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Curriculum (Germany)

Mathematics — Grade 2 of Elementary School

The 2nd grade mathematics curriculum: numbers up to 100, addition and subtraction with regrouping, the beginning of multiplication tables, comparing differences, money, and time. Ready-to-print worksheet templates for every topic.

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What does a child learn in 2nd grade math?

In 2nd grade, the number range expands to 100. The child calculates across tens, learns the multiplication tables, compares differences ("how much more"), and calculates with money and time.

Important note on educational standards: The KMK educational standards describe the competencies at the end of grade 4. In the curriculum section below, they are listed completely including citations; the assignment to the specific school year is our pedagogical decision.

Curriculum scope

  1. KMK.ZO (our numbering) · Teaching content · checked against the act

    Numbers and Operations

    our translation · original wording (DE): Zahl und Operation

    KMK Bildungsstandards Mathematik Primarbereich (23.06.2022), Leitidee Zahl und Operation

  2. KMK.ZO.1 (our numbering) · Teaching content · checked against the act

    Understand number representations and number relationships

    our translation · original wording (DE): Zahldarstellungen und Zahlbeziehungen verstehen

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Zahldarstellungen und Zahlbeziehungen verstehen”

  3. KMK.ZO.2 (our numbering) · Teaching content · checked against the act

    understand and master arithmetic operations

    our translation · original wording (DE): Rechenoperationen verstehen und beherrschen

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”

  4. KMK.ZO.3 (our numbering) · Teaching content · checked against the act

    Apply arithmetic operations in contexts

    our translation · original wording (DE): Rechenoperationen in Kontexten anwenden

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen in Kontexten anwenden”

  5. KMK.ZO.1.1 (our numbering) · Teaching content · checked against the act

    recognize, explain, and use the structure of the decimal place value system (e.g., bundling principle, place value principle)

    our translation · original wording (DE): erkennen, erklären und nutzen den Aufbau des dezimalen Stellenwertsystems (z. B. Bündelungsprinzip, Stellenwertprinzip)

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Zahldarstellungen und Zahlbeziehungen verstehen”, Spiegelstrich 1

    Number range: liczby naturalne do 1000 w naszym zakresie; dokument siega miliona

  6. KMK.ZO.2.1 (our numbering) · Teaching content · checked against the act

    have an understanding of operations for the four basic arithmetic operations and recognize and use the relationships between the operations

    our translation · original wording (DE): verfügen über ein Operationsverständnis zu den vier Grundrechenarten und erkennen und nutzen die Zusammenhänge zwischen den Operationen

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 1

    Number range: cztery dzialania w zakresie 100

    Checking results using the inverse operation (we teach in grade 2-4) · Addition within 100 (we teach in grade 1-4) · Multiplication tables up to 100 (we teach in grade 2-4)

  7. KMK.ZO.3.1 (our numbering) · Teaching content · checked against the act

    apply arithmetic operations in word problems and describe the relationships between the real-world context and the individual solution steps

    our translation · original wording (DE): wenden bei Sachaufgaben Rechenoperationen an und beschreiben die Beziehungen zwischen der Sache und den einzelnen Lösungsschritten

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen in Kontexten anwenden”, Spiegelstrich 1

    Number range: zadania z trescia w zakresie 100-1000

    Solving simple word problems (we teach in grade 1-4)

  8. KMK.ZO.1.2 (our numbering) · Teaching content · checked against the act

    represent numbers up to 1 000 000 in different ways (e.g. visual aids, stepped notation, place value chart, numeral representation) and relate them to one another

    our translation · original wording (DE): stellen Zahlen bis 1 000 000 auf verschiedene Weise dar (z. B. Anschauungsmittel, Stufenschrift, Stellenwerttabelle, Zifferndarstellung) und setzen diese zueinander in Beziehung

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Zahldarstellungen und Zahlbeziehungen verstehen”, Spiegelstrich 2

    Number range: dokument mowi do 1 000 000; nasza tresc konczy sie na 1000

  9. KMK.ZO.2.2 (our numbering) · Teaching content · checked against the act

    master the basic facts of mental arithmetic (among others, number bonds, addition facts, multiplication tables) from memory and reliably derive their inverses

    our translation · original wording (DE): beherrschen die Grundaufgaben des Kopfrechnens (u. a. Zahlzerlegungen, Einspluseins, Einmaleins) gedächtnismäßig und leiten deren Umkehrungen sicher ab

