity property for multiplication or addition, return to the unit (our translation)
Curriculum point CM1.P.1 (our numbering) Identify a situation of proportionality (our translation)
Curriculum point CM1.P.2 (our numbering) Being able to solve a proportionality problem (our translation)
Curriculum point CM2.P.1 (our numbering) Identify a situation of proportionality (our translation)
Curriculum point CM2.P.2 (our numbering) Be able to solve a proportionality problem (our translation)

In CM2, to solve a proportionality problem, pupils learn to use the unit-value method (return to the unit). Faced with a global measure (a price, a mass, a duration) associated with several identical objects, the pupil uses division to determine the exact value of a single item, whether the number is a whole number or a decimal.

The most common error is reversing the terms of the division, for example dividing the number of items by the total price instead of dividing the price by the number of items. Some pupils also fall into the trap of additive reasoning, trying to subtract a difference rather than dividing to find the unit share.

In worksheets based on the model How much for one?, the pupil reads a real-life problem (for example, the cost of 4 identical notebooks or the mass of 5 juice cartons) and must write the calculation needed to isolate the value of one unit before possibly calculating other quantities.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Value for one unit: find the mistake · Value for one unit: true or false · Price per item step by step · Price per item: extra data · Unit rate: word problem, the value for one · Value for one unit: choose the result · Unit price: where is it cheaper?

Long division by a single-digit number

The student learns to set up and carry out the division of a whole number by a one-digit divisor to determine the quotient and the remainder.

Curriculum point CM1.NC.52 (our numbering) Perform Euclidean divisions with a one-digit divisor, setting them out and carrying them out. (our translation)
Curriculum point CM2.NC.55 (our numbering) Pose and carry out decimal divisions with a whole-number dividend and a one-digit divisor (our translation)

In CM2, the child consolidates mastery of long division with the "potence" layout. They practise dividing a whole number by a one-digit divisor, calculating each digit of the quotient step by step while carrying down and reducing the remainder at each stage.

The most frequent mistake occurs when, after bringing down a digit, the number obtained is smaller than the divisor. The pupil often has the reflex of bringing down the next digit directly, forgetting to write a 0 in the quotient, which completely distorts the value of the result. Another classic difficulty is continuing the calculation with an intermediate remainder greater than or equal to the divisor.

In training, the activities of the Long division by a one-digit number template offer pre-filled potence layouts in which the child performs the successive subtractions and clearly notes the quotient obtained as well as the final remainder.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Long division: choose the dividend · Long division: the missing dividend · Long division by a one-digit number · Long division in a word problem · Long division: a zero in the quotient — choose

Comparing data in a bar chart

In Year 5 (CM2), your child learns to read a bar chart and compare the heights of the bars to identify quantities and answer precise questions.

Curriculum point 1re.AUT.13 (our numbering) Read a graph, a histogram, a bar chart or pie chart, a box plot or any other representation (identify the origin of the axes, the units of the graduations or the scales, etc.). (our translation)
Curriculum point 1re.AUT.14 (our numbering) Move from the graph to the data and vice versa. (our translation)
Curriculum point 2de.AUT.24 (our numbering) Read and comment on common graphs: • bar chart; • pie chart, semi-circular chart; • curve, scatter plot (Cartesian diagram). (our translation)
Curriculum point 5e.OGD.2 (our numbering) Calculer des effectifs et des fréquences (exprimées sous forme décimale, fractionnaire ou de pourcentage).Calculate absolute frequencies and relative frequencies (expressed as decimals, fractions or percentages). (our translation)
Curriculum point 5e.OGD.3 (our numbering) Read and interpret information presented in the form of tables, diagrams and graphs. (our translation)
Curriculum point 6e.OGD.4 (our numbering) Make a choice by filtering the data in a table according to a criterion (our translation)
Curriculum point CM1.OGD.2 (our numbering) Read and interpret data from a single- or double-entry table, a bar chart or a line graph (our translation)
Curriculum point CM1.OGD.3 (our numbering) Solve one- or multi-step problems using data from a single- or double-entry table, a bar chart or a line graph (our translation)
Curriculum point CM2.OGD.2 (our numbering) Read and interpret data from a table, a bar chart, a pie chart or a line graph (our translation)
Curriculum point CM2.OGD.3 (our numbering) Solve one- or two-step problems using data from a table, a bar chart, a pie chart or a line graph (our translation)

In CM2 (the final year of primary school), pupils learn to read and interpret data presented as bar charts. Your child looks at the different columns, identifies the quantities shown and compares values directly to solve small one- or two-step problems.

