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Curriculum (Poland)

Mathematics — Grade 2 of primary school

Scope of grade 2 elementary school mathematics: numbers up to 100, addition and subtraction with regrouping, the beginning of the multiplication table, difference comparison, money, and time. Printable task templates ready for each topic.

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What does a child learn in 2nd grade math?

In grade 2, the number range expands up to 100. The child adds and subtracts with regrouping across tens, learns the multiplication table, learns difference comparison ("how much more"), as well as money and clock calculations.

Important note about the curriculum: the Polish core curriculum for early childhood education is formulated in blocks — it defines what the student knows at the end of grade 3. In the "Curriculum Scope" section below, you will find the complete block for grades 1–3 with quotes from the regulation — and the task template list shows what from this block is covered specifically in grade 2.

Curriculum scope

  1. Curriculum point EW.MAT.I-III.1 · Teaching content · checked against the act

    Achievements in understanding spatial relations and size characteristics.

    our translation · original wording (PL): Osiągnięcia w zakresie rozumienia stosunków przestrzennych i cech wielkościowych.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 1

  2. Curriculum point EW.MAT.I-III.1.1 · Teaching content · checked against the act

    determines and presents the relative position of objects on a plane and in space; determines and presents the direction of movement of objects and people; determines the position of an object to the right/to the left of a person seen from the front (also shown in a photograph or picture);

    our translation · original wording (PL): określa i prezentuje wzajemne położenie przedmiotów na płaszczyźnie i w przestrzeni; określa i prezentuje kierunek ruchu przedmiotów oraz osób; określa położenie przedmiotu na prawo/na lewo od osoby widzianej z przodu (także przedstawionej na fotografii czy obrazku);

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 1 pkt 1

  3. Curriculum point EW.MAT.I-III.1.2 · Teaching content · checked against the act

    compares objects with respect to a distinguished size attribute, e.g. length or mass; classifies objects;

    our translation · original wording (PL): porównuje przedmioty pod względem wyróżnionej cechy wielkościowej, np. długości czy masy; dokonuje klasyfikacji przedmiotów;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 1 pkt 2

    Comparing the lengths of objects (we teach in grade 1-3)

  4. Curriculum point EW.MAT.I-III.1.3 · Teaching content · checked against the act

    uses the concepts: vertical, horizontal, diagonal.

    our translation · original wording (PL): posługuje się pojęciami: pion, poziom, skos.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 1 pkt 3

    Recognizing directions: vertical, horizontal, and diagonal (we teach in grade 1-3)

  5. Curriculum point EW.MAT.I-III.2 · Teaching content · checked against the act

    Achievements in understanding numbers and their properties.

    our translation · original wording (PL): Osiągnięcia w zakresie rozumienia liczb i ich własności.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 2

  6. Curriculum point EW.MAT.I-III.2.1 · Teaching content · checked against the act

    counts (forwards and backwards) from a given number by 1, by 2, by 10, etc.;

    our translation · original wording (PL): liczy (w przód i wstecz) od podanej liczby po 1, po 2, po 10 itp.;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 2 pkt 1

    Number range: liczby naturalne do 1000

    Counting forward and backward by a fixed step (we teach in grade 1-3)

  7. Curriculum point EW.MAT.I-III.2.2 · Teaching content · checked against the act

    reads and writes, using digits, numbers from zero to one thousand and selected numbers up to one million (e.g. 1 500, 10 000, 800 000);

    our translation · original wording (PL): odczytuje i zapisuje, za pomocą cyfr, liczby od zera do tysiąca oraz wybrane liczby do miliona (np. 1 500, 10 000, 800 000);

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 2 pkt 2

    Number range: od zera do tysiąca; wybrane liczby do miliona (odczyt)

  8. Curriculum point EW.MAT.I-III.2.3 · Teaching content · checked against the act

    explains the meaning of digits in the notation of a number; indicates ones, tens, hundreds, etc., determines order using an ordinal number;

    our translation · original wording (PL): wyjaśnia znaczenie cyfr w zapisie liczby; wskazuje jedności, dziesiątki, setki itd., określa kolejność, posługując się liczbą porządkową;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 2 pkt 3

    Number range: liczby trzycyfrowe

    Determining the order using ordinal numbers (we teach in grade 1-3)

  9. Curriculum point EW.MAT.I-III.2.4 · Teaching content · checked against the act

    compares numbers; orders numbers from smallest to largest and vice versa; understands formulations of the type: a number 7 greater, a number 10 smaller; uses the symbols: <, =, >.

    our translation · original wording (PL): porównuje liczby; porządkuje liczby od najmniejszej do największej i odwrotnie; rozumie sformułowania typu: liczba o 7 większa, liczba o 10 mniejsza; stosuje znaki: <, =, >.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 2 pkt 4

    Number range: liczby naturalne do 1000

    Comparing numbers up to 100 (we teach in grade 1-3) · Difference comparison: how many more (we teach in grade 2-3)

  10. Curriculum point EW.MAT.I-III.3 · Teaching content · checked against the act

    Achievements in the area of using numbers.

    our translation · original wording (PL): Osiągnięcia w zakresie posługiwania się liczbami.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 3

  11. Curriculum point EW.MAT.I-III.3.1 · Teaching content · checked against the act

    explains the essence of mathematical operations – addition, subtraction, multiplication, division and the relationships between them; intuitively uses the properties of operations;

    our translation · original wording (PL): wyjaśnia istotę działań matematycznych – dodawania, odejmowania, mnożenia, dzielenia oraz związki między nimi; korzysta intuicyjnie z własności działań;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 3 pkt 1

    Checking results using inverse operations (we teach in grade 2-3) · Convenient calculation using properties of operations (we teach in grade 1-3)

