Curriculum (Switzerland)

Mathematics — Grade 3

Imaginesis: printable math worksheets for this grade (Switzerland) — 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.

Mathematics in 3rd grade primary school: number range up to 1000, multiplication tables, written addition and subtraction, units of measurement, perimeter and symmetry. For each topic, there are sample exercises for printable worksheets with solutions.

What does a child learn in 3rd grade mathematics?

In Year 3, the number range extends to 1000: counting in steps, ordering, and rounding to tens and hundreds. The child learns the whole small multiplication table, division as the inverse operation, and written addition and subtraction. They calculate with francs and Rappen, convert between neighbouring units of measurement (m, cm, mm; kg, g; l, dl), determine durations, measure and calculate the perimeter of polygons, and reflect figures across axes.

About the curriculum: The basis is the Lehrplan 21, subject area Mathematics (template from the German-speaking Swiss Conference of Cantonal Ministers of Education, revised version of 29.02.2016). It describes competences not year by year but in cycles; Year 3 belongs to the 2nd cycle (Years 3 to 6). The assignment of tasks to Year 3 comes from us and follows the usual structure of the material. The competence levels of the cycle appear verbatim in the block below; cantonal curricula may differ slightly.

Curriculum scope

Curriculum point MA.1.A.1 · Teaching content · checked against the act

The students understand and use arithmetic terms and symbols. They read and write numbers.

our translation · original wording (DE): Die Schülerinnen und Schüler verstehen und verwenden arithmetische Begriffe und Symbole. Sie lesen und schreiben Zahlen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.1
Curriculum point MA.1.A.1.d · Teaching content · checked against the act

understand and use the term "divided by" and the symbol :.

our translation · original wording (DE): verstehen und verwenden den Begriff durch und das Symbol :.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.1.d

Division as the Inverse of Multiplication (we teach it in grade 3–6)
Curriculum point MA.1.A.1.e · Teaching content · checked against the act

understand and use the terms addition, subtraction, multiplication, division, remainder, number line, square number, hundreds, thousands, place values. can read and write natural numbers up to 1'000.

our translation · original wording (DE): verstehen und verwenden die Begriffe Addition, Subtraktion, Multiplikation, Division, Rest, Zahlenstrahl, Quadratzahl, Hunderter, Tausender, Stellenwerte. können natürliche Zahlen bis 1'000 lesen und schreiben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.1.e

Place values in three-digit numbers (we teach it in grade 3–6) · Reading and writing numbers up to 1000 (we teach it in grade 1–6) · Tens Jump on the Number Line (we teach it in grade 1–6)
Curriculum point MA.1.A.1.f · Teaching content · checked against the act

understand and use the terms addend, sum, difference, factor, product, quotient. can read and write natural numbers up to 1 million.

our translation · original wording (DE): verstehen und verwenden die Begriffe Summand, Summe, Differenz, Faktor, Produkt, Quotient. können natürliche Zahlen bis 1 Million lesen und schreiben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.1.f
Curriculum point MA.1.A.1.g · Teaching content · checked against the act

understand and use the terms fraction, percent, factor, multiples, numerator, denominator, estimate, round. use the symbols %, ≈. can read and write decimal numbers and fractions.

our translation · original wording (DE): verstehen und verwenden die Begriffe Bruch, Prozent, Teiler, Vielfache, Zähler, Nenner, überschlagen, runden. verwenden die Symbole %, ≈. können Dezimalzahlen und Brüche lesen und schreiben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.1.g

Halves and Quarters: Parts of a Whole (we teach it in grade 1–6) · Finding Divisors and Multiples of a Number (we teach it in grade 3–9) · Reading and writing decimal numbers (we teach it in grade 3–6)
Curriculum point MA.1.A.2 · Teaching content · checked against the act

Students can count flexibly, order numbers by size and estimate results.

our translation · original wording (DE): Die Schülerinnen und Schüler können flexibel zählen, Zahlen nach der Grösse ordnen und Ergebnisse überschlagen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.2
Curriculum point MA.1.A.2.d · Teaching content · checked against the act

can count forwards and backwards from any numbers within the number range up to 100. can count forwards and backwards from any multiples of 10 in steps of 2, 5 and 10 within the number range up to 100.

our translation · original wording (DE): können im Zahlenraum bis 100 von beliebigen Zahlen aus vorwärts und rückwärts zählen. können im Zahlenraum bis 100 von beliebigen 10er-Zahlen aus in 2er-, 5er- und 10er-Schritten vorwärts und rückwärts zählen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.2.d

Counting forwards and backwards in steps (we teach it in grade 1–6) · Successors and predecessors: Finding neighbouring numbers (we teach it in grade 1–6)
Curriculum point MA.1.A.2.e · Teaching content · checked against the act

can count forwards and backwards in the number range up to 1'000 in 1s, 2s, 10s and 100s, starting from any number. can order numbers up to 1'000.

our translation · original wording (DE): können im Zahlenraum bis 1'000 von beliebigen Zahlen aus in 1er-, 2er-, 10er- und 100er-Schritten vorwärts und rückwärts zählen. können Zahlen bis 1'000 ordnen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.2.e

Comparing and ordering numbers up to 1000 (we teach it in grade 3–6) · Counting forwards and backwards in steps (we teach it in grade 1–6)
Curriculum point MA.1.A.2.f · Teaching content · checked against the act

can count forwards and backwards in appropriate steps within the number range up to 1 million, starting from any numbers (e.g. from 320'000 in steps of 20'000). can order numbers up to 1 million (e.g. determine the approximate position of 72'000 on a number line).

our translation · original wording (DE): können im Zahlenraum bis 1 Million von beliebigen Zahlen aus in angemessenen Schritten vorwärts und rückwärts zählen (z.B. von 320'000 in 20'000er-Schritten). können Zahlen bis 1 Million ordnen (z.B. die ungefähre Position von 72'000 auf einem Zahlenstrahl bestimmen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.2.f

Tens Jump on the Number Line (we teach it in grade 1–6)
Curriculum point MA.1.A.2.g · Teaching content · checked against the act

can count forwards and backwards from any decimal numbers in appropriate steps (e.g. from 0.725 in steps of 0.005). can order fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50, 100. can order decimal numbers (e.g. 1.043; 1.43; 1.05; 1.5; 1.403). can estimate basic operations with natural numbers (e.g. 13'567 + 28'902 ≈ 40'000; 592'000 : 195 ≈ 600'000 : 200).

our translation · original wording (DE): können von beliebigen Dezimalzahlen aus in angemessenen Schritten vorwärts und rückwärts zählen (z.B. von 0.725 in 0.005er-Schritten). können Brüche mit den Nennern 2, 3, 4, 5, 6, 8, 10, 20, 50, 100 ordnen. können Dezimalzahlen ordnen (z.B. 1.043; 1.43; 1.05; 1.5; 1.403). können Grundoperationen mit natürlichen Zahlen überschlagen (z.B. 13'567 + 28'902 ≈ 40'000; 592'000 : 195 ≈ 600'000 : 200).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.2.g

Estimating: Estimating results and checking them (we teach it in grade 3–9)
Curriculum point MA.1.A.3 · Teaching content · checked against the act

The students can add, subtract, multiply, divide and exponentiate.

our translation · original wording (DE): Die Schülerinnen und Schüler können addieren, subtrahieren, multiplizieren, dividieren und potenzieren.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.3
Curriculum point MA.1.A.3.c · Teaching content · checked against the act

can double, halve, add and subtract in the number range up to 100. know products from the small multiplication table with the factors 2, 5 and 10. can decompose products from the small multiplication table into factors (e.g. 36 = 6 · 6 = 4 · 9).

our translation · original wording (DE): können im Zahlenraum bis 100 verdoppeln, halbieren, addieren und subtrahieren. kennen Produkte aus dem kleinen Einmaleins mit den Faktoren 2, 5 und 10. können Produkte aus dem kleinen Einmaleins in Faktoren zerlegen (z.B. 36 = 6 · 6 = 4 · 9).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.3.c

Addition up to 100 with Crossing the Tens (we teach it in grade 1–6) · The Small Multiplication Table: Knowing the Products with Confidence (we teach it in grade 3–6)
Curriculum point MA.1.A.3.d · Teaching content · checked against the act

can note down calculation methods when adding and subtracting and check the results. can add and subtract in writing. know the products of the small multiplication table.

our translation · original wording (DE): können beim Addieren und Subtrahieren Rechenwege notieren und Ergebnisse überprüfen. können schriftlich addieren und subtrahieren. kennen die Produkte des kleinen Einmaleins.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.3.d

Written addition and subtraction up to 1000 (we teach it in grade 3–6) · Adding and subtracting in writing within the number range 1000 (we teach it in grade 3–6) · The Small Multiplication Table: Knowing the Products with Confidence (we teach it in grade 3–6) · Division as the Inverse of Multiplication (we teach it in grade 3–6) · Adding larger numbers in writing and checking the result (we teach it in grade 3–6) · Adding and subtracting full hundreds (we teach it in grade 3–6)
Curriculum point MA.1.A.3.e · Teaching content · checked against the act

can add and subtract up to 4 significant digits mentally (e.g. 320'000 + 38'000; 402 + 90). can multiply up to 4 significant digits (mentally or by writing down own calculation methods, e.g. 45 · 240). can divide natural numbers by one-digit divisors (mentally or by writing down own calculation methods, e.g. 231 : 7).

our translation · original wording (DE): können bis 4 Wertziffern im Kopf addieren und subtrahieren (z.B. 320'000 + 38'000; 402 + 90). können bis 4 Wertziffern multiplizieren (im Kopf oder mit Notieren eigener Rechenwege, z.B. 45 · 240). können natürliche Zahlen durch einstellige Divisoren dividieren (im Kopf oder mit Notieren eigener Rechenwege, z.B. 231 : 7).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.3.e

Calculating Smartly: Reshaping Numbers Strategically (we teach it in grade 3–6) · Single-digit number times tens number (we teach it in grade 3–6) · Multiplying two-digit numbers by 2 (we teach it in grade 3–6) · Multiplying single-digit numbers in writing (we teach it in grade 3–6) · Dividing by a one-digit number in writing (we teach it in grade 3–6)
Curriculum point MA.1.A.3.f · Teaching content · checked against the act

can add and subtract decimal numbers with up to 5 significant digits (mentally or by writing down their own calculation methods, e.g. 30.8 + 5.6). can simplify, expand, add and subtract fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50, 100 using the rectangle model. can carry out basic operations with a calculator.

our translation · original wording (DE): können Dezimalzahlen bis 5 Wertziffern addieren und subtrahieren (im Kopf oder mit Notieren eigener Rechenwege, z.B. 30.8 + 5.6). können Brüche mit den Nennern 2, 3, 4, 5, 6, 8, 10, 20, 50, 100 am Rechteckmodell kürzen, erweitern, addieren und subtrahieren. können Grundoperationen mit dem Rechner ausführen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.3.f

Expanding fractions: same value, new denominator (we teach it in grade 3–6) · Adding and subtracting fractions with the same denominator (we teach it in grade 3–6)
Curriculum point MA.1.A.4 · Teaching content · checked against the act

The students can compare and transform terms, solve equations, apply laws and rules.

our translation · original wording (DE): Die Schülerinnen und Schüler können Terme vergleichen und umformen, Gleichungen lösen, Gesetze und Regeln anwenden.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.4
Curriculum point MA.1.A.4.d · Teaching content · checked against the act

can use relationships between products (e.g. 6 · 8 is 8 greater than 5 · 8 or with the commutative law: e.g. 8 · 3 = 3 · 8).

our translation · original wording (DE): können Beziehungen zwischen Produkten nutzen (z.B. 6 · 8 ist um 8 grösser als 5 · 8 oder mit dem Kommutativgesetz: z.B. 8 · 3 = 3 · 8).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.4.d

The Small Multiplication Table: Knowing the Products with Confidence (we teach it in grade 3–6) · Calculating sums cleverly: order and grouping (we teach it in grade 1–6)
Curriculum point MA.1.A.4.e · Teaching content · checked against the act

understand division as the inverse operation of multiplication and the connection to addition (e.g. 28 : 7 = 4 → 28 = 4 · 7 → 28 = 7 + 7 + 7 + 7). can use relationships between the small times tables and the tens times tables.

our translation · original wording (DE): verstehen die Division als Umkehroperation der Multiplikation und den Zusammenhang zur Addition (z.B. 28 : 7 = 4 → 28 = 4 · 7 → 28 = 7 + 7 + 7 + 7). können Beziehungen zwischen dem kleinen Einmaleins und dem Zehnereinmaleins nutzen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.4.e

Division as the Inverse of Multiplication (we teach it in grade 3–6) · Checking Calculations with the Inverse Operation (we teach it in grade 1–6) · Multiplying numbers under 20 by 10 (we teach it in grade 3–6)
Curriculum point MA.1.A.4.f · Teaching content · checked against the act

can transform products by doubling and halving (e.g. 8 · 26 = 4 · 52 = 2 · 104). can use the associative law for sums and products (e.g. 136 + 58 + 42 = 136 + (58 + 42); 38 · 4 · 25 = 38 · (4 · 25)). can round natural numbers to 10s, 100s and 1'000s.

our translation · original wording (DE): können Produkte durch Verdoppeln und Halbieren umformen (z.B. 8 · 26 = 4 · 52 = 2 · 104). können das Assoziativgesetz bei Summen und Produkten nutzen (z.B. 136 + 58 + 42 = 136 + (58 + 42); 38 · 4 · 25 = 38 · (4 · 25)). können natürliche Zahlen auf 10er, 100er und 1'000er runden.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.4.f

Calculating Smartly: Reshaping Numbers Strategically (we teach it in grade 3–6) · Rounding to tens and hundreds (we teach it in grade 3–6)
Curriculum point MA.1.A.4.g · Teaching content · checked against the act

recognise numbers that are divisible by 2, 5, 10, 100, 1'000. can round decimal numbers (e.g. 17'456 to the nearest hundred; 1.745 to the nearest tenth).

our translation · original wording (DE): erkennen Zahlen, die durch 2, 5, 10, 100, 1'000 teilbar sind. können Dezimalzahlen runden (z.B. 17'456 auf 100er; 1.745 auf Zehntel).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.A.4.g
Curriculum point MA.1.B.1 · Teaching content · checked against the act

The students can explore number and operation relationships as well as arithmetic patterns and exchange findings.

our translation · original wording (DE): Die Schülerinnen und Schüler können Zahl- und Operationsbeziehungen sowie arithmetische Muster erforschen und Erkenntnisse austauschen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.1
Curriculum point MA.1.B.1.d · Teaching content · checked against the act

can systematically vary products and describe the effects or show them with visual aids (e.g. 3 · 3, 6 · 3; 3 · 4, 6 · 4; 3 · 5, 6 · 5). look for their own solution strategies and exchange them.

our translation · original wording (DE): können Produkte systematisch variieren und Auswirkungen beschreiben bzw. mit Anschauungsmaterial zeigen (z.B. 3 · 3, 6 · 3; 3 · 4, 6 · 4; 3 · 5, 6 · 5). suchen eigene Lösungswege und tauschen sie aus.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.1.d
Curriculum point MA.1.B.1.e · Teaching content · checked against the act

can systematically vary operations and exchange insights (e.g. with 3 numbers < 10 form the same results: 30 = 8 · 3 + 6 = 7 · 4 + 2 = 7 · 3 + 9; 32 = ...).

our translation · original wording (DE): können Operationen systematisch variieren und Erkenntnisse austauschen (z.B. mit 3 Zahlen < 10 gleiche Ergebnisse bilden: 30 = 8 · 3 + 6 = 7 · 4 + 2 = 7 · 3 + 9; 32 = ...).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.1.e
Curriculum point MA.1.B.1.f · Teaching content · checked against the act

engage in open tasks, explore relationships, formulate conjectures and look for alternative solutions.

our translation · original wording (DE): lassen sich auf offene Aufgaben ein, erforschen Beziehungen, formulieren Vermutungen und suchen Lösungsalternativen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.1.f
Curriculum point MA.1.B.1.g · Teaching content · checked against the act

are able to explore and describe operational relationships between natural numbers (e.g. the difference of 2 reverse numbers is a multiple of 9: 41 - 14 = 27; 83 - 38 = 45).

our translation · original wording (DE): können operative Beziehungen zwischen natürlichen Zahlen erforschen und beschreiben (z.B. die Differenz von 2 Umkehrzahlen ist ein Vielfaches von 9: 41 - 14 = 27; 83 - 38 = 45).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.1.g
Curriculum point MA.1.B.1.h · Teaching content · checked against the act

can use heuristic strategies: trying out, looking for examples, forming analogies, investigating regularities, making assumptions, formulating conjectures. can form, continue, modify and describe systematic task sequences (e.g. on a number table, cover 5 numbers with a figure and calculate the sum. Shift the figure by one, two, three, ... position(s)).

our translation · original wording (DE): können heuristische Strategien verwenden: ausprobieren, Beispiele suchen, Analogien bilden, Regelmässigkeiten untersuchen, Annahmen treffen, Vermutungen formulieren. können systematische Aufgabenfolgen bilden, weiterführen, verändern und beschreiben (z.B. auf einer Zahlentafel 5 Zahlen mit einer Figur abdecken und die Summe berechnen. Die Figur um eine, zwei, drei, ... Position(en) verschieben).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.1.h
Curriculum point MA.1.B.2 · Teaching content · checked against the act

Students can explain, verify and justify statements, conjectures and results about numbers and variables.

our translation · original wording (DE): Die Schülerinnen und Schüler können Aussagen, Vermutungen und Ergebnisse zu Zahlen und Variablen erläutern, überprüfen, begründen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.2
Curriculum point MA.1.B.2.d · Teaching content · checked against the act

can check quotients using the inverse operation (e.g. 21 : 3 = 7 → 7 · 3 = 21).

our translation · original wording (DE): können Quotienten mit der Umkehroperation überprüfen (z.B. 21 : 3 = 7 → 7 · 3 = 21).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.2.d

Checking Calculations with the Inverse Operation (we teach it in grade 1–6)
Curriculum point MA.1.B.2.e · Teaching content · checked against the act

can justify divisions with remainder using the inverse operation (e.g. 32 : 6 leaves a remainder because 32 is not a number in the 6 times table).

our translation · original wording (DE): können Divisionen mit Rest mit der Umkehroperation begründen (z.B. 32 : 6 gibt Rest, weil 32 keine Zahl aus der 6er-Reihe ist).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.2.e

Checking Calculations with the Inverse Operation (we teach it in grade 1–6)
Curriculum point MA.1.B.2.f · Teaching content · checked against the act

Can check results using estimation calculations. Can investigate and justify the number of digits of products and quotients.

our translation · original wording (DE): können Ergebnisse mit Überschlagsrechnungen überprüfen. können die Anzahl Stellen von Produkten und Quotienten erforschen und begründen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.2.f

Estimating: Estimating results and checking them (we teach it in grade 3–9)
Curriculum point MA.1.B.2.g · Teaching content · checked against the act

can check results of basic operations by simplifying (e.g. 8 · 13 = 4 · 26 = 2 · 52), decomposing (e.g. 17.8 + 23.5 = 17 + 3 + 20 + 1.3) and using inverse operations

our translation · original wording (DE): können Ergebnisse zu Grundoperationen durch Vereinfachen (z.B. 8 · 13 = 4 · 26 = 2 · 52), Zerlegen (z.B. 17.8 + 23.5 = 17 + 3 + 20 + 1.3) und Umkehroperationen überprüfen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.2.g

Finding and correcting calculation errors (we teach it in grade 2–6) · Calculating Smartly: Reshaping Numbers Strategically (we teach it in grade 3–6)
Curriculum point MA.1.B.3 · Teaching content · checked against the act

Pupils can use aids when exploring arithmetic patterns.

our translation · original wording (DE): Die Schülerinnen und Schüler können beim Erforschen arithmetischer Muster Hilfsmittel nutzen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.3
Curriculum point MA.1.B.3.c · Teaching content · checked against the act

can use place-value charts when exploring arithmetic structures (e.g. placing counters into the place-value chart and moving them).

our translation · original wording (DE): können Stellenwerttafel beim Erforschen arithmetischer Strukturen nutzen (z.B. Plättchen in die Stellenwerttafel legen und verschieben).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.3.c
Curriculum point MA.1.B.3.d · Teaching content · checked against the act

can follow instructions for sequences of actions (e.g. in flowcharts) and use them when exploring arithmetic structures (e.g. 1. Start with a two-digit number / 2. If the number is even: Divide by 2, otherwise: Multiply by 3 and add 1 / 3. Repeat 2.).

our translation · original wording (DE): können Anweisungen zu Handlungssequenzen (z.B. in Flussdiagrammen) befolgen und beim Erforschen arithmetischer Strukturen nutzen (z.B. 1. Starte mit einer zweistelligen Zahl / 2. Wenn die Zahl gerade ist: Dividiere durch 2, sonst: Multipliziere mit 3 und addiere 1 / 3. Wiederhole 2.).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.B.3.d
Curriculum point MA.1.C.1 · Teaching content · checked against the act

The students can present, describe, exchange and follow calculation methods.

