English
Curriculum (Poland)

Mathematics — Grade 4

Grade 4 mathematics according to the new core curriculum (2026, Compass of Tomorrow reform). The first unit is ready: common fractions — a fraction as part of a whole, expanding and simplifying, mixed numbers, comparing, as well as adding and subtracting fractions with like denominators. Subsequent Grade 4 units are being added gradually. Ready-to-print worksheet templates are available for each topic.

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What does a child learn in 4th-grade mathematics?

In Grade 4, students perform written calculations with multi-digit numbers and apply the order of operations, learn common fractions (expanding, simplifying, mixed numbers, comparing, addition with like denominators), and are introduced to decimals. They convert units of length and mass, recognize acute, right, and obtuse angles, calculate the area of a rectangle and the perimeter of a polygon, and read data from charts.

Important note on the curriculum: the new core curriculum (Journal of Laws 2026, item 378) applies to Grade 4 starting from the 2026/2027 school year — rolling out year by year. The curriculum for Grades 4–6 is block-based — it defines what a student should know by the end of Grade 6. Assigning topics to a specific grade is our decision based on a typical syllabus pacing; in the “Curriculum Scope” section, you can see the entire Grades 4–6 block with quotes from the ministerial regulation.

Page status: sections on natural numbers and written calculations, common and decimal fractions, divisibility, units, geometry (angles, areas, perimeters, rectangular cuboids), data, and the coordinate system are ready. Symmetry and geometric constructions are being added subsequently.

Curriculum scope

  1. Curriculum point MAT.IV-VI.1 · Teaching content · checked against the act

    Numbers

    our translation · original wording (PL): Liczby

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, treści nauczania kl. IV–VI, dział 1

  2. Curriculum point MAT.IV-VI.1.1 · Teaching content · checked against the act

    uses the decimal system of writing natural numbers, including comparing and rounding natural numbers and interpreting them on a number line

    our translation · original wording (PL): stosuje dziesiątkowy system zapisu liczb naturalnych, w tym porównuje i zaokrągla liczby naturalne oraz interpretuje je na osi liczbowej

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 1

    Writing and comparing large numbers (we teach in grade 4-6) · Rounding numbers to thousands and ten thousands (we teach in grade 4-6)

  3. Curriculum point MAT.IV-VI.1.2 · Teaching content · checked against the act

    reads and writes natural numbers in the Roman numeral system in the range from 1 to 3000

    our translation · original wording (PL): odczytuje i zapisuje liczby naturalne w systemie rzymskim w zakresie od 1 do 3000

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 2

    Roman numerals up to 3000 (we teach in grade 4-6)

  4. Curriculum point MAT.IV-VI.1.3 · Teaching content · checked against the act

    recognizes numbers divisible by 2, 3, 4, 5, 9, 10

    our translation · original wording (PL): rozpoznaje liczby podzielne przez 2, 3, 4, 5, 9, 10

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 3

  5. Curriculum point MAT.IV-VI.1.4 · Teaching content · checked against the act

    knows the concept of a prime number and recognizes a composite number when it is a single-digit or two-digit number, as well as when a divisibility rule indicates the existence of a divisor

    our translation · original wording (PL): zna pojęcie liczby pierwszej i rozpoznaje liczbę złożoną, gdy jest ona jednocyfrowa lub dwucyfrowa, a także gdy na istnienie dzielnika wskazuje cecha podzielności

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 4

  6. Curriculum point MAT.IV-VI.1.5 · Teaching content · checked against the act

    factors one- or two-digit numbers into prime factors

    our translation · original wording (PL): rozkłada liczby jedno- lub dwucyfrowe na czynniki pierwsze

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 5

  7. Curriculum point MAT.IV-VI.1.6 · Teaching content · checked against the act

    finds common factors and common multiples of two single- or two-digit numbers, including the greatest common factor and the least common multiple

    our translation · original wording (PL): znajduje wspólne dzielniki i wspólne wielokrotności dwóch liczb jedno- lub dwucyfrowych, w tym największy wspólny dzielnik i najmniejszą wspólną wielokrotność

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 6

  8. Curriculum point MAT.IV-VI.1.7 · Teaching content · checked against the act

    uses factors and multiples of numbers in calculations and reasoning

    our translation · original wording (PL): posługuje się dzielnikami i wielokrotnościami liczb w obliczeniach i rozumowaniach

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 7

  9. Curriculum point MAT.IV-VI.1.8 · Teaching content · checked against the act

    determines the cardinality of a set of numbers from a certain small range, described by certain conditions

    our translation · original wording (PL): określa liczebność zbioru liczb z pewnego niewielkiego zakresu, opisanego za pomocą pewnych warunków

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 8

  10. Curriculum point MAT.IV-VI.1.9 · Teaching content · checked against the act

    adds and subtracts natural numbers mentally or with written intermediate calculations

    our translation · original wording (PL): dodaje i odejmuje liczby naturalne w pamięci lub z zapisem obliczeń pośrednich

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 9

    Column addition and subtraction of numbers (we teach in grade 4-6)

  11. Curriculum point MAT.IV-VI.1.10 · Teaching content · checked against the act

    multiplies and divides a natural number by a one-digit, two-digit, or three-digit number mentally or by recording intermediate calculations

    our translation · original wording (PL): mnoży i dzieli liczbę naturalną przez liczbę jednocyfrową, dwucyfrową lub trzycyfrową w pamięci lub z zapisem obliczeń pośrednich

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 10

    Long multiplication by a single-digit number (we teach in grade 4-6) · Long multiplication of multi-digit numbers (we teach in grade 4-6) · Long division by a single-digit number (we teach in grade 4-6)

  12. Curriculum point MAT.IV-VI.1.11 · Teaching content · checked against the act

    interprets division of natural numbers as sharing and as grouping

    our translation · original wording (PL): interpretuje dzielenie liczb naturalnych jako podział oraz jako mieszczenie

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 11

    Long division by a single-digit number (we teach in grade 4-6)

  13. Curriculum point MAT.IV-VI.1.12 · Teaching content · checked against the act

    performs operations on natural numbers, using strategies convenient for themselves that facilitate calculations, including the commutative and associative properties of addition and multiplication and the distributive property of multiplication and division over addition and subtraction

    our translation · original wording (PL): wykonuje działania na liczbach naturalnych, stosując wygodne dla siebie strategie ułatwiające obliczenia, w tym własności przemienności i łączności dodawania i mnożenia oraz rozdzielność mnożenia i dzielenia względem dodawania i odejmowania

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 12

    Clever addition and multiplication of numbers (we teach in grade 4-6)

  14. Curriculum point MAT.IV-VI.1.13 · Teaching content · checked against the act

    performs division with remainder of natural numbers and uses the properties of remainders

    our translation · original wording (PL): wykonuje dzielenie z resztą liczb naturalnych i korzysta z własności reszt

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 13

    Long division by a single-digit number (we teach in grade 4-6)

  15. Curriculum point MAT.IV-VI.1.14 · Teaching content · checked against the act

    compares natural numbers by difference and by quotient

    our translation · original wording (PL): porównuje różnicowo i ilorazowo liczby naturalne

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 14

    Comparing numbers: by how much and how many times (we teach in grade 4-6)

  16. Curriculum point MAT.IV-VI.1.15 · Teaching content · checked against the act

    calculates powers of natural numbers with positive integer exponents, among two-digit numbers recognizes numbers that are squares and cubes of integers

    our translation · original wording (PL): oblicza potęgi liczb naturalnych o wykładnikach całkowitych dodatnich, wśród liczb dwucyfrowych rozpoznaje liczby będące kwadratami i sześcianami liczb całkowitych

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 15

    Squares and cubes of numbers and fractions (we teach in grade 4-6)

  17. Curriculum point MAT.IV-VI.1.16 · Teaching content · checked against the act

    uses integers also in situations arising from everyday life, compares integers and performs simple mental calculations on them, interprets integers on a number line and calculates the distance between two integers on a number line

    our translation · original wording (PL): posługuje się liczbami całkowitymi także w sytuacjach wynikających z życia codziennego, porównuje liczby całkowite i wykonuje na nich proste rachunki pamięciowe, interpretuje liczby całkowite na osi liczbowej oraz oblicza odległość dwóch liczb całkowitych na osi liczbowej

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 16

  18. Curriculum point MAT.IV-VI.1.17 · Teaching content · checked against the act

    represents a part of a given whole as a fraction and interprets a proper fraction as a part of a given whole

    our translation · original wording (PL): przedstawia część danej całości za pomocą ułamka oraz interpretuje ułamek właściwy jako część danej całości

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 17

    A fraction as a part of a whole and a set (we teach in grade 4-6) · Understanding halves and quarters of a whole (we teach in grade 4-6)

  19. Curriculum point MAT.IV-VI.1.18 · Teaching content · checked against the act

    interprets a fraction as the quotient of natural numbers

    our translation · original wording (PL): interpretuje ułamek jako iloraz liczb naturalnych

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 18

  20. Curriculum point MAT.IV-VI.1.19 · Teaching content · checked against the act

    simplifies and expands common fractions, brings fractions to a common denominator

    our translation · original wording (PL): skraca i rozszerza ułamki zwykłe, sprowadza ułamki do wspólnego mianownika

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 19

    Expanding common fractions (we teach in grade 4-6) · Simplifying common fractions (we teach in grade 4-6)

  21. Curriculum point MAT.IV-VI.1.20 · Teaching content · checked against the act

    represents an improper fraction as a mixed number, and a mixed number as an improper fraction

    our translation · original wording (PL): przedstawia ułamek niewłaściwy w postaci liczby mieszanej, a liczbę mieszaną w postaci ułamka niewłaściwego

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 20

    Converting improper fractions and mixed numbers (we teach in grade 4-6)