  12. Curriculum point EW.MAT.I-III.3.2 · Teaching content · checked against the act

    adds mentally to a given number and subtracts mentally from a given number: a one-digit number, the number 10, the number 100, and multiples of 10 and 100 (in simpler examples);

    our translation · original wording (PL): dodaje do podanej liczby w pamięci i od podanej liczby odejmuje w pamięci: liczbę jednocyfrową, liczbę 10, liczbę 100 oraz wielokrotności 10 i 100 (w prostszych przykładach);

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 3 pkt 2

    Number range: dodawanie i odejmowanie w pamięci; wielokrotności 10 i 100

    Not required at this stage: algorytmy pisemne (dodawanie i odejmowanie pod kreską) — podstawa wymaga obliczeń pamięciowych i zapisu cząstkowego

    Mental addition within 100 (we teach in grade 1-3) · Subtracting two-digit numbers up to 100 (we teach in grade 2-3)

  13. Curriculum point EW.MAT.I-III.3.3 · Teaching content · checked against the act

    multiplies and divides mentally within the multiplication table; multiplies numbers less than 20 by 10 mentally; solves equations with an unknown written in the form of a box (fills in the box); uses own strategies when performing calculations; uses the equals sign and the signs of the four basic operations;

    our translation · original wording (PL): mnoży i dzieli w pamięci w zakresie tabliczki mnożenia; mnoży w pamięci przez 10 liczby mniejsze od 20; rozwiązuje równania z niewiadomą zapisaną w postaci okienka (uzupełnia okienko); stosuje własne strategie, wykonując obliczenia; posługuje się znakiem równości i znakami czterech podstawowych działań;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 3 pkt 3

    Number range: tabliczka mnożenia; mnożenie przez 10 liczb < 20

    Not required at this stage: dzielenie pisemne, dzielenie z resztą

    Mental multiplication and division up to 100 (we teach in grade 2-3)

  14. Curriculum point EW.MAT.I-III.3.4 · Teaching content · checked against the act

    adds and subtracts two-digit numbers, writing down partial results of operations if necessary or, performing operations mentally, gives the result immediately; calculates sums and differences of larger numbers in simple examples such as: 250 + 50, 180 – 30; multiplies two-digit numbers by 2, writing down partial results of operations if they need to; uses their own strategies in calculations.

    our translation · original wording (PL): dodaje i odejmuje liczby dwucyfrowe, zapisując w razie potrzeby cząstkowe wyniki działań lub, wykonując działania w pamięci, od razu podaje wynik; oblicza sumy i różnice większych liczb w prostych przykładach typu: 250 + 50, 180 – 30; mnoży liczby dwucyfrowe przez 2, zapisując, jeśli ma taką potrzebę, cząstkowe wyniki działań; przy obliczeniach stosuje własne strategie.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 3 pkt 4

    Number range: liczby dwucyfrowe; proste przykłady typu 250 + 50

    Not required at this stage: algorytmy pisemne

    Addition up to 100 with regrouping (we teach in grade 2-3) · Subtracting two-digit numbers up to 100 (we teach in grade 2-3)

  15. Curriculum point EW.MAT.I-III.4 · Teaching content · checked against the act

    Achievements in the area of reading mathematical texts.

    our translation · original wording (PL): Osiągnięcia w zakresie czytania tekstów matematycznych.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 4

  16. Curriculum point EW.MAT.I-III.4.1 · Teaching content · checked against the act

    analyzes and solves simple and selected complex word problems; recognizes a mathematical problem and creates their own strategy for solving it, appropriate to the conditions of the problem; describes the solution using operations, equations with a box, a drawing, or in another way of their choice;

    our translation · original wording (PL): analizuje i rozwiązuje zadania tekstowe proste i wybrane złożone; dostrzega problem matematyczny oraz tworzy własną strategię jego rozwiązania, odpowiednią do warunków zadania; opisuje rozwiązanie za pomocą działań, równości z okienkiem, rysunku lub w inny wybrany przez siebie sposób;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 4 pkt 1

    Solving simple word problems (we teach in grade 1-3)

  17. Curriculum point EW.MAT.I-III.4.2 · Teaching content · checked against the act

    poses problems and solves them, creates mathematical puzzles, uses their own artistic, technical, and construction activity in this process; carries out selected activities using simple computer applications.

    our translation · original wording (PL): układa zadania i je rozwiązuje, tworzy łamigłówki matematyczne, wykorzystuje w tym procesie własną aktywność artystyczną, techniczną, konstrukcyjną; wybrane działania realizuje za pomocą prostych aplikacji komputerowych.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 4 pkt 2

  18. Curriculum point EW.MAT.I-III.5 · Teaching content · checked against the act

    Achievements in understanding geometric concepts.

    our translation · original wording (PL): Osiągnięcia w zakresie rozumienia pojęć geometrycznych.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 5

  19. Curriculum point EW.MAT.I-III.5.1 · Teaching content · checked against the act

    recognises – in the natural environment (including on the faces of solid figures) and in drawings – geometric figures: rectangle, square, triangle, circle; distinguishes these figures from other figures; draws line segments and broken lines using a ruler; draws rectangles (including squares) freehand, using a square grid;

    our translation · original wording (PL): rozpoznaje – w naturalnym otoczeniu (w tym na ścianach figur przestrzennych) i na rysunkach – figury geometryczne: prostokąt, kwadrat, trójkąt, koło; wyodrębnia te figury spośród innych figur; kreśli przy linijce odcinki i łamane; rysuje odręcznie prostokąty (w tym kwadraty), wykorzystując sieć kwadratową;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 5 pkt 1

    Recognizing geometric shapes (we teach in grade 1-3) · Drawing line segments and broken lines using a ruler (we teach in grade 1-3)

  20. Curriculum point EW.MAT.I-III.5.2 · Teaching content · checked against the act

    measures the lengths of line segments, sides of geometric figures, etc.; states the measurement result using units of length: centimeter, meter, millimeter; explains the relationships between units of length; uses compound units; explains the concept of the kilometer;

    our translation · original wording (PL): mierzy długości odcinków, boków figur geometrycznych itp.; podaje wynik pomiaru, posługując się jednostkami długości: centymetr, metr, milimetr; wyjaśnia związki między jednostkami długości; posługuje się wyrażeniami dwumianowanymi; wyjaśnia pojęcie kilometr;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 5 pkt 2