our translation · original wording (DE): Die Schülerinnen und Schüler können Rechenwege darstellen, beschreiben, austauschen und nachvollziehen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.1
Curriculum point MA.1.C.1.d · Teaching content · checked against the act

recognize multiplicative relationships in graphic models, in particular doublings and 1 · more or 1 · less (e.g. 3 · 4 and 6 · 4 in a dot array as a doubling).

our translation · original wording (DE): erkennen in grafischen Modellen multiplikative Beziehungen, insbesondere Verdoppelungen und 1 · mehr bzw. 1 · weniger (z.B. 3 · 4 und 6 · 4 in einem Punktefeld als Verdoppelung).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.1.d

The Small Multiplication Table: Knowing the Products with Confidence (we teach it in grade 3–6)
Curriculum point MA.1.C.1.e · Teaching content · checked against the act

can represent, exchange and comprehend calculation methods for the basic operations (e.g. 80 + 5 + 5 + 5 + 5 = 80 + 4 · 5; 347 - 160 → 160 + 40 + 147 = 347).

our translation · original wording (DE): können Rechenwege zu den Grundoperationen darstellen, austauschen und nachvollziehen (z.B. 80 + 5 + 5 + 5 + 5 = 80 + 4 · 5; 347 - 160 → 160 + 40 + 147 = 347).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.1.e

Calculating Smartly: Reshaping Numbers Strategically (we teach it in grade 3–6)
Curriculum point MA.1.C.1.f · Teaching content · checked against the act

can represent, exchange and follow calculation methods for basic operations with decimal numbers (e.g. decompose 35.7 + 67.8 into several addends and represent it on the number line).

our translation · original wording (DE): können Rechenwege zu Grundoperationen mit Dezimalzahlen darstellen, austauschen und nachvollziehen (z.B. 35.7 + 67.8 in mehrere Summanden zerlegen und auf dem Rechenstrich darstellen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.1.f
Curriculum point MA.1.C.2 · Teaching content · checked against the act

Students can illustrate, describe and generalize quantities, number sequences and terms.

our translation · original wording (DE): Die Schülerinnen und Schüler können Anzahlen, Zahlenfolgen und Terme veranschaulichen, beschreiben und verallgemeinern.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.2
Curriculum point MA.1.C.2.d · Teaching content · checked against the act

can illustrate basic operations with actions, situational pictures, arithmetic stories and graphic structures, and interpret illustrations. can show and describe relationships in and between basic operations (e.g. the change in the products 1 · 3, 2 · 4, 3 · 5, 4 · 6, ...).

our translation · original wording (DE): können Grundoperationen mit Handlungen, Sachbildern, Rechengeschichten und grafischen Strukturen veranschaulichen und Veranschaulichungen interpretieren. können Beziehungen in und zwischen Grundoperationen zeigen und beschreiben (z.B. die Veränderung der Produkte 1 · 3, 2 · 4, 3 · 5, 4 · 6, ...).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.2.d

Understanding and Solving Word Problems (we teach it in grade 1–6) · The Small Multiplication Table: Knowing the Products with Confidence (we teach it in grade 3–6)
Curriculum point MA.1.C.2.e · Teaching content · checked against the act

are able to represent the meaning of the digits in the place-value system (e.g. 2 hundred flats, 5 ten rods and 7 unit cubes represent 257).

our translation · original wording (DE): können die Bedeutung der Ziffern im Stellenwertsystem darstellen (z.B. 2 100er-Platten, 5 10-er-Stäbe und 7 1er-Würfel stellen 257 dar).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.2.e

Place values in three-digit numbers (we teach it in grade 3–6)
Curriculum point MA.1.C.2.f · Teaching content · checked against the act

can illustrate number sequences and products (e.g. 14 · 14 with the multiplication grid; the number sequence 1, 3, 6, 10, ... with dots).

our translation · original wording (DE): können Zahlenfolgen und Produkte veranschaulichen (z.B. 14 · 14 mit dem Malkreuz; die Zahlenfolge 1, 3, 6, 10, ... mit Punkten).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.2.f
Curriculum point MA.1.C.2.g · Teaching content · checked against the act

can illustrate regularities in the domain of natural numbers with examples (e.g. square numbers have an odd number of divisors → 16: 1, 2, 4, 8, 16). can represent fractions with denominators 2, 3, 4, 5, 6, 8, 10 and compare them, as well as interpret representations (e.g. circle and rectangle models, number line). can describe number sequences with positive rational numbers (e.g. ½, ¼, ⅛, ...; 0.7, 0.77, 0.777, ...).

our translation · original wording (DE): können Gesetzmässigkeiten im Bereich der natürlichen Zahlen mit Beispielen konkretisieren (z.B. Quadratzahlen haben eine ungerade Anzahl Teiler → 16: 1, 2, 4, 8, 16). können Brüche mit den Nennern 2, 3, 4, 5, 6, 8, 10 darstellen und vergleichen sowie Darstellungen interpretieren (z.B. Kreis-, Rechteckmodell, Zahlenstrahl). können Zahlenfolgen mit positiven rationalen Zahlen beschreiben (z.B. ½, ¼, ⅛, ...; 0.7, 0.77, 0.777, ...).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.1.C.2.g

Finding Divisors and Multiples of a Number (we teach it in grade 3–9) · Halves and Quarters: Parts of a Whole (we teach it in grade 1–6)
Curriculum point MA.2.A.1 · Teaching content · checked against the act

The students understand and use terms and symbols.

our translation · original wording (DE): Die Schülerinnen und Schüler verstehen und verwenden Begriffe und Symbole.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.1
Curriculum point MA.2.A.1.d · Teaching content · checked against the act

understand and use the terms figure, length, width, area, body, reflect, shift.

our translation · original wording (DE): verstehen und verwenden die Begriffe Figur, Länge, Breite, Fläche, Körper, spiegeln, verschieben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.1.d

Recognizing and naming plane figures (we teach it in grade 1–6)
Curriculum point MA.2.A.1.e · Teaching content · checked against the act

understand and use the terms point, corner, edge, face, cube, cuboid.

our translation · original wording (DE): verstehen und verwenden die Begriffe Punkt, Ecke, Kante, Seitenfläche, Würfel, Quader.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.1.e

Recognizing and naming bodies by their properties (we teach it in grade 1–6)
Curriculum point MA.2.A.1.f · Teaching content · checked against the act

recognize and name geometric solids (cube, cuboid, sphere, cylinder, pyramid) and shapes in the environment and in pictures.

our translation · original wording (DE): erkennen und benennen geometrische Körper (Würfel, Quader, Kugel, Zylinder, Pyramide) und Figuren in der Umwelt und auf Bildern.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.1.f

Recognizing and naming bodies by their properties (we teach it in grade 1–6) · Recognizing and naming geometric solids (we teach it in grade 3–6)
Curriculum point MA.2.A.1.g · Teaching content · checked against the act

understand and use the terms side, diagonal, diameter, radius, area, centre, parallel, line, straight line, line segment, grid, point of intersection, intersect, perpendicular, symmetry, reflection in an axis, perimeter, angle, right-angled, translation, geo-triangle. use the symbols for right angles and parallel lines.

our translation · original wording (DE): verstehen und verwenden die Begriffe Seite, Diagonale, Durchmesser, Radius, Flächeninhalt, Mittelpunkt, Parallele, Linie, Gerade, Strecke, Raster, Schnittpunkt, schneiden, Senkrechte, Symmetrie, Achsenspiegelung, Umfang, Winkel, rechtwinklig, Verschiebung, Geodreieck. verwenden die Symbole für rechte Winkel und parallele Linien.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.1.g

Parallel or Perpendicular: Lines on the Grid (we teach it in grade 3–6) · Axial symmetry: reflect across an axis (we teach it in grade 3–9) · Classifying angles by their size (we teach it in grade 3–6)
Curriculum point MA.2.A.2 · Teaching content · checked against the act

Students can depict, decompose and compose figures and bodies.

our translation · original wording (DE): Die Schülerinnen und Schüler können Figuren und Körper abbilden, zerlegen und zusammensetzen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.2
Curriculum point MA.2.A.2.d · Teaching content · checked against the act

can enlarge, reduce and move figures in grids. can decompose polygons into triangles and quadrilaterals and compose figures (e.g. lay figures with triangles).

our translation · original wording (DE): können Figuren in Rastern vergrössern, verkleinern und verschieben. können Vielecke in Drei- und Vierecke zerlegen und Figuren zusammensetzen (z.B. mit Dreiecken Figuren legen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.2.d
Curriculum point MA.2.A.2.e · Teaching content · checked against the act

can tile in different ways with basic shapes (e.g. with triangles or pentominoes). can reflect figures across axes and sketch mirror images.

our translation · original wording (DE): können mit Grundfiguren verschieden parkettieren (z.B. mit Dreiecken oder Pentominos). können Figuren an Achsen spiegeln und Spiegelbilder skizzieren.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.2.e

Axial symmetry: reflect across an axis (we teach it in grade 3–9)
Curriculum point MA.2.A.2.f · Teaching content · checked against the act

can move, tilt and turn real objects (bodies) and recognise the corresponding transformations (e.g. tilt a cube twice).

our translation · original wording (DE): können reale Körper verschieben, kippen, drehen und erkennen entsprechende Abbildungen (z.B. einen Würfel zwei Mal kippen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.2.f
Curriculum point MA.2.A.3 · Teaching content · checked against the act

The students can determine and calculate lengths, areas and volumes.

our translation · original wording (DE): Die Schülerinnen und Schüler können Längen, Flächen und Volumen bestimmen und berechnen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.3
Curriculum point MA.2.A.3.c · Teaching content · checked against the act

can compare side lengths and areas of triangles and quadrilaterals as well as volumes of cubes and cuboids (e.g. by covering two rectangles of different sizes with squares)

our translation · original wording (DE): können Seitenlängen und Flächeninhalte von Drei- und Vierecken sowie Volumen von Würfeln und Quadern vergleichen (z.B. in zwei verschieden grosse Rechtecke mit Quadraten belegen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.3.c

Measuring Areas with Squares and Grid Cells (we teach it in grade 3–6) · COMPARING SIZES: LONGER, HEAVIER, LIGHTER (we teach it in grade 1–6)
Curriculum point MA.2.A.3.d · Teaching content · checked against the act

can count areas using unit squares (e.g. the classroom floor using square metres).

our translation · original wording (DE): können Flächen mit Einheitsquadraten auszählen (z.B. das Schulzimmer mit Meterquadraten).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.3.d

Measuring Areas with Squares and Grid Cells (we teach it in grade 3–6)
Curriculum point MA.2.A.3.e · Teaching content · checked against the act

can measure and calculate the perimeter of polygons. can calculate the area of squares and rectangles. can build cuboids from a given number of cubes and decompose cuboids into a certain number of cuboids.

our translation · original wording (DE): können den Umfang von Vielecken messen und berechnen. können den Flächeninhalt von Quadraten und Rechtecken berechnen. können Quader aus einer gegebenen Anzahl Würfeln bilden und Quader in eine bestimmte Anzahl Quader zerlegen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.A.3.e

Perimeter of Polygons and Missing Sides (we teach it in grade 3–6)
Curriculum point MA.2.B.1 · Teaching content · checked against the act

The students can explore geometric relationships, in particular between lengths, areas and volumes, formulate conjectures and exchange findings.

our translation · original wording (DE): Die Schülerinnen und Schüler können geometrische Beziehungen, insbesondere zwischen Längen, Flächen und Volumen, erforschen, Vermutungen formulieren und Erkenntnisse austauschen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.1
Curriculum point MA.2.B.1.d · Teaching content · checked against the act

explore figures and solids and can formulate relationships (e.g. the side faces of a cuboid are rectangles).

our translation · original wording (DE): erforschen Figuren und Körper und können Beziehungen formulieren (z.B. die Seitenflächen eines Quaders sind Rechtecke).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.1.d

Recognizing and naming bodies by their properties (we teach it in grade 1–6)
Curriculum point MA.2.B.1.e · Teaching content · checked against the act

can form figures with a given perimeter (e.g. lay triangles with 5, 6, or 7 matchsticks)

our translation · original wording (DE): können Figuren mit gegebenem Umfang bilden (z.B. Dreiecke mit 5, 6, oder 7 Streichhölzern legen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.1.e

Perimeter of Polygons and Missing Sides (we teach it in grade 3–6)
Curriculum point MA.2.B.1.f · Teaching content · checked against the act

can explore relationships between side lengths and area of rectangles on a grid.

our translation · original wording (DE): können Beziehungen zwischen Seitenlängen und Flächeninhalt bei Rechtecken in einem Raster erforschen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.1.f
Curriculum point MA.2.B.1.g · Teaching content · checked against the act

can systematically vary line segments on figures, explore the effects, formulate and exchange conjectures (e.g. the area of a rectangle with a given perimeter using a grid)

our translation · original wording (DE): können Strecken an Figuren systematisch variieren, Auswirkungen erforschen, Vermutungen formulieren und austauschen (z.B. Flächeninhalt eines Rechtecks bei gegebenem Umfang mit einem Raster).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.1.g
Curriculum point MA.2.B.2 · Teaching content · checked against the act

The students can check statements and formulas about geometric relationships, support them with examples, and justify them.

our translation · original wording (DE): Die Schülerinnen und Schüler können Aussagen und Formeln zu geometrischen Beziehungen überprüfen, mit Beispielen belegen und begründen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.2
Curriculum point MA.2.B.2.a · Teaching content · checked against the act

can explore and describe properties of figures and solids (e.g. halving a square produces, among others, triangles or rectangles).

our translation · original wording (DE): können Eigenschaften von Figuren und Körpern erforschen und beschreiben (z.B. beim Halbieren eines Quadrates entstehen u.a. Dreiecke oder Rechtecke).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.2.a
Curriculum point MA.2.B.2.b · Teaching content · checked against the act

can use heuristic strategies: change lines and angles, sketch examples, compare figures and solids. can check nets of cubes and cuboids by folding.

our translation · original wording (DE): können heuristische Strategien verwenden: Linien und Winkel verändern, Beispiele skizzieren, Figuren und Körper vergleichen. können Würfel- und Quadernetze durch Falten überprüfen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.2.b
Curriculum point MA.2.B.2.c · Teaching content · checked against the act

can check statements about geometric relationships in triangles, quadrilaterals and circles (e.g. a circle and a quadrilateral can intersect in more than 4 points).

our translation · original wording (DE): können Aussagen zu geometrischen Beziehungen im Dreieck, Viereck und Kreis überprüfen (z.B. ein Kreis und ein Viereck können sich in mehr als 4 Punkten schneiden).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.B.2.c
Curriculum point MA.2.C.1 · Teaching content · checked against the act

The students can represent bodies and spatial relationships.

our translation · original wording (DE): Die Schülerinnen und Schüler können Körper und räumliche Beziehungen darstellen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.1
Curriculum point MA.2.C.1.d · Teaching content · checked against the act

can draw the top view (plan) of cube buildings on squared paper.

our translation · original wording (DE): können die Aufsicht von Würfelgebäuden auf Karopapier zeichnen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.1.d
Curriculum point MA.2.C.1.e · Teaching content · checked against the act

can sketch the top view, front view and side view of cuboids and cube buildings. can build cube buildings according to the top view and side view and describe them.

our translation · original wording (DE): können die Aufsicht, Vorderansicht und Seitenansicht von Quadern und Würfelgebäuden skizzieren. können Würfelgebäude entsprechend der Aufsicht und Seitenansicht bauen und beschreiben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.1.e
Curriculum point MA.2.C.1.f · Teaching content · checked against the act

can sketch cubes and cuboids in oblique projection.

our translation · original wording (DE): können Würfel und Quader im Schrägbild skizzieren.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.1.f
Curriculum point MA.2.C.1.g · Teaching content · checked against the act

can build cubes and cuboids from squares and rectangles and vice versa, and draw the net of cubes and cuboids by unfolding.

our translation · original wording (DE): können aus Quadraten und Rechtecken Würfel und Quader herstellen und umgekehrt das Netz von Würfeln und Quadern durch Abwickeln zeichnen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.1.g
Curriculum point MA.2.C.2 · Teaching content · checked against the act

Students can fold, sketch, draw and construct figures, as well as exchange and check representations of plane geometry.

our translation · original wording (DE): Die Schülerinnen und Schüler können Figuren falten, skizzieren, zeichnen und konstruieren sowie Darstellungen zur ebenen Geometrie austauschen und überprüfen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.2
Curriculum point MA.2.C.2.d · Teaching content · checked against the act

can fold paper following pictorial instructions (e.g. a boat).

our translation · original wording (DE): können nach bildlicher Anleitung falten (z.B. ein Schiff).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.2.d
Curriculum point MA.2.C.2.e · Teaching content · checked against the act

can draw rectangles with given side lengths. can draw, modify and describe area ornaments with compass and ruler.

our translation · original wording (DE): können Rechtecke mit gegebenen Seitenlängen zeichnen. können Flächenornamente mit Zirkel und Lineal zeichnen, verändern und beschreiben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.2.e
Curriculum point MA.2.C.2.f · Teaching content · checked against the act

can draw with grids, compass and set square (e.g. parallel lines, right angles, right-angled triangles, squares and rectangles).

our translation · original wording (DE): können mit Rastern, Zirkel und Geodreieck zeichnen (z.B. parallele Linien, rechte Winkel, rechtwinklige Dreiecke, Quadrate und Rechtecke).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.2.f
Curriculum point MA.2.C.3 · Teaching content · checked against the act

Students can visualize figures and solids in different positions in their minds, represent and describe changes (mental geometry).

our translation · original wording (DE): Die Schülerinnen und Schüler können sich Figuren und Körper in verschiedenen Lagen vorstellen, Veränderungen darstellen und beschreiben (Kopfgeometrie).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.3
Curriculum point MA.2.C.3.d · Teaching content · checked against the act

can change the position of a figure or a cuboid in their imagination as well as describe changes (e.g. rotate a desk by 180° in their imagination). can check cube and cuboid nets in their imagination.

our translation · original wording (DE): können die Lage einer Figur oder eines Quaders in der Vorstellung verändern sowie Veränderungen beschreiben (z.B. ein Pult im Kopf um 180° drehen). können Würfel- und Quadernetze in der Vorstellung überprüfen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.3.d
Curriculum point MA.2.C.3.e · Teaching content · checked against the act

can mentally decompose and recompose solids (e.g. replicate a given figure from two pieces of the Soma cube). can carry out operations on a model and describe the results (e.g. tilt a die 4 times so that the same number of pips is facing up again).

our translation · original wording (DE): können Körper in der Vorstellung zerlegen und zusammenfügen (z.B. eine vorgegebene Figur aus zwei Teilen des Somawürfels nachbauen). können Operationen am Modell ausführen und Ergebnisse beschreiben (z.B. einen Würfel 4 Mal kippen, so dass die gleiche Augenzahl wieder oben liegt).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.3.e
Curriculum point MA.2.C.4 · Teaching content · checked against the act

The students can determine the coordinates of figures and solids in a coordinate system or represent figures and solids based on their coordinates, as well as read and draw plans.

our translation · original wording (DE): Die Schülerinnen und Schüler können in einem Koordinatensystem die Koordinaten von Figuren und Körpern bestimmen bzw. Figuren und Körper aufgrund ihrer Koordinaten darstellen sowie Pläne lesen und zeichnen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.4
Curriculum point MA.2.C.4.c · Teaching content · checked against the act

can represent objects on a plan (e.g. seating arrangement in the classroom).

our translation · original wording (DE): können Objekte in einem Plan darstellen (z.B. Sitzordnung im Klassenzimmer).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.4.c
Curriculum point MA.2.C.4.d · Teaching content · checked against the act

can draw figures in a coordinate system, shift them horizontally and vertically, and state the coordinates of their vertices.

our translation · original wording (DE): können Figuren in einem Koordinatensystem zeichnen, horizontal und vertikal verschieben sowie die Koordinaten der Eckpunkte angeben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.4.d
Curriculum point MA.2.C.4.e · Teaching content · checked against the act

can read and use plans and photographs for orientation in space.

our translation · original wording (DE): können Pläne und Fotografien zur Orientierung im Raum lesen und nutzen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.4.e
Curriculum point MA.2.C.4.f · Teaching content · checked against the act

can draw figures in a coordinate system and determine the coordinates of points (e.g. span figures on the geoboard according to coordinates and draw them).

our translation · original wording (DE): können zu Koordinaten Figuren zeichnen sowie die Koordinaten von Punkten bestimmen (z.B. Figuren auf dem Geobrett nach Koordinaten aufspannen und zeichnen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.2.C.4.f
Curriculum point MA.3.A.1 · Teaching content · checked against the act

The students understand and use terms and symbols for quantities, functions, data and chance.

our translation · original wording (DE): Die Schülerinnen und Schüler verstehen und verwenden Begriffe und Symbole zu Grössen, Funktionen, Daten und Zufall.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.1
Curriculum point MA.3.A.1.d · Teaching content · checked against the act

can lay out amounts with coins and banknotes up to 100 francs.

our translation · original wording (DE): können mit Münzen und Noten bis 100 Fr. Beträge legen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.1.d

Calculating with Francs up to 20 (we teach it in grade 1–6)
Curriculum point MA.3.A.1.e · Teaching content · checked against the act

understand and use the terms weight, capacity, point in time, duration, second. can orient themselves by reference quantities: 1 km, 1 dm, 1 mm, 1 kg, 100 g, 1 l, 1 dl, 1 h, 1 min (e.g. associate 1 kg with a packet of flour). can name and use units of measurement and their abbreviations: lengths (km, dm, mm), capacity measures (l, dl), weights (kg, g), time (h, min).