The most common mistake concerns reading the scale on the vertical axis. Pupils often count the squares one by one without checking the scale, whereas a graduation may increase by 2, 5, 10 or 100 units. Another frequent difficulty is confusing the name of the category (on the horizontal axis) with the quantity being measured.

Through the activity Compare les barres du diagramme, the child practises observing a graph in concrete terms to quickly identify the largest or smallest value, rank categories or calculate the difference between two bars.

Create a worksheet for this skill Multiple-choice test

Task types: Bar chart – how many more: find the mistake · Bar chart: compare the bars · Bar chart: how many more — true or false · Reading a bar chart: choose the total · Mean from a dot plot (grade 7–8) · Mean of four bars in a chart (grade 7–8) · Mean of four bars in a chart: choose the result (grade 7–8) · Scaled pictogram: how many more (grade 7–8) · Share of a bar in the total as a percentage (grade 7–8)

Reading and writing decimal numbers

In CM2 (the last year of primary school in France), your child learns to read and write decimal numbers up to the thousandth and to identify the exact value of each digit according to its position.

Curriculum point 6e.NC.1 (our numbering) Know and use the value of digits according to their position in the writing of a number (our translation)
Curriculum point 6e.NC.2 (our numbering) Know the links between the numeration units: unit, ten, hundred, thousand, tenth, hundredth, thousandth (our translation)
Curriculum point 6e.NC.4 (our numbering) Recognise a decimal number (our translation)
Curriculum point CM1.NC.23 (our numbering) Interpret, represent, write and read decimal fractions (our translation)
Curriculum point CM1.NC.24 (our numbering) Know and use the relationships between simple units, tenths and hundredths (our translation)
Curriculum point CM1.NC.27 (our numbering) Write a decimal fraction greater than 1 as the sum of a whole number and decimal fractions having a numerator less than 10 (our translation)
Curriculum point CM1.NC.31 (our numbering) Interpret, represent, write and read decimal numbers (decimal notation) (our translation)
Curriculum point CM2.NC.23 (our numbering) Interpret, represent, write and read decimal fractions (our translation)
Curriculum point CM2.NC.24 (our numbering) Know and use the relationships between simple units, tenths, hundredths and thousandths (our translation)
Curriculum point CM2.NC.27 (our numbering) Write a decimal fraction greater than 1 as the sum of a whole number and decimal fractions having a numerator less than 10 (our translation)
Curriculum point CM2.NC.31 (our numbering) Interpret, represent, write and read decimal numbers (decimal notation) (our translation)

In Grade 5 (CM2), students consolidate their mastery of decimal notation, directly linked to decimal fractions. They learn to distinguish and name the different places that make up the number: the whole-number part (units, tens, hundreds), but above all the decimal part with tenths, hundredths and thousandths.

A classic difficulty lies in confusing the place values, in particular tenths and hundredths, or in mixing up tens and tenths because the words sound similar. Many students also tend to read the part after the decimal point as an independent whole number, forgetting that the position of the zero (as in 4.05 compared with 4.5) completely changes the value of the hundredths.

Through concrete exercises such as Find the hundredths digit, students practise analysing a given decimal number so that they can identify, without hesitation, the digit occupying the requested place.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Find the digit in the hundredths place · Decimal place value: choose the thousandths digit · Decimal place value: expanded form · Decimal place value: value of a digit · Decimal: choose the value of a digit

Reading a decimal number on a number line

In grade 5 (CM2), pupils learn to read and locate a decimal number written with a decimal comma on a graduated number line.