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 2

    Number range: Einspluseins do 20, Einmaleins do 100

    Addition up to 20 without regrouping (we teach in grade 1-4) · Multiplication tables up to 100 (we teach in grade 2-4)

  10. KMK.ZO.3.2 (our numbering) · Teaching content · checked against the act

    round and estimate appropriately

    our translation · original wording (DE): runden und überschlagen sachadäquat

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen in Kontexten anwenden”, Spiegelstrich 2

    Number range: zaokraglanie do dziesiatek i setek

  11. KMK.ZO.1.3 (our numbering) · Teaching content · checked against the act

    orient themselves in the number range up to 1 000 000 (e.g. order numbers by size, determine neighbouring numbers)

    our translation · original wording (DE): orientieren sich im Zahlenraum bis 1 000 000 (z. B. Zahlen der Größe nach ordnen, Nachbarzahlen bestimmen)

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Zahldarstellungen und Zahlbeziehungen verstehen”, Spiegelstrich 3

    Number range: dokument do 1 000 000; nasza tresc do 1000

    Counting forwards and backwards in steps (we teach in grade 1-4)

  12. KMK.ZO.2.3 (our numbering) · Teaching content · checked against the act

    transfer the basic problems of mental arithmetic to analogous problems in the number range up to one million

    our translation · original wording (DE): übertragen die Grundaufgaben des Kopfrechnens auf analoge Aufgaben im Zahlenraum bis zur Million

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 3

    Number range: dokument: analogie az do miliona; my: wielokrotnosci 10 i 100

  13. KMK.ZO.2.4 (our numbering) · Teaching content · checked against the act

    understand mental and semi-written calculation strategies for the four basic operations and use them flexibly

    our translation · original wording (DE): verstehen mündliche und halbschriftliche Rechenstrategien zu den vier Grundrechenarten und setzen diese flexibel ein

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 4

    Number range: rachunek pamieciowy i polpisemny do 1000

    Not required at this stage: algorytm pisemny pod kreska (to osobny punkt ZO.2.7)

    Addition up to 100 with regrouping (we teach in grade 2-4) · Subtraction problems within 100 (we teach in grade 2-4)

  14. KMK.ZO.2.5 (our numbering) · Teaching content · checked against the act

    describe, compare and evaluate different calculation methods; find, explain and correct calculation errors

    our translation · original wording (DE): beschreiben, vergleichen und bewerten verschiedene Rechenwege; finden, erklären und berichtigen Rechenfehler

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 5

    Number range: bledy w dzialaniach do 100

    Finding calculation errors within the number range up to 100 (we teach in grade 2-4)

  15. KMK.ZO.2.6 (our numbering) · Teaching content · checked against the act

    recognize, explain and use laws of arithmetic (e.g. commutative law: turnaround facts)

    our translation · original wording (DE): erkennen, erklären und nutzen Rechengesetze (z. B. Kommutativgesetz: Tauschaufgaben)

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 6

    Number range: przemiennosc i lacznosc w zakresie 100

    Using calculation strategies and comparing sums (we teach in grade 1-4)

  16. KMK.ZO.2.7 (our numbering) · Teaching content · checked against the act

    understand written methods of addition, subtraction and multiplication, describe the algorithm, carry it out fluently and apply it to suitable tasks

    our translation · original wording (DE): verstehen schriftliche Verfahren der Addition, Subtraktion und Multiplikation, beschreiben den Algorithmus, führen diesen geläufig aus und wenden ihn bei geeigneten Aufgaben an

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 7

    Number range: algorytmy pisemne dodawania, odejmowania i mnozenia (kl. 3-4 w DE)

  17. KMK.ZO.2.8 (our numbering) · Teaching content · checked against the act

    check solutions through suitable procedures (e.g. estimation, inverse operation)

    our translation · original wording (DE): kontrollieren Lösungen durch geeignete Vorgehensweisen (z. B. Überschlagsrechnung, Umkehroperation)