our translation · original wording (DE): verstehen und verwenden die Begriffe Gewicht, Inhalt, Zeitpunkt, Zeitdauer, Sekunde. können sich an Referenzgrössen orientieren: 1 km, 1 dm, 1 mm, 1 kg, 100 g, 1 l, 1 dl, 1 h, 1 min (z.B. 1 kg mit einer Packung Mehl assoziieren). können Masseinheiten und deren Abkürzungen benennen und verwenden: Längen (km, dm, mm), Hohlmasse (l, dl ), Gewichte (kg, g), Zeit (h, min).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.1.e

Units of mass: grams and kilograms in everyday life (we teach it in grade 3–6) · Calculating Durations and Times (we teach it in grade 1–6)
Curriculum point MA.3.A.1.f · Teaching content · checked against the act

can name and use units of measurement and their abbreviations: capacity (l, dl, cl, ml), weights (t, kg, g, mg), time (h, min, s). can orient themselves to reference quantities: 1 s, 1 min. can understand and use prefixes: kilo, deci, centi, milli.

our translation · original wording (DE): können Masseinheiten und deren Abkürzungen benennen und verwenden: Hohlmasse (l, dl, cl, ml), Gewichte (t, kg, g, mg), Zeit (h, min, s). können sich an Referenzgrössen orientieren: 1 s, 1 min. können Vorsätze verstehen und verwenden: Kilo, Dezi, Centi, Milli.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.1.f

Converting Weights: Grams and Kilograms (we teach it in grade 3–6) · Calculating with Clock Times and Durations (we teach it in grade 3–6)
Curriculum point MA.3.A.1.g · Teaching content · checked against the act

understand and use the terms (un)likely, (im)possible, certain.

our translation · original wording (DE): verstehen und verwenden die Begriffe (un)wahrscheinlich, (un)möglich, sicher.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.1.g

Certain, Possible, or Impossible: Judging Events (we teach it in grade 1–5)
Curriculum point MA.3.A.1.h · Teaching content · checked against the act

understand and use the terms proportionality, area, volume, capacity, mean, pie chart, bar chart, line graph, data, frequency, chance, memory. can orient themselves to reference quantities: 1 m², 1 dm², 1 cm², 1 mm², 1 bit, 1 byte, 1 kB. can name units of measurement and use their abbreviations: area units (km², m², dm², cm², mm²), time (d, h, min, s).

our translation · original wording (DE): verstehen und verwenden die Begriffe Proportionalität, Flächeninhalt, Volumen, Inhalt, Mittelwert, Kreisdiagramm, Säulendiagramm, Liniendiagramm, Daten, Häufigkeit, Zufall, Speicher. können sich an Referenzgrössen orientieren: 1 m², 1 dm², 1 cm², 1 mm², 1 bit, 1 Byte, 1 kB. können Masseinheiten benennen und deren Abkürzungen verwenden: Flächenmasse (km², m², dm², cm², mm²), Zeit (d, h, min, s).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.1.h
Curriculum point MA.3.A.2 · Teaching content · checked against the act

The students can estimate, measure, convert, round and calculate with quantities.

our translation · original wording (DE): Die Schülerinnen und Schüler können Grössen schätzen, messen, umwandeln, runden und mit ihnen rechnen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.2
Curriculum point MA.3.A.2.d · Teaching content · checked against the act

can form, add and subtract amounts of money in Fr. and Rp. (e.g. form 20 Fr. with 2 · 5 Fr. + 5 · 2 Fr.; 25 Fr. 60 Rp. + 14 Fr. 30 Rp.). can determine analogue and digital times.

our translation · original wording (DE): können Geldbeträge mit Fr. und Rp. bilden, addieren und subtrahieren (z.B. 20 Fr. mit 2 · 5 Fr. + 5 · 2 Fr. bilden; 25 Fr. 60 Rp. + 14 Fr. 30 Rp.). können analoge und digitale Uhrzeiten bestimmen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.2.d

Calculating with Money: Budget, Change and Offers (we teach it in grade 3–9) · Calculating with Francs up to 20 (we teach it in grade 1–6) · Reading the clock: full and half hours (we teach it in grade 1–6)
Curriculum point MA.3.A.2.e · Teaching content · checked against the act

can estimate, measure and convert between neighbouring units of measurement: l, dl; m, cm, mm; kg, g (e.g. 2'000 g = 2 kg). can add, subtract and multiply quantities: l, dl; m, cm, mm; kg, g (e.g. 3 cm 5 mm + 2 cm 7 mm). can estimate lengths, volumes and weights and compare them with representative examples.

our translation · original wording (DE): können Grössen schätzen, messen und in benachbarte Masseinheiten umwandeln: l, dl; m, cm, mm; kg, g (z.B. 2'000 g = 2 kg). können Grössen addieren, subtrahieren und vervielfachen: l, dl; m, cm, mm; kg, g (z.B. 3 cm 5 mm + 2 cm 7 mm). können Längen, Volumen und Gewichte schätzen und mit Repräsentanten vergleichen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.2.e

Converting lengths: m, cm and mm (we teach it in grade 3–9) · Converting Weights: Grams and Kilograms (we teach it in grade 3–6) · Estimating in Everyday Life (we teach it in grade 3–6)
Curriculum point MA.3.A.2.f · Teaching content · checked against the act

can estimate and measure lengths, weights, capacities, points in time and durations, and state them with a suitable unit of measurement.

our translation · original wording (DE): können Längen, Gewichte, Inhalte, Zeitpunkte und Zeitdauern schätzen und messen sowie mit einer geeigneten Masseinheit angeben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.2.f

Estimating in Everyday Life (we teach it in grade 3–6) · Calculating Durations and Times (we teach it in grade 1–6)
Curriculum point MA.3.A.2.g · Teaching content · checked against the act

can calculate with lengths, weights, volumes and time specifications and convert corresponding quantities into neighbouring units of measurement.

our translation · original wording (DE): können mit Längen, Gewichten, Volumen und Zeitangaben rechnen sowie entsprechende Grössen in benachbarte Masseinheiten umwandeln.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.2.g

Converting lengths: m, cm and mm (we teach it in grade 3–9) · Calculating Durations and Times (we teach it in grade 1–6) · Calculating with Clock Times and Durations (we teach it in grade 3–6)
Curriculum point MA.3.A.2.h · Teaching content · checked against the act

can estimate, determine, compare and round measures (money, lengths, weight or mass, time, volume [l]), calculate with them, convert them into neighbouring units of measurement, and write them in compound units.

our translation · original wording (DE): können Grössen (Geld, Längen, Gewicht bzw. Masse, Zeit, Volumen [l]) schätzen, bestimmen, vergleichen, runden, mit ihnen rechnen, in benachbarte Masseinheiten umwandeln und in zweifach benannten Einheiten schreiben.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.2.h

Calculating with Money: Budget, Change and Offers (we teach it in grade 3–9) · Converting Weights: Grams and Kilograms (we teach it in grade 3–6)
Curriculum point MA.3.A.3 · Teaching content · checked against the act

Pupils can describe functional relationships and determine function values.

our translation · original wording (DE): Die Schülerinnen und Schüler können funktionale Zusammenhänge beschreiben und Funktionswerte bestimmen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.3
Curriculum point MA.3.A.3.c · Teaching content · checked against the act

can continue linear and non-linear number sequences (e.g. 90, 81, 70, 57, ...; 1, 4, 9, 16, ...; 1, 3, 6, 10, 15, ...).

our translation · original wording (DE): können lineare und nichtlineare Zahlenfolgen weiterführen (z.B. 90, 81, 70, 57, ...; 1, 4, 9, 16, ...; 1, 3, 6, 10, 15, ...).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.3.c
Curriculum point MA.3.A.3.d · Teaching content · checked against the act

can describe and continue value tables of proportional relationships with money amounts (e.g. 100 g → 5.40 Fr.; 200 g → 10.80 Fr.; 300 g → 16.20 Fr., ...).

our translation · original wording (DE): können Wertetabellen zu proportionalen Zusammenhängen mit Geldbeträgen beschreiben und weiterführen (z.B. 100 g → 5.40 Fr.; 200 g → 10.80 Fr.; 300 g → 16.20 Fr., ...).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.3.d

Filling in Value Tables: Finding and Applying the Rule (we teach it in grade 2–6)
Curriculum point MA.3.A.3.e · Teaching content · checked against the act

can record functional relationships in tables of values (e.g. distances covered at a speed of 4.5 km/h after 10 min, 20 min, 30 min, ...). can work with proportional relationships (e.g. 300 g of cheese at 20 Fr./kg; fuel consumption for 700 km at 6 l/100 km).

our translation · original wording (DE): können funktionale Zusammenhänge in Wertetabellen erfassen (z.B. zurückgelegte Distanzen bei einer Geschwindigkeit von 4.5 km/h nach 10 min, 20 min, 30 min, ...). können mit proportionalen Beziehungen rechnen (z.B. 300 g Käse zu 20 Fr./kg; Treibstoffverbrauch für 700 km zu 6 l/100 km).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.A.3.e
Curriculum point MA.3.B.1 · Teaching content · checked against the act

Students can formulate questions about relationships between quantities and functional relationships, investigate these, and check and justify their results.

our translation · original wording (DE): Die Schülerinnen und Schüler können zu Grössenbeziehungen und funktionalen Zusammenhängen Fragen formulieren, diese erforschen sowie Ergebnisse überprüfen und begründen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.B.1
Curriculum point MA.3.B.1.d · Teaching content · checked against the act

can check relationships between lengths, prices and times (e.g. larger objects are more expensive or greater distances take more time).

our translation · original wording (DE): können Beziehungen zwischen Längen, Preisen und Zeiten überprüfen (z.B. grössere Gegenstände sind teurer oder weitere Wege brauchen mehr Zeit).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.B.1.d
Curriculum point MA.3.B.1.e · Teaching content · checked against the act

can formulate questions about relationships between quantities, investigate them, and check functional relationships (e.g. the fill level of ½ litre, 1 litre, 2 litres in different containers; the ratio between price and weight of a product; the weight of a light drink and a lemonade).

our translation · original wording (DE): können zu Beziehungen zwischen Grössen Fragen formulieren, erforschen, und funktionale Zusammenhänge überprüfen (z.B. die Füllhöhe von ½ Liter, 1 Liter, 2 Liter in verschiedenen Gefässen; das Verhältnis zwischen Preis und Gewicht eines Produkts; das Gewicht eines Lightgetränks und einer Limonade).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.B.1.e

Filling in Value Tables: Finding and Applying the Rule (we teach it in grade 2–6)
Curriculum point MA.3.B.2 · Teaching content · checked against the act

The students can investigate real-life situations involving statistics, combinatorics and probability, formulate conjectures and test them.

our translation · original wording (DE): Die Schülerinnen und Schüler können Sachsituationen zur Statistik, Kombinatorik und Wahrscheinlichkeit erforschen, Vermutungen formulieren und überprüfen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.B.2
Curriculum point MA.3.B.2.b · Teaching content · checked against the act

can systematically combine and vary (e.g. pairings with 6 children). can pose and answer questions about statistical data (e.g. the longest route to school is more than twice as long as the shortest; most children live less than 1 km away from school).

our translation · original wording (DE): können systematisch kombinieren und variieren (z.B. Paarbildungen mit 6 Kindern). können zu statistischen Daten Fragen stellen und beantworten (z.B. der längste Schulweg ist mehr als doppelt so lang wie der kürzeste; die meisten Kinder wohnen weniger als 1 km von der Schule entfernt).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.B.2.b
Curriculum point MA.3.B.2.c · Teaching content · checked against the act

can explore countable combinations and permutations, record observations and check statements (e.g. combinations of numbers on a bicycle lock; permutations with the letters ADEN, ADNE, AEDN, ...).

our translation · original wording (DE): können auszählbare Kombinationen und Permutationen erforschen, Beobachtungen festhalten und Aussagen überprüfen (z.B. Kombinationen von Zahlen beim Veloschloss; Permutationen mit Buchstaben ADEN, ADNE, AEDN, ...).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.B.2.c
Curriculum point MA.3.C.1 · Teaching content · checked against the act

The students can collect, order, represent, evaluate and interpret data on statistics, combinatorics and probability.

our translation · original wording (DE): Die Schülerinnen und Schüler können Daten zu Statistik, Kombinatorik und Wahrscheinlichkeit erheben, ordnen, darstellen, auswerten und interpretieren.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.1
Curriculum point MA.3.C.1.c · Teaching content · checked against the act

can represent lengths and prices graphically (e.g. 1 Fr. or 1 cm with one square each).

our translation · original wording (DE): können Längen und Preise grafisch darstellen (z.B. 1 Fr. oder 1 cm mit je einem Karo).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.1.c

Presenting Data in Tables and Charts (we teach it in grade 1–6)
Curriculum point MA.3.C.1.d · Teaching content · checked against the act

can represent and interpret data on lengths, capacities, weights, durations, quantities and prices in tables and diagrams (e.g. on pets). can carry out random experiments, record results and interpret them (e.g. throw two dice 50 times).

our translation · original wording (DE): können Daten zu Längen, Inhalten, Gewichten, Zeitdauern, Anzahlen und Preisen in Tabellen und Diagrammen darstellen und interpretieren (z.B. zu Haustieren). können Zufallsexperimente durchführen, Ergebnisse protokollieren und interpretieren (z.B. 50 mal zwei Würfel werfen).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.1.d

Presenting Data in Tables and Charts (we teach it in grade 1–6)
Curriculum point MA.3.C.1.e · Teaching content · checked against the act

can collect, sort, represent and interpret data statistically (e.g. school routes: distance, means of transport, duration).

our translation · original wording (DE): können Daten statistisch erfassen, ordnen, darstellen und interpretieren (z.B. Schulwege: Distanz, Transportmittel, Zeitdauer).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.1.e
Curriculum point MA.3.C.1.f · Teaching content · checked against the act

can analyze data sets according to criteria and determine the mean, maximum and minimum in data sets.

our translation · original wording (DE): können Datensätze nach Kriterien auswerten und in Datensätzen Mittelwert, Maximum und Minimum bestimmen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.1.f
Curriculum point MA.3.C.2 · Teaching content · checked against the act

The students can mathematize real-life situations, represent them, calculate, and interpret and check the results.

our translation · original wording (DE): Die Schülerinnen und Schüler können Sachsituationen mathematisieren, darstellen, berechnen sowie Ergebnisse interpretieren und überprüfen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.2
Curriculum point MA.3.C.2.c · Teaching content · checked against the act

can form basic operations with placeholders or inverse operations for arithmetic stories, solve them and interpret them (e.g. a present costs CHF 36, CHF 23 has been saved. How much is still missing?).

our translation · original wording (DE): können zu Rechengeschichten Grundoperationen mit Platzhaltern bzw. Umkehroperationen bilden, diese lösen und interpretieren (z.B. ein Geschenk kostet 36 Fr., 23 Fr. wurden gespart. Wie viel fehlt noch?).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.2.c

Equations with Boxes: Finding the Missing Number (we teach it in grade 1–6) · Understanding and solving word problems (we teach it in grade 3–6)
Curriculum point MA.3.C.2.d · Teaching content · checked against the act

can ask questions about texts, tables and diagrams, carry out their own calculations, and interpret and check the results.

our translation · original wording (DE): können zu Texten, Tabellen und Diagrammen Fragen stellen, eigene Berechnungen ausführen sowie Ergebnisse interpretieren und überprüfen.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.2.d

Understanding and solving word problems (we teach it in grade 3–6)
Curriculum point MA.3.C.2.e · Teaching content · checked against the act

recognise proportional relationships in real-life situations (e.g. between number of steps and distance). can process information from factual texts, tables, diagrams and pictures from the media.

our translation · original wording (DE): erkennen in Sachsituationen Proportionalitäten (z.B. zwischen Anzahl Schritten und Distanz). können Informationen aus Sachtexten, Tabellen, Diagrammen und Bildern aus den Medien verarbeiten.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.2.e
Curriculum point MA.3.C.3 · Teaching content · checked against the act

The students can make terms, formulas, equations and tables concrete with real-life situations.

our translation · original wording (DE): Die Schülerinnen und Schüler können Terme, Formeln, Gleichungen und Tabellen mit Sachsituationen konkretisieren.

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.3
Curriculum point MA.3.C.3.d · Teaching content · checked against the act

can relate equations with a placeholder to story problems or pictures (e.g. 28 + _ = 50 → a bus has 50 seats, 28 of which are already taken).

our translation · original wording (DE): können Gleichungen mit einem Platzhalter durch Rechengeschichten oder Bilder konkretisieren (z.B. 28 + _ = 50 → ein Bus hat 50 Sitzplätze, 28 sind bereits besetzt).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.3.d

Equations with Boxes: Finding the Missing Number (we teach it in grade 1–6) · Inventing Your Own Math Stories (we teach it in grade 2–6)
Curriculum point MA.3.C.3.e · Teaching content · checked against the act

can give meaning to arithmetic expressions and tables (e.g. 125 Fr. + 4 Fr. + 4 Fr. + 4 Fr. - 34 Fr. → 125 Fr. savings. 3 weeks at 4 francs pocket money each. Purchase of a ball for 34 Fr.).

our translation · original wording (DE): können Rechentermen und Tabellen eine Bedeutung geben (z.B. 125 Fr. + 4 Fr. + 4 Fr. + 4 Fr. - 34 Fr. → 125 Fr. Ersparnisse. 3 Wochen zu je 4 Franken Sackgeld. Kauf eines Balles für 34 Fr.).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.3.e

Understanding and solving word problems (we teach it in grade 3–6) · Calculating with Money: Budget, Change and Offers (we teach it in grade 3–9)
Curriculum point MA.3.C.3.f · Teaching content · checked against the act

can describe relationships in a proportional table of values (e.g. the number of min per km travelled).

our translation · original wording (DE): können zu einer proportionalen Wertetabelle Zusammenhänge beschreiben (z.B. die Anzahl min je zurückgelegtem km).

Lehrplan 21, Fachbereichslehrplan Mathematik (Vorlage der D-EDK, freigegeben 31.10.2014, bereinigte Fassung 29.02.2016), MA.3.C.3.f

Filling in Value Tables: Finding and Applying the Rule (we teach it in grade 2–6)

Skills step by step

Addition up to 100 with Crossing the Tens

Your child learns to add two numbers within the number range up to 100, even when the ones go over 10, and to show the calculation steps in a clear, traceable way.

Your child adds numbers within the range up to 100 where the ones digits together give more than 10, for example 18 + 14. The Lehrplan 21 requires that children can represent and follow calculation paths for additions. An example of this is the number line, on which one shows 18 + 14 step by step.

A typical mistake: the ones and the tens are added separately, and the ten from the ones is forgotten. For 18 + 14, the ones give 8 + 4 = 12, but the 12 is not read as 1 ten and 2 ones. The result then becomes 22 instead of 32. This often happens because bundling into tens is not yet secure: the child sees the numbers as digits rather than as quantities made up of tens and ones.

In Year 3, children mainly encounter these task types:

Addition within 100 with crossing a ten: direct calculations with crossing a ten.
Complete to the next ten: how much is missing? and Complete to the ten and continue calculating: calculation paths via the full ten.
Addition up to 100 with crossing a ten: choose the result and Addition up to 100: check the result, find the error: compare and check calculation paths and results.

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

Measuring Areas with Squares and Grid Cells

The child learns to determine the area of a figure by covering it with equally sized squares and counting the squares.

Curriculum point MA.2.A.3.c can compare side lengths and areas of triangles and quadrilaterals as well as volumes of cubes and cuboids (e.g. by covering two rectangles of different sizes with squares) (our translation)
Curriculum point MA.2.A.3.d can count areas using unit squares (e.g. the classroom floor using square metres). (our translation)

The child can state the area of a shape by counting how many equal-sized unit squares cover it. In this way the child can also compare the areas of two shapes and determine which one is larger. The curriculum does not name a number range for this skill and describes it across the whole stage. For Grade 3, the task templates show what is practised concretely: laying shapes out on a grid or with tiles and counting the squares that are covered.

A typical mistake is that children add up the sides or count the squares along the edge instead of covering the area. This often comes from confusing area with perimeter, because both involve the side lengths. Partial squares at the edge are also sometimes counted incorrectly or left out. Tasks in which someone else's result has to be corrected help children recognise such mistakes.

In practice, a task might look like this:

Rectangle area: How many squares cover the rectangle?
Area on a grid: How many squares cover the shape?
Area of two shapes: How much larger is one of the two?
Area with tiles: How many pairs of tiles or how many missing tiles are needed?
Area and one side: How long is the other side?
Area by laying out: true or false, or choose the correct answer
Shape made of two rectangles: How large is the area of the whole shape?
Draw a rectangle with the given area.

Create a worksheet for this skill Multiple-choice test

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

Division as the Inverse of Multiplication

Your child learns to solve division problems within the multiplication tables by recognizing division as the opposite of multiplication and checking the result with a matching multiplication problem.