    Number range: milimetr, centymetr, metr; kilometr jako pojęcie

  21. Curriculum point EW.MAT.I-III.5.3 · Teaching content · checked against the act

    measures the perimeters of various figures using measuring tools, also in everyday life contexts; calculates the perimeter of a triangle and a rectangle (including also a square) with given sides;

    our translation · original wording (PL): mierzy obwody różnych figur za pomocą narzędzi pomiarowych, także w kontekstach z życia codziennego; oblicza obwód trójkąta i prostokąta (w tym także kwadratu) o danych bokach;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 5 pkt 3

    Number range: wyniki w zakresie 100

  22. Curriculum point EW.MAT.I-III.5.4 · Teaching content · checked against the act

    notices symmetry in the natural environment, in applied art and other human creations present in the child's surroundings.

    our translation · original wording (PL): dostrzega symetrię w środowisku przyrodniczym, w sztuce użytkowej i innych wytworach człowieka obecnych w otoczeniu dziecka.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 5 pkt 4

  23. Curriculum point EW.MAT.I-III.6 · Teaching content · checked against the act

    Achievements in applying mathematics in real-life situations and in other areas of education.

    our translation · original wording (PL): Osiągnięcia w zakresie stosowania matematyki w sytuacjach życiowych oraz w innych obszarach edukacji.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6

  24. Curriculum point EW.MAT.I-III.6.1 · Teaching content · checked against the act

    classifies objects and various elements of the social and natural environment based on identified features; notices rhythm in the natural environment, applied art and other human creations present in the child's environment;

    our translation · original wording (PL): klasyfikuje obiekty i różne elementy środowiska społeczno-przyrodniczego z uwagi na wyodrębnione cechy; dostrzega rytm w środowisku przyrodniczym, sztuce użytkowej i innych wytworach człowieka, obecnych w środowisku dziecka;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 1

    Discovering and continuing patterns in numbers (we teach in grade 1-3)

  25. Curriculum point EW.MAT.I-III.6.2 · Teaching content · checked against the act

    divides into two and four equal parts, e.g. a sheet of paper, chocolate; uses the terms: half, two and a half, four equal parts, fourth part or quarter;

    our translation · original wording (PL): dzieli na dwie i cztery równe części, np. kartkę papieru, czekoladę; używa pojęć: połowa, dwa i pół, cztery równe części, czwarta część lub ćwierć;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 2

  26. Curriculum point EW.MAT.I-III.6.3 · Teaching content · checked against the act

    performs money calculations; converts zlotys into grosze and vice versa, distinguishes denominations on coins and banknotes, indicates differences in their purchasing power;

    our translation · original wording (PL): wykonuje obliczenia pieniężne; zamienia złote na grosze i odwrotnie, rozróżnia nominały na monetach i banknotach, wskazuje różnice w ich sile nabywczej;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 3

    Number range: kwoty do 100 zł

    Money calculations and giving change (we teach in grade 2-3) · Converting zlotys to groszy (we teach in grade 1-3)

  27. Curriculum point EW.MAT.I-III.6.4 · Teaching content · checked against the act

    reads time on an analogue clock and a digital clock (displaying digits in a 24-hour system); performs simple calculations related to time; uses units of time: 24-hour day, hour, minute, second; uses a stopwatch, phone, tablet, and computer applications; writes dates, e.g. their date of birth or the current date; uses a calendar; reads and writes Roman numerals at least up to XII;

    our translation · original wording (PL): odczytuje godziny na zegarze ze wskazówkami oraz elektronicznym (wyświetlającym cyfry w systemie 24-godzinnym); wykonuje proste obliczenia dotyczące czasu; posługuje się jednostkami czasu: doba, godzina, minuta, sekunda; posługuje się stoperem, aplikacjami telefonu, tabletu, komputera; zapisuje daty np. swojego urodzenia lub datę bieżącą; posługuje się kalendarzem; odczytuje oraz zapisuje znaki rzymskie co najmniej do XII;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 4

    Number range: doba, godzina, minuta, sekunda; znaki rzymskie do XII

    Reading time on an analog and digital clock (we teach in grade 1-3)

  28. Curriculum point EW.MAT.I-III.6.5 · Teaching content · checked against the act

    measures temperature using a thermometer and reads it;

    our translation · original wording (PL): mierzy temperaturę za pomocą termometru oraz odczytuje ją;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 5

  29. Curriculum point EW.MAT.I-III.6.6 · Teaching content · checked against the act

    makes estimated calculations in various real-life situations;

    our translation · original wording (PL): dokonuje obliczeń szacunkowych w różnych sytuacjach życiowych;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 6

  30. Curriculum point EW.MAT.I-III.6.7 · Teaching content · checked against the act

    weighs; uses the terms: kilogram, decagram, gram, tonne; knows the relationships between these units; measures liquids; uses the terms: litre, half a litre, quarter of a litre;

    our translation · original wording (PL): waży; używa określeń: kilogram, dekagram, gram, tona; zna zależności między tymi jednostkami; odmierza płyny; używa określeń: litr, pół litra, ćwierć litra;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 7

  31. Curriculum point EW.MAT.I-III.6.8 · Teaching content · checked against the act

    uses checkers, chess and other board or logic games to develop strategic and logical thinking skills, understanding of rules, etc.; transforms games, creating their own strategies and organizational rules;

    our translation · original wording (PL): wykorzystuje warcaby, szachy i inne gry planszowe lub logiczne do rozwijania umiejętności myślenia strategicznego, logicznego, rozumienia zasad itd.; przekształca gry, tworząc własne strategie i zasady organizacyjne;

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 8

  32. Curriculum point EW.MAT.I-III.6.9 · Teaching content · checked against the act

    uses acquired skills for problem-solving, creative activities and exploration of the world, taking care of one's own development and creating individual learning strategies.

    our translation · original wording (PL): wykorzystuje nabyte umiejętności do rozwiązywania problemów, działań twórczych i eksploracji świata, dbając o własny rozwój i tworząc indywidualne strategie uczenia się.

    Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 6 pkt 9

  33. EW.MAT.I-III.WR.1 (our numbering) · How it is taught

    At this stage, calculations are carried out mentally, with the support of partial recording — the core curriculum does not require written algorithms (column addition, written division); this is material for stage II of education.

    our translation · original wording (PL): Na tym etapie obliczenia prowadzi się pamięciowo, ze wsparciem zapisu cząstkowego — podstawa nie wymaga algorytmów pisemnych (dodawania pod kreską, dzielenia pisemnego); to materiał II etapu edukacyjnego.

    our summary of the point · Dz.U. 2017 poz. 356, zal. nr 2, II. Edukacja matematyczna, ust. 3 pkt 2 i 4 — nasz wniosek z brzmienia punktów

    Not required at this stage: algorytmy pisemne, dzielenie pisemne, dzielenie z resztą

  34. EW.MAT.I-III.WR.2 (our numbering) · How it is taught

    We introduce concepts in the order: manipulation of concrete objects, drawing and diagram (number line, place value chart, bar chart), only then symbolic notation.

    our translation · original wording (PL): Pojęcia wprowadzamy w kolejności: manipulacja konkretami, rysunek i schemat (oś liczbowa, tabela pozycyjna, diagram słupkowy), dopiero potem zapis symboliczny.

    our summary of the point · Nasza nota dydaktyczna (model Brunera), nie tekst rozporządzenia

Skills step by step

Addition up to 100 with regrouping

The child learns to mentally add two-digit numbers with regrouping across tens up to 100, using their own strategies and recording intermediate results.

Curriculum point EW.MAT.I-III.OS.3 (our numbering) The student adds and subtracts mentally two-digit numbers and multiples of 10 and 100. (our translation)
Curriculum point EW.MAT.I-III.3.4 adds and subtracts two-digit numbers, writing down partial results of operations if necessary or, performing operations mentally, gives the result immediately; calculates sums and differences of larger numbers in simple examples such as: 250 + 50, 180 – 30; multiplies two-digit numbers by 2, writing down partial results of operations if they need to; uses their own strategies in calculations. (our translation)

In Grade 2, a child mentally adds two-digit numbers up to 100 when the sum of the ones crosses into the next ten (for example, 37 + 25 or 48 + 6). The student does not need to know column addition algorithms yet. They can give the final result right away or help themselves by writing down their own partial results on paper—most often by first bridging to the next ten or by adding tens and ones separately.

The most common mistake at this stage is losing the newly formed ten. A child skillfully adds the ones (for example, 7 + 5 = 12), but in the final result, they only combine the initial tens with just the ending 2, getting 52 instead of 62. It is also challenging to smoothly decompose the second addend in order to first efficiently bridge the first one to a full ten.

Tasks that practice this skill take various forms: from simple calculations, to questions asking how much is missing to make a full ten, to finding the missing number at the beginning of an operation. Children also solve classic word problems (including those with extraneous information), compare two expressions without calculating everything from scratch, and verify the correctness of others' calculations to spot errors in them.

Create a worksheet for this skill

Task types: Choose the correct result · How much is missing to the next ten · True or false · Addition within 100 with regrouping · Bridge through ten and finish the calculation · How much is missing to the target (within 100) · Word problem — addition (change) · Correct someone else's result · Number sequence — give the next term (within 100) · Unknown starting amount (within 100) · Which sum is larger (within 100) · Balancing both sides (within 100) · Check the result and find the mistake (within 100) · Two operations in a row (within 100) · Word problem with one number too many (within 100)

Comparing numbers up to 100

The child learns to compare two-digit numbers up to 100, order them, and correctly use the less-than, greater-than, and equal-to signs: <, >, and =.

Curriculum point EW.MAT.I-III.2.4 compares numbers; orders numbers from smallest to largest and vice versa; understands formulations of the type: a number 7 greater, a number 10 smaller; uses the symbols: <, =, >. (our translation)

In Grade 2, children learn to compare quantities up to 100. They can efficiently identify which value is greater or smaller, arrange numbers in ascending or descending order, and write these relationships using mathematical symbols: <, >, and =. Although the entire core curriculum for Grades 1–3 ultimately covers numbers up to 1000, mastering the structure of two-digit numbers up to 100 is crucial at this stage.

A common challenge for second graders is confusing the symbols < and > themselves, as well as focusing solely on the ones digit instead of the tens digit. When comparing, for example, 38 and 52, a child might consider the first number to be greater simply because eight is larger than two, forgetting to check the tens digit.

Exercises for this skill include, among others:

  • inserting the correct symbol (<, >, or =) between two numbers or after counting objects,
  • finding the missing digit in an inequality with a blank box (e.g., listing all digits that make the statement true),
  • identifying a number that meets an additional condition, such as finding an even number that lies between two given thresholds.
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Task types: Insert the sign: <, > or = · Comparing numbers within 100 · Compute, then insert the sign · How much is missing to one hundred · Order five numbers · Order the numbers from greatest · Which group collected the least · An even number between two numbers · How many digits fit in the box · List the digits that fit

Mental multiplication and division up to 100

The child learns to multiply and divide from memory within the multiplication table, multiply numbers less than 20 by 10, and fill in missing numbers in open sentences with a box.

Curriculum point EW.MAT.I-III.OS.4 (our numbering) The student gives from memory the results of multiplication and division within the multiplication table and checks division using multiplication. (our translation)
Curriculum point EW.MAT.I-III.3.3 multiplies and divides mentally within the multiplication table; multiplies numbers less than 20 by 10 mentally; solves equations with an unknown written in the form of a box (fills in the box); uses own strategies when performing calculations; uses the equals sign and the signs of the four basic operations; (our translation)

In grade 2, a child begins to calculate mentally with ease within the multiplication table and multiply numbers less than 20 by 10 (up to 100). They also learn division within the same range and check its result using multiplication. The student applies their own memory strategies, uses the signs of the four basic operations, and is able to solve a simple equation where the unknown is represented by an empty box.