  22. Curriculum point MAT.IV-VI.1.21 · Teaching content · checked against the act

    marks common fractions and decimals on a number line and reads common fractions and decimals marked on a number line

    our translation · original wording (PL): zaznacza ułamki zwykłe i dziesiętne na osi liczbowej oraz odczytuje ułamki zwykłe i dziesiętne zaznaczone na osi liczbowej

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 21

    Reading fractions on a number line (we teach in grade 4-6) · Reading decimals on a number line (we teach in grade 4-6)

  23. Curriculum point MAT.IV-VI.1.22 · Teaching content · checked against the act

    writes terminating decimals in the form of common fractions

    our translation · original wording (PL): zapisuje ułamki dziesiętne skończone w postaci ułamków zwykłych

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 22

    Converting decimals to fractions (we teach in grade 4-6) · Reading hundredths in decimals (we teach in grade 4-6)

  24. Curriculum point MAT.IV-VI.1.23 · Teaching content · checked against the act

    converts common fractions with denominators that are divisors of the numbers 10, 100, 1000, etc. into decimals

    our translation · original wording (PL): zamienia ułamki zwykłe o mianownikach będących dzielnikami liczb 10, 100, 1000 itd. na ułamki dziesiętne

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 23

    Converting common fractions to decimals (we teach in grade 4-6)

  25. Curriculum point MAT.IV-VI.1.24 · Teaching content · checked against the act

    writes common fractions whose denominators are not divisors of the numbers 10, 100, 1000, etc., in the form of an infinite decimal expansion in cases not requiring complicated calculations

    our translation · original wording (PL): zapisuje ułamki zwykłe, których mianowniki nie są dzielnikami liczb 10, 100, 1000 itd., w postaci rozwinięcia dziesiętnego nieskończonego w przypadkach niewymagających skomplikowanych rachunków

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 24

  26. Curriculum point MAT.IV-VI.1.25 · Teaching content · checked against the act

    rounds decimals

    our translation · original wording (PL): zaokrągla ułamki dziesiętne

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 25

  27. Curriculum point MAT.IV-VI.1.26 · Teaching content · checked against the act

    compares fractions (common and decimal)

    our translation · original wording (PL): porównuje ułamki (zwykłe i dziesiętne)

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 26

    Comparing fractions with the same denominator (we teach in grade 4-6) · Comparing decimals (we teach in grade 4-6)

  28. Curriculum point MAT.IV-VI.1.27 · Teaching content · checked against the act

    adds, subtracts, multiplies and divides common fractions with one- and two-digit denominators

    our translation · original wording (PL): dodaje, odejmuje, mnoży i dzieli ułamki zwykłe o mianownikach jedno- i dwucyfrowych

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 27

    Adding and subtracting fractions with like denominators (we teach in grade 4-6)

  29. Curriculum point MAT.IV-VI.1.28 · Teaching content · checked against the act

    performs calculations with decimals mentally or with written intermediate calculations within the scope of:

    our translation · original wording (PL): wykonuje obliczenia na ułamkach dziesiętnych w pamięci lub z zapisem obliczeń pośrednich w zakresie:

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 28

  30. Curriculum point MAT.IV-VI.1.29 · Teaching content · checked against the act

    calculates powers of common and decimal fractions with positive integer exponents, also using a calculator

    our translation · original wording (PL): oblicza potęgi o wykładnikach całkowitych dodatnich ułamków zwykłych i dziesiętnych, także za pomocą kalkulatora

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 29

    Squares and cubes of numbers and fractions (we teach in grade 4-6)

  31. Curriculum point MAT.IV-VI.1.30 · Teaching content · checked against the act

    compares fractions by difference

    our translation · original wording (PL): porównuje różnicowo ułamki

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 30

    Adding and subtracting fractions with like denominators (we teach in grade 4-6)

  32. Curriculum point MAT.IV-VI.1.31 · Teaching content · checked against the act

    calculates a fraction of a given quantity

    our translation · original wording (PL): oblicza ułamek danej wielkości

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 31

  33. Curriculum point MAT.IV-VI.1.32 · Teaching content · checked against the act

    performs uncomplicated calculations involving rational numbers

    our translation · original wording (PL): wykonuje nieskomplikowane rachunki, w których występują liczby wymierne

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 32

  34. Curriculum point MAT.IV-VI.1.33 · Teaching content · checked against the act

    interprets 100 % of a given quantity as a whole, 50 % – as a half, 25 % – as one quarter, 10 % – as one tenth, 1 % – as one hundredth part of this quantity

    our translation · original wording (PL): interpretuje 100 % danej wielkości jako całość, 50 % – jako połowę, 25 % – jako jedną czwartą, 10 % – jako jedną dziesiątą, 1 % – jako jedną setną część tej wielkości

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 33

  35. Curriculum point MAT.IV-VI.1.34 · Teaching content · checked against the act

    calculates a percentage of a given quantity in cases set in a practical context

    our translation · original wording (PL): oblicza procent danej wielkości w przypadkach osadzonych w kontekście praktycznym

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 34

  36. Curriculum point MAT.IV-VI.1.35 · Teaching content · checked against the act

    calculates the unit price and the cost of purchasing several items of goods, compares the cost-effectiveness of different purchase options (e.g. discount, promotion, bundle purchase) – economic and financial module

    our translation · original wording (PL): oblicza cenę jednostkową i koszt zakupu kilku sztuk towaru, porównuje opłacalność różnych opcji zakupu (np. rabat, promocja, zakup w pakiecie) – moduł ekonomiczno-finansowy

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 35

    Planning expenses and choosing the cheaper offer (we teach in grade 4-6)

  37. Curriculum point MAT.IV-VI.1.36 · Teaching content · checked against the act

    applies the rules regarding the order of operations

    our translation · original wording (PL): stosuje reguły dotyczące kolejności wykonywania działań

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 36

    Order of operations: calculations with parentheses (we teach in grade 4-6)

  38. Curriculum point MAT.IV-VI.1.37 · Teaching content · checked against the act

    estimates the results of operations

    our translation · original wording (PL): szacuje wyniki działań

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 37

    Estimating addition results (we teach in grade 4-6)

  39. Curriculum point MAT.IV-VI.1.38 · Teaching content · checked against the act

    uses a calculator in tasks where calculations are complex and performing them is not the main goal of the task, for example in problems based on real-world data.

    our translation · original wording (PL): używa kalkulatora w zadaniach, w których obliczenia są złożone, a ich wykonywanie nie jest głównym celem zadania, na przykład w problemach opartych na rzeczywistych danych.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 38

  40. Curriculum point MAT.IV-VI.1.28.a · Teaching content · checked against the act

    adds, subtracts, and multiplies decimals in cases where the decimals have at most three decimal places

    our translation · original wording (PL): dodaje, odejmuje i mnoży ułamki dziesiętne w przypadkach, gdy ułamki mają co najwyżej trzy cyfry po przecinku

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 28 lit. a

    Adding and subtracting decimals (we teach in grade 4-6)

  41. Curriculum point MAT.IV-VI.1.28.b · Teaching content · checked against the act

    divides decimal fractions in cases reducible to division by a natural number with at most three digits

    our translation · original wording (PL): dzieli ułamki dziesiętne w przypadkach dających się sprowadzić do dzielenia przez liczbę naturalną co najwyżej trzycyfrową

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 1 pkt 28 lit. b

  42. Curriculum point MAT.IV-VI.2 · Teaching content · checked against the act

    Measures

    our translation · original wording (PL): Miary

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, treści nauczania kl. IV–VI, dział 2

  43. Curriculum point MAT.IV-VI.2.1 · Teaching content · checked against the act

    measures line segments with an accuracy of 1 mm and estimates their lengths in practical situations

    our translation · original wording (PL): mierzy odcinki z dokładnością do 1 mm i szacuje ich długości w sytuacjach praktycznych

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 1

  44. Curriculum point MAT.IV-VI.2.2 · Teaching content · checked against the act

    uses units of length: millimetre, centimetre, decimetre, metre and kilometre, in practical situations converts these units from one to another

    our translation · original wording (PL): posługuje się jednostkami długości: milimetr, centymetr, decymetr, metr i kilometr, w sytuacjach praktycznych przelicza te jednostki z jednej na drugą

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 2

    Converting units of length (we teach in grade 4-6)

  45. Curriculum point MAT.IV-VI.2.3 · Teaching content · checked against the act

    measures angles less than 180° to the nearest degree and draws any angles when their measure is given in whole degrees

    our translation · original wording (PL): mierzy kąty mniejsze niż 180° z dokładnością do jednego stopnia oraz rysuje dowolne kąty, gdy ich miara jest podana w pełnych stopniach

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 3

    Recognizing types of angles (we teach in grade 4-6)

  46. Curriculum point MAT.IV-VI.2.4 · Teaching content · checked against the act

    uses units of area: mm2, cm2, dm2, m2, km2, are, hectare

    our translation · original wording (PL): stosuje jednostki pola: mm2, cm2, dm2, m2, km2, ar, hektar

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 4

  47. Curriculum point MAT.IV-VI.2.5 · Teaching content · checked against the act

    uses units of volume and capacity: cm3, dm3, m3, millilitre, litre

    our translation · original wording (PL): stosuje jednostki objętości i pojemności: cm3, dm3, m3, mililitr, litr

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 5

  48. Curriculum point MAT.IV-VI.2.6 · Teaching content · checked against the act

    converts units of area and units of volume in practical contexts

    our translation · original wording (PL): przelicza jednostki pola i jednostki objętości w kontekstach praktycznych

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 6

  49. Curriculum point MAT.IV-VI.2.7 · Teaching content · checked against the act

    uses, including converting, units of mass in practical contexts: gram, decagram, kilogram, tonne

    our translation · original wording (PL): stosuje, w tym przelicza, jednostki masy w kontekstach praktycznych: gram, dekagram, kilogram, tona

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 7

    Converting units of mass to smaller units (we teach in grade 4-6)