Curriculum point MA.1.A.1.d understand and use the term "divided by" and the symbol :. (our translation)
Curriculum point MA.1.A.3.d can note down calculation methods when adding and subtracting and check the results. can add and subtract in writing. know the products of the small multiplication table. (our translation)
Curriculum point MA.1.A.4.e understand division as the inverse operation of multiplication and the connection to addition (e.g. 28 : 7 = 4 → 28 = 4 · 7 → 28 = 7 + 7 + 7 + 7). can use relationships between the small times tables and the tens times tables. (our translation)

Your child learns that division is the reverse of multiplication. The task 28 : 7 = 4 means "28 divided by 7" and can be checked with the multiplication 4 · 7 = 28. The same relationship also shows up in addition: 28 = 7 + 7 + 7 + 7. In the number range up to 100, the child relies on the products of the small multiplication table.

A typical mistake is swapping the numbers. 28 : 7 and 7 : 28 look similar but have very different results. Some children also just look for any multiplication fact that happens to fit, instead of finding the number that was divided by. It helps to check each result by working backwards: does the multiplication fact match the original number?

In Year 3, your child will encounter tasks such as:

Division within the times tables (up to 100)
Which number was divided by (division table)
Sharing into equal parts and Distributing evenly
How many packs does this make and How many in one row
Checking a division and finding the error
Division with an extra number that is not needed

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

Task types: Division facts: choose the result · Division within the table (to 100) · Division: how many packs will there be · Share into equal parts · Share them out evenly · Division: how many in one row · Division with one number too many · Division: check and find the mistake · Missing divisor: choose the number · What was it divided by (division table) · Division: which sharing gives more per person?

Calculating Durations and Times

The child learns to calculate time spans and clock times and to convert hours into minutes.

Curriculum point MA.3.A.1.e understand and use the terms weight, capacity, point in time, duration, second. can orient themselves by reference quantities: 1 km, 1 dm, 1 mm, 1 kg, 100 g, 1 l, 1 dl, 1 h, 1 min (e.g. associate 1 kg with a packet of flour). can name and use units of measurement and their abbreviations: lengths (km, dm, mm), capacity measures (l, dl), weights (kg, g), time (h, min). (our translation)
Curriculum point MA.3.A.2.f can estimate and measure lengths, weights, capacities, points in time and durations, and state them with a suitable unit of measurement. (our translation)
Curriculum point MA.3.A.2.g can calculate with lengths, weights, volumes and time specifications and convert corresponding quantities into neighbouring units of measurement. (our translation)
Curriculum point MA.3.B.1.c can explore real-life situations involving quantities, distances, points in time, durations and prices, and describe and ask about relationships (e.g. compare the duration of the outward and return journey with the outward journey) (our translation)

In Grade 3, the child can work with time in hours (h) and minutes (min). It can estimate and measure points in time and durations, describe related everyday situations, and formulate questions, for example how long the way there takes compared to the way back. In addition, it can convert hours into minutes and calculate with such values. The curriculum does not name a separate number range for time; the Grade 3 mathematics area works in the number range up to 1000.

The units are often confused: the child calculates with hours as if they were tens and then arrives at answers such as "2 h 30 min equals 230 min" or believes an hour has 100 minutes. Mistakes also happen when calculating across the full hour, for example from 10:50 to 11:10, because the minutes are simply added without counting up to the full hour.

Typical tasks in this area, with printable worksheets and solutions, are:

Calculate the duration
At what time did it start?
Time: how many minutes have passed? (word problem)
Convert hours into minutes and Hours into minutes: choose the correct answer or true or false
Daily schedule: order the times
Duration: how much longer did one take?

Create a worksheet for this skill Multiple-choice test

Task types: Convert hours into minutes · The day plan: put the times in order · Hours to minutes: choose the correct answer · Hours to minutes: true or false · Time duration (how long?) · Time: how many minutes have passed? (word problem) · What time did it start? · Duration: how much longer did one last?

Equations with Boxes: Finding the Missing Number

The child learns to find the missing number in equations with an empty box, for example 28 + _ = 50, and to check it using stories or pictures.

The child learns to determine the missing number in an equation with an empty box (placeholder), for example 28 + _ = 50. To do this, it can use a word problem or a picture as help: A bus has 50 seats, and 28 are already taken. How many are still missing? The examples for this skill in the curriculum work with numbers up to 50. The number range for Grade 3 extends up to 1000.

A typical mistake: The child reads the equals sign as an instruction to calculate and simply adds the known numbers together, even when the task requires subtraction. For 28 + _ = 50, it would then calculate 28 + 50. It often helps to read the equation as a story or to think of the inverse: If 28 is added to the number we are looking for and the result is 50, then the number we are looking for is 50 - 28.

Such tasks appear in this form:

Missing addend (placeholder task) and Equation with a box: missing first addend
Equation with a box: choose the missing number and fill in both boxes
Equation with a box: true or false and Sum of three numbers
Scale in balance and Equality of both sides: how much to add, where the two sides must have equal weight or equal size

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

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

The Small Multiplication Table: Knowing the Products with Confidence

Children learn to know the products of the small multiplication table, use relationships between them, and find missing factors.

Curriculum point MA.1.A.3.c can double, halve, add and subtract in the number range up to 100. know products from the small multiplication table with the factors 2, 5 and 10. can decompose products from the small multiplication table into factors (e.g. 36 = 6 · 6 = 4 · 9). (our translation)
Curriculum point MA.1.A.3.d can note down calculation methods when adding and subtracting and check the results. can add and subtract in writing. know the products of the small multiplication table. (our translation)
Curriculum point MA.1.A.4.d can use relationships between products (e.g. 6 · 8 is 8 greater than 5 · 8 or with the commutative law: e.g. 8 · 3 = 3 · 8). (our translation)
Curriculum point MA.1.C.1.d recognize multiplicative relationships in graphic models, in particular doublings and 1 · more or 1 · less (e.g. 3 · 4 and 6 · 4 in a dot array as a doubling). (our translation)
Curriculum point MA.1.C.2.d can illustrate basic operations with actions, situational pictures, arithmetic stories and graphic structures, and interpret illustrations. can show and describe relationships in and between basic operations (e.g. the change in the products 1 · 3, 2 · 4, 3 · 5, 4 · 6, ...). (our translation)

The curriculum describes this goal across several school years. In the number range up to 100, children should know products of the small multiplication table and calculate with them confidently. In Year 3, the worksheets mainly focus on multiplications up to 100, for example 6 · 8 or 7 · 9.

Children should use relationships between products instead of memorising each one separately. Anyone who knows 5 · 8 can derive 6 · 8, because it is 8 more. Swapping the factors also helps: 8 · 3 gives the same result as 3 · 8. This includes breaking products down into factors, for example 36 = 6 · 6 = 4 · 9, and recognising doublings in dot arrays, such as 3 · 4 and 6 · 4.

A typical stumbling block arises when products are stored only as isolated individual facts. The child then confuses neighbouring results such as 6 · 7 and 6 · 8, or 7 · 8 and 7 · 9. Anyone who uses a known product as a starting point and follows the difference can more easily spot and correct such confusions.

On the worksheets, the multiplication table appears in different task formats. These include Einmaleins (bis 100), Fehlender Faktor (kleines Einmaleins) and Fehlender Faktor: wähle die Zahl. Comparison tasks such as Multiplikation: welches Produkt ist grösser, um wie viel? and dot arrays such as Multiplikation: wie viele Punkte im Punktefeld draw on the relationships between products. With Multiplikation: prüfen und Fehler finden, children check results. The worksheets contain solutions, so parents can check the answers themselves.

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

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

Calculating sums cleverly: order and grouping

The child recognizes that addends can be swapped and cleverly grouped together without changing the result, and uses this when adding.

Curriculum point MA.1.A.4.b can decompose numbers up to 20 in different ways (e.g. 5 = 1 + 4 = 3 + 2 = 3 + 1 + 1) and transform them (commutative law: e.g. 5 + 3 = 3 + 5). (our translation)
Curriculum point MA.1.A.4.c can use addition as the inverse operation of subtraction (e.g. 18 - 15 = 3, because 15 + 3 = 18). can use relationships between additions with the commutative law (e.g. 2 + 18 = 18 +2) and the associative law (e.g. 17 + 18 = 17 + 3 + 15 = 20 + 15). (our translation)
Curriculum point MA.1.A.4.d can use relationships between products (e.g. 6 · 8 is 8 greater than 5 · 8 or with the commutative law: e.g. 8 · 3 = 3 · 8). (our translation)

The child learns that the order of the addends does not change the result: 3 + 5 and 5 + 3 both give 8. The child can use this relationship to rearrange sums, and sees that numbers can also be grouped in other ways, for example 17 + 18 = 17 + 3 + 15 = 20 + 15. The curriculum points describe this for the whole stage. In Year 3, the focus is mainly on addition up to 100.

A typical mistake arises when regrouping: a number is split, but the separated part is not added back in. From 17 + 18 one then gets 17 + 3 + 13, and the result is no longer correct. Many children cling too closely to the written form and forget that the sum must stay the same. Some also believe that 5 + 3 and 3 + 5 are two different tasks.

In the tasks for this year group, this appears in the following forms:

Swapping addends: comparing two sums, children check whether two calculations give the same amount.
The same sum, sides swapped: what is hidden, a number is missing, and the child finds it via the swapped side.
Properties of addition: missing term in the equation, one part of the equation is empty.
Smart addition: choosing the order and Smart addition: choosing the result, the child chooses a convenient order or a suitable result.
Convenient order when adding: right or wrong, the child judges calculation methods.
Four addends, two convenient pairs, the child forms two simple pairs from four numbers.
Addition up to 100: explaining a smart calculation strategy, the child justifies their method in their own words.

Relationships between multiplications also belong to this stage, but they are not offered separately in the tasks for this year group and are therefore not described here.

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

Task types: Convenient order of adding: choose the order · Swapping addends: compare the two sums · A handy order of adding: true or false · Addition within 100: easy strategy and explanation · Convenient order of adding: choose the result · The same total, sides swapped — what is hidden · Four terms, two convenient pairs · Properties of addition: missing term in an equality

Multiplying numbers under 20 by 10

The child learns to multiply numbers under 20 by 10 and, in doing so, to use the connection between the small multiplication tables and the tens multiplication tables.

Curriculum point MA.1.A.4.e understand division as the inverse operation of multiplication and the connection to addition (e.g. 28 : 7 = 4 → 28 = 4 · 7 → 28 = 7 + 7 + 7 + 7). can use relationships between the small times tables and the tens times tables. (our translation)

The Lehrplan 21 requires that children can use relationships between the small multiplication table and the multiplication table of ten. For this topic, the specific focus is on numbers under 20 multiplied by 10, for example 7 · 10 = 70 or 14 · 10 = 140. The digits stay the same, but they move one place to the left, because each digit is now worth ten times as much.

A typical mistake: 14 · 10 is written as 104, because the zero is simply attached to the 14 instead of shifting the digits. Another mistake is adding 10 to the number, so calculating 14 · 10 = 24. Both errors show that the pattern is not yet understood and that only a rule is being applied.

Suitable worksheets with solutions:

Multiplying by 10: the basic tasks.
Multiplying by 10: true or false: The child checks solutions such as 104 and explains why they cannot be correct.
Multiplying by 10: choosing the correct result: The child compares several possible answers.
Multiplying by 10: one unnecessary piece of information: The child recognises an unnecessary number in the task and leaves it out.
Multiplying by 10: a chain of changes: The child multiplies by 10 several times in succession.
Ten times ten, so two places further: 10 · 10 = 100 shows that shifting by two places works.
Tens: how many full tens fit in?: This supports understanding of tens, on which the multiplication table of ten is built.

Create a worksheet for this skill Multiple-choice test

Task types: Multiplying by 10 · Multiplying by 10: choose the correct result · Multiplying by 10: true or false · Multiplying by 10: a chain of changes · Multiplying by 10: one number too many · Tens: how many whole tens fit? · Ten times ten, or two places further

Filling in Value Tables: Finding and Applying the Rule

Curriculum point MA.3.A.3.a can describe value tables (e.g. 1 bottle → 2 francs; 2 bottles → 4 francs; 3 bottles → 6 francs). (our translation)
Curriculum point MA.3.A.3.b can describe and continue linear number sequences and value tables with integers (e.g. 0, 9, 18, 27, 36, ...; 1 m → 8 Fr.; 2 m → 16 Fr.; 3 m → 24 Fr., ...). (our translation)
Curriculum point MA.3.A.3.d can describe and continue value tables of proportional relationships with money amounts (e.g. 100 g → 5.40 Fr.; 200 g → 10.80 Fr.; 300 g → 16.20 Fr., ...). (our translation)
Curriculum point MA.3.B.1.e can formulate questions about relationships between quantities, investigate them, and check functional relationships (e.g. the fill level of ½ litre, 1 litre, 2 litres in different containers; the ratio between price and weight of a product; the weight of a light drink and a lemonade). (our translation)
Curriculum point MA.3.C.3.f can describe relationships in a proportional table of values (e.g. the number of min per km travelled). (our translation)

The child learns to recognise, from a table of values, the rule that turns one number into another, and so to fill in the missing numbers. In Grade 3 this involves numbers up to 1000 and the small multiplication table, for example sequences such as 0, 9, 18, 27, 36.

A typical mistake: the child looks only at the last completed row and continues the sequence by guesswork, instead of checking the rule against every row. With a multiplication rule such as "times 9", for example, it calculates 3 → 12 (3 + 9) instead of 3 → 27. It also often happens that input and output are swapped when the rule is read from the arrows.

In lessons and on the worksheets, these task types appear most often:

Function table: fill in using the multiplication rule
Function table: calculation program
Value table: find the rule
Rule table: which number went in
Rule table (subtraction): complete the results
Rule table: correct the errors
Rule table: choose the machine's result
Rule of the machine: choose the number

The curriculum points on money tables (e.g. 100 g → 5.40 Fr.) and on relationships such as "minutes per km" refer to the whole level and go beyond this grade. For Grade 3, the tasks listed above are the main focus here.

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

Task types: Function table: fill in using the multiplying rule · Rule table (subtraction): fill in the results · Function table: find the rule · Machine rule: choose the number · Rule table: choose what comes out of the machine · Rule table: correct the mistake · Rule table: which number went in · Function table: calculation program (grade 4–6)

Place values in three-digit numbers

The child recognizes the value of each digit of a number up to 1000, and can combine hundreds, tens and ones to form a number or break a number down into them.

In 3rd grade, your child works with numbers up to 1000. Here, your child should understand what each digit means: in 257 there are 2 hundreds, 5 tens and 7 ones. This can be shown with blocks, i.e. 2 hundred flats, 5 ten rods and 7 one cubes, and conversely the child can read the number from such blocks. The curriculum also requires that three-digit numbers can be read and written.

A typical mistake occurs when there is a zero in the middle of a number. Someone with 3 hundreds and 5 ones will often write 35 instead of 305, because the missing tens are simply overlooked. This usually stems from the idea that each digit is a number on its own, regardless of the position it occupies.

The tasks on the worksheets on this topic include, for example:

Place value: put together a number from H, T and O
Place value: how many full tens does the number have?
Split the number into hundreds and the remainder
Place value: how many ones in total?
Read the number from the blocks
Place value: true or false

The worksheets contain solutions, so you can easily check your child's answers.

Create a worksheet for this skill Multiple-choice test

Task types: Place value: how many ones altogether? · Read the number from the blocks · Split the number into hundreds and the rest · Place value: build a number from hundreds, tens, ones · Place value: how many whole tens · Place value: how many whole tens in a three-digit number? · Place value: true or false

Adding and subtracting full hundreds

The child calculates with whole hundreds in the number range up to 1000 and checks whether its result is correct.

Curriculum point MA.1.A.3.d can note down calculation methods when adding and subtracting and check the results. can add and subtract in writing. know the products of the small multiplication table. (our translation)

In the number range up to 1000, the child learns to add and subtract whole hundreds such as 200, 500 or 800. The focus is on place value: the child recognises that 300 + 400 makes seven hundreds, so 700. The calculation steps are written down, and the child should be able to check their result.

A typical mistake happens when the hundreds are treated only as single digits. The child then calculates 3 + 4 = 7 and writes 7 instead of 700, because they do not keep the place value in mind. Similarly, in subtraction it can happen that only the digits are compared without checking the result against the hundreds grid.

In practice, the worksheets on this topic include, for example:

Adding hundreds: How many hundreds were added?
Subtracting whole hundreds: Calculations in which whole hundreds are taken away.
Whole hundreds: find the mistake: An incorrect calculation is searched for and corrected, which practises checking.
Jumping by whole hundreds: Starting from a number, the child jumps forwards or backwards by whole hundreds, including two jumps in a row.
Missing hundreds and whole hundreds, how much is missing to make equality: The missing number is filled in or chosen from given options.

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

Task types: Jumping by full hundreds · Jumping by full hundreds: choose the correct result · Taking away full hundreds · Adding hundreds: how many hundreds were added? · Full hundreds: fix the mistake · Jumping by full hundreds: two jumps in a row · Missing hundreds: choose the number · Whole hundreds: how much is missing to balance

Halves and Quarters: Parts of a Whole

The child learns to divide wholes into equal parts and to recognise, name and compare halves and quarters.

Curriculum point MA.1.A.1.g understand and use the terms fraction, percent, factor, multiples, numerator, denominator, estimate, round. use the symbols %, ≈. can read and write decimal numbers and fractions. (our translation)
Curriculum point MA.1.C.2.g can illustrate regularities in the domain of natural numbers with examples (e.g. square numbers have an odd number of divisors → 16: 1, 2, 4, 8, 16). can represent fractions with denominators 2, 3, 4, 5, 6, 8, 10 and compare them, as well as interpret representations (e.g. circle and rectangle models, number line). can describe number sequences with positive rational numbers (e.g. ½, ¼, ⅛, ...; 0.7, 0.77, 0.777, ...). (our translation)
Curriculum point MA.2.C.2.b can halve the area of squares and rectangles (e.g. fold a rectangle into four equal strips and colour 2 of the 4 strips). (our translation)
Curriculum point MA.2.C.2.c can fold squares, rectangles, and circles into 2, 4, 8 or 16 equal parts. (our translation)

The child can fold shapes such as squares, rectangles and circles into equal parts and so recognise one half or one quarter. The curriculum describes this area across several school years: squares, rectangles and circles are divided into 2, 4, 8 or 16 equal parts, and the area of a rectangle is halved, for example by folding it into four equal strips and colouring two of them. The tasks in this class mainly work with halves and quarters.

A typical mistake: the child counts the coloured parts and gives that as the answer, even though the question asks about the parts that are not coloured. Just as often, the parts look halved but are not equal in size, for example when one strip is wider than the others after folding. Then the fraction is wrong, even if the number of parts is right. It helps to refold the parts and lay them side by side.

On the worksheet, these skills appear in the following task types:

Part of a whole (half and quarter): Which part is coloured?
Fraction of a set: how many make up one part: How many objects belong to one half or one quarter?
Fraction of a set: choose how many there are: Which number fits a given fraction?
Part of a set: find the mistake: What is wrong with an incorrect solution?
Fraction of a set: how many are there in total?: The whole is determined from a known part.
Invent sets for the same division: The child invents their own sets with the same fraction.
How many parts stay uncoloured: true or false: A statement about the uncoloured parts is checked.

Create a worksheet for this skill Multiple-choice test

Task types: Part of a whole (halves and quarters) · A fraction of a set: fix the mistake · Fraction of a set: choose how many · Fraction of a set: how many altogether? · Fraction of a set: how many is one part · How many parts left unshaded: true or false · Invent sets that split into equal parts

Written addition and subtraction up to 1000

Children learn to write three-digit numbers one above the other, to add and subtract them in writing, and to check their results.

In Grade 3, children calculate with written methods within the number range up to 1000. They write three-digit numbers one above the other, calculate place by place, and note down their method. They should also learn to check their result.

The typical mistake in written subtraction arises when something slips during borrowing. For 52 − 27, the top row has 2 and the bottom row has 7. Instead of borrowing a ten from the tens place, the child then calculates 7 − 2 = 5, and the result is wrong. It also often happens that the ten from the neighboring place is forgotten. This is often because the place values get lost from view when the numbers are written one above the other.

The worksheets include, among others, these task types:

Written addition step by step and Add three-digit numbers in writing practice calculating with carrying.
Add three numbers in writing and Written subtraction up to 1000 extend the method.
Correct the mistake in written subtraction and Choose the result of written subtraction train checking: the child finds the error in a calculation or decides which result is correct.
Missing addend in written addition requires thinking through the calculation from the other side.

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

Task types: Add three-digit numbers in columns · Three-digit written addition: choose the result · Column addition step by step · Written subtraction within 1000 · Add three numbers in columns · Column subtraction: choose the result · Column subtraction: correct the mistake · Missing addend in column addition

Checking Calculations with the Inverse Operation

The child learns to check addition and subtraction results using the corresponding inverse operation, and to use multiplication and division as related calculations.