A typical problem at this stage is confusing multiplication with repeated addition of identical numbers—for example, writing the operation 4 · 3 as the addition of different quantities or incorrectly determining how many times a given addend was taken. Intuitive reversal of operations also poses a difficulty: when a child remembers the result of multiplication, but gets lost when finding the missing factor in an equation with a box or in related division.

In practice, the exercises involve working with specific task templates. Children solve tasks such as:

  • Missing factor — entering the correct number into an empty box to make the equation true;
  • How many times the addend was taken — converting repeated addition into a multiplication expression;
  • Which multiplication yields more and by how much — comparing the results of two operations with each other;
  • Check the multiplication and find the mistake and Multiplication with an unnecessary number — spotting errors in calculations and discarding data not needed for the calculations.
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Task types: Equal groups altogether · How many dots in the array · How many times was it taken · Multiplication table (to 100) · Missing factor (multiplication table) · Check the multiplication and find the mistake · Multiplication with one number too many · Which product is larger and by how much

Subtracting two-digit numbers up to 100

The child learns to subtract two-digit numbers mentally, writing down intermediate results if necessary and using their own calculation strategies.

Curriculum point EW.MAT.I-III.OS.3 (our numbering) The student adds and subtracts mentally two-digit numbers and multiples of 10 and 100. (our translation)
Curriculum point EW.MAT.I-III.3.2 adds mentally to a given number and subtracts mentally from a given number: a one-digit number, the number 10, the number 100, and multiples of 10 and 100 (in simpler examples); (our translation)
Curriculum point EW.MAT.I-III.3.4 adds and subtracts two-digit numbers, writing down partial results of operations if necessary or, performing operations mentally, gives the result immediately; calculates sums and differences of larger numbers in simple examples such as: 250 + 50, 180 – 30; multiplies two-digit numbers by 2, writing down partial results of operations if they need to; uses their own strategies in calculations. (our translation)

In 2nd grade, children subtract two-digit numbers up to 100, as well as multiples of 10 and simple examples with larger numbers, such as 180 – 30. At this stage, column subtraction is not yet used. Students calculate mentally and provide the result directly, or write down convenient intermediate steps, for instance by breaking the subtrahend into tens and ones.

A typical difficulty is crossing the tens boundary (regrouping). Children often confuse the order of the digits in the ones place and subtract the smaller digit from the larger one regardless of the operation (for example, in 52 – 17 they calculate 7 – 2 instead of correctly subtracting 10 first, and then 7). Losing track of tens during multi-step mental calculations is also common.

Exercises targeting this skill take various forms—from simple calculations to spotting mistakes in completed work. Children solve problems involving two consecutive subtractions, word problems requiring them to determine how many there were at the beginning, and tasks combining adding and removing items where they must filter out unnecessary numerical information.

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Task types: Subtract within 10: how many are left? · Jumping back on the hundred grid · Subtraction within 100 · Subtraction step by step · Subtraction within 100: choose the correct result · How many there were at the start (subtraction within 100) · Some left, some arrived — what remains (within 100) · Subtraction within 100: correct someone else's result · Two subtractions in a row (within 100) · Check the subtraction and find the mistake (within 100) · Subtraction with one number too many (within 100)

Money calculations and giving change

The child learns to pay for purchases, select the appropriate coins and banknotes, and calculate change up to 100 PLN.

Curriculum point EW.MAT.I-III.OS.9 (our numbering) The student performs money, clock, and calendar calculations in everyday situations. (our translation)
Curriculum point EW.MAT.I-III.6.3 performs money calculations; converts zlotys into grosze and vice versa, distinguishes denominations on coins and banknotes, indicates differences in their purchasing power; (our translation)

In grade 2, children perform everyday money calculations up to 100 zł. They recognize the denominations of coins and banknotes, convert zlotys to groszy and vice versa, and understand the differences in their purchasing power. They can calculate the total cost of several items, check whether they have enough money for purchases, and calculate how much change they should receive from a given banknote.

A common mistake at this stage is confusing zlotys with groszy when adding, for example, treating 1 zł and 10 gr as 11 zł. Calculating the missing amount or change from whole tens also poses difficulty, especially when it requires subtraction across a ten (e.g., paying with a 50 zł banknote for purchases worth 34 zł).

The exercises are based on practical shopping situations. Children solve worksheet tasks in which they determine:

  • Whether there is enough money for selected items and how much more is needed to buy a more expensive item,
  • how to calculate purchases and change when paying with a specific banknote,
  • how much several pieces of the same product cost,
  • which coins to pay with to make up the exact required amount.
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Task types: How much do several items cost · How much is still missing · Is there enough money · Change: choose the right amount · Change: fix the mistake · Shopping and change · Which coins to pay with · Which coins to pay with (cents)

Mental addition within 100

The child learns to mentally add numbers up to 100, including adding single-digit numbers and whole tens, also crossing the tens threshold.

Curriculum point EW.MAT.I-III.3.2 adds mentally to a given number and subtracts mentally from a given number: a one-digit number, the number 10, the number 100, and multiples of 10 and 100 (in simpler examples); (our translation)

In Grade 2, children perform mental calculations within 100 without using written algorithms (column addition). Students efficiently add single digits and whole tens to a given number, using partial recording or breaking numbers apart when needed.

A typical challenge at this stage is crossing the tens boundary, for example in operations like 47 + 8. Children often lose track of the full ten or only add the ones digit to the ones of the first addend, forgetting to increase the tens place (resulting in an incorrect answer of 45 instead of 55).

The exercises are based on a variety of visual and mental formats. Children complete tasks using a number line, fill in result tables, add three addends at once in a single operation, and compare expressions to identify the one that produces a different result from the rest.