  50. Curriculum point MAT.IV-VI.2.8 · Teaching content · checked against the act

    performs simple calendar calculations in days, weeks, months and years

    our translation · original wording (PL): wykonuje proste obliczenia kalendarzowe w dniach, tygodniach, miesiącach i latach

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 8

    Calendar calculations: how many days is that? (we teach in grade 4-6)

  51. Curriculum point MAT.IV-VI.2.9 · Teaching content · checked against the act

    performs simple clock calculations in hours, minutes, and seconds

    our translation · original wording (PL): wykonuje proste obliczenia zegarowe w godzinach, minutach i sekundach

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 9

    Clock calculations: hours, minutes, and seconds (we teach in grade 4-6)

  52. Curriculum point MAT.IV-VI.2.10 · Teaching content · checked against the act

    converts compound units into decimals, and decimals into compound units

    our translation · original wording (PL): zamienia wyrażenia dwumianowane na ułamki dziesiętne, a ułamki dziesiętne na wyrażenia dwumianowane

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 10

  53. Curriculum point MAT.IV-VI.2.11 · Teaching content · checked against the act

    calculates the actual length of a line segment when its length to scale is given, and calculates the length of a line segment to scale when its actual length is given

    our translation · original wording (PL): oblicza rzeczywistą długość odcinka, gdy dana jest jego długość w skali, oraz oblicza długość odcinka w skali, gdy dana jest jego rzeczywista długość

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 11

  54. Curriculum point MAT.IV-VI.2.12 · Teaching content · checked against the act

    in a practical context calculates: distance given speed and time, speed given distance and time, time given distance and speed, and uses the units of speed km/h and m/s

    our translation · original wording (PL): w kontekście praktycznym oblicza: drogę przy danej prędkości i czasie, prędkość przy danej drodze i czasie, czas przy danej drodze i prędkości oraz stosuje jednostki prędkości km/h oraz m/s

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 12

  55. Curriculum point MAT.IV-VI.2.13 · Teaching content · checked against the act

    performs monetary calculations related to everyday expenses, budget, saving, currency exchange and comparing prices, interprets documents with units of measurement and prices – economic and financial module

    our translation · original wording (PL): wykonuje obliczenia pieniężne związane z codziennymi wydatkami, budżetem, oszczędzaniem, wymianą walut i porównywaniem cen, interpretuje dokumenty z jednostkami miar i cenami – moduł ekonomiczno-finansowy

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 13

    Planning expenses and choosing the cheaper offer (we teach in grade 4-6)

  56. Curriculum point MAT.IV-VI.2.14 · Teaching content · checked against the act

    uses simple applications and digital tools to solve problems related to measurements and unit conversion.

    our translation · original wording (PL): stosuje proste aplikacje i narzędzia cyfrowe do rozwiązywania problemów związanych z pomiarami i przeliczaniem jednostek.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 2 pkt 14

  57. Curriculum point MAT.IV-VI.3 · Teaching content · checked against the act

    Algebra

    our translation · original wording (PL): Algebra

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, treści nauczania kl. IV–VI, dział 3

  58. Curriculum point MAT.IV-VI.3.1 · Teaching content · checked against the act

    describes quantities and relationships between quantities using algebraic expressions based on information set in a practical context

    our translation · original wording (PL): opisuje wielkości oraz zależności między wielkościami za pomocą wyrażeń algebraicznych na podstawie informacji osadzonych w kontekście praktycznym

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 3 pkt 1

  59. Curriculum point MAT.IV-VI.3.2 · Teaching content · checked against the act

    calculates the values of simple algebraic expressions in situations not requiring complicated calculations and compares, analyzes and interprets the obtained results

    our translation · original wording (PL): oblicza wartości prostych wyrażeń algebraicznych w sytuacjach niewymagających skomplikowanych rachunków oraz porównuje, analizuje i interpretuje otrzymane wyniki

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 3 pkt 2

  60. Curriculum point MAT.IV-VI.3.3 · Teaching content · checked against the act

    uses simple formulas in which letter symbols appear

    our translation · original wording (PL): korzysta z nieskomplikowanych wzorów, w których występują oznaczenia literowe

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 3 pkt 3

  61. Curriculum point MAT.IV-VI.3.4 · Teaching content · checked against the act

    sets up equations based on information given in the problem

    our translation · original wording (PL): układa równania na podstawie informacji podanych w zadaniu

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 3 pkt 4

  62. Curriculum point MAT.IV-VI.3.5 · Teaching content · checked against the act

    solves simple linear equations with one unknown appearing on one side of the equation.

    our translation · original wording (PL): rozwiązuje proste równania pierwszego stopnia z jedną niewiadomą występującą po jednej stronie równania.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 3 pkt 5

  63. Curriculum point MAT.IV-VI.4 · Teaching content · checked against the act

    Figures

    our translation · original wording (PL): Figury

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, treści nauczania kl. IV–VI, dział 4

  64. Curriculum point MAT.IV-VI.4.1 · Teaching content · checked against the act

    recognizes and names figures: point, line, ray, line segment

    our translation · original wording (PL): rozpoznaje i nazywa figury: punkt, prosta, półprosta, odcinek

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 1

  65. Curriculum point MAT.IV-VI.4.2 · Teaching content · checked against the act

    recognises, names and draws angles, distinguishes between acute, right, obtuse, straight, full, reflex and convex angles, indicates the vertex and arms of an angle

    our translation · original wording (PL): rozpoznaje, nazywa i rysuje kąty, rozróżnia kąt ostry, prosty, rozwarty, półpełny, pełny, wklęsły i wypukły, wskazuje wierzchołek i ramiona kąta

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 2

    Recognizing types of angles (we teach in grade 4-6)

  66. Curriculum point MAT.IV-VI.4.3 · Teaching content · checked against the act

    recognises and draws perpendicular and parallel lines and line segments, also on squared paper

    our translation · original wording (PL): rozpoznaje oraz rysuje proste i odcinki prostopadłe i równoległe, także na kartce w kratkę

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 3

  67. Curriculum point MAT.IV-VI.4.4 · Teaching content · checked against the act

    recognises adjacent, vertically opposite, corresponding and alternate angles and applies their properties

    our translation · original wording (PL): rozpoznaje kąty przyległe, wierzchołkowe, odpowiadające i naprzemianległe oraz stosuje ich własności

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 4

  68. Curriculum point MAT.IV-VI.4.5 · Teaching content · checked against the act

    recognises, names and draws polygons, identifies their vertices and interior angles, sides, diagonals

    our translation · original wording (PL): rozpoznaje, nazywa i rysuje wielokąty, wskazuje ich wierzchołki i kąty wewnętrzne, boki, przekątne

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 5

  69. Curriculum point MAT.IV-VI.4.6 · Teaching content · checked against the act

    recognises, names and draws a disc and a circle, indicates their centre, radius, diameter, chord, draws a chord of a disc and a circle, as well as (given the centre) a radius and diameter

    our translation · original wording (PL): rozpoznaje, nazywa i rysuje koło i okrąg, wskazuje ich środek, promień, średnicę, cięciwę, rysuje cięciwę koła i okręgu, a także (przy danym środku) promień i średnicę

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 6

  70. Curriculum point MAT.IV-VI.4.7 · Teaching content · checked against the act

    recognises, names, draws an acute-angled, right-angled and obtuse-angled triangle as well as a scalene, isosceles and equilateral triangle

    our translation · original wording (PL): rozpoznaje, nazywa, rysuje trójkąt ostrokątny, prostokątny i rozwartokątny oraz różnoboczny, równoramienny i równoboczny

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 7

  71. Curriculum point MAT.IV-VI.4.8 · Teaching content · checked against the act

    applies the theorems on the sum of the measures of the angles in a triangle and the sum of the measures of the angles in a quadrilateral

    our translation · original wording (PL): stosuje twierdzenia o sumie miar kątów w trójkącie i sumie miar kątów w czworokącie

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 8

  72. Curriculum point MAT.IV-VI.4.9 · Teaching content · checked against the act

    identifies the legs of an isosceles triangle, uses the equality of the base angles of an isosceles triangle and the equality of its legs

    our translation · original wording (PL): wskazuje ramiona trójkąta równoramiennego, korzysta z równości kątów przy podstawie trójkąta równoramiennego oraz z równości jego ramion

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 9

  73. Curriculum point MAT.IV-VI.4.10 · Teaching content · checked against the act

    constructs a triangle with given sides, determines the possibility of constructing a triangle with given side lengths

    our translation · original wording (PL): konstruuje trójkąt o podanych bokach, ustala możliwość zbudowania trójkąta o danych długościach boków

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 10

  74. Curriculum point MAT.IV-VI.4.11 · Teaching content · checked against the act

    recognises, names, draws a square, rectangle, rhombus, parallelogram, trapezium, including an isosceles and right-angled trapezium, and applies their properties

    our translation · original wording (PL): rozpoznaje, nazywa, rysuje kwadrat, prostokąt, romb, równoległobok, trapez, w tym trapez równoramienny i prostokątny, oraz stosuje ich własności

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 11

  75. Curriculum point MAT.IV-VI.4.12 · Teaching content · checked against the act

    recognises and draws axially symmetric figures, identifies and draws their axes of symmetry

    our translation · original wording (PL): rozpoznaje i rysuje figury osiowosymetryczne, wskazuje i rysuje ich osie symetrii

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 12

  76. Curriculum point MAT.IV-VI.4.13 · Teaching content · checked against the act

    recognizes and draws heights in a triangle, parallelogram, trapezoid

    our translation · original wording (PL): rozpoznaje i rysuje wysokości w trójkącie, równoległoboku, trapezie

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 13

  77. Curriculum point MAT.IV-VI.4.14 · Teaching content · checked against the act

    calculates the area of a triangle, square, rectangle, rhombus, parallelogram, trapezoid and the areas of figures that can be built from them

    our translation · original wording (PL): oblicza pole trójkąta, kwadratu, prostokąta, rombu, równoległoboku, trapezu oraz pola figur, które można z nich zbudować