    KMK Bildungsstandards (23.06.2022), Leitidee Zahl und Operation, Bereich „Rechenoperationen verstehen und beherrschen”, Spiegelstrich 8

    Number range: kontrola wyniku szacowaniem i dzialaniem odwrotnym

    Checking results using the inverse operation (we teach in grade 2-4)

  18. KMK.GM (our numbering) · Teaching content · checked against the act

    Quantities and measurement

    our translation · original wording (DE): Größen und Messen

    KMK Bildungsstandards Mathematik Primarbereich (23.06.2022), Leitidee Größen und Messen

  19. KMK.GM.1 (our numbering) · Teaching content · checked against the act

    Have concepts of measurement

    our translation · original wording (DE): Über Größenvorstellungen verfügen

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Über Größenvorstellungen verfügen”

  20. KMK.GM.2 (our numbering) · Teaching content · checked against the act

    Measure quantities and determine measurements

    our translation · original wording (DE): Größen messen und Maßangaben bestimmen

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Größen messen und Maßangaben bestimmen”

  21. KMK.GM.3 (our numbering) · Teaching content · checked against the act

    Work with quantities in contexts

    our translation · original wording (DE): Mit Größen in Kontexten umgehen

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Mit Größen in Kontexten umgehen”

  22. KMK.GM.1.1 (our numbering) · Teaching content · checked against the act

    compare and order quantities (monetary values, lengths, time spans, masses, areas and volumes)

    our translation · original wording (DE): vergleichen und ordnen Größen (Geldwerte, Längen, Zeitspannen, Massen, Flächeninhalte und Volumina)

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Über Größenvorstellungen verfügen”, Spiegelstrich 1

    Number range: porownywanie bez rachunku: dluzszy, ciezszy, dluzej trwa

    Comparing and ordering quantities (we teach in grade 1-4)

  23. KMK.GM.2.1 (our numbering) · Teaching content · checked against the act

    understand and use (among other things, areas by covering with unit squares, volumes by measuring with unit cubes) the basic principle of measurement (select non-standard and standard units of measurement, use repeatedly, and where applicable relate to subunits)

    our translation · original wording (DE): verstehen und nutzen (u. a. Flächeninhalte durch Auslegen mit Einheitsquadraten, Rauminhalte durch Messen mit Einheitswürfeln) das Grundprinzip des Messens (nicht-standardisierte und standardisierte Einheitsmaße auswählen, wiederholt nutzen und ggf. in Beziehung zu Untereinheiten setzen)

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Größen messen und Maßangaben bestimmen”, Spiegelstrich 1

    Number range: pole przez wykladanie kwadratami jednostkowymi, objetosc szescianami

  24. KMK.GM.3.1 (our numbering) · Teaching content · checked against the act

    estimate quantities appropriately and with reference to suitable benchmarks

    our translation · original wording (DE): schätzen Größen sachadäquat und mit Bezug zu geeigneten Repräsentanten

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Mit Größen in Kontexten umgehen”, Spiegelstrich 1

    Number range: szacowanie wielkosci z odniesieniem do wzorca

  25. KMK.GM.1.2 (our numbering) · Teaching content · checked against the act

    know standard units (for monetary values, lengths, time spans, capacities, and mass) and relate these to one another within the respective measurement domain

    our translation · original wording (DE): kennen Standardeinheiten (zu Geldwerten, Längen, Zeitspannen, Hohlmaßen und zur Masse) und setzen diese im jeweiligen Größenbereich zueinander in Beziehung

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Über Größenvorstellungen verfügen”, Spiegelstrich 2

    Number range: mm, cm, m, km; g, kg; ml, l; s, min, h

  26. KMK.GM.2.2 (our numbering) · Teaching content · checked against the act

    measure lengths, time spans, masses and capacities appropriately using suitable units and different measuring instruments

    our translation · original wording (DE): messen Längen, Zeitspannen, Massen und Hohlmaße mit geeigneten Einheiten und unterschiedlichen Messgeräten sachgerecht

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Größen messen und Maßangaben bestimmen”, Spiegelstrich 2

    Number range: pomiar linijka, waga, miarka, zegar

    Reading the time correctly (we teach in grade 1-4)