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Task types: Adding two-digit numbers · Addition on the number line · Addition on the number line within 100 · Choose the result of the addition within 100 · Fill in the results table · Is the total right? Addition within 100 · Jumping on the hundred grid · Correct the mistake in an addition within 100 · Match each sum to its result · Number pyramid · The addition code · Three parts at once (within 100) · Which one has a different result

Solving simple word problems

The child learns to understand the content of a simple word problem, choose addition or subtraction for it, and write down the solution.

Curriculum point EW.MAT.I-III.4.1 analyzes and solves simple and selected complex word problems; recognizes a mathematical problem and creates their own strategy for solving it, appropriate to the conditions of the problem; describes the solution using operations, equations with a box, a drawing, or in another way of their choice; (our translation)

In Grade 2, a child manages simple one-step word problems within 100, using addition and subtraction (including regrouping across tens). The student can identify the problem in a story they read, plan their own way to solve it, and write it down using a traditional operation, a drawing, or a missing-number equation.

A common problem at this stage is mechanically picking numbers from the text and adding them together without understanding the meaning of the situation. Children get lost especially when they need to determine the initial amount—seeing a decrease in the text, they instinctively subtract the given numbers instead of combining what is left with what was taken away.

In practice, the child works with specific real-life situations. Typical tasks involve calculating how much is left after giving away some items, or figuring out how much there was at the beginning. The child also practices identifying which of the given operations correctly describes a given story—for example, choosing the right equation to calculate the total number of items.

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Task types: Simple word problem — how many are left · A word problem with an extra number — how many are left · Choose the correct result · Which operation solves the problem · Which operation solves the problem (altogether) · How many were there at the start

Recognizing geometric shapes

The child recognizes and names circles, triangles, rectangles, and squares in drawings and in their surroundings.

Curriculum point EW.MAT.I-III.OS.7 (our numbering) The student recognizes geometric figures and distinguishes them from among others. (our translation)
Curriculum point EW.MAT.I-III.5.1 recognises – in the natural environment (including on the faces of solid figures) and in drawings – geometric figures: rectangle, square, triangle, circle; distinguishes these figures from other figures; draws line segments and broken lines using a ruler; draws rectangles (including squares) freehand, using a square grid; (our translation)

In Grade 2, the student proficiently recognizes and distinguishes basic geometric shapes: circle, triangle, rectangle, and square. They point them out in flat drawings, on the faces of 3D solids, and in everyday objects. They can distinguish these shapes from other figures and use their names correctly.

A common challenge at this stage is recognizing shapes that are rotated—for example, a triangle pointing downwards is sometimes mistaken for another shape, and a rotated square is sometimes mistakenly called a rhombus. Children also tend to overlook the fact that every square is also a rectangle, which makes classifying them correctly more difficult.

In practice, the child solves tasks that involve naming a presented shape in the template What is the name of the drawn shape. In the exercise How many triangles are in the picture, the student analyzes a complex illustration, finds, and counts the shapes hidden in it, distinguishing them from the other graphic elements.

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Task types: How many triangles are in the picture · Correct the name of the drawn figure · Is it this figure? True or false · What is the drawn figure called · What is this figure called? Choose · What is this turned figure called?

Counting forward and backward by a fixed step

The child learns to count forwards and backwards by a constant value, for example by 2 or by 10, within the number range up to 100.

Curriculum point EW.MAT.I-III.2.1 counts (forwards and backwards) from a given number by 1, by 2, by 10, etc.; (our translation)

In Grade 2, children learn to skip-count fluently along the number line up to 100. Instead of counting only by ones, they can start from any number and count forward or backward by a constant step—for example, by 2s or by 10s. Although the curriculum expects counting this way up to 1,000 by the end of Grade 3, in the second year of school, mastering this pattern with two-digit numbers is key.

Children struggle most with crossing tens boundaries, especially when counting backward. A common mistake occurs at points such as counting backward by 2 from 41—a child loses track of the correct ten and says 49 or 38 instead of 39. Maintaining a steady rhythm can also be problematic when the step does not start from a multiple of ten, but from an odd number.

In practice, using the Skip-count by a constant step template, children complete number sequences according to a given rule. The task consists of entering the next missing values when the starting number and the step size (forward or backward) are known.

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Task types: Counting in steps: choose the next number · Keep counting by the same step · Count backwards in equal steps · Counting in steps: correct the wrong number · How many times you must count on to get there

Convenient calculation using properties of operations

The child learns to cleverly rearrange and combine numbers in addition up to 100 to make mental math easier.

Curriculum point EW.MAT.I-III.3.1 explains the essence of mathematical operations – addition, subtraction, multiplication, division and the relationships between them; intuitively uses the properties of operations; (our translation)

In Grade 2, children intuitively use the properties of addition within 100. Instead of adding numbers in order, they can spot addends that are easy to combine—for example, those that make a whole ten. They understand that changing the order of addition does not affect the final result, which allows for faster and error-free mental calculation.

A common mistake children make is strictly sticking to the written order and adding numbers only from left to right. An example such as 17 + 8 + 3 is often calculated as the more difficult 17 + 8, and only then is the three added. The child gets lost in calculations that cross the tens boundary, instead of first combining 17 and 3 to make an even 20.

Tasks from the template Choose a convenient order involve pairing numbers that make whole tens before completing the rest of the operation. The student rewrites the calculations in a new, more convenient order or connects the relevant addends with brackets, making it easier to efficiently add the remaining values.

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Task types: Choose the convenient order · Compare the two sums · A handy order of adding: choose the correct answer · A handy order of adding: true or false · Add the easy way and explain your steps · The same total, sides swapped — what is hidden · Four terms, two convenient pairs · What is missing on the other side to make it equal

Converting zlotys to groszy

The child learns to convert whole amounts in zlotys to groszy up to 100 PLN, based on the principle that one zloty is equal to one hundred groszy.