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 14

    Area of a rectangle and finding the missing side (we teach in grade 4-6)

  78. Curriculum point MAT.IV-VI.4.15 · Teaching content · checked against the act

    calculates the perimeter of a polygon with given side lengths

    our translation · original wording (PL): oblicza obwód wielokąta o podanych długościach boków

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 15

    Calculating the perimeter of a polygon and a missing side (we teach in grade 4-6)

  79. Curriculum point MAT.IV-VI.4.16 · Teaching content · checked against the act

    plots points with given integer coordinates in a coordinate system and reads the coordinates of marked lattice points

    our translation · original wording (PL): zaznacza w układzie współrzędnych punkty o podanych współrzędnych całkowitych oraz odczytuje współrzędne zaznaczonych punktów kratowych

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 16

  80. Curriculum point MAT.IV-VI.4.17 · Teaching content · checked against the act

    calculates the distance between points in a coordinate system whose first or second coordinates are the same

    our translation · original wording (PL): oblicza odległość między punktami w układzie współrzędnych, których pierwsze lub drugie współrzędne są takie same

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 17

  81. Curriculum point MAT.IV-VI.4.18 · Teaching content · checked against the act

    recognizes a pyramid, a prism, including a cuboid and a cube, recognizes a cylinder, a cone and a sphere

    our translation · original wording (PL): rozpoznaje ostrosłup, graniastosłup, w tym prostopadłościan i sześcian, rozpoznaje walec, stożek i kulę

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 18

  82. Curriculum point MAT.IV-VI.4.19 · Teaching content · checked against the act

    identifies vertices, edges, lateral faces and bases of prisms and pyramids

    our translation · original wording (PL): wskazuje wierzchołki, krawędzie, ściany boczne i podstawy graniastosłupów i ostrosłupów

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 19

  83. Curriculum point MAT.IV-VI.4.20 · Teaching content · checked against the act

    recognizes and draws a net of a right prism, including a cube, of a regular square or triangular pyramid, makes a model of a right prism and a pyramid from a given or self-created net

    our translation · original wording (PL): rozpoznaje i rysuje siatkę graniastosłupa prostego, w tym sześcianu, ostrosłupa prawidłowego czworokątnego lub trójkątnego, wykonuje model graniastosłupa prostego i ostrosłupa z podanej lub samodzielnie stworzonej siatki

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 20

  84. Curriculum point MAT.IV-VI.4.21 · Teaching content · checked against the act

    calculates the surface area of a rectangular prism

    our translation · original wording (PL): oblicza pole powierzchni prostopadłościanu

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 21

  85. Curriculum point MAT.IV-VI.4.22 · Teaching content · checked against the act

    calculates the volume of a rectangular prism with given edge lengths and the volume of a solid composed of several rectangular prisms.

    our translation · original wording (PL): oblicza objętość prostopadłościanu o podanych długościach jego krawędzi i objętość bryły zbudowanej z kilku prostopadłościanów.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 4 pkt 22

  86. Curriculum point MAT.IV-VI.5 · Teaching content · checked against the act

    Data

    our translation · original wording (PL): Dane

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, treści nauczania kl. IV–VI, dział 5

  87. Curriculum point MAT.IV-VI.5.1 · Teaching content · checked against the act

    interprets data presented in text and using tables, diagrams, and graphs, including graphs drawn with a continuous line, in particular compares prices, costs, and expenses presented in tables, on graphs, or on receipts – economic and financial module

    our translation · original wording (PL): interpretuje dane przedstawione w tekście oraz za pomocą tabel, diagramów i wykresów, w tym wykresów wykonanych za pomocą linii ciągłej, w szczególności porównuje ceny, koszty i wydatki przedstawione w tabelach, na wykresach lub paragonach – moduł ekonomiczno-finansowy

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 5 pkt 1

    Comparing data on bar charts (we teach in grade 4-6)

  88. Curriculum point MAT.IV-VI.5.2 · Teaching content · checked against the act

    conducts simple statistical investigations: collects data, records them in an organized form and presents conclusions resulting from the collected information

    our translation · original wording (PL): przeprowadza proste badania statystyczne: zbiera dane, zapisuje je w uporządkowanej formie i przedstawia wnioski wynikające z zebranych informacji

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 5 pkt 2

    Comparing data on bar charts (we teach in grade 4-6)

  89. Curriculum point MAT.IV-VI.5.3 · Teaching content · checked against the act

    calculates the arithmetic mean when describing everyday phenomena

    our translation · original wording (PL): oblicza średnią arytmetyczną przy opisie zjawisk z życia codziennego

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 5 pkt 3

  90. Curriculum point MAT.IV-VI.5.4 · Teaching content · checked against the act

    interprets data on expenses, calculates their average value, and formulates conclusions regarding the cost-effectiveness of different solutions – economic-financial module.

    our translation · original wording (PL): interpretuje dane dotyczące wydatków, oblicza ich średnią wartość oraz formułuje wnioski dotyczące opłacalności różnych rozwiązań – moduł ekonomiczno-finansowy.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 5 pkt 4

    Comparing data on bar charts (we teach in grade 4-6)

  91. Curriculum point MAT.IV-VI.6 · Teaching content · checked against the act

    Mathematical thinking

    our translation · original wording (PL): Myślenie matematyczne

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, treści nauczania kl. IV–VI, dział 6

  92. Curriculum point MAT.IV-VI.6.1 · Teaching content · checked against the act

    applies general methods of solving mathematical problems, including:

    our translation · original wording (PL): stosuje ogólne metody rozwiązywania problemów matematycznych, w tym:

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 1

  93. Curriculum point MAT.IV-VI.6.2 · Teaching content · checked against the act

    explains their way of thinking when solving a mathematical problem, including:

    our translation · original wording (PL): wyjaśnia swój sposób myślenia przy rozwiązywaniu problemu matematycznego, w tym:

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 2

  94. Curriculum point MAT.IV-VI.6.3 · Teaching content · checked against the act

    conducts mathematical reasoning, including:

    our translation · original wording (PL): prowadzi rozumowania matematyczne, w tym:

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 3

  95. Curriculum point MAT.IV-VI.6.1.a · Teaching content · checked against the act

    records relationships between data in a task (e.g., using a drawing, diagram, or other shorthand way of presenting data)

    our translation · original wording (PL): zapisuje związki między danymi w zadaniu (np. za pomocą rysunku, diagramu lub innego skrótowego sposobu przedstawiania danych)

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 1 lit. a

  96. Curriculum point MAT.IV-VI.6.2.a · Teaching content · checked against the act

    talks about their way of solving the problem

    our translation · original wording (PL): opowiada o swoim sposobie rozwiązania zadania

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 2 lit. a

  97. Curriculum point MAT.IV-VI.6.3.a · Teaching content · checked against the act

    gives examples of mathematical objects satisfying given conditions and objects not satisfying them

    our translation · original wording (PL): podaje przykłady obiektów matematycznych spełniających dane warunki oraz obiektów ich niespełniających

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 3 lit. a

  98. Curriculum point MAT.IV-VI.6.1.b · Teaching content · checked against the act

    creates a strategy for solving a problem by dividing the solution into stages

    our translation · original wording (PL): tworzy strategię rozwiązania problemu przez dzielenie rozwiązania na etapy

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 1 lit. b

  99. Curriculum point MAT.IV-VI.6.2.b · Teaching content · checked against the act

    provides arguments justifying successive steps of the solution

    our translation · original wording (PL): podaje argumenty uzasadniające kolejne kroki rozwiązania

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 2 lit. b

  100. Curriculum point MAT.IV-VI.6.3.b · Teaching content · checked against the act

    uses the trial-and-error method

    our translation · original wording (PL): stosuje metodę prób i poprawek

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 3 lit. b

  101. Curriculum point MAT.IV-VI.6.1.c · Teaching content · checked against the act

    assesses the reasonableness of the solution (e.g. by estimating, checking all conditions of the problem, assessing the order of magnitude of the obtained result)

    our translation · original wording (PL): ocenia sensowność rozwiązania (np. przez szacowanie, sprawdzanie wszystkich warunków zadania, ocenianie rzędu wielkości otrzymanego wyniku)

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 1 lit. c

  102. Curriculum point MAT.IV-VI.6.3.c · Teaching content · checked against the act

    considers all cases

    our translation · original wording (PL): rozważa wszystkie przypadki

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 3 lit. c

  103. Curriculum point MAT.IV-VI.6.3.d · Teaching content · checked against the act

    uses proportional reasoning, also as a method facilitating multiplication and division.

    our translation · original wording (PL): używa rozumowania proporcjonalnego, także jako metody ułatwiającej mnożenie i dzielenie.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, kl. IV–VI, dział 6 pkt 3 lit. d

  104. Curriculum point MAT.IV-VI.WO.1 · General aims · checked against the act

    Using mathematical tools – understanding and using mathematical concepts and properties also in a new situation, noticing relationships between properties as well as differences and similarities between mathematical objects.

    our translation · original wording (PL): Korzystanie z narzędzi matematycznych – rozumienie i używanie pojęć oraz własności matematycznych także w nowej sytuacji, dostrzeganie związków między własnościami oraz różnic i podobieństw między obiektami matematycznymi.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, cele kształcenia — wymagania ogólne, kl. IV-VI, pkt 1

  105. Curriculum point MAT.IV-VI.WO.2 · General aims · checked against the act

    Performing calculations mentally or using various forms of notation; using in calculations not only learned procedures, but also one's own calculation strategies; analyzing errors and understanding the causes of their occurrence.

    our translation · original wording (PL): Wykonywanie obliczeń w pamięci lub z zastosowaniem różnych form zapisu; stosowanie w obliczeniach nie tylko wyuczonych procedur, ale także własnych strategii obliczeń; analizowanie błędów i rozumienie przyczyn ich powstania.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, cele kształcenia — wymagania ogólne, kl. IV-VI, pkt 2