Curriculum point 5e.EG.1 (our numbering) On a number line: - read the coordinate of a given point; - place a point with a given coordinate. (our translation)
Curriculum point 6e.NC.29 (our numbering) Graduate a segment of a given length (our translation)
Curriculum point 6e.NC.7 (our numbering) Place on a graduated half-line a point whose abscissa is a decimal number (our translation)
Curriculum point 6e.NC.8 (our numbering) Locate a decimal number on a graduated half-line (our translation)
Curriculum point CM1.NC.25 (our numbering) Place a decimal fraction on a graduated half-line and locate a point on a graduated half-line by a decimal fraction (our translation)
Curriculum point CM1.NC.32 (our numbering) Place a decimal number written with a decimal comma on a graduated half-line, and locate a point on a graduated half-line by a decimal number (our translation)
Curriculum point CM2.NC.25 (our numbering) Place a decimal fraction on a graduated half-line and locate a point on a graduated half-line by a decimal fraction (our translation)
Curriculum point CM2.NC.32 (our numbering) Place a decimal number written with a decimal comma on a graduated half-line, and identify a point on a graduated half-line by a number written with a decimal comma (our translation)

In grade 5 (CM2), students strengthen their understanding of numbers by learning to locate a point represented by a decimal number on a graduated number line. They rely on the regular division of the unit into tenths or hundredths to determine precisely the position of a value lying between two whole numbers or two decimals.

The most common mistake is simply counting the small tick marks without first identifying the value of each interval. A child might, for example, read 3.4 at the fourth graduation after 3, without noticing that each step actually represents a hundredth (which would correspond to 3.04), or count the graduations as if they were always whole units.

Through the exercise Read the decimal number on the number line, a number line is presented with a few labelled reference points and a mark indicating a specific location. The student observes the gap between the given reference points to calculate the value of a subdivision, then enters the exact decimal number corresponding to the indicated position.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Decimals on a number line: choose the distance · Decimals on a number line: choose the midpoint · Decimals on a number line: distance between two numbers · Read a decimal on a number line · Decimals on a number line: the midpoint

Reading a fraction on a number line

In CM2 (the final year of French primary school), your child learns to locate a point on a graduated half-line and to express its position using a fraction or the sum of a whole number and a fraction.

Curriculum point 2de.NC.11 (our numbering) Read the abscissa of a real number on a graduated number line and place a real number with a given abscissa. (our translation)
Curriculum point 6e.NC.28 (our numbering) Place a fraction on a graduated number line in simple cases (our translation)
Curriculum point 6e.NC.29 (our numbering) Graduate a segment of a given length (our translation)
Curriculum point CE2.NC.12 (our numbering) Divide a unit of length into fractions of the unit and measure non-integer lengths relative to that unit. (our translation)
Curriculum point CM1.NC.18 (our numbering) Know how to place a fraction or the sum of a whole number and a fraction less than one on a graduated half-line (our translation)
Curriculum point CM1.NC.19 (our numbering) Know how to locate a point on a graduated ray by a fraction or by the sum of a whole number and a fraction (our translation)
Curriculum point CM2.NC.17 (our numbering) Locate a fraction, or the sum of a whole number and a fraction less than one, on a graduated number line (our translation)
Curriculum point CM2.NC.18 (our numbering) Locate a point on a graduated half-line by a fraction or by the sum of a whole number and a fraction (our translation)

In CM2 (the final year of primary school), students consolidate their use of the graduated number line to work with numbers. They learn to precisely locate the position of a point and to name it either as a fraction or as the sum of a whole number and a fraction less than one (for example, to identify a mark located beyond 1 or beyond 2).

The classic difficulty lies in correctly identifying the denominator. Quite often, the child counts the vertical marks rather than the intervals, or counts all the visible graduations on the line instead of looking only at how one single unit (the space between 0 and 1) is divided.

In practice, in exercises of the type "Read the fraction on the number line", a regular graduated number line is presented with whole-number markers and an arrow or a target point. The student must first determine into how many equal parts each unit is divided in order to find the denominator, then count the number of parts from the origin or from the preceding whole number to write the requested fraction.

Create a worksheet for this skill Multiple-choice test

Task types: A fraction on a number line: choose the fraction · A fraction on a number line: true or false · Read a fraction on a number line

Parallel and Perpendicular Segments on a Grid

Your child is learning to identify whether line segments drawn on a grid are parallel or perpendicular.