Curriculum point EW.MAT.I-III.6.3 performs money calculations; converts zlotys into grosze and vice versa, distinguishes denominations on coins and banknotes, indicates differences in their purchasing power; (our translation)

In grade 2, children learn basic money conversions up to 100 PLN. They use the key relationship: 1 PLN = 100 gr. At this stage, the student efficiently converts full amounts given in zlotys into the corresponding number of groszy, understanding the value relationship between these units.

The most common problem is mechanically adding zeros without understanding the scale, or confusing currency units. Sometimes children treat the notation 1 PLN as the equivalent of 10 gr instead of 100 gr, carrying over associations from the base-10 counting system to coins.

In practice, using the Converting zlotys to groszy template, the child solves tasks involving completing equations, for example entering the number of groszy for a given amount in zlotys (e.g. 2 PLN = … gr), or matching appropriate groszy values to given banknotes and coins.

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Task types: Converting zloty to grosz · How much is missing to a whole unit of currency · How many whole units of currency is that · Zloty to grosz: choose the correct answer · Zloty to grosz: true or false

Difference comparison: how many more

The child learns to determine how much greater one number is than another within 100, writing the difference using subtraction.

Curriculum point EW.MAT.I-III.OS.2 (our numbering) The student compares and orders numbers, using the signs <, = and >. (our translation)
Curriculum point EW.MAT.I-III.2.4 compares numbers; orders numbers from smallest to largest and vice versa; understands formulations of the type: a number 7 greater, a number 10 smaller; uses the symbols: <, =, >. (our translation)

In 2nd grade, children learn to precisely compare two quantities up to 100. They not only identify which number is greater, but can also calculate the exact difference between them. They understand the phrase how much greater and know that finding this difference requires subtracting the smaller number from the greater one. Although the entire curriculum for grades 1–3 ultimately covers the range up to 1,000, at this stage children practice these relationships with numbers up to 100.

A common mistake children make is associating the word more exclusively with addition. Seeing the question "how much more," students instinctively add the two given numbers together instead of calculating the difference between them. Setting up the equation itself can also be difficult, namely remembering that we always subtract the smaller value from the greater one.

Exercises from the How much more template involve comparing two numbers or sets of objects and calculating the difference. The child sets up the appropriate subtraction equation (e.g., 15 − 9 = 6) and writes down the conclusion that the first number is that much greater than the second.

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Task types: How many more · How many more: choose the correct answer · How many more: true or false · How many the other one has, when it has that many more · How many the other one has, when the first has that many more

Reading time on an analog and digital clock

The child learns to tell time on an analog clock and on a digital display in a 24-hour format, using their knowledge of hours and minutes.

Curriculum point EW.MAT.I-III.6.4 reads time on an analogue clock and a digital clock (displaying digits in a 24-hour system); performs simple calculations related to time; uses units of time: 24-hour day, hour, minute, second; uses a stopwatch, phone, tablet, and computer applications; writes dates, e.g. their date of birth or the current date; uses a calendar; reads and writes Roman numerals at least up to XII; (our translation)

In 2nd grade, children learn to tell time on both a traditional analog clock and a digital clock that displays digits in a 24-hour format. Students use basic units of time, such as the hour and minute, and also read clock faces with Roman numerals up to XII.

The most common difficulty at this stage is confusing the short hour hand with the long minute hand, as well as incorrectly associating the positions of the hands with digital times in the afternoon (e.g., reading 15:00 as 3:00 on a 24-hour clock). Children also sometimes struggle to determine the exact number of minutes as the long hand moves past each number on the dial.

In the Reading the Clock exercise, the child solves tasks that involve entering the correct time below an illustration of a traditional clock face or matching an analog clock face to the corresponding time on a digital clock.

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Task types: Reading a clock: true or false · Reading a clock: which time is on the dial · Reading the clock · Correct the mistake in reading the clock · How many minutes to the full hour · Which clock shows the earlier time

Checking results using inverse operations

A child learns to check their own calculations and understand how addition relates to subtraction, and division to multiplication.

Curriculum point EW.MAT.I-III.OS.4 (our numbering) The student gives from memory the results of multiplication and division within the multiplication table and checks division using multiplication. (our translation)
Curriculum point EW.MAT.I-III.3.1 explains the essence of mathematical operations – addition, subtraction, multiplication, division and the relationships between them; intuitively uses the properties of operations; (our translation)

In grade 2, children discover that mathematical operations are interconnected and can be reversed. In practice, this means that students can check the correctness of addition using subtraction within the range of numbers up to 100, and also recall from memory multiplication and division facts within the multiplication table, checking division with the corresponding multiplication.

A common problem at this stage is the mechanical copying of numbers from the first operation without understanding their roles. A child asked to check addition using subtraction might subtract an addend from another addend instead of from the obtained result (sum). It also happens that a student automatically writes the expected number without actually recalculating, thus missing an error made in the first operation.

In tasks such as Checking Addition with Subtraction, the child first calculates the result of the addition, and then sets up the checking operation: they subtract one of the addends from the obtained sum to ensure that the result equals the other addend.

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Task types: Checking addition by subtraction · Check a subtraction by adding · Correct the mistake in checking a subtraction · How many were there before sharing · Is the check of the subtraction right? · What number was it subtracted from? Choose · What was it multiplied by

Determining the order using ordinal numbers

The child learns to identify the position of objects in a series and determine the order of a given element from the beginning.

Curriculum point EW.MAT.I-III.2.3 explains the meaning of digits in the notation of a number; indicates ones, tens, hundreds, etc., determines order using an ordinal number; (our translation)

In Grade 2, children learn to precisely name the position of elements in an ordered sequence. Instead of answering the question "how many items are there?", they identify a specific place in a line using ordinal numbers (e.g., first, second, fifth). Although the curriculum covers three-digit numbers by the end of Grades 1–3, tasks at this stage focus on clearly determining order within the everyday range of numbers up to 100.