Curriculum point MA.1.A.4.c can use addition as the inverse operation of subtraction (e.g. 18 - 15 = 3, because 15 + 3 = 18). can use relationships between additions with the commutative law (e.g. 2 + 18 = 18 +2) and the associative law (e.g. 17 + 18 = 17 + 3 + 15 = 20 + 15). (our translation)
Curriculum point MA.1.A.4.e understand division as the inverse operation of multiplication and the connection to addition (e.g. 28 : 7 = 4 → 28 = 4 · 7 → 28 = 7 + 7 + 7 + 7). can use relationships between the small times tables and the tens times tables. (our translation)
Curriculum point MA.1.B.2.c can check products using a sum (e.g. 3 · 4 = 4 + 4 + 4). can check differences using the inverse operation (e.g. 27 - 6 = 21 → 21 + 6 = 27). (our translation)
Curriculum point MA.1.B.2.d can check quotients using the inverse operation (e.g. 21 : 3 = 7 → 7 · 3 = 21). (our translation)
Curriculum point MA.1.B.2.e can justify divisions with remainder using the inverse operation (e.g. 32 : 6 leaves a remainder because 32 is not a number in the 6 times table). (our translation)

The child recognises that addition and subtraction belong together: a subtraction can be checked with an addition and vice versa. For example, 18 − 15 = 3 is correct because 15 + 3 = 18. For written calculations in the number range up to 1000, the child uses this check to verify its result. Likewise, in the small multiplication table, it links multiplication and division, for example 21 : 3 = 7, because 7 · 3 = 21.

A typical mistake: the check is done by repeating the first calculation, or the numbers are swapped in the check, so that the check does not really test anything. This often happens because addition and subtraction are learned as two separate operations rather than as two directions of the same relationship.

In Year 3, the child mainly encounters these types of tasks:

Checking addition by subtraction
Checking subtraction: with addition
Checking subtraction: true or false
From which number was subtracted? Choose
Checking subtraction: correcting errors
Multiplication and division: how many before sharing
Multiplication and division: what was multiplied

The curriculum points describe a standard across several school years. The ten times table and divisions with remainders are not included in the task templates for this class and do not belong to the tasks here.

Create a worksheet for this skill Multiple-choice test

Task types: Checking addition by subtraction · Checking subtraction: by adding · Checking subtraction: correct the mistake · Checking subtraction: true or false · Multiplication and division: how many before sharing · Multiplication and division: what it was multiplied by · What number was it subtracted from? Choose

Calculating with Francs up to 20

Your child learns to show amounts of money up to 20 francs with coins and banknotes and to add and subtract with them.

Curriculum point MA.3.A.1.b understand and use the terms money, coins and banknotes between 1 and 20 francs. can describe differences between objects and situations using comparative and superlative forms, in particular with regard to prices, lengths, points in time, durations, weights and contents (e.g. B is heavier than A, C is the heaviest). (our translation)
Curriculum point MA.3.A.1.c understand and use the terms length, metre, centimetre, time, hours, minutes, francs, Rappen, price. can orient themselves by reference quantities: 1 centimetre, 1 metre. can use units of measurement for money and length and the abbreviations Fr., Rp., cm, m. (our translation)
Curriculum point MA.3.A.1.d can lay out amounts with coins and banknotes up to 100 francs. (our translation)
Curriculum point MA.3.A.2.b can lay out whole franc amounts up to 20 francs as well as add and subtract them. can determine the time to the half hour. (our translation)
Curriculum point MA.3.A.2.c can estimate, measure and add lengths up to 1 m (e.g. 15 cm + 35 cm). can double and halve lengths and amounts of money, divide 1 metre into 2, 5 and 10 equal parts, and lay out whole franc amounts up to 100 Fr. using coins and banknotes. (our translation)
Curriculum point MA.3.A.2.d can form, add and subtract amounts of money in Fr. and Rp. (e.g. form 20 Fr. with 2 · 5 Fr. + 5 · 2 Fr.; 25 Fr. 60 Rp. + 14 Fr. 30 Rp.). can determine analogue and digital times. (our translation)
Curriculum point MA.3.B.1.b can vary quantities and prices and investigate the effects (e.g. 3 balls at 4 francs and 5 balls at 2 francs). (our translation)

Your child can lay out amounts of money up to 20 francs with coins and notes and calculate with them, for example adding two notes and one coin together or subtracting the price from the money handed over. The Lehrplan 21 also mentions amounts in francs and centimes as well as amounts up to 100 francs. These goals belong to a longer learning pathway and are only touched on briefly in this class.

A typical mistake is to simply count coins instead of calculating with their value: three coins are counted as three francs, even though one of them is worth five francs. When working out change, the calculation is often reversed, because one has to think from the price back to the amount handed over, instead of finding the difference.

In Year 3, your child will encounter tasks such as:

Money in a picture: how much is it?
Coins: which coins to pay with?
Shopping: is the money enough?
Shopping: what do several items cost?
Money: how much is still missing for the purchase?
Change: find the mistake or choose the correct amount
Shopping and change as a combination of both steps

Create a worksheet for this skill Multiple-choice test

Task types: Money in a picture: how much is there? · Money: how much is still missing to buy it · Shopping: how much do several items cost? · Shopping: is there enough money? · Change: choose the right amount · Change: fix the mistake · Coins: which coins to pay with? · Shopping and change

Comparing and ordering numbers up to 1000

Your child learns to compare three-digit numbers up to 1000 with one another and to put them in the correct order.

Curriculum point MA.1.A.2.e can count forwards and backwards in the number range up to 1'000 in 1s, 2s, 10s and 100s, starting from any number. can order numbers up to 1'000. (our translation)

The child can compare and order numbers within the range up to 1000. They decide which number is greater or smaller and arrange several numbers in the correct order, for example from smallest to largest.

A typical mistake: some children only look at the last digit. For 352 and 298, they then say 352 is smaller because 2 is smaller than 8. However, the hundreds digit matters first: 352 has 3 hundreds, while 298 has only 2. Comparing the digits from left to right helps avoid this mistake.

In practice, the child encounters these types of tasks:

Fill in the sign: numbers up to 1000 (with <, > or =)
Compare numbers up to 1000: which one is the largest?
Compare numbers up to 1000: how much larger?
Order numbers up to 1000: starting from the smallest

Create a worksheet for this skill Multiple-choice test

Task types: Insert the relation sign: numbers to 1000 · Comparing numbers within 1000: how much greater? · Comparing numbers within 1000: which is greatest? · How many more within 1000: choose the correct answer · How many more within 1000: true or false · Ordering numbers within 1000: from least

Understanding and Solving Word Problems

The child solves short word problems by finding the matching calculation, working it out, and relating the result back to the story.

Curriculum point MA.1.C.2.b can represent numbers up to 20 in a structured way (e.g. based on fives and tens: 9 = 5 + 4; 12 = 10 + 2). can make additions and subtractions concrete using actions, number stories and pictures. (our translation)
Curriculum point MA.1.C.2.d can illustrate basic operations with actions, situational pictures, arithmetic stories and graphic structures, and interpret illustrations. can show and describe relationships in and between basic operations (e.g. the change in the products 1 · 3, 2 · 4, 3 · 5, 4 · 6, ...). (our translation)
Curriculum point MA.3.B.1.c can explore real-life situations involving quantities, distances, points in time, durations and prices, and describe and ask about relationships (e.g. compare the duration of the outward and return journey with the outward journey) (our translation)
Curriculum point MA.3.C.2.b can write down basic operations for real-life situations, arithmetic stories and pictures, solve them and interpret the results (e.g. 13 girls and 5 boys as 18 children; 1 book costs 10 Fr. → 5 books cost 5 · 10 Fr.). recognise essential and non-essential information for solving problems (e.g. a book is 5 cm thick, has 75 pages and is free. How much does one pay for it?). (our translation)
Curriculum point MA.3.C.3.b can give meaning to additions and subtractions with arithmetic stories, pictures and actions (e.g. 12 + 8 → on the playground there are 12 girls and 8 boys). (our translation)
Curriculum point MA.3.C.3.c can give meaning to basic operations and tables with arithmetic stories, pictures and actions (e.g. 5 · 8 → a child builds 5 houses with 8 blocks each). (our translation)

In grade 3, the child solves word problems involving addition and subtraction within the number range up to 1000. They write down the matching calculation, work it out, and explain what the result means in the story, for example: 13 girls and 5 boys are 18 children together. To do this, they use pictures or actions to follow the story. Word problems with the small multiplication table also belong to this topic.

A typical sign is that the child focuses on individual words or numbers instead of understanding the whole story. For example, if the word "together" appears in the text, the child adds, even though something is being taken away. Or the child simply adds all the numbers in the text. With tasks that include a number that plays no role in the question, the child often finds it hard to decide which information is important.

The worksheets mainly include these task types:

Simple word problem – how many are left: a subtraction from a short story.
Choose the operation: addition (together) and subtraction (taken away): the child decides for themselves which calculation fits the story.
Word problem: how many were there at the start: the child must think backwards from the result.
Word problem with an unnecessary number: the child recognises which piece of information is not needed for the question.
Word problem: choose the correct result: the child checks which result fits the story.

Create a worksheet for this skill Multiple-choice test

Task types: Simple word problem — how many are left · A word problem with an extra number — how many are left · Choose the operation: addition (altogether) · Choose the operation: subtraction (take away) · Word problem: choose the correct answer · Word problem: how many were there at the start

Recognizing and naming plane figures

The child learns to recognize and correctly name plane shapes such as circle, triangle, rectangle and square, even when they are rotated.

Curriculum point MA.2.A.1.a can draw and sort lines (e.g. short, long, straight, wavy lines). can name circle, triangle, rectangle, square, cube and sphere. (our translation)
Curriculum point MA.2.A.1.b can order and describe line segments, circles, triangles, squares, rectangles as well as spheres and cubes. They use the terms longer, shorter, longest, shortest, bigger, smaller, biggest, smallest. can identify and name overlapping figures (e.g. by tracing the outline). (our translation)
Curriculum point MA.2.A.1.d understand and use the terms figure, length, width, area, body, reflect, shift. (our translation)
Curriculum point MA.2.A.2.b can trace triangles, squares, rectangles and circles and draw them without a template, as well as shape spheres and cubes. can compose figures and solids from pieces. (our translation)

The Lehrplan 21 describes this skill across several school years. In Year 3, the worksheets mainly show that the child recognises and names plane shapes such as circle, triangle, rectangle and square. The child should also be able to find a shape again even when it is positioned differently.

It is typical for children to judge a shape by its position instead of by its sides and corners. A rotated shape then seems like a completely different shape. It is also often confused whether it is a plane shape or a solid: a circle is flat, a sphere is three-dimensional. In pictures with overlapping shapes, one shape easily gets lost, so a triangle is overlooked.

Typical tasks on the worksheets are:

What is the name of the drawn shape? The child names a drawing.
What is the name of this rotated shape? The child recognises a rotated shape.
Shapes in the picture: how many triangles? The child counts a particular shape in a picture with overlapping shapes.
Plane shapes: true or false The child checks statements about shapes.
What is this shape called? Choose The child selects the matching name.
Plane shapes: correct the name of the shape The child finds and corrects a wrong name.

Create a worksheet for this skill Multiple-choice test

Task types: Shapes in a drawing: how many triangles? · Plane shapes: correct the name of the drawn shape · Plane shapes: true or false · What is the drawn figure called · What is this figure called? Choose · What is this turned figure called?

Reading and writing numbers up to 1000

The child reads and writes numbers up to 1000 in digits and in words, even when a zero is in the middle, for example 305.

Curriculum point MA.1.A.1.c understand and use the terms times, greater than, less than, even, odd, complement, halve, double, tens, ones and the symbols ·, <, >. can read and write natural numbers up to 100. (our translation)
Curriculum point MA.1.A.1.e understand and use the terms addition, subtraction, multiplication, division, remainder, number line, square number, hundreds, thousands, place values. can read and write natural numbers up to 1'000. (our translation)

Your child can read and write numbers up to 1000 in digits and in words. This includes three-digit numbers such as 305, 470 or 982. They learn to recognise which digit stands for the hundreds, the tens and the ones.

A zero is often lost in three-digit numbers. For example, three hundred and five then becomes 35 instead of 305, because the empty tens place is overlooked. The reason is that number words do not say, digit by digit, where each digit belongs. The zero in the middle is therefore especially error-prone.

Exercises for this are available as printable worksheets with solutions. Typical task types are:

Write the number in digits
Read the number in words
Zero in the middle: correct the way the number is written
Number words: correct the errors
Number words: choose the digit notation
Number words: true or false

Create a worksheet for this skill Multiple-choice test

Task types: Write the number in digits · Numbers in words: choose the digits · Numbers in words: true or false · Read the number in words · Numbers in words: correct the mistake · Zero in the middle: fix how the number is written

Estimating in Everyday Life

The child learns to estimate approximate sums, differences and prices in everyday life by rounding to the nearest ten and checking whether a result fits the situation.

Curriculum point MA.3.A.2.e can estimate, measure and convert between neighbouring units of measurement: l, dl; m, cm, mm; kg, g (e.g. 2'000 g = 2 kg). can add, subtract and multiply quantities: l, dl; m, cm, mm; kg, g (e.g. 3 cm 5 mm + 2 cm 7 mm). can estimate lengths, volumes and weights and compare them with representative examples. (our translation)
Curriculum point MA.3.A.2.f can estimate and measure lengths, weights, capacities, points in time and durations, and state them with a suitable unit of measurement. (our translation)

In the number range up to 1000, the child can estimate in everyday situations. It rounds numbers to the nearest ten to estimate a sum or difference, and it considers how much several items cost together. In doing so, it also checks whether an exact result fits the situation.

A typical mistake: 47 is rounded down to 40 instead of up to 50, because the child only looks at the ones digit or does not know which ten is closer. The estimate then becomes too low, and the child trusts it anyway. A second common misconception is the belief that an estimate must be exactly equal to the exact result. An estimate should, however, only be in the right order of magnitude.

A task on this topic might look like this, for example. The templates for this area are:

Estimate costs by rounding up
Estimate: find prices that match the estimate
Estimate a difference: round to the nearest ten
Estimate: does the result fit?
Roughly how much do we pay together
Estimate a sum: round to the nearest ten

Estimating lengths and weights is also part of the curriculum, but it is not practised specifically on these worksheets.

Create a worksheet for this skill Multiple-choice test

Task types: Estimation: will the result fit · About how much will we pay in total · Estimate the difference: round to the nearest ten · Estimate the sum: round to the nearest ten · Estimating a cost by rounding up · Estimation: find prices that match the estimate

Finding and correcting calculation errors

The child learns to recognize an incorrect calculation result, check it with a second calculation, and correct it.

Curriculum point MA.1.B.2.c can check products using a sum (e.g. 3 · 4 = 4 + 4 + 4). can check differences using the inverse operation (e.g. 27 - 6 = 21 → 21 + 6 = 27). (our translation)
Curriculum point MA.1.B.2.g can check results of basic operations by simplifying (e.g. 8 · 13 = 4 · 26 = 2 · 52), decomposing (e.g. 17.8 + 23.5 = 17 + 3 + 20 + 1.3) and using inverse operations (our translation)

The child checks calculations by doing a second calculation. For a subtraction, this is the reverse: someone who works out 27 − 6 = 21 checks with 21 + 6 and sees whether 27 comes out. For a multiplication, the product can be checked as a sum, for example 3 · 4 = 4 + 4 + 4. The curriculum points describe this ability for the stage as a whole. For Year 3, the worksheets mainly show subtractions within the number range up to 1000 and multiplications with the small times table.

A typical mistake when subtracting in columns: the child subtracts the smaller digit from the larger one in every column, even when the larger digit is on the bottom, or forgets to carry over. Someone who has calculated this way often checks using the same method and does not find the mistake. The reverse calculation helps because it takes a different route. In multiplication, the mistake usually lies in the times table, for example 6 · 7 = 36 instead of 42. If you recount 6 · 7 as 7 + 7 + 7 + 7 + 7 + 7, the mistake becomes noticeable.

The worksheets on this topic include, among others, these task types with solutions:

Subtraction: correct a wrong result
Multiplication: correct a wrong result
Correct subtraction result: decide whether it is right or wrong
Correct subtraction result: choose the matching answer
Addition and subtraction: find the mistake in two steps
Subtraction: find out how much someone has been mistaken by, for example correct 232, written 242, error 10

Create a worksheet for this skill Multiple-choice test

Task types: Addition and subtraction: fix a mistake in two steps · Correct subtraction result: choose the answer · Correct subtraction result: true or false · Multiplication: correct the wrong result · Subtraction: correct the wrong result · Subtraction: by how much someone was wrong

Adding larger numbers in writing and checking the result

The child learns to add three-digit numbers in writing, to record their calculation method, and to check the result.

This class deals with additions in the number range up to 1000. The tasks show three-digit numbers that are added without carrying. The curriculum also mentions written subtraction, but the tasks at hand concern mainly addition.

A typical mistake occurs when the numbers are not written neatly one below the other: the ones then do not stand under the ones, and the tens not under the tens. The result is already wrong when read off. A second common mistake is to simply accept the first solution without checking it. This is exactly where the curriculum comes in when it requires results to be checked.

A task in this area looks, for example, like this:

True or false: The child decides whether a given addition is correct.
Correct the wrong result: The child finds and corrects a mistake in the calculation.
Choose the right result: The child chooses the correct solution from several options.
Three addends: The child adds three numbers one after another.
Find two numbers with the given sum: The child looks for suitable addends.

The tasks on correcting and checking are particularly suitable for practising checking.

Create a worksheet for this skill Multiple-choice test

Task types: Add three-digit numbers (no regrouping) · Addition within 1000: choose the correct result · Addition within 1000: three terms · Addition within 1000: true or false · Invent two numbers with the given sum · Addition within 1000: correct someone else's result

Units of mass: grams and kilograms in everyday life

The child learns to read weights in grams (g) and kilograms (kg), to convert between them, and to complete them, for example by working out how many grams are missing to reach a full kilogram.

In the third school year, the child works with weights in the number range up to 1000. They learn to use grams and kilograms and to relate them to each other, for example that 1 kg is the same as 1000 g. The curriculum refers to everyday reference quantities for this, for example a bag of flour weighing 1 kg or 100 g as a comparison. The curriculum item also covers lengths, liquid volumes and time. The tasks in this area revolve mainly around weights.

A typical mistake occurs when converting: children apply the pattern of the base-ten system incorrectly and write, for example, 1 kg = 100 g, because they have remembered 100 g as a comparison quantity. When completing to a full kilogram, calculations often go wrong when crossing the hundreds, for example 1000 g − 650 g = 450 g instead of 350 g.

Typical tasks in this area are:

Scale: How many grams does it show?
Kilograms in smaller units: correct or incorrect?
Convert kilograms into smaller units of mass
Units of mass from kilograms: choose the result
Mass: How much is missing to the full kilogram, or how many grams are missing up to the kilogram?
How many portions does the pack suffice for?

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

Task types: Converting kilograms to smaller units of mass · Mass: how many grams are missing to a kilogram? · Mass: how much is missing to a full kilogram? · Scale: how many grams does it show? · Kilograms to smaller units: true or false · Mass units from kilograms: choose the answer · How many portions the package makes

Reading the clock: full and half hours

Your child learns to tell the time to the full hour and the half hour, both on an analogue clock face and on a digital display.

Curriculum point MA.3.A.1.c understand and use the terms length, metre, centimetre, time, hours, minutes, francs, Rappen, price. can orient themselves by reference quantities: 1 centimetre, 1 metre. can use units of measurement for money and length and the abbreviations Fr., Rp., cm, m. (our translation)
Curriculum point MA.3.A.2.b can lay out whole franc amounts up to 20 francs as well as add and subtract them. can determine the time to the half hour. (our translation)
Curriculum point MA.3.A.2.d can form, add and subtract amounts of money in Fr. and Rp. (e.g. form 20 Fr. with 2 · 5 Fr. + 5 · 2 Fr.; 25 Fr. 60 Rp. + 14 Fr. 30 Rp.). can determine analogue and digital times. (our translation)

Your child learns to determine the time on the hour and the half hour, both on an analogue clock face with hands and on a digital display. To do this, they must tell apart the short hour hand and the long minute hand and read both together.

Often only the hour hand is noticed, while the minutes are ignored or misinterpreted. At the half hour, the hour hand also sits between two numbers, which easily leads to the wrong hour. Language can also be confusing: "half past three" means 3:30 and not 4:30. The task "Clock: correcting reading errors" targets exactly these points.

In class, your child will encounter the following task types, which are available as printable worksheets with solutions:

Read the clock: true or false: A time shown is judged as correct or incorrect.
Clock: correcting reading errors: An incorrectly read time is corrected.
Read the clock: The displayed time is determined.
Clock: how many minutes until the full hour?: The minutes until the next full hour are counted.
Clock: which clock shows the earlier time?: From two clocks, the one showing the earlier time is identified.
Read the clock: which time does the clock face show: For a clock face, the matching time is chosen.

Create a worksheet for this skill Multiple-choice test

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

Counting forwards and backwards in steps

The child learns to count forwards and backwards in fixed steps such as 2, 5 or 10, starting from any number, and to continue number sequences.