  27. KMK.GM.3.2 (our numbering) · Teaching content · checked against the act

    calculate appropriately with approximate values in real-world situations and check results for plausibility

    our translation · original wording (DE): rechnen in Sachsituationen angemessen mit Näherungswerten und prüfen Ergebnisse auf Plausibilität

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Mit Größen in Kontexten umgehen”, Spiegelstrich 2

    Number range: rachunek na wartosciach przyblizonych, ocena sensownosci wyniku

  28. KMK.GM.1.3 (our numbering) · Teaching content · checked against the act

    develop and use mental representations of benchmarks for standard units and quantities significant in everyday life (e.g. height of the door, duration of the school lesson)

    our translation · original wording (DE): entwickeln und nutzen Vorstellungen über Repräsentanten für Standardeinheiten und im Alltag bedeutsame Größen (z. B. Höhe der Tür, Dauer der Schulstunde)

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Über Größenvorstellungen verfügen”, Spiegelstrich 3

    Number range: wzorce z otoczenia: wysokosc drzwi, czas lekcji

  29. KMK.GM.2.3 (our numbering) · Teaching content · checked against the act

    name measurements with different units and represent them in different notations (e.g. 2,5 km | 2500 m | 2 km 500 m)

    our translation · original wording (DE): benennen Größenangaben mit verschiedenen Einheiten und stellen diese in unterschiedlichen Schreibweisen (z. B. 2,5 km | 2500 m | 2 km 500 m) dar

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Größen messen und Maßangaben bestimmen”, Spiegelstrich 3

    Number range: zapis mieszany i przeliczenia dlugosci

  30. KMK.GM.3.3 (our numbering) · Teaching content · checked against the act

    solve word problems with measurements

    our translation · original wording (DE): lösen Sachaufgaben mit Größen

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Mit Größen in Kontexten umgehen”, Spiegelstrich 3

    Number range: zadania z trescia na pieniadze, czas i dlugosc

    Calculating with money in everyday life (we teach in grade 2-4) · Solving simple word problems (we teach in grade 1-4)

  31. KMK.GM.1.4 (our numbering) · Teaching content · checked against the act

    know and understand simple fractions commonly used in everyday life in connection with measurements (e.g. 1 2 m, three-quarters of an hour, 1 4 l)

    our translation · original wording (DE): kennen und verstehen im Alltag gebräuchliche einfache Brüche im Zusammenhang mit Größen (z. B. 1 2 m, Dreiviertelstunde, 1 4 l)

    KMK Bildungsstandards (23.06.2022), Leitidee Größen und Messen, Bereich „Über Größenvorstellungen verfügen”, Spiegelstrich 4

    Number range: polowa, cwiartka, trzy czwarte przy wielkosciach

  32. KMK.MS (our numbering) · Teaching content · checked against the act

    Patterns, structures and functional relationship

    our translation · original wording (DE): Muster, Strukturen und funktionaler Zusammenhang

    KMK Bildungsstandards Mathematik Primarbereich (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang

  33. KMK.MS.1 (our numbering) · Teaching content · checked against the act

    recognize, describe and represent regularities

    our translation · original wording (DE): Gesetzmäßigkeiten erkennen, beschreiben und darstellen

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Gesetzmäßigkeiten erkennen, beschreiben und darstellen”

  34. KMK.MS.2 (our numbering) · Teaching content · checked against the act

    Recognise, describe and represent functional relationships

    our translation · original wording (DE): Funktionale Beziehungen erkennen, beschreiben und darstellen

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Funktionale Beziehungen erkennen, beschreiben und darstellen”

  35. KMK.MS.1.1 (our numbering) · Teaching content · checked against the act

    understand and use structures in arithmetic and geometric representations (e.g. in number representations, visual aids)

    our translation · original wording (DE): verstehen und nutzen Strukturen in arithmetischen und geometrischen Darstellungen (z. B. in Zahldarstellungen, Anschauungsmitteln)

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Gesetzmäßigkeiten erkennen, beschreiben und darstellen”, Spiegelstrich 1

    Number range: struktury w zapisie liczb i w ukladach geometrycznych

    Continuing number sequences and rhythms (we teach in grade 1-4)