Curriculum point CE1.EG.12 (our numbering) Know and use the code for right angles. (our translation)
Curriculum point CE2.EG.11 (our numbering) Know and use the notation for a right angle and the notation showing that segments have the same length. (our translation)
Curriculum point CM1.EG.3 (our numbering) Know the common codes used in geometry (our translation)
Curriculum point CM1.EG.5 (our numbering) Recognise and use the notion of perpendicularity (our translation)
Curriculum point CM1.EG.6 (our numbering) Recognise and use the notion of parallelism (our translation)
Curriculum point CM2.EG.3 (our numbering) Know the usual notations and codes used in geometry (our translation)
Curriculum point CM2.EG.4 (our numbering) Recognise and use the notion of perpendicularity (our translation)
Curriculum point CM2.EG.5 (our numbering) Recognise and use the concept of parallelism (our translation)

In CM2, the pupil consolidates the study of geometric relationships by learning to recognize and concretely use parallelism and perpendicularity. Using the reference lines of a grid, they check whether two segments intersect forming a right angle, or whether they keep a regular spacing without ever crossing.

A common mistake is judging the position of the drawn lines only by eye, especially when the segments do not touch or are oblique relative to the lines of the grid. The pupil then risks declaring segments that are merely intersecting to be perpendicular, instead of using the count of squares to check the angle or the spacing.

In the exercise Parallèles ou perpendiculaires ? (Parallel or perpendicular?), the child observes different lines or segments drawn on a grid. They examine the designated pairs and determine for each one whether the segments are parallel, perpendicular, or whether they satisfy neither of these two properties.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Parallel or perpendicular? · Distance of parallel lines: find the mistake (grade 6–7) · Distance of parallel lines: true or false (grade 6–7) · Parallel lines: choose the distance (grade 6–7) · Parallel lines: distance (grade 6–7)

Reflection of a point across a line

In grade 5 (CM2), students learn to determine and locate the exact position of the reflection of a point across a given line.

Curriculum point 6e.EG.20 (our numbering) Know the definition of the reflection of a point in a line (our translation)
Curriculum point 6e.EG.21 (our numbering) Know and use the properties of axial symmetry to carry out constructions (our translation)
Curriculum point CE2.EG.12 (our numbering) Recognise whether a figure has one or more axes of symmetry by using folding or tracing paper. (our translation)
Curriculum point CE2.EG.13 (our numbering) Complete, on squared or dotted paper, a simple figure so that it becomes symmetrical with respect to a given axis. (our translation)
Curriculum point CM1.EG.11 (our numbering) Recognise whether a figure has one or more axes of symmetry (our translation)
Curriculum point CM1.EG.12 (our numbering) Complete a figure so that it is symmetrical with respect to a given line, horizontal or vertical (our translation)
Curriculum point CM1.EG.13 (our numbering) Construct, on squared paper, the figure symmetrical to a given figure with respect to a horizontal or vertical line (our translation)
Curriculum point CM2.EG.12 (our numbering) Construct, on squared paper, the figure symmetrical to a given figure with respect to a vertical, horizontal or diagonal line of the grid (our translation)

In grade 5 (CM2), after identifying axes and completing simple figures on grid paper in earlier years, students practise constructing the symmetric of a point with respect to a line. They learn that the symmetric point lies on the other side of the line, at the same distance from it, and along a line perpendicular to the axis.

The classic mistake is to shift the point in a straight line without taking the axis into account, as if it were a simple slide, or to measure the distance at an angle instead of measuring perpendicularly to the reference line.

Worksheets on the symmetric of a point with respect to a line show a drawn line and one or more isolated points. The student must locate or mark the exact position of the corresponding symmetric point.

Create a worksheet for this skill Drill sheet (numbers only)Multiple-choice test

Task types: Line symmetry: find the mistake · Line symmetry: how many lines of symmetry · Line symmetry: reflect across a vertical line · Line symmetry: true or false · Reflect a point in a line · Reflection in a vertical line: choose the coordinate · Line symmetry: axis of a pair of points

Recognizing and naming common solids

Your child is learning to identify and precisely name solids: cube, cuboid, right prism, pyramid, cylinder, cone and sphere.

Curriculum point CM1.EG.14 (our numbering) Name a cube, a sphere, a cuboid, a cone, a pyramid, a cylinder and a right prism (our translation)
Curriculum point CM2.EG.13 (our numbering) Name a cube, a sphere, a cuboid, a cone, a pyramid, a cylinder or a right prism (our translation)

In grade 5 (CM2), the student consolidates their knowledge of solids in space. They are able to recognize and name without ambiguity the shapes in the curriculum: the cube, the cuboid, the right prism, the pyramid, the cylinder, the cone and the sphere.