Curriculum point MA.1.A.2.b can count forward and backward from any numbers in the number range up to 20. can count forward in steps of 2, from 2 to 20. can spontaneously show finger patterns from 1 to 10 as well as recognize quantities up to 5 without counting. (our translation)
Curriculum point MA.1.A.2.c can count forward in 1s, 2s, 5s and 10s in the number range up to 100. can order numbers in the 100s number range (e.g. on the number line and on the 100 chart). (our translation)
Curriculum point MA.1.A.2.d can count forwards and backwards from any numbers within the number range up to 100. can count forwards and backwards from any multiples of 10 in steps of 2, 5 and 10 within the number range up to 100. (our translation)
Curriculum point MA.1.A.2.e can count forwards and backwards in the number range up to 1'000 in 1s, 2s, 10s and 100s, starting from any number. can order numbers up to 1'000. (our translation)
Curriculum point MA.1.B.1.b can systematically vary additions up to 20, describe their effects or show them with visual materials (e.g. 8 + 8 = 16, 8 + 9 = 17; the sum increases by 1 because the second addend increases by 1). can form, continue and modify number sequences (figurate numbers) (e.g. 1, 2, 3 / 2, 3, 4 / 3, 4, 5 / 4, 5, 6). (our translation)
Curriculum point MA.3.A.3.b can describe and continue linear number sequences and value tables with integers (e.g. 0, 9, 18, 27, 36, ...; 1 m → 8 Fr.; 2 m → 16 Fr.; 3 m → 24 Fr., ...). (our translation)

The child can count forwards and backwards in equal steps from any number. The curriculum objectives for this span several school years: first the number range up to 20, then up to 100 in steps of 1s, 2s, 5s and 10s, and finally up to 1000 in steps of 1s, 2s, 10s and 100s. In Year 3, the number range up to 1000 is the focus, and the tasks show how these step sequences also work with larger numbers.

A typical mistake occurs when counting on crosses a tens or hundreds boundary. The child then often changes only the last digit or counts the digits individually, for example 98, 99, 900 instead of 98, 99, 100. The reason is usually that the child does not yet think of the place values as a unit.

Tasks on this topic look, for example, like this:

Continue counting in the same step: The sequence is continued with a constant difference.
Count backwards in equal steps: The numbers get smaller again, starting from a large number.
Counting in steps: choose the next number: The child determines which number comes next in the sequence.
Counting on: how many steps are needed? The child works out how many steps it takes to get from one number to another.
How often added: choose the number: The child recognises how many times a step was added.
Counting in steps: correct the wrong number: One number in a number sequence is wrong, and the child finds and corrects it.

The worksheets for these tasks each include solutions, so that parents can check the results.

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

Task types: Counting in steps: choose the next number · Keep counting by the same step · Count backwards in equal steps · Counting in steps: correct the wrong number · Counting on: how many times to reach the number? · How many times added: choose the number · Count by tens: choose the result (grade 1) · Count by tens: true or false (grade 1) · Count by tens: what comes next? (grade 1)

Multiplying two-digit numbers by 2

The child learns to multiply a two-digit number by 2, for example 34 · 2 = 68, by doubling the tens and the ones separately.

In Year 3, the child can multiply a two-digit number by 2, for example 34 · 2 or 47 · 2, within the number range up to 1000. The child doubles the tens and the ones and combines the partial results, such as 30 · 2 = 60 and 4 · 2 = 8, which together make 68. The curriculum points on multiplying by up to four significant digits, such as 45 · 240, go beyond this year. Here the focus is only on the part with a two-digit number times 2.

A typical mistake is forgetting the carry. For 46 · 2, 6 · 2 = 12: you write down the 2 and carry the 1 to the tens. If the 1 is forgotten, the result becomes 82 instead of 92. Another common error is writing the tens and the ones separately: for 35 · 2, the 6 and the 10 then become "610" instead of 70.

In practice, this topic appears on worksheets in several forms:

Two-digit number times 2: direct calculations such as 28 · 2.
Doubling: which number doubled gives this? The task works in reverse: Which number doubled gives 58?
Multiplying by 2: true or false: A given result is checked, for example whether 27 · 2 = 54 is correct.
Multiplying by 2: choosing the correct result: The matching answer is selected from several solutions.
Doubling: how much more after doubling both? Two numbers are doubled, and it is asked how much bigger one is than the other afterwards.

Create a worksheet for this skill Multiple-choice test

Task types: Multiplying a two-digit number by 2 · Multiplying by 2: choose the correct result · Multiplying by 2: true or false · Doubling: which number doubled gives this one? · Doubling: how much more after doubling both numbers?

COMPARING SIZES: LONGER, HEAVIER, LIGHTER

Your child learns to compare objects by a size property, such as length or weight, to name the difference, and to arrange them in order.

Curriculum point MA.2.A.1.b can order and describe line segments, circles, triangles, squares, rectangles as well as spheres and cubes. They use the terms longer, shorter, longest, shortest, bigger, smaller, biggest, smallest. can identify and name overlapping figures (e.g. by tracing the outline). (our translation)
Curriculum point MA.2.A.3.a experience the constancy of lengths and volumes when the shape changes (e.g. the length remaining the same after bending wires). can compare the lengths of different line courses (e.g. paths on squared paper). (our translation)
Curriculum point MA.2.A.3.c can compare side lengths and areas of triangles and quadrilaterals as well as volumes of cubes and cuboids (e.g. by covering two rectangles of different sizes with squares) (our translation)
Curriculum point MA.3.A.1.a can describe objects and situations using long/short (temporal and spatial), fast/slow, before/after, wide/narrow, thick/thin, big/small, heavy/light. (our translation)
Curriculum point MA.3.A.1.b understand and use the terms money, coins and banknotes between 1 and 20 francs. can describe differences between objects and situations using comparative and superlative forms, in particular with regard to prices, lengths, points in time, durations, weights and contents (e.g. B is heavier than A, C is the heaviest). (our translation)
Curriculum point MA.3.A.2.a can distribute lengths and volumes (e.g. cut a string into roughly equal parts or share water out into cups). can divide the course of the day into morning, noon, afternoon, evening and night (e.g. assign activities to the parts of the day). (our translation)
Curriculum point MA.3.B.1.a can compare quantities, lengths, areas and volumes with one another. (our translation)

Your child compares two or more objects by a property, for example by length or weight. In doing so, they use words such as longer, shorter, longest and shortest, and arrange objects from the lightest to the heaviest or from the longest to the shortest. The curriculum points apply to a whole stage and not only to Year 3. The types of tasks below show what is practised specifically in this year.

A typical confusion occurs with the question of by how much something is longer. The child then names the longer object instead of determining the difference. So they recognise which ribbon is longer, but do not work out how much length is added. Even with three or more objects, longer and longest are often mixed up.

In Year 3, your child mainly encounters these types of tasks:

Comparing lengths: which is the longest? The child recognises the longest distance or the longest object.
Comparing lengths: how much longer is the ribbon? The child determines the difference between two lengths.
By how much longer: choose the right answer and By how much longer: true or false The child checks statements about the length difference.
Mass: order from the lightest The child puts objects into an order according to their weight.

At home, your child can lay two strings side by side and say by how much one is longer. This is a separate suggestion and does not replace the tasks.

Create a worksheet for this skill Multiple-choice test

Task types: Comparing lengths: how much longer is the ribbon? · Comparing lengths: which one is the longest? · Mass: order from lightest · How much longer: choose the correct answer · How much longer: true or false

Inventing Your Own Math Stories

The child invents a matching word problem for an arithmetic expression or a picture and checks whether an answer fits the task.

Curriculum point MA.3.C.3.c can give meaning to basic operations and tables with arithmetic stories, pictures and actions (e.g. 5 · 8 → a child builds 5 houses with 8 blocks each). (our translation)
Curriculum point MA.3.C.3.d can relate equations with a placeholder to story problems or pictures (e.g. 28 + _ = 50 → a bus has 50 seats, 28 of which are already taken). (our translation)

The child learns to give meaning to basic operations and tables. For a calculation such as 5 · 8, the child might tell a story: A child builds 5 houses, and each house has 8 bricks. Equations with a placeholder such as 28 + _ = 50 can also be made understandable through a story or picture, for example: A bus has 50 seats, and 28 are already taken. In this topic area, Grade 3 works with the number range up to 1000 and the small multiplication table.

It is typical that the story and the calculation do not match. The child first chooses the numbers and then writes a story that belongs to a different operation, or the question at the end of the story does not fit the calculation. For example, a story meant as "gets more" often goes with a calculation that is a subtraction. The reason: the child pays attention to the numbers, not to the situation they describe.

On the worksheets for this topic area, such tasks appear in several forms:

Make up a problem for these numbers: A suitable story is written for the given numbers.
Make up a problem with the given result: The result is fixed, and the story must fit it.
Make up problems: does the answer fit the problem? and which answer fits? The child checks whether an answer belongs to the story.
Make up problems: correct the answer: A wrong answer is checked against the text of the problem and corrected.

Create a worksheet for this skill Multiple-choice test

Task types: Making up problems: does the answer fit? · Make up a problem for these numbers · Making up problems: correct the answer · Making up problems: which answer fits? · Make up a problem with the given answer

Certain, Possible, or Impossible: Judging Events

The child learns to decide, for simple statements, whether something is certain, possible or impossible, and can justify their choice.

Curriculum point MA.3.A.1.g understand and use the terms (un)likely, (im)possible, certain. (our translation)
Curriculum point MA.3.B.2.a can vary, order and record arrangements (e.g. two-digit numbers with the digits 1, 2, 3; equally long paths on a schematic city map; seating arrangements of three children). can assess the influenceability of situations (e.g. influenceability of the weather; influenceability of the duration of the journey to school). (our translation)

The child can judge whether an event is certain, possible, or impossible, and uses these terms in their own words. An example is the statement "A ball from this bag is red," which can be certain, possible, or impossible depending on what is in the bag. The curriculum also names the terms likely and unlikely. However, the tasks in this area focus on certain, possible, and impossible.

Children often confuse "possible" with "certain": they say "That will definitely happen," even though a different outcome is also conceivable. Likewise, they consider something impossible just because it rarely happens. A helpful question is: Could it turn out differently? If not, it is certain or impossible. If so, it is possible.

Typical tasks on the worksheets are:

Fill the bag: certain, possible, or impossible: The child fills a bag so that a particular outcome is certain, possible, or impossible.
Certain, possible, or impossible: The child assigns statements to one of these three categories.
Certain, possible, or impossible? True or false: The child checks whether a given classification is correct.
Correct it: certain, possible, or impossible: The child corrects an incorrect classification.
Certain, possible, or impossible? Choose: The child selects the appropriate answer from a set of options.

The worksheets include solutions, so parents can check the answers directly.

Create a worksheet for this skill Multiple-choice test

Task types: Certain, possible or impossible · Certain, possible or impossible? Choose · Certain, possible or impossible? True or false · Fill the bag: certain, possible or impossible · Correct it: certain, possible or impossible

Successors and predecessors: Finding neighbouring numbers

The child learns to name, for a given number, the number that is one more (its successor) and the number that is one less (its predecessor).

The child can reliably name, for a given number, which number comes directly after it and which comes directly before it. The curriculum points refer to the number range up to 20 and up to 100 and thus describe a level of competence that spans several school years. What is concretely practised in Year 3 is shown by the task templates: determining the successor and predecessor of a given number.

A typical error occurs when crossing a multiple of ten. If the child is looking at the number 40, they sometimes name 30 as the predecessor, because they change the tens digit instead of the ones digit. Similarly, the successor of 19 is often given as 29 or 10. This usually stems from an uncertain idea of the counting sequence at the point where the tens change, and not from a lack of calculation ability.

Typical tasks in this area are:

Which number is 1 greater: The child names the successor of a given number.
Which number is 1 less: The child names the predecessor of a given number.
Successor plus predecessor: choose the correct answer: The child selects the matching sum from several solutions.
Successor plus predecessor: true or false: The child checks given calculations and decides whether they are correct.
Sum of successor and predecessor: The child calculates the sum of the two neighbouring numbers.

When comparing the solutions, it becomes apparent that the sum of successor and predecessor always equals twice the starting number. This is an observation that can be discovered together with children, and not a requirement of the task templates.

Create a worksheet for this skill Multiple-choice test

Task types: Sum of the successor and the predecessor · Successor plus predecessor: choose the correct answer · Successor plus predecessor: true or false · Which number is 1 greater · Which number is 1 smaller

Recognizing and naming bodies by their properties

The child recognizes geometric solids such as cubes, cuboids, spheres, cylinders and pyramids by their properties, such as corners, edges and faces, and names them correctly.

Curriculum point MA.2.A.1.a can draw and sort lines (e.g. short, long, straight, wavy lines). can name circle, triangle, rectangle, square, cube and sphere. (our translation)
Curriculum point MA.2.A.1.e understand and use the terms point, corner, edge, face, cube, cuboid. (our translation)
Curriculum point MA.2.A.1.f recognize and name geometric solids (cube, cuboid, sphere, cylinder, pyramid) and shapes in the environment and in pictures. (our translation)
Curriculum point MA.2.B.1.d explore figures and solids and can formulate relationships (e.g. the side faces of a cuboid are rectangles). (our translation)

The child recognises and names solid shapes that they see in their surroundings or in pictures: cube, cuboid, sphere, cylinder and pyramid. In doing so, they use the terms point, corner, edge and face, and can formulate simple relationships, for example that the faces of a cuboid are rectangles. The curriculum points describe a goal that spans several school years. The tasks in Year 3 mainly show how well a child names and classifies solid shapes. No number range is specified for this topic.

It is typical for children to confuse a solid shape with a flat figure they see on it. A sphere is then called a "circle", and a cube a "square". The reason: the names sound similar, and the shape appears flat in the picture or the object. A helpful question is whether the solid has corners, edges and faces. A cube does, a sphere does not. Many children also find it hard to tell a cube from a cuboid, because a cube is a special cuboid in which all faces are squares.

You will find tasks on this topic in the following forms:

What is this solid called: The child names a solid shown in the picture.
What solid is this? True or false: The child checks whether a statement about a solid is correct.
What solid is this? Choose: The child selects the matching name from several options.
Solids: find an object in the shape of the solid: The child looks for an everyday object that has the shape of a solid.
Solids: correct the name of the solid: The child finds an incorrect name and corrects it.

Create a worksheet for this skill Multiple-choice test

Task types: What is this solid called · Solids: correct the name of the solid · Solids: find an object shaped like the solid · Which solid is it? Choose · Which solid is it? True or false

Presenting Data in Tables and Charts

The child learns to present counting results, such as tally marks, lengths, or prices, in tables and simple pictograms, and to read the total number from them.

Curriculum point MA.3.C.1.b can collect, record, order and interpret frequencies, lengths and prices (e.g. tally lists of dice throws; body heights). can represent quantities from the environment (e.g. 7 blond children with 7 squares, 5 brown-haired children with 5 squares). (our translation)
Curriculum point MA.3.C.1.c can represent lengths and prices graphically (e.g. 1 Fr. or 1 cm with one square each). (our translation)
Curriculum point MA.3.C.1.d can represent and interpret data on lengths, capacities, weights, durations, quantities and prices in tables and diagrams (e.g. on pets). can carry out random experiments, record results and interpret them (e.g. throw two dice 50 times). (our translation)

In the 3rd grade, the child collects frequencies, lengths or prices, records them in tally charts or tables, and displays them graphically. The curriculum gives examples such as dice face counts, body heights or pets. One square can represent, for example, one child, 1 cm or 1 CHF. The examples work with small numbers such as 5 and 7. The curriculum does not give a more precise statement about the number range for this topic at this point.

A typical mistake happens in the pictograph: one picture stands for several units, but the child only counts the pictures. Then three pictures that each mean five children are wrongly read as the number 3 instead of 15. When adding up the table, a row is also often overlooked because the values are not summed systematically from top to bottom.

The worksheets on this topic contain these task types:

How many in total in the table: The child adds all the values in a table.
Pictograph: one picture stands for several: The child works out how many units the pictures represent together.
The missing row when the total is known: The child determines a missing value because the total is given.
Total from the table: choose the correct answer: The child selects the correct total from several options.
Total from the table: true or false: The child checks whether a given total is correct.

The curriculum also mentions random experiments such as rolling dice with a record. For this topic, however, there is no task template in these worksheets.

Create a worksheet for this skill Multiple-choice test

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

Converting lengths: m, cm and mm

The child learns to convert lengths between neighbouring units, for example 1 m = 100 cm and 1 cm = 10 mm.

Curriculum point MA.3.A.2.e can estimate, measure and convert between neighbouring units of measurement: l, dl; m, cm, mm; kg, g (e.g. 2'000 g = 2 kg). can add, subtract and multiply quantities: l, dl; m, cm, mm; kg, g (e.g. 3 cm 5 mm + 2 cm 7 mm). can estimate lengths, volumes and weights and compare them with representative examples. (our translation)
Curriculum point MA.3.A.2.g can calculate with lengths, weights, volumes and time specifications and convert corresponding quantities into neighbouring units of measurement. (our translation)
Curriculum point MA.3.A.2.j can use the decimal system of units (SI system) and assign the prefixes mega, kilo, deci, centi and milli to the powers of ten. (our translation)

In 3rd grade, children practise converting lengths from one unit into a neighbouring unit, for example from metres into centimetres or from centimetres into millimetres. The numbers are within the number range up to 1000. The important relationships are 1 m = 100 cm and 1 cm = 10 mm.

A typical mistake concerns the direction of the conversion. When changing from metres to centimetres, some children divide by 100 instead of multiplying by 100, because the number is supposed to get bigger. Likewise, 100 and 10 are confused, so that 1 cm is calculated as 100 mm. A helpful idea is that a smaller unit gives more pieces.

The tasks in this grade look like this:

Convert into a larger length unit and Convert into a smaller length unit, for example 400 cm = ? m or 6 cm = ? mm.
Length units: choose the converted value, where the correct conversion is found from several given options.
State the length in one unit and Length in one unit: true or false, where it is checked whether a statement is correct.
Add lengths in two units, for example 3 cm 5 mm + 2 cm 7 mm.
Length units: compare, where two lengths in different units are put in order of size, for example 2 m and 150 cm.

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

Task types: A length in one unit: find the mistake (grade 4–5) · A length in one unit: true or false (grade 4–5) · Convert to a larger unit of length (grade 4–6) · Convert to a smaller unit of length (grade 4–6) · Units of length: choose the converted value (grade 4–5) · Units of length: compare (grade 4–5) · Write a length in one unit (grade 4–6) · Adding lengths given in two units (grade 4–5)

Calculating with Clock Times and Durations

Your child learns to determine durations in minutes and seconds, convert minutes into seconds, and compare time spans with one another.

At the end of Year 3, children should be able to calculate with time values and convert quantities into the neighbouring unit of measurement. This concerns hours (h), minutes (min) and seconds (s). Reference quantities such as 1 s and 1 min serve as orientation.

A common mistake: time values are treated like decimal numbers. A child writes 1 min 30 s as the number 130, or calculates 1 min as 100 s. The reason is that minutes and seconds are counted in steps of 60, not in tens.

The tasks in this area work mainly with minutes and seconds. The printed worksheets with solutions cover roughly the following task types:

Word problem on duration: How long did it take?
Clock time: How many minutes have passed?
Time span: Choose the appropriate time span and determine how many minutes have passed.
Durations: Compare two durations.
Minutes and seconds in seconds: Convert a value into seconds.
Minutes and seconds: Decide whether statements are true or false.

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

Task types: Minutes and seconds to seconds (grade 4–6) · Durations: compare (grade 4–5) · Elapsed time word problem: how long did it last (grade 4–6) · Elapsed time: choose how many minutes passed (grade 4–5) · Minutes and seconds: find the mistake (grade 4–5) · Minutes and seconds: true or false (grade 4–5) · Time on a clock: how many minutes passed (grade 4–6)

Understanding and solving word problems

The child reads a math word problem, translates it into an equation with a placeholder or an inverse operation, solves it, and checks whether the result fits the story.

Curriculum point MA.3.C.2.c can form basic operations with placeholders or inverse operations for arithmetic stories, solve them and interpret them (e.g. a present costs CHF 36, CHF 23 has been saved. How much is still missing?). (our translation)
Curriculum point MA.3.C.2.d can ask questions about texts, tables and diagrams, carry out their own calculations, and interpret and check the results. (our translation)
Curriculum point MA.3.C.3.e can give meaning to arithmetic expressions and tables (e.g. 125 Fr. + 4 Fr. + 4 Fr. + 4 Fr. - 34 Fr. → 125 Fr. savings. 3 weeks at 4 francs pocket money each. Purchase of a ball for 34 Fr.). (our translation)

In Year 3, within the number range up to 1000, the child learns to solve everyday word problems. They form a matching calculation for a story, for example with a placeholder or an inverse operation, solve it, and interpret the result again in the context of the problem. An example: A gift costs 36 francs and 23 francs have been saved. The question is how much is still missing. The calculation 36 − 23 = 13 gives the answer: 13 francs are still missing.

A common mistake is that the child picks the numbers out of the text and combines them with the first operation that comes to mind. For the question "How much is still missing?", the child then calculates 36 + 23 instead of thinking about how much of the price is still left. The mistake arises because the story was not understood first. It is therefore helpful to first say in your own words what happens in the problem.

The worksheets at this level mainly feature these task types:

Multi-step word problem (combining): Several pieces of information from the text are combined into one calculation.
Supply and sets: It is asked how many sets are possible at most, or which number can be chosen.
Three-day word problem: The matching result is chosen, or a statement is judged as true or false. This way the result can be checked.