  106. Curriculum point MAT.IV-VI.WO.3 · General aims · checked against the act

    Reading and critically interpreting provided information and transforming the form of its presentation in order to facilitate the interpretation of data.

    our translation · original wording (PL): Odczytywanie i krytyczne interpretowanie podanych informacji oraz przetwarzanie formy ich prezentacji w celu ułatwienia interpretacji danych.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, cele kształcenia — wymagania ogólne, kl. IV-VI, pkt 3

  107. Curriculum point MAT.IV-VI.WO.4 · General aims · checked against the act

    Recognizing mathematics in issues from various fields and building confidence in one's own effectiveness in applying mathematical methods, formulating a mathematical description of simple situations, particularly in everyday life.

    our translation · original wording (PL): Dostrzeganie matematyki w zagadnieniach z różnych dziedzin i budowanie przekonania o własnej skuteczności w stosowaniu metod matematycznych, formułowanie opisu matematycznego prostych sytuacji, w szczególności w życiu codziennym.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, cele kształcenia — wymagania ogólne, kl. IV-VI, pkt 4

  108. Curriculum point MAT.IV-VI.WO.5 · General aims · checked against the act

    Solving mathematical problems independently and in collaboration with others, seeking solutions that go beyond ordinary applications of known schemes.

    our translation · original wording (PL): Rozwiązywanie problemów matematycznych samodzielnie i we współpracy z innymi, poszukiwanie rozwiązań wykraczających poza zwykłe zastosowania znanych schematów.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, cele kształcenia — wymagania ogólne, kl. IV-VI, pkt 5

  109. Curriculum point MAT.IV-VI.WO.6 · General aims · checked against the act

    Developing the need to justify mathematical facts, formulating understandable arguments justifying the correctness of simple reasoning, verifying arguments provided by others.

    our translation · original wording (PL): Kształtowanie potrzeby uzasadniania faktów matematycznych, formułowanie zrozumiałych argumentów uzasadniających poprawność prostych rozumowań, weryfikowanie argumentów podawanych przez innych.

    Dz.U. 2026 poz. 378, zal. nr 2, Matematyka, cele kształcenia — wymagania ogólne, kl. IV-VI, pkt 6

Skills step by step

Understanding halves and quarters of a whole

The child learns to identify and mark a half and a quarter of a single object or a group of objects, as well as reconstruct the whole based on its parts.

Curriculum point MAT.IV-VI.1.17 represents a part of a given whole as a fraction and interprets a proper fraction as a part of a given whole (our translation)

In fourth grade, children learn to represent halves and quarters using common fractions and identify them in specific examples. This skill includes both dividing a single shape into equal parts and finding a fraction of a set of objects (e.g., a quarter of 12 crayons). Students also practice reasoning in reverse: determining the total number of items when they know what half or a quarter of them is.

The most common issue is ignoring the condition of equal parts—students divide a shape into two or four pieces using arbitrary lines and incorrectly consider them to be halves or quarters. Another frequent mistake is not paying attention to the instructions and counting shaded parts instead of unshaded ones, as well as difficulty transferring the concept of a fraction from a single circle or rectangle to a set of multiple separate objects.

In practice, tasks involve, among other things, determining a fraction of a group of objects, evaluating the correctness of divisions in true-or-false questions, and finding errors in drawings. Students also solve tasks where they must calculate the total size of a group based on a given fraction or come up with their own sets that can be divided into equal halves and quarters.

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

Roman numerals up to 3000

The child learns to read and correctly write Roman numerals up to 3000.

Curriculum point MAT.IV-VI.1.2 reads and writes natural numbers in the Roman numeral system in the range from 1 to 3000 (our translation)

In 4th grade, students learn the rules for writing numbers using Roman numerals and gradually master the range up to 3000 (the target for grades 4–6). Children combine basic symbols (such as I, V, X, L, C, D, M), converting familiar Arabic numerals into Roman numerals and reading values written in this ancient system.

The most common problem at this stage is the correct order of symbols when adding and subtracting values. Children often confuse the rules for forming numbers such as IV or IX, writing them in reverse (e.g., as VI or XI), or forget that a smaller symbol before a larger one means subtraction rather than addition.

In practice, exercises are based on simple tasks from ready-made templates: Read the Roman numeral, where the student provides the Arabic value for a given notation, and Write the number in Roman numerals, in which they convert a given number into Roman symbols.

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Task types: Read a Roman numeral · Write a number in Roman numerals

Adding and subtracting decimals

The child learns to add and subtract decimals with up to three decimal places and apply these calculations when adding masses.

Curriculum point MAT.IV-VI.1.28.a adds, subtracts, and multiplies decimals in cases where the decimals have at most three decimal places (our translation)

In Grade 4, students perform addition and subtraction of decimals that have at most three decimal places. The student practices performing these operations fluently with numbers alone as well as with units of measurement.

The most common difficulty is losing place value when adding numbers with a different number of decimal places (e.g., in the problem 1.2 + 0.35). Children often tend to mechanically right-align the numbers instead of following the line up the decimal points rule, which leads them to add tenths to hundredths.

In practice, the student encounters worksheets such as Add decimals and Subtract decimals, as well as problems set in the context of shopping or measurements, such as Add masses written as decimals.

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Task types: Add decimals · Subtract decimals · Add masses written as decimals

Comparing numbers: by how much and how many times

The child learns to compare natural numbers by determining how much greater one is than the other, or how many times greater it is.

Curriculum point MAT.IV-VI.1.14 compares natural numbers by difference and by quotient (our translation)

In grade 4, the student compares natural numbers with each other using two different operations. They distinguish between a situation where they check the difference between two quantities using subtraction, and a situation where they examine their multiple using division.

The most common mistake at this stage is confusing the questions "how many more/less" and "how many times". Children often automatically subtract the smaller number from the larger one, even when the task wording requires division and calculating a multiple.

In practice, the tasks are based on simple question templates: How much greater?, How many times more?, and How many times greater?. Based on the given numerical data, the student must choose the correct operation — subtraction or division — and record the result correctly.

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Task types: How many times as large? · How many times as many? · How much greater?

Adding and subtracting fractions with like denominators

The child learns to add and subtract common fractions with like denominators, performing operations on the numerators and keeping the common denominator.

Curriculum point MAT.IV-VI.1.27 adds, subtracts, multiplies and divides common fractions with one- and two-digit denominators (our translation)
Curriculum point MAT.IV-VI.1.30 compares fractions by difference (our translation)

In Grade 4, children perform addition and subtraction of common fractions with the same one- or two-digit denominators. The student performs the operation solely on the numerators of the fractions, keeping the common denominator unchanged.

A common mistake at this stage is mechanically adding or subtracting denominators (for example, calculating 1/5 + 2/5 = 3/10). In doing so, children carry over habits from operations on natural numbers, forgetting that the denominator merely indicates the size and number of equal parts of a whole.

In practice, the student practices this skill using exercises from the templates Add fractions with like denominators and Subtract fractions with like denominators, training the correct notation of sums and differences.

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Task types: Add fractions with like denominators · Subtract fractions with like denominators

Converting units of length

The child learns to convert lengths between millimeters, centimeters, decimeters, meters, and kilometers and to write compound measurements in a single unit.

Curriculum point MAT.IV-VI.2.2 uses units of length: millimetre, centimetre, decimetre, metre and kilometre, in practical situations converts these units from one to another (our translation)

In Grade 4, students use units of length: millimeter, centimeter, decimeter, meter, and kilometer. They learn to recognize relationships between them and efficiently convert values in practical situations, remembering basic relationships (e.g., 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m).

A typical problem at this stage is confusing the number of zeros when converting units of different multiples—for example, treating a meter as 10 centimeters or a kilometer as 100 meters. Deciding whether to multiply (add zeros) or divide (drop zeros) when converting to another unit is also challenging.

Worksheets and exercises in this grade cover three main types of tasks:

  • convert to a smaller unit of length (e.g., converting meters to centimeters or kilometers to meters),
  • convert to a larger unit of length (e.g., converting whole hundreds of centimeters to meters),
  • express length in a single unit (e.g., converting 3 m 40 cm into centimeters only).
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Task types: Convert to a larger unit of length · Convert to a smaller unit of length · Write a length in one unit

Clock calculations: hours, minutes, and seconds

The child learns to calculate elapsed time and convert minutes and seconds in simple everyday situations.

Curriculum point MAT.IV-VI.2.9 performs simple clock calculations in hours, minutes, and seconds (our translation)

In 4th grade, children perform simple clock calculations involving hours, minutes, and seconds. They learn to accurately determine how much time has passed between two events, as well as how to convert minutes and seconds into seconds only.

A common mistake at this stage is treating the passage of time like standard decimal addition. Children forget that an hour has 60 minutes, and a minute has 60 seconds, which leads them, for example, to add 45 minutes to 12:30 and give the incorrect result of 12:75 instead of 13:15.

In practice, the tasks involve working with specific intervals of time. Children solve exercises such as:

  • How many minutes have passed? — reading the time difference between two given times,
  • How long did it take? — calculating the duration of a specific activity or journey,
  • Minutes and seconds to seconds — converting mixed units of time into seconds only.
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Task types: Minutes and seconds to seconds · How long did it last? · How many minutes have passed?

Converting improper fractions and mixed numbers

The child learns to convert improper fractions into mixed numbers and to write mixed numbers as improper fractions.

Curriculum point MAT.IV-VI.1.20 represents an improper fraction as a mixed number, and a mixed number as an improper fraction (our translation)

In 4th grade, children learn to convert fluently between two ways of writing quantities greater than one: improper fractions (where the numerator is greater than or equal to the denominator) and mixed numbers (consisting of a whole number and a fractional part). The student determines how many wholes are contained in a fraction and can also convert wholes back into fractional parts.