The most common mistake is confusing rounded solids with polyhedral solids that share a similar silhouette, for example taking a cone for a pyramid or a cylinder for a right prism. Students also sometimes have the reflex of using the vocabulary of plane figures, calling for example a "circle" or "disk" a sphere drawn on a sheet of paper.

Through the exercise "What is this solid?", the student observes a perspective representation of a volume and simply has to associate it with the correct geometric name among those studied.

Create a worksheet for this skill Multiple-choice test

Task types: Which solid is it? · Which solid is it? Choose the name · Edges of a solid: find the mistake · Edges of a solid: true or false

Recognizing a net of a cube

The student learns to determine whether an arrangement of six squares can be folded into a cube.

Curriculum point 5e.EG.4 (our numbering) Know how to relate a representation in cavalier perspective and a net of a cuboid, a right prism or a right circular cylinder. (our translation)
Curriculum point CM1.EG.20 (our numbering) Recognise a net of a cube (our translation)
Curriculum point CM1.EG.21 (our numbering) Construct a net of a cube (our translation)
Curriculum point CM2.EG.15 (our numbering) Recognise a net of a cube (our translation)
Curriculum point CM2.EG.16 (our numbering) Construct a net of a cube (our translation)
Curriculum point CM2.EG.17 (our numbering) Recognize a net of a rectangular prism (our translation)

In grade 5 (CM2), your child consolidates their study of solids by learning to recognize a cube net. They must determine whether a flat geometric arrangement made of six square faces, once folded, closes the solid completely without gaps or overlaps.

The most common mistake is simply counting six squares. The child then concludes too quickly that the figure forms a cube, without checking by mental folding that two faces risk overlapping and leaving one face empty.

In the exercise Is it a net of a cube?, a flat arrangement of squares joined by their sides is presented. The student must analyze the layout to indicate whether it matches the complete unfolding of a cube.

Create a worksheet for this skill Multiple-choice test

Free sample worksheets for this grade (PDF)

Grade 5 (France) — printable math worksheet

Task templates to print

Every task type, grouped by skill. Clicking one opens the worksheet generator with it already selected.

Prisms and pyramids: faces, vertices and edges

Comparing chances in simple situations

A bag of marbles: which is more likely (grade 2–4)
Chance: correct the comparison (grade 2–4)
Chance: is the comparison correct? (grade 2–4)
Chance: what are you most likely to draw? (grade 2–4)
Chance: which is bigger? Choose (grade 2–4)
Fill the bag: bigger, smaller or equal chance (grade 2–4)

Reading the exact time on an analog clock

Reading a clock: true or false (grade 2–3)
Reading a clock: which time is on the dial (grade 2–3)
Reading the clock (grade 3)
Clock: correct the mistake in reading (grade 2–3)
Clock: how many minutes to the full hour? (grade 3)
Clock: which shows the earlier time? (grade 3)

Organizing data in a table

Table: how many altogether? (grade 2–4)
Tally chart – total: find the mistake (grade 1–3)
Tally chart – two rows together: find the mistake (grade 1–2)
Tally chart: count the marks (K – grade 1)
Tally chart: how many more (grade 1–3)
Tally chart: how many more: choose the result (grade 1–3)
Tally chart: read a row (grade 1–3)
Tally chart: the biggest row (grade 1–2)
Tally chart: the biggest row: choose the result (grade 1–2)
Tally chart: total (grade 1–3)
Tally chart: total: true or false (grade 1–3)
Tally chart: two rows together (grade 1–2)
Tally chart: two rows together: true or false (grade 1–2)
Tally chart – most minus least: find the mistake (grade 2–4)
Tally chart: four rows altogether (grade 2–4)
Tally chart: four rows altogether: choose the result (grade 2–4)
Tally chart: how many marks to add (grade 1–2)
Tally chart: most minus least (grade 2–4)
Tally chart: most minus least: true or false (grade 2–4)
Tally chart: the hidden row (grade 2–3)
Tally chart: the hidden row: choose the result (grade 2–3)
Pictogram: one picture stands for several (grade 2–4)
The missing row when the total is known (grade 2–4)
Total from a table: choose the correct answer (grade 2–4)
Total from a table: true or false (grade 2–4)