  36. KMK.MS.2.1 (our numbering) · Teaching content · checked against the act

    recognize and describe functional relationships in real-world situations (e.g. quantity - price)

    our translation · original wording (DE): erkennen und beschreiben funktionale Beziehungen in Sachsituationen (z. B. Menge - Preis)

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Funktionale Beziehungen erkennen, beschreiben und darstellen”, Spiegelstrich 1

    Number range: zaleznosc ilosc - cena

    Calculating with money in everyday life (we teach in grade 2-4) · Multiplication tables up to 100 (we teach in grade 2-4)

  37. KMK.MS.1.2 (our numbering) · Teaching content · checked against the act

    recognise and describe structures in geometric and arithmetic patterns (e.g. number sequences, pentominoes) and use these in mathematical contexts (e.g. encryptions)

    our translation · original wording (DE): erkennen und beschreiben Strukturen in geometrischen und arithmetischen Mustern (z. B. Zahlenfolgen, Pentominos) und nutzen diese in mathematischen Kontexten (z. B. Verschlüsselungen)

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Gesetzmäßigkeiten erkennen, beschreiben und darstellen”, Spiegelstrich 2

    Number range: ciagi liczbowe i wzory geometryczne

    Counting forwards and backwards in steps (we teach in grade 1-4) · Continuing number sequences and rhythms (we teach in grade 1-4)

  38. KMK.MS.2.2 (our numbering) · Teaching content · checked against the act

    recognize, describe and represent functional relationships in tables

    our translation · original wording (DE): erkennen, beschreiben und stellen funktionale Beziehungen in Tabellen dar

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Funktionale Beziehungen erkennen, beschreiben und darstellen”, Spiegelstrich 2

    Number range: tabela zaleznosci z jedna regula

  39. KMK.MS.1.3 (our numbering) · Teaching content · checked against the act

    recognize, represent equality of mathematical expressions and use this (e.g. expressing numbers through different expressions, comparing expressions)

    our translation · original wording (DE): erkennen, stellen Gleichheit von mathematischen Ausdrücken dar und nutzen diese (z. B. Zahlen durch verschiedene Terme ausdrücken, Terme vergleichen)

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Gesetzmäßigkeiten erkennen, beschreiben und darstellen”, Spiegelstrich 3

    Number range: rownosc wyrazen, okienko w rownaniu

    Using calculation strategies and comparing sums (we teach in grade 1-4)

  40. KMK.MS.2.3 (our numbering) · Teaching content · checked against the act

    solve word problems involving functional relationships (e.g. proportionality)

    our translation · original wording (DE): lösen Sachaufgaben zu funktionalen Zusammenhängen (z. B. Proportionalität)

    KMK Bildungsstandards (23.06.2022), Leitidee Muster, Strukturen und funktionaler Zusammenhang, Bereich „Funktionale Beziehungen erkennen, beschreiben und darstellen”, Spiegelstrich 3

    Number range: zadania na proporcjonalnosc prosta

  41. KMK.RF (our numbering) · Teaching content · checked against the act

    Space and shape

    our translation · original wording (DE): Raum und Form

    KMK Bildungsstandards Mathematik Primarbereich (23.06.2022), Leitidee Raum und Form

  42. KMK.RF.1 (our numbering) · Teaching content · checked against the act

    Have spatial visualization ability

    our translation · original wording (DE): Über räumliches Vorstellungsvermögen verfügen

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Über räumliches Vorstellungsvermögen verfügen”

  43. KMK.RF.2 (our numbering) · Teaching content · checked against the act

    Recognize, name and represent geometric figures

    our translation · original wording (DE): Geometrische Figuren erkennen, benennen und darstellen

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Figuren erkennen, benennen und darstellen”

  44. KMK.RF.3 (our numbering) · Teaching content · checked against the act

    Identify, name and represent geometric transformations

    our translation · original wording (DE): Geometrische Abbildungen erkennen, benennen und darstellen

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Abbildungen erkennen, benennen und darstellen”

  45. KMK.RF.1.1 (our numbering) · Teaching content · checked against the act

    orient themselves in space (e.g. paths, plans, views)

    our translation · original wording (DE): orientieren sich im Raum (z. B. Wege, Pläne, Ansichten)