A common mistake when converting a mixed number to a fraction is adding the whole number directly to the numerator instead of first multiplying it by the denominator. Conversely, when extracting wholes from an improper fraction, correctly calculating the remainder from division—which should become the new numerator while keeping the denominator unchanged—can be challenging.

Exercises practicing this skill appear in two clear template formats: Convert fraction to mixed number (e.g., converting a fraction into a result with extracted wholes) and Convert mixed number to fraction (where the student combines the whole number and the fraction into a single fractional representation).

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Task types: Write a mixed number as a fraction · Write an improper fraction as a mixed number

Area of a rectangle and finding the missing side

The child learns to calculate the area of a rectangle and determine the length of its side when the area and the other side are known.

Curriculum point MAT.IV-VI.4.14 calculates the area of a triangle, square, rectangle, rhombus, parallelogram, trapezoid and the areas of figures that can be built from them (our translation)

In grade 4, students take their first steps within the grades 4–6 requirements regarding the areas of geometric figures, focusing on rectangles and squares. Children calculate the area of figures by multiplying the lengths of two adjacent sides. They also learn the inverse operation: when given the area of a rectangle and the length of one side, they determine the missing dimension using division.

A typical mistake at this stage is confusing area with perimeter—students often add the side lengths together instead of multiplying them. When finding a missing side, a common error is subtracting the known side from the given area instead of correctly dividing the area by that dimension.

In practice, the exercises include the following types of tasks:

  • Area of a rectangle – simple arithmetic exercises based on multiplying the given dimensions of adjacent sides,
  • Missing side of a rectangle – problems requiring dividing the area by the known side to find the second edge,
  • Area of a rectangle in everyday life – word problems set in real-life contexts, such as planning the area of a room, a lawn, or a tiled floor.
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Task types: Area of a rectangle · Area of a rectangle in everyday life · Missing side of a rectangle

Planning expenses and choosing the cheaper offer

The child learns to calculate the cost of purchases, check how much change will be left from the available budget, and compare offers to choose the more cost-effective one.

Curriculum point MAT.IV-VI.1.35 calculates the unit price and the cost of purchasing several items of goods, compares the cost-effectiveness of different purchase options (e.g. discount, promotion, bundle purchase) – economic and financial module (our translation)
Curriculum point MAT.IV-VI.2.13 performs monetary calculations related to everyday expenses, budget, saving, currency exchange and comparing prices, interprets documents with units of measurement and prices – economic and financial module (our translation)

In 4th grade, a child performs practical calculations related to everyday shopping. At this stage, they learn to determine the total cost of multiple items, calculate how much money will be left from a given amount (e.g., from pocket money), and compare the cost-effectiveness of different options—buying single items or a promotional multipack.

A common mistake among children is comparing only the final prices of packages rather than the cost per single item. Students are often convinced that a larger package is always more expensive, forgetting to calculate the unit price. It also happens that, when planning expenses, they subtract the price of a single item from the budget instead of the total cost of all the items being purchased.

Exercises practicing this skill are based on everyday situations in the following templates:

  • How much money will be left? – the student calculates the cost of selected items and checks whether the given budget is enough for the purchase and how much change will be returned;
  • Which offer is cheaper? – the child compares two options (e.g., individual snack bars versus a multipack) and identifies the better value choice.
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Task types: How much money is left? · Which offer is the better deal?

Expanding common fractions

The child learns to multiply the numerator and denominator of a fraction by the same number to write it in a new form without changing its value.

Curriculum point MAT.IV-VI.1.19 simplifies and expands common fractions, brings fractions to a common denominator (our translation)

In 4th grade, children learn how to expand fractions, which means multiplying both the numerator and the denominator by the same non-zero natural number. This helps them discover that the same fraction and the same part of a whole can be written using different, proportionally larger numbers.

A typical mistake at this stage is multiplying only one part of the fraction—most often the numerator—and leaving the denominator unchanged (for example, writing that expanding the fraction 1/3 by 2 results in 2/3 instead of 2/6). Another common error is adding the specified number to the numerator and denominator instead of multiplying.

In practice, on worksheets from the Expand the fraction template, children complete exercises that involve expanding a given fraction by a specific number or filling in the missing numerator or denominator in an equality of two fractions.

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Writing and comparing large numbers

The child learns to correctly write multi-digit numbers, compare their values, and understand the meaning of individual place values.

Curriculum point MAT.IV-VI.1.1 uses the decimal system of writing natural numbers, including comparing and rounding natural numbers and interpreting them on a number line (our translation)

In 4th grade, children consolidate their understanding of the decimal place value system and begin to work fluently with multi-digit numbers. They learn to read and compare large natural numbers, as well as understand how a digit's position affects its value—for example, how many times greater a digit in the thousands place is than the same digit in the hundreds or tens place.

A common mistake at this stage is comparing numbers solely by the first digit on the left, without first counting how many digits each number has. Children are sometimes convinced, for instance, that 987 is greater than 1234 because it starts with a higher digit, ignoring the higher order of magnitude in the four-digit number.

Exercises in this area have a very clear format. In activities like Compare multi-digit numbers, students insert less than, greater than, or equal signs between given pairs of numbers. Meanwhile, worksheets such as How many times greater? Place values help students understand the structure of the base-ten system by comparing the values of the same digits in different positions.

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Task types: Compare multi-digit numbers · How many times as large? Place value

Simplifying common fractions

The child learns to divide the numerator and denominator of a common fraction by the same number to write it in a simpler form with smaller numbers.

Curriculum point MAT.IV-VI.1.19 simplifies and expands common fractions, brings fractions to a common denominator (our translation)

In Grade 4, children learn to simplify fractions by dividing the numerator and denominator by their common divisor. The student notices that despite changing the numbers to smaller ones, the value of the fraction remains exactly the same—the fraction still describes the same part of the whole.

A common problem at this stage is dividing the numerator and denominator by two different numbers, or dividing only one part of the fraction. Children also sometimes confuse division with subtraction and try to "simplify" a fraction by subtracting the same value from the numerator and denominator.

In practice, on worksheets from the Simplify the fraction template, the child receives a fraction to simplify. The task is to find a common divisor for the numerator and denominator, perform the division, and correctly enter the fraction in its new, simplified form.

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Clever addition and multiplication of numbers

The child learns to conveniently transform operations on natural numbers, using the properties of addition and multiplication.

Curriculum point MAT.IV-VI.1.12 performs operations on natural numbers, using strategies convenient for themselves that facilitate calculations, including the commutative and associative properties of addition and multiplication and the distributive property of multiplication and division over addition and subtraction (our translation)

In grade 4, children perform calculations with natural numbers, choosing their own convenient strategies. Instead of calculating sequentially, they notice and group numbers into easier pairs (for example, numbers that add up to full tens or hundreds), applying the commutative and associative properties of addition and multiplication in practice.

A common mistake is mechanically calculating from left to right, which leads to arithmetic errors with more difficult numbers. Children also sometimes struggle with correctly applying the distributive property of multiplication over addition—they are able to break down a number, but forget to multiply each of the terms.

The exercises in the Add cleverly and Multiply cleverly templates involve rearranging numbers or breaking down a more difficult factor so that the calculation can be done mentally, for example by pairing numbers that add up to 100 or first multiplying factors that make 10.

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Task types: Add the smart way · Multiply the smart way

Converting decimals to fractions

The child learns to convert terminating decimals into common fraction form, choosing the appropriate denominator.

Curriculum point MAT.IV-VI.1.22 writes terminating decimals in the form of common fractions (our translation)

In grade 4, children learn to convert decimal notation into common fraction form with a numerator and a denominator. Students convert terminating decimals by recognizing that the digits after the decimal point represent tenths, hundredths, or thousandths, respectively, and assign them the correct denominator: 10, 100, or 1000.

The most common difficulty is incorrectly linking the number of decimal digits to the size of the denominator. Children tend to write a denominator of 10 regardless of the number of decimal places (for example, writing the decimal 0.07 as 7/10 instead of 7/100) or drop the zeros right after the decimal point.

In practice, in exercises from the template Convert decimal to common fraction, the student is given a decimal number and enters its equivalent using a fraction bar as a common fraction or a mixed number.

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Column addition and subtraction of numbers

The child learns to add and subtract multi-digit natural numbers using the traditional column method.

Curriculum point MAT.IV-VI.1.9 adds and subtracts natural numbers mentally or with written intermediate calculations (our translation)

In 4th grade, students perform addition and subtraction of multi-digit natural numbers using column methods. Instead of calculating solely by mental arithmetic, they write the operations in vertical columns, which allows for efficient and orderly calculations with larger numbers.

The most common problem is aligning the digits incorrectly underneath each other — for example, aligning numbers to the left instead of by the ones place value. Students also get confused when crossing tens boundaries, forgetting to add carried tens in addition or to borrow from the next place value in subtraction, especially when there is a zero along the way.

In practice, the child solves tasks from the Add vertically and Subtract vertically templates. The exercises involve correctly placing the given numbers into the grid boxes and determining the final result while taking into account carrying and borrowing marks above the column.

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Task types: Add using the column method · Subtract using the column method

Squares and cubes of numbers and fractions

The child calculates the second and third powers of numbers and fractions, and also identifies squares and cubes among two-digit numbers.

Curriculum point MAT.IV-VI.1.15 calculates powers of natural numbers with positive integer exponents, among two-digit numbers recognizes numbers that are squares and cubes of integers (our translation)
Curriculum point MAT.IV-VI.1.29 calculates powers of common and decimal fractions with positive integer exponents, also using a calculator (our translation)

In 4th grade, students are introduced to the concept of exponentiation as repeated multiplication of the same number by itself. Children calculate squares (second power) and cubes (third power) of natural numbers, as well as common fractions and decimals. Across grades 4–6, they also learn to quickly identify which two-digit numbers are squares or cubes of integers (e.g., 16, 27, or 64).