Drawing a ball from a box (grade 7–8)
Rolling a die (grade 7–8)
Chances in two bags: compare (grade 7–8)
Drawing a numbered card (grade 7–8)
Probability of the complement (grade 7–8)
Probability: choose the result (grade 7–8)
Probability: find the mistake (grade 7–8)
Probability: true or false (grade 7–8)
Probability: how many balls of that colour (grade 7–8)
Drawing without looking: what is the probability? (grade 7–8)

Classify the angle
Complementary angles: find the other angle
Supplementary angles: choose the other angle
Supplementary angles: find the other angle
Vertical angles: choose the measure
A half turn of a clock hand (grade 2–3)
A half turn of a clock hand: true or false (grade 2–3)
A quarter turn anticlockwise (grade 2–3)
A quarter turn clockwise (grade 2–3)
A quarter turn clockwise: choose the result (grade 2–3)
A three-quarter turn clockwise (grade 2–3)

Factors of a number: choose how many
List all factors of a number
Factors: how many are there?
Factors: smallest number with k factors (grade 6–7)
Smallest number with k divisors: find the mistake (grade 6–7)
Smallest number with k divisors: true or false (grade 6–7)

Multiplying a digit by a multiple of 10

Multiplying by tens: choose the result (grade 3)
Multiply by a multiple of ten (grade 3)
Multiplying by tens: true or false (grade 3)

Understanding and calculating a fraction of a quantity

Fraction of a set: choose how many items (grade 3)
Fraction of a set: a/b of the whole (grade 3)
One part of a set: choose the number (grade 3)

Locating points on a number ray

Jump by tens on the number line (grade 2)
Jump by tens: choose the number (grade 2)
Jump by tens: true or false (grade 2)

Bar chart – how many more: find the mistake
Bar chart: compare the bars
Bar chart: how many more — true or false
Reading a bar chart: choose the total
Mean from a dot plot (grade 7–8)
Mean of four bars in a chart (grade 7–8)
Mean of four bars in a chart: choose the result (grade 7–8)
Scaled pictogram: how many more (grade 7–8)
Share of a bar in the total as a percentage (grade 7–8)

Parallel or perpendicular?
Distance of parallel lines: find the mistake (grade 6–7)
Distance of parallel lines: true or false (grade 6–7)
Parallel lines: choose the distance (grade 6–7)
Parallel lines: distance (grade 6–7)

Net of a cube: is it a net?

Other task types

Create a worksheet for this curriculum

Outside the curriculum — extra tasks

Tasks that this grade's curriculum does not include, but other countries teach at this level. Free, like everything here, and never mixed into the topics or the ready-made tests of the curriculum.