The solutions are enclosed, so that you can check with the child whether the calculation and the answer fit the story.

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

Task types: Two-step word problem (combine) · Word problem, three days: choose the result · Word problem, three days: true or false · Stock and sets: choose the number of sets (grade 4–6) · Stock and sets: the most sets you can make (grade 4–6)

Adding and subtracting fractions with the same denominator

The child learns to add and subtract fractions with the same denominator, for example 2/5 + 1/5 = 3/5.

Curriculum point MA.1.A.3.f can add and subtract decimal numbers with up to 5 significant digits (mentally or by writing down their own calculation methods, e.g. 30.8 + 5.6). can simplify, expand, add and subtract fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50, 100 using the rectangle model. can carry out basic operations with a calculator. (our translation)

In 3rd grade, the child calculates with fractions that have the same denominator, for example 2/5 + 1/5 or 7/8 − 3/8. The denominator shows into how many equal parts the whole is divided. Only the numerators, that is, the number of parts, are added or subtracted. The curriculum point on which this topic builds describes the level across several school years. It names the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50 and 100 as well as the rectangle model as a representation. The tasks in this grade build on fractions with the same denominator.

A typical mistake is adding both the numerator and the denominator. Then 1/4 + 1/4 wrongly becomes 2/8. The child treats the fraction like two separate numbers and overlooks that the denominator sets the size of the parts and stays the same. The same thing happens when subtracting, if the denominator is changed.

The worksheets include task formats such as these:

Adding: "Add fractions with the same denominator" and "Fractions with the same denominator: sum greater than 1"
Subtracting: "Subtract fractions: take away from the whole", "Subtract fractions: missing numerator" and "Subtract fractions: compare differences"
Comparing and checking: "Fractions with the same denominator: compare sums", "Fractions with the same denominator: choose the sum", "Fractions with the same denominator: true or false" and "Fractions: how much is missing from the whole?"

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

Adding and subtracting in writing within the number range 1000

The child learns to write numbers in the number range up to 1000 one below the other, to add and subtract them in written form, and to check their calculation method.

In Grade 3, the child works with multi-digit numbers in columns within the number range up to 1000: ones go under ones, tens under tens, and hundreds under hundreds. In doing so, the child writes down their calculation method and checks whether the result is correct.

A typical mistake when adding is that a ten that arises when adding the ones is forgotten and not added to the tens. When subtracting, the digits are often swapped: instead of 3 − 8, 8 − 3 is calculated. The reason is usually that the child does not regroup at this point, i.e. does not break one ten into ten ones before calculating.

Typical tasks on this topic are:

Adding in columns and Subtracting in columns: solve tasks written in columns yourself.
Written addition: choose the result and Written addition: right or wrong: select a result or check a calculation.
Written subtraction: regrouping across zeros: subtractions where a zero is in the way.
Written subtraction: right or wrong: check a given calculation and find an error.

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

Task types: Add using the column method (grade 4–6) · Column addition: choose the result (grade 4–5) · Column addition: find the mistake (grade 4–5) · Column addition: true or false (grade 4–5) · Subtract using the column method (grade 4–6) · Written subtraction: find the mistake (grade 4–5) · Written subtraction: true or false (grade 4–5) · Numbers to a million: addition word problem (grade 4–5) · Numbers to a million: subtraction word problem (grade 4–5) · Written subtraction: borrowing across zeros (grade 4–5)

Rounding to tens and hundreds

Your child learns to round numbers to the nearest ten or hundred by looking at the digit to the right of the rounding place.

Curriculum point MA.1.A.4.f can transform products by doubling and halving (e.g. 8 · 26 = 4 · 52 = 2 · 104). can use the associative law for sums and products (e.g. 136 + 58 + 42 = 136 + (58 + 42); 38 · 4 · 25 = 38 · (4 · 25)). can round natural numbers to 10s, 100s and 1'000s. (our translation)

Your child learns to round natural numbers to the nearest ten or the nearest hundred, for example 468 to 470 or to 500. The curriculum also mentions rounding to thousands. However, the tasks in this class only show tens and hundreds in the number range up to 1000.

A typical mistake is truncating: the child simply drops the last digit and so turns 468 into 460 instead of 470. The correct approach is to look at the digit to the right of the rounding place. If it is 5 or more, round up; otherwise, round down.

On the worksheets, these task types appear, for example:

Round to the nearest ten and Round to the nearest hundred: The child rounds a number independently.
Rounding to tens: choose the result and Rounding to hundreds: choose the result: The child selects the correct rounded number from several options.
Rounding to tens: true or false: The child checks a given rounding and decides whether it is correct.

Create a worksheet for this skill Multiple-choice test

Task types: Round to the nearest ten · Rounding to tens: choose the result · Rounding to tens: true or false · Round to the nearest hundred · Rounding to hundreds: choose the result

Perimeter of Polygons and Missing Sides

Your child learns to determine the perimeter of a polygon by adding up all the side lengths, and to calculate a missing side from a given perimeter.

Curriculum point MA.2.A.3.e can measure and calculate the perimeter of polygons. can calculate the area of squares and rectangles. can build cuboids from a given number of cubes and decompose cuboids into a certain number of cuboids. (our translation)
Curriculum point MA.2.B.1.e can form figures with a given perimeter (e.g. lay triangles with 5, 6, or 7 matchsticks) (our translation)

Your child learns to measure and calculate the perimeter of a polygon. The perimeter is the length of the boundary all the way around, that is, the sum of all sides. This also includes determining a missing side from a known perimeter and the remaining sides. The curriculum gives the example of laying out triangles with 5, 6 or 7 matchsticks. In this way, the perimeter becomes visible as a concrete number of length units.

A side is often left out when adding up, or a side is counted twice. When finding the missing side, people often add instead of subtract: the child calculates the perimeter plus the known sides, even though they should subtract the known sides from the perimeter. The reason lies in the concept: the perimeter is the total length all the way around, and the missing side is the remainder that is left after subtracting the known sides.

In this topic there are two types of tasks:

Perimeter of a polygon: All sides are given, the perimeter is to be found.
Missing side from the perimeter: The perimeter and all sides except one are given, the missing side is to be found.

The tasks are available as printable worksheets with solutions, so that you can work through the calculations together at home.

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

Task types: Perimeter of a polygon (grade 4–6) · Missing side from the perimeter (grade 4–6) · Missing side from the perimeter: choose the side (grade 4–6) · Perimeter of a polygon: choose the result (grade 4–5) · Perimeter of a rectangle step by step (grade 4–6) · Perimeter of a rectangle: extra data (grade 4–6) · Perimeter of a regular polygon: find the side (grade 4–6) · Perimeters of a rectangle and a square: compare (grade 4–6) · Perimeter of a polygon: word problem (fence) (grade 4–5)

Calculating with Money: Budget, Change and Offers

The child calculates with francs and centimes, plans a small budget, works out the change after shopping and compares offers.

Curriculum point MA.3.A.1.j understand and use the terms coordinate system, currency, arithmetic mean (extension: inverse proportionality). can use units of measurement and their abbreviations and orient themselves to reference quantities: area measures (km², ha, a, m², dm², cm², mm²), volume measures (km³, m³, dm³, cm³, mm³), money (CHF, €, $). (our translation)
Curriculum point MA.3.A.2.d can form, add and subtract amounts of money in Fr. and Rp. (e.g. form 20 Fr. with 2 · 5 Fr. + 5 · 2 Fr.; 25 Fr. 60 Rp. + 14 Fr. 30 Rp.). can determine analogue and digital times. (our translation)
Curriculum point MA.3.A.2.h can estimate, determine, compare and round measures (money, lengths, weight or mass, time, volume [l]), calculate with them, convert them into neighbouring units of measurement, and write them in compound units. (our translation)
Curriculum point MA.3.C.3.e can give meaning to arithmetic expressions and tables (e.g. 125 Fr. + 4 Fr. + 4 Fr. + 4 Fr. - 34 Fr. → 125 Fr. savings. 3 weeks at 4 francs pocket money each. Purchase of a ball for 34 Fr.). (our translation)

In 3rd grade, children calculate with amounts of money in francs and centimes (Rappen) in the number range up to 1000. They build amounts from partial amounts, for example 20 Fr. from 2 · 5 Fr. + 5 · 2 Fr., and add or subtract amounts such as 25 Fr. 60 Rp. + 14 Fr. 30 Rp. The examples in the curriculum revolve around 125 francs.

Part of this is understanding that a calculation has a meaning. The expression 125 Fr. + 4 Fr. + 4 Fr. + 4 Fr. − 34 Fr. stands for savings, three weeks of pocket money, and the purchase of a ball for 34 francs. The child should be able to explain what each number means and what is left over at the end.

A typical mistake occurs when the Rappen exceed 100. For 70 Rp. + 50 Rp., children often write 120 Rp. and forget that this becomes 1 Fr. 20 Rp. Francs and Rappen are then treated like two separate numbers, and the carry-over is missing.

The matching tasks in this subject's worksheet range, each with solutions, are:

Compare offers: Which is cheaper?
Money word problem: How much is left after the purchase?
The cheaper offer: choose the unit price or decide true/false
Budget: choose how much is left over, or decide true/false

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

Task types: Budget: find the mistake (grade 4–6) · Budget: true or false (grade 4–6) · Budget: choose how much is left (grade 4–6) · Money word problem: how much is left after shopping (grade 4–6) · The better offer: find the mistake (grade 4–6) · The better offer: true or false (grade 4–6) · Comparing offers: word problem, which is the better deal (grade 4–6) · The better offer: choose the price of one item (grade 4–6)

Calculating Smartly: Reshaping Numbers Strategically

Your child learns to make calculations simpler when working with numbers close to 100 or with round hundreds, by cleverly rearranging and grouping the numbers.

Curriculum point MA.1.A.3.e can add and subtract up to 4 significant digits mentally (e.g. 320'000 + 38'000; 402 + 90). can multiply up to 4 significant digits (mentally or by writing down own calculation methods, e.g. 45 · 240). can divide natural numbers by one-digit divisors (mentally or by writing down own calculation methods, e.g. 231 : 7). (our translation)
Curriculum point MA.1.A.4.f can transform products by doubling and halving (e.g. 8 · 26 = 4 · 52 = 2 · 104). can use the associative law for sums and products (e.g. 136 + 58 + 42 = 136 + (58 + 42); 38 · 4 · 25 = 38 · (4 · 25)). can round natural numbers to 10s, 100s and 1'000s. (our translation)
Curriculum point MA.1.B.2.g can check results of basic operations by simplifying (e.g. 8 · 13 = 4 · 26 = 2 · 52), decomposing (e.g. 17.8 + 23.5 = 17 + 3 + 20 + 1.3) and using inverse operations (our translation)
Curriculum point MA.1.C.1.e can represent, exchange and comprehend calculation methods for the basic operations (e.g. 80 + 5 + 5 + 5 + 5 = 80 + 4 · 5; 347 - 160 → 160 + 40 + 147 = 347). (our translation)

Your child can rewrite tasks in the number range up to 1000 so that they become easier. For example, they combine addends into round hundreds, or when multiplying by a number close to 100, they calculate via 100 and adjust the result. The curriculum points on this topic extend beyond Grade 3. For this grade, the worksheets show the following task types.

A typical mistake occurs during the adjustment. For 4 · 98, a child often calculates 400 − 2, because they recognise 98 as 100 minus 2. However, they forget that each of the four groups is 2 too large, so a total of 8 must be subtracted. It helps to use a sketch or groups of 98 to think about exactly what was calculated too much.

In practice, your child will encounter these task types on the worksheets:

Adding cleverly: Sums are rearranged so that suitable numbers are combined first.
Adding cleverly: full hundreds: Your child chooses the correct answer.
Multiplying cleverly: Products are made simpler by rewriting them.
Calculating cleverly: times a number close to 100: Your child uses the closeness to 100 for the calculation.
Multiplying cleverly: true or false: Your child checks whether a rewritten calculation method is correct.

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

Task types: Add the smart way (grade 4–6) · Multiply the smart way (grade 4–6) · Smart addition: whole hundreds: choose the answer (grade 4–6) · Clever multiplication: find the mistake (grade 4–5) · Clever multiplication: true or false (grade 4–5) · Mental maths: multiplying by a number close to 100 (grade 4–5)

Estimating: Estimating results and checking them

The child learns to roughly estimate sums within the number range up to 1000 by rounding the numbers to the nearest hundred, and so to recognise the order of magnitude in which the exact result lies.

Curriculum point MA.1.A.2.g can count forwards and backwards from any decimal numbers in appropriate steps (e.g. from 0.725 in steps of 0.005). can order fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50, 100. can order decimal numbers (e.g. 1.043; 1.43; 1.05; 1.5; 1.403). can estimate basic operations with natural numbers (e.g. 13'567 + 28'902 ≈ 40'000; 592'000 : 195 ≈ 600'000 : 200). (our translation)
Curriculum point MA.1.A.2.h can estimate sums and differences of decimal numbers (e.g. 0.723 - 0.04 ≈ 0.7; 23'268 + 4'785 ≈ 28'000). can estimate results in percentage calculations (e.g. 263 of 830 is about 30%; 45% of 13'000 is more than 5'000). (our translation)
Curriculum point MA.1.A.2.i Extension: can estimate products and quotients of decimal numbers. (e.g. 0.382 : 42.8 → 0.4 : 40 = 0.4 : 4 : 10 = 0.01; 32.7 : 0.085 → 30 : 0.1 = 300 : 1 = 300). (our translation)
Curriculum point MA.1.B.2.f Can check results using estimation calculations. Can investigate and justify the number of digits of products and quotients. (our translation)

In 3rd grade the child calculates with numbers up to 1000. They learn to first estimate a sum roughly: they round each number to hundreds and then calculate with the rounded numbers. This gives them an approximate value, for example for 287 + 419 the estimate 300 + 400 = 700. This allows the child to judge whether an exact result is plausible.

A typical mistake is that the child rounds only one of the two numbers or rounds both numbers inconsistently. Often the child also insists on calculating exactly and considers the estimate unnecessary. The result is then calculated correctly, but the child cannot check whether it is roughly right. It helps to practise the estimate as a separate step before calculating exactly.

The printable worksheets in this area include three task types with solutions:

Estimate a sum: The child estimates a sum by rounding the numbers and adding the rounded numbers.
Estimate a sum: choose the estimate: The child selects the suitable estimate from several options.
Estimate: choose the rounding to hundreds: The child practises rounding numbers in the range up to 1000 to hundreds before calculating.

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

Task types: Estimate a sum (grade 4–6) · Estimating a sum: choose the estimate (grade 4–6) · Estimating: choose the rounding to hundreds (grade 4–6)

Expanding fractions: same value, new denominator

The child learns to expand a fraction: the numerator and the denominator are multiplied by the same number, so that the fraction keeps the same value.

A fraction such as 1/2 keeps the same size if you multiply both the top (numerator) and the bottom (denominator) by the same number: 1/2 = 2/4 = 3/6. The rectangle model shows this: a rectangle with one half coloured is exactly the same size as a rectangle divided into four parts, of which two are coloured.

The curriculum point names the denominators 2, 3, 4, 5, 6, 8, 10, 20, 50 and 100 for fractions and links expanding with simplifying, adding and subtracting. However, it describes a longer period of time. The tasks this area offers for Year 3 mainly show expanding itself.

A typical mistake is to change only the denominator, or to add the same number to the numerator and denominator instead of multiplying. For example, 1/2 then becomes 1/4, or 1/2 becomes 3/4. Both change the value of the fraction. A helpful question is: What was the fraction multiplied by, and was the same thing done to the top and the bottom?

The worksheets on this topic (with solutions) include, among others:

Expanding fractions: bringing a fraction to a given larger denominator, e.g. 3/4 to denominator 8.
Missing denominator: tasks such as 2/3 = ?/6.
What was it expanded by? The child recognises the factor, e.g. for 2/5 = 6/15.
True or false: The child checks whether an expansion is correct, e.g. 1/2 = 2/4 or 1/2 = 1/4.
Choose the factor: The child chooses the suitable number from several numbers.

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

Task types: Expanding fractions: choose the multiplier (grade 4–6) · Expanding fractions: find the mistake (grade 4–6) · Expanding fractions: the missing denominator (grade 4–6) · Expanding fractions: true or false (grade 4–6) · Expanding fractions: what was it multiplied by? (grade 4–6) · Find the equivalent fraction (grade 4–6)

Classifying angles by their size

The child learns to classify angles by their size, for example to recognise right angles and to determine types of angles.

The child learns to classify angles by their size. The curriculum uses the term right angle for this, along with the symbol for right angles. The protractor set is among the tools that appear in this area. For angles, the curriculum excerpt does not specify a number range.

A common misconception is that an angle with longer arms is also larger. However, only the opening between the two arms matters, not their length. For this reason, two angles with arms of different lengths often look like different sizes, even though they are equal.

The worksheets on this topic contain tasks with the following templates:

Determine the type of angle: The child decides which type of angle is shown.
Complementary and supplementary angles, calculate the other angle: The child works out how large the missing angle is.
Supplementary angles, choose the other angle as well as Vertically opposite angles, choose the size: The child selects which angle or which size fits.

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

Task types: A half turn of a clock hand · A half turn of a clock hand: true or false · A quarter turn anticlockwise · A quarter turn clockwise · A quarter turn clockwise: choose the result · A three-quarter turn clockwise · Classify the angle (grade 4–6) · Complementary angles: find the other angle (grade 4–6) · Supplementary angles: choose the other angle (grade 4–6) · Supplementary angles: find the other angle (grade 4–6) · Vertical angles: choose the measure (grade 5–7)

Finding Divisors and Multiples of a Number

The child learns to find all the divisors of a number and to recognize how many divisors a number has, for example for 16: 1, 2, 4, 8 and 16.

Curriculum point MA.1.A.1.g understand and use the terms fraction, percent, factor, multiples, numerator, denominator, estimate, round. use the symbols %, ≈. can read and write decimal numbers and fractions. (our translation)
Curriculum point MA.1.A.4.h can solve equations with variables by substitution or inverse operations. can follow the calculation rules "multiplication before addition" and the bracket rules (e.g. 4 + 8 - 2 · 3 = 6; (4 + 8 - 2) · 3 = 30; 4 + (8 - 2) · 3 = 22). Extension: can use divisibility rules for 3, 4, 6, 8, 9, 25, 50 and determine divisors of natural numbers. (our translation)
Curriculum point MA.1.C.2.g can illustrate regularities in the domain of natural numbers with examples (e.g. square numbers have an odd number of divisors → 16: 1, 2, 4, 8, 16). can represent fractions with denominators 2, 3, 4, 5, 6, 8, 10 and compare them, as well as interpret representations (e.g. circle and rectangle models, number line). can describe number sequences with positive rational numbers (e.g. ½, ¼, ⅛, ...; 0.7, 0.77, 0.777, ...). (our translation)

The child understands the terms divisor and multiple and can find all divisors of a number. A divisor divides evenly without a remainder: 16 can be divided by 1, 2, 4, 8 and 16. A multiple is created by multiplying, for example 4, 8, 12, 16 ... are the multiples of 4. The numbers in the tasks remain natural numbers; the exact number range can be found on the respective worksheet.

A typical mistake: when looking for divisors, the numbers are found in pairs (1 and 16, 2 and 8), and often the 1 or the number itself is missing, or the 4 is counted only once for 16, even though it stands on its own. Another common mistake is confusion: when divisors are asked for, multiples are written down (16, 32, 48 ...). The check is helpful: "Does 16 divide evenly by this number without a remainder?"

Typical tasks on this worksheet are:

State all divisors of a number: write down all divisors of a given number.
Divisors: how many are there? do not determine the divisors themselves, only their number.
Divisors of a number: choose the count: select the correct number of divisors from given answers.
Divisors: smallest number with k divisors: find the smallest number that has exactly as many divisors as specified.
Smallest number with k divisors: true or false: check a statement about the smallest number with a certain number of divisors and justify it.

Divisibility rules (for example for 3, 4 or 9) are listed in the curriculum as an extension; there is no task template on this page for this topic.

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

Task types: Factors of a number: choose how many (grade 5–6) · List all factors of a number (grade 4–6) · Factors: how many are there? (grade 5–6) · 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)

Single-digit number times tens number

The child can multiply a single-digit number by a multiple of ten, for example 3 · 40 = 120, by calculating with the tens.

The child can multiply a single-digit number by a multiple of ten, for example 3 · 40, 5 · 70 or 2 · 300. In doing so, the child thinks about the tens: 40 consists of 4 tens, and 3 times 4 tens makes 12 tens, so 120. The curriculum point this area refers to extends to larger numbers such as 45 · 240. The tasks in this class stay with single-digit numbers times multiples of ten.

A typical mistake is to multiply only the digits and forget the zero. Then 3 · 40 becomes 12 instead of 120. This happens because the child only looks at the 4 and does not consider that it is about tens. A helpful question is: Is the result ten times as large as 3 · 4? If so, the zero must go back at the end.

On the worksheets, this area appears in three task types:

Multiplying with multiples of ten: The child works out the task themselves.
Times multiples of ten: right or wrong: The child checks whether a given solution is correct.
Times multiples of ten: choose the result: The child selects the correct answer from several options.