The most common mistake at this stage is confusing exponentiation with simple multiplication by the exponent. Children often write that 4 to the power of 2 is 8 instead of 16, or that the cube of 2 is 6 instead of 8. With fractions, another frequent issue is raising only the numerator to the power while forgetting the denominator.

In printable tasks, children practice these skills through worksheets such as Square and Cube of a Number and Square of a Fraction. These involve writing out powers as products of identical factors, calculating the final results, and identifying squares and cubes within a given set of numbers.

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Task types: Square and cube of a number · Square of a fraction

Reading fractions on a number line

The child learns to read common fractions marked on a number line by determining the division of the unit segment into equal parts.

Curriculum point MAT.IV-VI.1.21 marks common fractions and decimals on a number line and reads common fractions and decimals marked on a number line (our translation)

In Grade 4, children learn to interpret the position of points on a number line in relation to fractions. At this stage, students can determine how many equal parts a unit interval is divided into (for example, the segment from 0 to 1), and then correctly read and write the fraction corresponding to the marked point.

A common mistake is counting the vertical tick marks instead of the equal intervals created between them. A student who sees three tick marks dividing the segment between 0 and 1 often writes the number 3 in the denominator, forgetting that three marks inside divide the whole into 4 equal parts.

In tasks based on the template Read fraction from a number line, the child is given a drawn number line with marked reference points and an indicated location (e.g., with a dot or an arrow). Their task is to independently determine the denominator from the number of divisions and the numerator from the number of counted steps, and then enter the missing fraction.

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Calculating the perimeter of a polygon and a missing side

The child learns to add the lengths of all sides of a shape and to determine a missing side based on the known perimeter of a polygon.

Curriculum point MAT.IV-VI.4.15 calculates the perimeter of a polygon with given side lengths (our translation)

In Grade 4, students practice adding the lengths of all sides of a polygon to find its perimeter. They also develop the reverse skill: calculating the length of one missing side based on the given perimeter of the entire shape and the known dimensions of its edges.

A common mistake is omitting one of the sides in more complex shapes or adding up only some of the dimensions. When finding a missing side, on the other hand, the difficulty lies in the correct order of operations: the student must first add up all the given segments and only then subtract that result from the total perimeter.

Exercises for this topic prepare students to work with specific shapes and include two templates:

  • Perimeter of a polygon – the student reads the side lengths from the diagram of the shape or the problem text and calculates their total sum;
  • Missing side from perimeter – the student analyzes a polygon with a given total perimeter and calculates the length of the unknown segment.
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Task types: Perimeter of a polygon · Missing side from the perimeter

Rounding numbers to thousands and ten thousands

The child learns to correctly round natural numbers to the nearest thousand and ten thousand based on the analysis of the relevant digit.

Curriculum point MAT.IV-VI.1.1 uses the decimal system of writing natural numbers, including comparing and rounding natural numbers and interpreting them on a number line (our translation)

In 4th grade, students develop their understanding of the base-ten number system and learn how to round larger natural numbers. At this stage, children focus on rounding numbers to two specific place values: to the nearest thousand and to the nearest ten thousand. Students determine which multiple of the given place value is closest to the given number.

A typical issue is looking at the wrong digit when deciding how to round—for example, looking at the ones digit instead of the hundreds digit when rounding to the nearest thousand. Another common mistake is forgetting to change subsequent digits to zeros, causing students to modify only the specified place value while leaving the digits to its right unchanged.

Exercises for this topic consist of clear calculation practice. Children work with tasks such as Round to the nearest thousand and Round to the nearest ten thousand, where they identify the correct key digit for given multi-digit numbers and write down the rounded result ending with the appropriate number of zeros.

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Task types: Round to the nearest ten thousand · Round to the nearest thousand

Converting common fractions to decimals

The child learns to convert common fractions with denominators that are divisors of 10, 100, or 1000 into decimals written with a decimal point.

Curriculum point MAT.IV-VI.1.23 converts common fractions with denominators that are divisors of the numbers 10, 100, 1000, etc. into decimals (our translation)

In this topic, students convert common fractions into decimals. This skill covers fractions with denominators that are factors of 10, 100, 1000, etc. (e.g., 2, 4, 5, 20, 25, 50). Students first expand the fraction to get 10, 100, or 1000 in the denominator, and then write the result using a decimal point—for example, expanding the fraction 1/2 to 5/10 and writing it as 0.5.

A common mistake at this stage is mechanically copying the digits of the fraction after the decimal point without first expanding the denominator—for example, writing the fraction 1/4 as 0.4 or 0.14 instead of 0.25. Another difficulty is placing the digits correctly after the decimal point for fractions with denominators of 100 or 1000, which leads to writing the fraction 3/100 as 0.3 instead of the correct 0.03.

Tasks from the template Convert a fraction to a decimal involve providing the correct decimal form for a given fraction, which reinforces the method of expanding the denominator to powers of ten, such as tens, hundreds, or thousands.

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Order of operations: calculations with parentheses

The child learns to correctly calculate the value of arithmetic expressions, performing the operations written in parentheses first.

Curriculum point MAT.IV-VI.1.36 applies the rules regarding the order of operations (our translation)

In grade 4, students learn the primary role of parentheses in mathematical notation. By solving simple arithmetic expressions, children learn to identify and calculate first the operation enclosed in parentheses, and only then move on to the remaining operations.

The most common mistake at this stage is calculating mechanically from left to right, following the direction of reading text. Children often ignore the parentheses (for example, in the expression 20 – (5 + 3) they first subtract 5 from 20 and finally add 3), forgetting that the parentheses enforce the precedence of addition over subtraction.

In exercises from the Calculate the value of an expression with parentheses template, students work with ready-made examples where their goal is to find the intermediate result from the parentheses, and then correctly complete the entire calculation.

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Calendar calculations: how many days is that?

The child learns to perform simple calendar calculations, convert weeks and months into days, and determine how many days have passed between specified dates.

Curriculum point MAT.IV-VI.2.8 performs simple calendar calculations in days, weeks, months and years (our translation)

In 4th grade, a child performs simple calendar-related calculations, focusing on converting units of time into days and using the relationships between days, weeks, months, and years. The student works with basic calendar facts—they know, for example, that a week has 7 days, and a year has 365 or 366 days, and they can determine the length of a given period in days.

The most common mistake is the so-called off-by-one error when determining the passage of time between two dates. Children often mechanically subtract day numbers from each other, forgetting to include the starting day (for example, when counting how many days a trip lasts from Monday to Wednesday). Remembering the varying number of days in different months also poses a difficulty.

Exercises from the How many days is that? template involve converting a given number of weeks into days (for example, calculating how many days a three-week camp lasts) or determining the number of days between specific events shown on a calendar page.

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Comparing decimals

The child learns to compare numbers written with a decimal point and correctly indicate which one is greater, smaller, or whether they are equal.

Curriculum point MAT.IV-VI.1.26 compares fractions (common and decimal) (our translation)

In grade 4, as part of the requirements for grades 4–6, children learn to compare decimals. They examine and compare two decimal numbers, first analyzing the whole number parts, and when they are equal – the subsequent digits after the decimal point: tenths and hundredths.

The most common mistake at this stage is being misled by the length of the digits after the decimal point and treating them like a single whole number. Students often judge that, for example, 0.18 is greater than 0.3 because "18 is greater than 3". They forget to compare digits in the corresponding place values or to pad with zeros (comparing 0.18 and 0.30).

The tasks in the Compare Decimals worksheet involve inserting the correct symbol: <, >, or = between the two given decimals.

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Estimating addition results

The child learns to estimate the result of addition by rounding numbers before performing calculations.

Curriculum point MAT.IV-VI.1.37 estimates the results of operations (our translation)

In 4th grade, children learn to determine the approximate result of addition without having to perform tedious calculations. Instead of calculating accurately on paper, the student rounds numbers to easier, round values (e.g., to the nearest tens or hundreds) and efficiently adds them up mentally to estimate the expected magnitude of the sum.

The most common mistake is first adding the numbers accurately together, and only then rounding the final result. Children do this out of fear of making a mistake, not realizing that estimation is meant to simplify calculations before starting them, rather than serve as an additional step after completing the full operation.

Worksheets based on the Estimate the sum template present the student with tasks where they must quickly identify the approximate value of an addition or choose the appropriate number range, which develops the habit of checking the plausibility of the results they obtain.

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Reading hundredths in decimals

The child learns to identify digits at the appropriate decimal places, including correctly recognizing the hundredths digit in a decimal number.

Curriculum point MAT.IV-VI.1.22 writes terminating decimals in the form of common fractions (our translation)

In grade 4, children learn the place value structure of decimals and how to identify digits in specific decimal places. Confidently distinguishing place values, especially the hundredths place, is a key step toward easily connecting terminating decimals with common fractions with a denominator of 100.

A common issue is confusing the order of places after the decimal point. Students often identify the first digit after the decimal point as hundredths or confuse whole numbers (e.g., tens before the decimal point) with the fractional part of the number.

In practice, students complete exercises based on the template Identify the hundredths digit. The task involves analyzing a given decimal number and accurately identifying the digit in the second decimal place.

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Comparing fractions with the same denominator

The child learns to compare common fractions with the same denominators and indicate which of them represents a larger part of the whole.

Curriculum point MAT.IV-VI.1.26 compares fractions (common and decimal) (our translation)

At this stage of learning, the child compares simple fractions that have the same denominator. They understand that if two identical wholes are divided into the same number of equal parts, the larger fraction is the one with the larger numerator—that is, the one from which more pieces were taken.

A common mistake stems from looking at the fraction notation mechanically. Children sometimes get confused about which number determines the size of the portion and are influenced solely by the bottom of the fraction, assuming, for example, that fractions with identical denominators must be equal to each other, regardless of the numerators.

Exercises from the template Compare fractions with the same denominator involve entering the correct symbol: <, >, or = between two numbers, for example, when comparing 2/8 and 5/8.