Distance from a point to a line (in the curriculum of: Poland)
Rounding multi-digit numbers to the nearest hundred (in the curriculum of: Switzerland, Germany, Spain +4)
Diagonals from a vertex: choose the number (in the curriculum of: Poland)
Diagonals of a polygon step by step (in the curriculum of: Poland)
Diagonals of a polygon: extra data (in the curriculum of: Poland)
Diagonals of a polygon: from one vertex (in the curriculum of: Poland)
Distance from a point to a line: vertical line (in the curriculum of: Poland)
Expressions: how many times as large, no calculating (in the curriculum of: Austria, Spain, Poland +1)
Fraction line plot – difference: find the mistake (in the curriculum of: United States)
Fraction line plot: difference, true or false (in the curriculum of: United States)
Gigabytes to megabytes (in the curriculum of: Switzerland, Netherlands)
Grid: area after enlarging (in the curriculum of: Switzerland, Spain, Italy +1)
Grid: area after enlarging: choose the result (in the curriculum of: Switzerland, Spain, Italy +1)
Grid: side after enlarging (in the curriculum of: Switzerland, Spain, Italy +1)
Grid: side after reducing (in the curriculum of: Switzerland, Spain, Italy +1)
Grid: the scale factor (in the curriculum of: Switzerland, Spain, Italy +1)
Line plot: longest minus shortest (in the curriculum of: United States)
Measure in the larger unit: choose the decimal (in the curriculum of: Austria, Switzerland, Spain +4)
Measure in the larger unit: find the mistake (in the curriculum of: Austria, Switzerland, Spain +4)
Measure in the larger unit: true or false (in the curriculum of: Austria, Switzerland, Spain +4)
Megabytes to gigabytes: choose the result (in the curriculum of: Switzerland, Netherlands)
Point-line distance (horizontal): choose the answer (in the curriculum of: Poland)
Read a Roman numeral (in the curriculum of: Austria, United Kingdom, Italy +1)
Roman numerals to 3000: choose the value (in the curriculum of: Austria, United Kingdom, Italy +1)
Roman numerals to 3000: find the mistake (in the curriculum of: Austria, United Kingdom, Italy +1)
Roman numerals to 3000: true or false (in the curriculum of: Austria, United Kingdom, Italy +1)
Round to the nearest ten thousand (in the curriculum of: Switzerland, Germany, Spain +4)
Round to the nearest thousand (in the curriculum of: Switzerland, Germany, Spain +4)
Rounding to the nearest thousand: choose the result (in the curriculum of: Switzerland, Germany, Spain +4)
Rounding to the nearest thousand: find the mistake (in the curriculum of: Switzerland, Germany, Spain +4)
Rounding to the nearest thousand: true or false (in the curriculum of: Switzerland, Germany, Spain +4)
Units of data: choose the converted value (in the curriculum of: Switzerland, Netherlands)
Units of data: compare (in the curriculum of: Switzerland, Netherlands)
Value of a formula for given numbers (in the curriculum of: Austria, Spain, Poland +1)
Value of an expression with a letter (in the curriculum of: Austria, Spain, Poland +1)
Value of an expression with a letter: choose the result (in the curriculum of: Austria, Spain, Poland +1)
Value of an expression with a letter: find the mistake (in the curriculum of: Austria, Spain, Poland +1)
Value of an expression with a letter: true or false (in the curriculum of: Austria, Spain, Poland +1)
Write a length as a decimal (in the curriculum of: Austria, Switzerland, Spain +4)
Write a number in Roman numerals (in the curriculum of: Austria, United Kingdom, Italy +1)
Common multiples: how many are divisible by both (in the curriculum of: Spain, Poland)
Diagonals of a polygon: choose the number (in the curriculum of: Poland)
Diagonals of a polygon: how many are there? (in the curriculum of: Poland)
Diagonals of a polygon: how many triangles? (in the curriculum of: Poland)
Expression with a letter: compare two expressions (in the curriculum of: Austria, Spain, Poland +1)
Fraction line plot: choose the difference (in the curriculum of: United States)
Fraction line plot: choose the equal share (in the curriculum of: United States)
Fraction line plot: choose the total (in the curriculum of: United States)
Line plot: total of the measurements (in the curriculum of: United States)
Multiples in a range: find the mistake (in the curriculum of: Spain, Poland)
Multiples in a range: how many are divisible (in the curriculum of: Spain, Poland)
Multiples in a range: true or false (in the curriculum of: Spain, Poland)
Numbers divisible by two numbers: choose the result (in the curriculum of: Spain, Poland)
Numbers to a million: rounding to thousands in a story (in the curriculum of: Switzerland, Germany, Spain +4)
Point-line distance (vertical): choose the answer (in the curriculum of: Poland)
Point-line distance (vertical): find the mistake (in the curriculum of: Poland)
Point-line distance (vertical): true or false (in the curriculum of: Poland)
Roman numerals to 3000: compare (in the curriculum of: Austria, United Kingdom, Italy +1)
Roman numerals to 3000: the sum (in the curriculum of: Austria, United Kingdom, Italy +1)
Two patterns: find the mistake (in the curriculum of: Spain, Netherlands, United States)
Two patterns: missing term in the table (in the curriculum of: Spain, Netherlands, United States)
Two patterns: the difference: choose the answer (in the curriculum of: Spain, Netherlands, United States)
Two patterns: the term in the same position (in the curriculum of: Spain, Netherlands, United States)
Two patterns: true or false (in the curriculum of: Spain, Netherlands, United States)
Line plot with fractions: equal share (in the curriculum of: United States)
Rounding to the nearest thousand: the smallest such number (in the curriculum of: Switzerland, Germany, Spain +4)