The most common mistake students make is confusing ordinal numbers with cardinal numbers. Children often answer "five" instead of "fifth" or count objects from the wrong side, ignoring where the beginning of the row is. It also happens that a child skips the first element and starts counting from the second one as the "first indicated".

In tasks like Which one in line from the start, the student sees a sequence of illustrations (e.g., animals or objects arranged in a line) and is asked to identify, mark, or write out in words which position from the left side the indicated object occupies.

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Task types: Which position from the start · Which position from the front: choose the correct answer · Which position from the front: true or false · How many are between two given places · How many there are, given the place from both ends

Drawing line segments and broken lines using a ruler

A child learns to use a ruler to precisely draw straight line segments and join them into polygonal chains.

Curriculum point EW.MAT.I-III.5.1 recognises – in the natural environment (including on the faces of solid figures) and in drawings – geometric figures: rectangle, square, triangle, circle; distinguishes these figures from other figures; draws line segments and broken lines using a ruler; draws rectangles (including squares) freehand, using a square grid; (our translation)

In Grade 2, children learn how to use a ruler proficiently. They can hold the tool firmly against the paper, draw straight line segments, and form broken lines by connecting consecutive sections at various angles.

The most common problem at this stage is the ruler slipping while drawing a line. Children often press the pencil too hard while holding the ruler with only one finger at the edge, causing the line to become crooked or slip underneath the tool.

In practice, this skill goes hand in hand with drawing geometric shapes. Tasks include, among other things, drawing a rectangle with given side lengths, where the child must measure equal segments and connect them into a closed figure using a ruler or on a grid.

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Task types: Correct the length of the broken line · Draw a broken line of the given length · Draw a rectangle with the given sides · How long is the broken line? Choose · Is the broken line this long? True or false

Discovering and continuing patterns in numbers

The child learns to notice repeating rules in number sequences up to 100 and write in their subsequent elements independently.

Curriculum point EW.MAT.I-III.6.1 classifies objects and various elements of the social and natural environment based on identified features; notices rhythm in the natural environment, applied art and other human creations present in the child's environment; (our translation)

In second grade, children transfer the ability to recognize patterns from their surroundings and nature to the world of numbers up to 100. They can analyze a given sequence, discover the consistent rule by which the values increase or decrease, and then correctly fill in the missing numbers according to that rule.

A common mistake at this stage is focusing solely on the difference between the first two elements and ignoring the rest of the sequence. Children often lose the constant step, especially when the sequence requires crossing a tens boundary (for example, when repeatedly adding the same number: 18, 23, 28) or when the pattern is decreasing.

In practice, exercises from the Continue the Number Pattern template involve filling in missing fields in a number sequence. The child is given the beginning of a sequence of numbers, determines the rule behind it, and writes in the next appropriate values.

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Task types: Continue the countdown rhythm · Continue the number rhythm · Correct the wrongly continued pattern · Next term of the pattern: choose the correct answer · Next term of the pattern: true or false · Number pattern: which number is missing in the middle · What was the first term of the pattern · Find a term far along the pattern · Number pattern: how much does it grow each time · Which pattern grows faster and by how much

Recognizing directions: vertical, horizontal, and diagonal

The child learns to correctly identify and name lines and the arrangement of objects vertically, horizontally, and diagonally.

Curriculum point EW.MAT.I-III.1.3 uses the concepts: vertical, horizontal, diagonal. (our translation)

At this stage, the child comfortably uses the concepts: vertical, horizontal, and diagonal. They can identify these directions in space and on a sheet of paper, as well as correctly determine the orientation of drawn lines or objects.

A common problem is confusing horizontal and vertical lines or struggling to name a diagonal line when it deviates from a simple top-bottom or left-right orientation. Children intuitively see the difference, but they need reinforcement of the correct terms so they do not simply describe a diagonal line as "crooked".

In practice, using the exercise Vertical, Horizontal, or Diagonal, the second-grader analyzes the prepared drawings and decides which orientation the presented elements have. The task involves indicating the correct term for given lines, arrows, or arrangements of objects on the worksheet.

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Task types: Correct it: vertical, horizontal or oblique · Draw a line: vertical, horizontal or oblique · Vertical, horizontal or oblique · Vertical, horizontal or oblique? True or false · What kind of line is it? Choose

Comparing the lengths of objects

The child learns to compare objects based on their size and determine, using subtraction, by how much one is longer than the other within the range up to 100.

Curriculum point EW.MAT.I-III.1.2 compares objects with respect to a distinguished size attribute, e.g. length or mass; classifies objects; (our translation)

In 2nd grade, a student can compare two objects based on a specific attribute, such as length. They combine direct observation with calculations: not only do they identify which is longer, but they can also determine the difference using subtraction within 100.

A common mistake children make is simply stating that one object is longer than the other, without attempting to calculate the difference. Accurately aligning measurement units or reading data from an illustration can also be challenging, which leads children to add the two numbers together instead of subtracting the smaller value from the larger one.

In tasks such as How Much Longer Is the Ribbon, the child sees ribbons or strips of specific lengths drawn on the worksheet. Their goal is to compare their dimensions, write the appropriate subtraction equation, and determine the exact difference.

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Task types: How much longer is the ribbon · Put them in order from lightest · Which one is the longest · How much longer: choose the correct answer · How much longer: true or false

Task templates to print

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

Addition up to 100 with regrouping

Comparing numbers up to 100

Mental multiplication and division up to 100

Subtracting two-digit numbers up to 100

Money calculations and giving change

Mental addition within 100

Solving simple word problems

Recognizing geometric shapes

Counting forward and backward by a fixed step

Convenient calculation using properties of operations

Converting zlotys to groszy

Difference comparison: how many more

Reading time on an analog and digital clock

Checking results using inverse operations

Determining the order using ordinal numbers

Drawing line segments and broken lines using a ruler

Discovering and continuing patterns in numbers

Recognizing directions: vertical, horizontal, and diagonal

Comparing the lengths of objects

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