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A fraction as a part of a whole and a set

The child describes a part of a single shape or a group of objects using a proper fraction, indicating what part of the whole a given fragment represents.

Curriculum point MAT.IV-VI.1.17 represents a part of a given whole as a fraction and interprets a proper fraction as a part of a given whole (our translation)

In Grade 4, children learn to see a proper fraction as a specific part of a whole or a given set. They recognize that the denominator indicates how many equal parts the whole is divided into (or how many items make up the whole group), and the numerator indicates the number of selected parts.

A common mistake at this stage is comparing the selected elements to the remaining ones instead of to the entire group. For example, seeing 2 shaded circles and 3 unshaded ones, a student might mistakenly write the fraction 2/3 instead of 2/5, confusing the rest of the set with its total count.

In tasks from the template Fraction of a set: a/b of the whole, the child works with illustrations showing sets of objects. Their task is to count all the elements that make up the whole, identify the specified subgroup, and correctly write the result as a common fraction.

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Recognizing types of angles

The child learns to recognize and name different types of angles based on the size of their opening.

Curriculum point MAT.IV-VI.2.3 measures angles less than 180° to the nearest degree and draws any angles when their measure is given in whole degrees (our translation)
Curriculum point MAT.IV-VI.4.2 recognises, names and draws angles, distinguishes between acute, right, obtuse, straight, full, reflex and convex angles, indicates the vertex and arms of an angle (our translation)

In 4th grade, children learn to classify angles based on the relative positions of their arms. Throughout grades 4–6, students learn about acute, right, obtuse, straight, full, reflex, and convex angles, as well as identify the vertex and arms of an angle. In this area, children focus on correctly determining whether a given angle is smaller than a right angle (acute), equal to it (right), or larger than it (obtuse).

A common mistake at this stage is judging the size of an angle by the length of the drawn lines forming its arms, rather than by the degree of their opening. Another difficulty is recognizing an angle whose arms are drawn in an unusual position, for example rotated diagonally, which makes it harder for children to intuitively relate it to the vertical and horizontal lines of a right angle.

In the exercises from the Identify the type of angle template, the student looks at the drawn figure and assigns the correct name to it. This practice helps reinforce the appearance of each type of angle, regardless of the length of its arms or its orientation on the page.

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Reading decimals on a number line

The child learns to correctly read decimals indicated by points on a number line.

Curriculum point MAT.IV-VI.1.21 marks common fractions and decimals on a number line and reads common fractions and decimals marked on a number line (our translation)

In 4th grade, a child takes their first steps with decimals and learns their graphical representation. At this stage, the student can read the value of a decimal indicated on a number line, connecting decimal notation with the appropriate position between whole numbers.

A common problem is incorrectly determining the value of a single step on the line. Children often count the tick marks instead of the intervals between them, or automatically assume that each subsequent tick mark represents one tenth (0.1), without checking how many equal parts the unit interval has been divided into.

In tasks from the Read decimal from number line template, the student sees a number line with selected numbers labeled and a point marked. Their task is to determine the value of this point and enter the correct decimal.

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Converting units of mass to smaller units

The child learns to convert weight to a smaller unit, converting tonnes to kilograms, kilograms to decagrams or grams, and decagrams to grams.

Curriculum point MAT.IV-VI.2.7 uses, including converting, units of mass in practical contexts: gram, decagram, kilogram, tonne (our translation)

In Grade 4, children learn to convert units of mass into smaller ones, working with tons, kilograms, decagrams, and grams. They use basic relationships: one ton is 1000 kilograms, one kilogram is 100 decagrams or 1000 grams, and one decagram is 10 grams.

A typical difficulty is confusing the number of zeros when converting kilograms. Children often instinctively add three zeros with every conversion, making a mistake when converting from kilograms to decagrams (where the correct multiplier is 100) or confusing the relationship between a decagram and a gram.

In practice, when solving problems from the template Convert to a smaller unit of mass, the student enters the missing number in simple equations, for example converting 4 kg to decagrams, 6 dag to grams, or 3 t to kilograms.

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Long multiplication by a single-digit number

The child learns to multiply a multi-digit natural number by a single-digit number, using a clear written method with intermediate calculations.

Curriculum point MAT.IV-VI.1.10 multiplies and divides a natural number by a one-digit, two-digit, or three-digit number mentally or by recording intermediate calculations (our translation)

In Grade 4, children perform column multiplication of whole numbers by a single-digit number. Instead of calculating purely in their heads, students write the problem in a column and work out the result step by step, multiplying the digits from right to left and writing down intermediate calculations.

The most common mistake occurs with so-called carrying over. Children often forget to add the previously carried number to the result of the next multiplication or, conversely, add the carried digit first and only then multiply, which completely changes the result.

In practice, the exercises are based on the template Multiply in columns by a single-digit number. Students receive a problem in a column or in a single line (e.g. 348 · 6), rewrite it in the proper column format with a line, and fill in the missing digits of the result on their own.

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Long multiplication of multi-digit numbers

The child learns to multiply multi-digit numbers by one-, two-, or three-digit numbers using column multiplication with the correct recording of calculations.

Curriculum point MAT.IV-VI.1.10 multiplies and divides a natural number by a one-digit, two-digit, or three-digit number mentally or by recording intermediate calculations (our translation)

At this stage of learning, the child multiplies multi-digit numbers using long multiplication. In accordance with the curriculum requirements for grades 4–6, the student multiplies natural numbers by single-digit, two-digit, and three-digit numbers, organizing calculations into columns and writing down consecutive partial products.

The most common problem when multiplying by two- and three-digit numbers is losing the correct alignment in subsequent rows of calculations. Children often forget to add a zero or shift the second result one place to the left, which leads to incorrectly summing the columns. Carrying over digits mentally into subsequent columns can also be confusing.

In practice, the exercises from the Multiply multi-digit numbers using long multiplication template involve independently aligning the numbers under each other, performing partial multiplication for each digit of the second factor, and then adding the resulting partial products together.

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Long division by a single-digit number

The child learns to divide natural numbers by a single-digit number, writing down the full calculation steps and intermediate results.

Curriculum point MAT.IV-VI.1.10 multiplies and divides a natural number by a one-digit, two-digit, or three-digit number mentally or by recording intermediate calculations (our translation)
Curriculum point MAT.IV-VI.1.11 interprets division of natural numbers as sharing and as grouping (our translation)
Curriculum point MAT.IV-VI.1.13 performs division with remainder of natural numbers and uses the properties of remainders (our translation)

In grade 4, students divide natural numbers by a single-digit number, explicitly writing out the intermediate calculations. The child transitions from mental arithmetic to the long division algorithm: step by step, they divide parts of the number, multiply the result back, subtract it, and bring down the next digit of the dividend.

A typical mistake at this stage is omitting a zero in the result (quotient). This happens most often when, after bringing down the next digit, the resulting number is smaller than the divisor — children often immediately bring down the next digit, forgetting to write a zero in the corresponding place on top. Misaligning the vertical columns on grid paper is also common, which leads to subtraction errors.

In tasks based on the template Long division by a single-digit number, the student receives a written problem and space to work out the entire column calculation on their own. Step by step, they determine each digit of the result, keep track of the remainders from subtraction, and write down the final quotient.

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Comparing data on bar charts

A fourth grader learns to read values from a bar chart and compare individual bars with each other to determine where there is more and where there is less.

Curriculum point MAT.IV-VI.5.1 interprets data presented in text and using tables, diagrams, and graphs, including graphs drawn with a continuous line, in particular compares prices, costs, and expenses presented in tables, on graphs, or on receipts – economic and financial module (our translation)
Curriculum point MAT.IV-VI.5.2 conducts simple statistical investigations: collects data, records them in an organized form and presents conclusions resulting from the collected information (our translation)
Curriculum point MAT.IV-VI.5.4 interprets data on expenses, calculates their average value, and formulates conclusions regarding the cost-effectiveness of different solutions – economic-financial module. (our translation)

In grade 4, children learn to read information from bar charts and compare them. Although the curriculum for the entire grades 4–6 stage ultimately also includes analyzing line graphs or calculating average expenses, at the beginning of this journey, students focus on simple bar comparisons. They determine which value is the greatest or smallest and identify the differences between given categories.

A typical mistake at this stage is judging data purely "by eye" based on the height of a bar, while ignoring the numerical axis. Students get confused especially when the scale on the axis increases in intervals (e.g., by 2, 5, or 10 units) and a bar ends between grid lines—they then read the value of the nearest mark instead of estimating the actual number.

In practice, using the Compare Bar Chart Bars template, the child analyzes a clear bar chart. The task involves correctly reading data from the vertical and horizontal axes and then identifying the relationships between them—for example, which bar represents the greatest value or by how many units one category exceeds another.

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Task templates to print

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

Understanding halves and quarters of a whole

Roman numerals up to 3000

Adding and subtracting decimals

Comparing numbers: by how much and how many times

Adding and subtracting fractions with like denominators

Converting units of length

Clock calculations: hours, minutes, and seconds

Converting improper fractions and mixed numbers

Area of a rectangle and finding the missing side

Planning expenses and choosing the cheaper offer

Expanding common fractions

Writing and comparing large numbers

Simplifying common fractions

Clever addition and multiplication of numbers

Converting decimals to fractions

Column addition and subtraction of numbers

Squares and cubes of numbers and fractions

Reading fractions on a number line

Calculating the perimeter of a polygon and a missing side

Rounding numbers to thousands and ten thousands

Converting common fractions to decimals

Order of operations: calculations with parentheses

Calendar calculations: how many days is that?

Comparing decimals

Estimating addition results

Reading hundredths in decimals

Comparing fractions with the same denominator

A fraction as a part of a whole and a set

Recognizing types of angles

Reading decimals on a number line

Converting units of mass to smaller units

Long multiplication by a single-digit number

Long multiplication of multi-digit numbers

Long division by a single-digit number

Comparing data on bar charts

Other task types

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