Create a worksheet for this skill Multiple-choice test

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

Converting Weights: Grams and Kilograms

The child learns to convert weights between grams and kilograms, for example 2000 g = 2 kg.

Curriculum point MA.3.A.1.f can name and use units of measurement and their abbreviations: capacity (l, dl, cl, ml), weights (t, kg, g, mg), time (h, min, s). can orient themselves to reference quantities: 1 s, 1 min. can understand and use prefixes: kilo, deci, centi, milli. (our translation)
Curriculum point MA.3.A.2.e can estimate, measure and convert between neighbouring units of measurement: l, dl; m, cm, mm; kg, g (e.g. 2'000 g = 2 kg). can add, subtract and multiply quantities: l, dl; m, cm, mm; kg, g (e.g. 3 cm 5 mm + 2 cm 7 mm). can estimate lengths, volumes and weights and compare them with representative examples. (our translation)
Curriculum point MA.3.A.2.h can estimate, determine, compare and round measures (money, lengths, weight or mass, time, volume [l]), calculate with them, convert them into neighbouring units of measurement, and write them in compound units. (our translation)

The child converts weights into the neighbouring unit, that is, between g and kg. In doing so, they use the fact that one kilogram is 1000 grams, because the prefix "Kilo" means thousand. The curriculum gives this example: 2000 g = 2 kg. Understanding also involves estimating weights and comparing them with familiar objects.

A typical mistake: the child changes only the name of the unit and leaves the number as it is (3 kg = 3 g), or shifts the number by only one place and writes 3 kg = 300 g instead of 3000 g. This happens because "Kilo" sounds like a hundred, even though it means a thousand grams. It helps to always ask whether the new number has to get bigger or smaller: one kilogram is heavier than one gram, so you need more grams for the same mass.

Typical tasks in this class are:

Converting to a smaller mass unit, for example from kg to g.
Converting to a larger mass unit, for example from g to kg.
Mass in kilograms: choosing a decimal number, where the child finds the correct way to write a weight in kg.
Mass in kilograms: true or false, where statements about weights are checked.
Converting mass units: choosing the result, where the correct solution is sought among several options.

In addition, there are comparing mass units and stating mass in one unit.

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

Task types: Convert to a larger unit of weight (grade 4–5) · Convert to a smaller unit of weight (grade 4–6) · Converting units of weight: choose the result (grade 4–5) · Mass in kilograms: find the mistake (grade 5–6) · Mass in kilograms: true or false (grade 5–6) · Units of weight: compare (grade 4–5) · Write a weight in one unit (grade 4–5) · Mass in kilograms: choose the decimal (grade 5–6)

Tens Jump on the Number Line

Your child learns to jump in steps of ten on the number line and to read off the number reached correctly.

Curriculum point MA.1.A.1.e understand and use the terms addition, subtraction, multiplication, division, remainder, number line, square number, hundreds, thousands, place values. can read and write natural numbers up to 1'000. (our translation)
Curriculum point MA.1.A.2.c can count forward in 1s, 2s, 5s and 10s in the number range up to 100. can order numbers in the 100s number range (e.g. on the number line and on the 100 chart). (our translation)
Curriculum point MA.1.A.2.f can count forwards and backwards in appropriate steps within the number range up to 1 million, starting from any numbers (e.g. from 320'000 in steps of 20'000). can order numbers up to 1 million (e.g. determine the approximate position of 72'000 on a number line). (our translation)
Curriculum point MA.1.C.1.b can represent sums and understand representations (e.g. on the 20-frame or on the number line). (our translation)

In Year 3, your child jumps forward in whole tens on the number line, for example from 34 to 44 and then to 54. This is about numbers within the range up to 100 and about showing these jumps on the number line. A tens jump means moving forward ten units without counting each tick mark individually.

A typical mistake is that children count the tick marks one by one. For 47 + 10, they then land on 48 instead of 57. The reason: all the tick marks on the number line look the same, and the child measures the jump by the number of tick marks rather than by the place value of the number.

There are printable worksheets with solutions on this topic. They appear in three forms:

Tens jump on the number line: Your child marks the jump on a number line and reads off the result.
Tens jump: choose the number: From several numbers, the child selects the one that is reached after the tens jump.
Tens jump: true or false: Your child checks whether a given jump statement is correct.

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)

Multiplying single-digit numbers in writing

Your child learns to multiply a multi-digit number by a single-digit number in writing, for example 124 · 3, and can also write down their own calculation methods.

The curriculum describes for this area that numbers with up to 4 digits can be multiplied, either mentally or with self-written calculation steps. This point refers to the level reached at the end of the stage, not only to Year 3. In Year 3, the tasks in this area within the number range up to 1000 mainly involve written multiplication by a single-digit number, where the numbers are written one below the other in columns.

A typical mistake occurs with carrying. For 36 · 4, the child calculates 4 · 6 = 24, writes the 4 under the ones and forgets to add the 2 tens to the tens of the 3. It is equally common for the place values not to be lined up neatly, so that ones and tens get mixed up.

The worksheets in this area include these task types:

Multiply by a single-digit number in writing: The child works out the task in columns.
Written multiplication in a word problem: From a short text, the child must recognise that a multiplication is needed and solve it in writing.
The missing factor: For example, 3 · ? = 96. The child finds the number that is missing.
Choose the result: From several proposed solutions, the correct product is selected.
Choose the missing factor: From several numbers, the one that makes the equation correct is selected.

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

Task types: Multiply by a one-digit number (columns) (grade 4–6) · Written multiplication: choose the missing factor (grade 4–5) · Written multiplication: choose the result (grade 4–5) · Long multiplication in a word problem (grade 4–5) · Written multiplication: the missing factor (grade 4–5)

Dividing by a one-digit number in writing

The child learns to divide a number such as 231 by a single-digit number such as 7, and can state a remainder when needed.

The child can divide a natural number by a one-digit number, for example 231 : 7. For this, they may write down their own calculation methods or calculate in their head. The curriculum names this example; a larger number limit for division is not specified there. If the division does not work out evenly, a remainder remains, for instance with 214 : 7, which gives 30 remainder 4.

A typical mistake: if a place value in the result is zero, children often leave it out. Anyone who writes 3 remainder 4 instead of 30 remainder 4 for 214 : 7 has lost the place value. A second common mistake is starting with a digit that is smaller than the divisor. For 231 : 7, one must first calculate with 23, not with the 2 alone.

The worksheets for this topic contain tasks such as:

Dividing by a one-digit number in written form
Written division in word problems
Written division: zero in the result
Written division: the missing dividend
Written division: choose the dividend

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

Task types: Long division: choose the dividend (grade 4–5) · Long division: the missing dividend (grade 4–5) · Long division by a one-digit number (grade 4–6) · Long division in a word problem (grade 4–5) · Long division: a zero in the quotient — choose (grade 4–5)

Reading and writing decimal numbers

The child reads and writes decimal numbers with a comma and recognises the value of each digit, for example 3,47 as 3 wholes, 4 tenths and 7 hundredths.

The children read and write decimal numbers, that is, numbers with a decimal comma, for example 3,47. They recognise the value of each digit: in 3,47 the 4 stands for 4 tenths and the 7 for 7 hundredths. The tasks in this class go as far as the thousandths digit, for example in 0,058. The curriculum describes this skill across several school years; in Year 3 the worksheets show how far it goes here.

A typical mistake arises when children treat the places after the decimal comma as they would whole numbers. Then 0,35 seems larger than 0,4, because 35 is larger than 4. Another confusion concerns zero as a placeholder: 3,07 is read as 3,7, because only the digits are counted and their places are not considered.

The printable worksheets on this topic include the following task types, each with solutions:

Reading the hundredths digit: determine the digit in the hundredths place of a number.
Place value of decimals: value of a digit: name the value of a digit, for example 4 tenths in 3,47.
Place value of decimals: decomposition: split a number into ones, tenths and hundredths, for example 3,47 = 3 + 0,4 + 0,07.
Place value of decimals: choose the thousandths digit: select the digit in the thousandths place.
Decimal number: choose the value of the digit: select the matching value of a digit.

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

Task types: Find the digit in the hundredths place (grade 4–6) · Decimal place value: choose the thousandths digit (grade 4–5) · Decimal place value: expanded form (grade 4–5) · Decimal place value: value of a digit (grade 4–5) · Decimal: choose the value of a digit (grade 4–5)

Parallel or Perpendicular: Lines on the Grid

The child recognizes on a grid whether two line segments run parallel or stand perpendicular to each other, and names the position with the appropriate terms.

In Grade 3, the child learns to tell on a grid whether two line segments are parallel or perpendicular (at right angles) to each other. In doing so, they use the terms parallel line, perpendicular line, grid and intersection point. The curriculum also names the symbols for right angles and for parallel lines, as well as the set square.

A typical mistake arises when the child only pays attention to whether the segments touch. Two segments that do not meet are then considered parallel, even when they are perpendicular to each other, for example a horizontal and a vertical segment that are offset on the grid. What matters, however, is the direction: parallel segments have the same direction, while perpendicular segments form a right angle.

The worksheet “Parallel or perpendicular?” shows segments on a grid. For each pair, the child decides whether it is parallel or perpendicular. In this way the distinction is practiced with concrete pictures, with solutions for checking.

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

Task types: 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) · Parallel or perpendicular? (grade 4–6)

Axial symmetry: reflect across an axis

Your child learns to reflect points and figures across an axis, find the mirror point, and recognize axes of symmetry.

Curriculum point MA.2.A.1.g understand and use the terms side, diagonal, diameter, radius, area, centre, parallel, line, straight line, line segment, grid, point of intersection, intersect, perpendicular, symmetry, reflection in an axis, perimeter, angle, right-angled, translation, geo-triangle. use the symbols for right angles and parallel lines. (our translation)
Curriculum point MA.2.A.2.e can tile in different ways with basic shapes (e.g. with triangles or pentominoes). can reflect figures across axes and sketch mirror images. (our translation)
Curriculum point MA.2.A.2.g can draw lines and figures enlarged, reduced, reflected and shifted with a set square, and recognise corresponding transformations. (our translation)
Curriculum point MA.2.A.2.i can use a set square and ruler to reflect figures in an axis or a point, translate them, and rotate them by 90°, 180° and 270° using a compass and set square. (our translation)

Your child learns that a point is reflected across a line (the axis): the mirror point lies on the same perpendicular to the axis, the same distance from the axis, but on the other side. On the grid, this is counted in squares. The curriculum points also include sketching mirror images and rotating by 90°, 180° and 270°, as well as tessellating. These go beyond Grade 3. This text only describes what the tasks at this level show.

A typical mistake: the child counts the distance from the point to the axis inaccurately. For example, it counts the axis itself as well, or places the mirror point on the same side as the starting point. Or it shifts the point horizontally instead of perpendicular to the axis. With whole figures, the result often looks "roughly the same", and the child does not check each corner point individually.

The worksheet includes these task types:

Reflect a point across a line: enter the mirror point.
Axial symmetry: true or false: decide whether a figure is symmetric about the axis.
Reflection across a vertical line: choose the coordinate: select the correct value for the mirror point.
Axial symmetry: reflection across a vertical line: complete a figure across a vertical axis.
Axial symmetry: how many axes of symmetry: count the axes of a figure.
Axial symmetry: axis of a pair of points: find the axis with respect to which two points correspond to each other.

Home tip (not part of the curriculum requirements): A sheet of paper folded along the axis shows immediately whether two points lie on top of each other.

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

Task types: Line symmetry: find the mistake (grade 5–7) · Line symmetry: how many lines of symmetry (grade 4–6) · Line symmetry: reflect across a vertical line (grade 5–7) · Line symmetry: true or false (grade 5–7) · Reflect a point in a line (grade 5–8) · Reflection in a vertical line: choose the coordinate (grade 5–7) · Line symmetry: axis of a pair of points (grade 5–7)

Recognizing and naming geometric solids

The child recognizes cubes, cuboids, spheres, cylinders and pyramids in the environment and in pictures, and names them correctly.

Curriculum point MA.2.A.1.f recognize and name geometric solids (cube, cuboid, sphere, cylinder, pyramid) and shapes in the environment and in pictures. (our translation)

Your child learns to recognise the solid shapes cube, cuboid, sphere, cylinder and pyramid and to name them. This applies both to everyday objects, such as a box, a ball or a tin can, and to pictures. The curriculum does not specify a number range for this point, because it is about shapes and not numbers.

Cubes and cuboids are often confused because both have corners. The difference is that not all faces of a cuboid need to be the same size. Spheres and cylinders are also often confused because both can roll. However, a sphere has no flat faces, whereas a cylinder does.

A typical task is the worksheet "Which solid is this?" The child sees a solid shape in a picture or an object and names it. As an activity at home, you can collect packaging or tins and think together about which solid shape each one most closely resembles.

Create a worksheet for this skill Multiple-choice test

Task types: Which solid is it? (grade 4–5) · Which solid is it? Choose the name (grade 4–5) · Edges of a solid: find the mistake (grade 4–5) · Edges of a solid: true or false (grade 4–5)

Free sample worksheets for this grade (PDF)

Grade 3 (Switzerland) — printable math worksheet

Task templates to print

Every task type, grouped by skill. Clicking one opens the worksheet generator with it already selected.

A length in one unit: find the mistake (grade 4–5)
A length in one unit: true or false (grade 4–5)
Convert to a larger unit of length (grade 4–6)
Convert to a smaller unit of length (grade 4–6)
Units of length: choose the converted value (grade 4–5)
Units of length: compare (grade 4–5)
Write a length in one unit (grade 4–6)
Adding lengths given in two units (grade 4–5)

Calculating with Clock Times and Durations

Minutes and seconds to seconds (grade 4–6)
Durations: compare (grade 4–5)
Elapsed time word problem: how long did it last (grade 4–6)
Elapsed time: choose how many minutes passed (grade 4–5)
Minutes and seconds: find the mistake (grade 4–5)
Minutes and seconds: true or false (grade 4–5)
Time on a clock: how many minutes passed (grade 4–6)

Understanding and solving word problems

Adding and subtracting fractions with the same denominator

Add fractions with like denominators (grade 4–6)
Fractions with like denominators: choose the sum (grade 4–6)
Fractions with like denominators: find the mistake (grade 4–6)
Fractions with like denominators: the missing numerator (grade 4–6)
Fractions with like denominators: true or false (grade 4–6)
Fractions: how much is missing to make a whole? (grade 4–5)
Subtract fractions with like denominators (grade 4–6)
Subtracting fractions: choose the difference (grade 4–6)
Subtracting fractions: find the mistake (grade 4–6)
Subtracting fractions: take away from a whole (grade 4–5)
Subtracting fractions: the missing numerator (grade 4–6)
Subtracting fractions: true or false (grade 4–6)
Fractions with like denominators: a sum greater than 1 (grade 4–6)
Fractions with like denominators: compare the sums (grade 4–6)
Subtracting fractions: compare the differences (grade 4–6)
Fractions: how many pairs make a whole? (grade 4–6)

Adding and subtracting in writing within the number range 1000

Add using the column method (grade 4–6)
Column addition: choose the result (grade 4–5)
Column addition: find the mistake (grade 4–5)
Column addition: true or false (grade 4–5)
Subtract using the column method (grade 4–6)
Written subtraction: find the mistake (grade 4–5)
Written subtraction: true or false (grade 4–5)
Numbers to a million: addition word problem (grade 4–5)
Numbers to a million: subtraction word problem (grade 4–5)
Written subtraction: borrowing across zeros (grade 4–5)

Rounding to tens and hundreds

Single-digit number times tens number

Converting Weights: Grams and Kilograms

Convert to a larger unit of weight (grade 4–5)
Convert to a smaller unit of weight (grade 4–6)
Converting units of weight: choose the result (grade 4–5)
Mass in kilograms: find the mistake (grade 5–6)
Mass in kilograms: true or false (grade 5–6)
Units of weight: compare (grade 4–5)
Write a weight in one unit (grade 4–5)
Mass in kilograms: choose the decimal (grade 5–6)

Tens Jump on the Number Line

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)

Multiplying single-digit numbers in writing

Multiply by a one-digit number (columns) (grade 4–6)
Written multiplication: choose the missing factor (grade 4–5)
Written multiplication: choose the result (grade 4–5)
Long multiplication in a word problem (grade 4–5)
Written multiplication: the missing factor (grade 4–5)

Dividing by a one-digit number in writing

Long division: choose the dividend (grade 4–5)
Long division: the missing dividend (grade 4–5)
Long division by a one-digit number (grade 4–6)
Long division in a word problem (grade 4–5)
Long division: a zero in the quotient — choose (grade 4–5)

Reading and writing decimal numbers

Find the digit in the hundredths place (grade 4–6)
Decimal place value: choose the thousandths digit (grade 4–5)
Decimal place value: expanded form (grade 4–5)
Decimal place value: value of a digit (grade 4–5)
Decimal: choose the value of a digit (grade 4–5)

Parallel or Perpendicular: Lines on the Grid

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)
Parallel or perpendicular? (grade 4–6)

Axial symmetry: reflect across an axis

Line symmetry: find the mistake (grade 5–7)
Line symmetry: how many lines of symmetry (grade 4–6)
Line symmetry: reflect across a vertical line (grade 5–7)
Line symmetry: true or false (grade 5–7)
Reflect a point in a line (grade 5–8)
Reflection in a vertical line: choose the coordinate (grade 5–7)
Line symmetry: axis of a pair of points (grade 5–7)

Recognizing and naming geometric solids

Which solid is it? (grade 4–5)
Which solid is it? Choose the name (grade 4–5)
Edges of a solid: find the mistake (grade 4–5)
Edges of a solid: true or false (grade 4–5)

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.

Calendar: how many days between dates? (in the curriculum of: Austria, Germany, United Kingdom +2)
Calendar: how many days between the marked dates? (in the curriculum of: Austria, Germany, United Kingdom +2)
Correct it: vertical, horizontal or oblique (in the curriculum of: Austria, Spain, United Kingdom +3)
Draw a line: vertical, horizontal or oblique (in the curriculum of: Austria, Spain, United Kingdom +3)
Perimeter of a square (in the curriculum of: Austria, Germany, Spain +5)
Perimeter of a square on a grid (in the curriculum of: Austria, Germany, Spain +5)
Perimeter of a triangle (in the curriculum of: Austria, Germany, Spain +4)
Reading a thermometer: choose the correct temperature (in the curriculum of: Netherlands, Poland)
Reading a thermometer: true or false (in the curriculum of: Netherlands, Poland)
Reading the temperature from a thermometer (in the curriculum of: Netherlands, Poland)
Roman numerals (I-XII) (in the curriculum of: United Kingdom, Poland)
Roman numerals: choose the correct form (in the curriculum of: United Kingdom, Poland)
Roman numerals: true or false (in the curriculum of: United Kingdom, Poland)
Square side from the perimeter (in the curriculum of: Austria, Germany, Spain +5)
Temperature: how many degrees are missing? (in the curriculum of: Netherlands, Poland)
Vertical, horizontal or oblique (in the curriculum of: Austria, Spain, United Kingdom +3)
Vertical, horizontal or oblique? True or false (in the curriculum of: Austria, Spain, United Kingdom +3)
What kind of line is it? Choose (in the curriculum of: Austria, Spain, United Kingdom +3)
Add the Roman numerals (in the curriculum of: United Kingdom, Poland)
Calendar: correct the mistake in counting days (in the curriculum of: Austria, Germany, United Kingdom +2)
Calendar: which day of the week will it be? (in the curriculum of: Austria, Germany, United Kingdom +2)
How many days pass: choose the correct answer (in the curriculum of: Austria, Germany, United Kingdom +2)
How many days pass: true or false (in the curriculum of: Austria, Germany, United Kingdom +2)
Perimeter of a square: choose the correct answer (in the curriculum of: Austria, Germany, Spain +5)
Perimeter of a square: fix the mistake (in the curriculum of: Austria, Germany, Spain +5)
Perimeter of a square: true or false (in the curriculum of: Austria, Germany, Spain +5)
Perimeter of a triangle: choose the correct answer (in the curriculum of: Austria, Germany, Spain +4)
Perimeter of a triangle: true or false (in the curriculum of: Austria, Germany, Spain +4)
Roman numerals: correct the reading mistake (in the curriculum of: United Kingdom, Poland)
Roman numerals: put them in order (in the curriculum of: United Kingdom, Poland)
Temperature: correct the thermometer reading mistake (in the curriculum of: Netherlands, Poland)
Temperature: how much did it rise? (in the curriculum of: Netherlands, Poland)
Temperature: which reading is warmer? (in the curriculum of: Netherlands, Poland)
Third side of a triangle (in the curriculum of: Austria, Germany, Spain +4)
What day was it some days ago? (in the curriculum of: Austria, Germany, United Kingdom +2)
Which day of the week will it be? Choose (in the curriculum of: Austria, Germany, United Kingdom +2)
Give numbers containing this Roman symbol (in the curriculum of: United Kingdom, Poland)
Give two temperatures from this scale (in the curriculum of: Netherlands, Poland)
Perimeter of a square: how much do perimeters differ? (in the curriculum of: Austria, Germany, Spain +5)
Perimeter of a triangle: how much larger is one? (in the curriculum of: Austria, Germany, Spain +4)
Perimeter: how long is the leg of an isosceles triangle? (in the curriculum of: Austria, Germany, Spain +4)