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Über räumliches Vorstellungsvermögen verfügen”, Spiegelstrich 1

    Number range: plan, widok, droga

  46. KMK.RF.2.1 (our numbering) · Teaching content · checked against the act

    classify solids and plane figures according to properties, assign technical terms and describe relationships between geometric figures (e.g. square and rectangle)

    our translation · original wording (DE): klassifizieren Körper und ebene Figuren nach Eigenschaften, ordnen Fachbegriffe zu und beschreiben Beziehungen zwischen geometrischen Figuren (z. B. Quadrat und Rechteck)

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Figuren erkennen, benennen und darstellen”, Spiegelstrich 1

    Number range: figury plaskie i bryly, zaleznosci miedzy nimi

    Recognizing and naming plane figures (we teach in grade 1-4) · Identifying and naming geometric solids (we teach in grade 1-4)

  47. KMK.RF.3.1 (our numbering) · Teaching content · checked against the act

    transform plane figures geometrically (reduce, enlarge, and reflect)

    our translation · original wording (DE): bilden ebene Figuren geometrisch ab (verkleinern, vergrößern und spiegeln)

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Abbildungen erkennen, benennen und darstellen”, Spiegelstrich 1

    Number range: powiekszanie, pomniejszanie i odbicie na sieci kwadratowej

  48. KMK.RF.1.2 (our numbering) · Teaching content · checked against the act

    recognize, describe and use spatial relationships (e.g., relate two- and three-dimensional representations to one another, such as building plan and structure, solid and net)

    our translation · original wording (DE): erkennen, beschreiben und nutzen räumliche Beziehungen (z. B. zwei- und dreidimensionale Darstellungen zueinander in Beziehung setzen, wie Bauplan und Bauwerk, Körper und Netz)

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Über räumliches Vorstellungsvermögen verfügen”, Spiegelstrich 2

    Number range: bryla i jej siatka, plan budowli i budowla

  49. KMK.RF.2.2 (our numbering) · Teaching content · checked against the act

    recognise solids and plane figures in the environment

    our translation · original wording (DE): erkennen Körper und ebene Figuren in der Umwelt wieder

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Figuren erkennen, benennen und darstellen”, Spiegelstrich 2

    Number range: rozpoznawanie ksztaltow w otoczeniu

    Recognizing and naming plane figures (we teach in grade 1-4) · Identifying and naming geometric solids (we teach in grade 1-4)

  50. KMK.RF.3.2 (our numbering) · Teaching content · checked against the act

    recognize and describe properties of line symmetry and relate these to line reflection

    our translation · original wording (DE): erkennen und beschreiben Eigenschaften der Achsensymmetrie und setzen diese mit der Achsenspiegelung in Beziehung

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Abbildungen erkennen, benennen und darstellen”, Spiegelstrich 2

    Number range: os symetrii figury, odbicie wzgledem osi

  51. KMK.RF.1.3 (our numbering) · Teaching content · checked against the act

    operate (e.g., decompose, fold, rotate, reflect, build) mentally with geometric objects

    our translation · original wording (DE): operieren (z. B. zerlegen, falten, drehen, spiegeln, bauen) mit geometrischen Objekten gedanklich

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Über räumliches Vorstellungsvermögen verfügen”, Spiegelstrich 3

    Number range: skladanie, obracanie, odbijanie w wyobrazni

  52. KMK.RF.2.3 (our numbering) · Teaching content · checked against the act

    make models of solids (solid models, surface models, edge models) and plane figures and investigate them (e.g. build, lay out, take apart, put together, cut out, fold), also using digital tools

    our translation · original wording (DE): stellen Modelle von Körpern (Vollmodelle, Flächenmodelle, Kantenmodelle) und ebenen Figuren her und untersuchen (z. B. bauen, legen, zerlegen, zusammenfügen, ausschneiden, falten) diese, auch unter Nutzung digitaler Werkzeuge

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Figuren erkennen, benennen und darstellen”, Spiegelstrich 3

    Number range: modele bryl: pelne, scienne, krawedziowe

  53. KMK.RF.3.3 (our numbering) · Teaching content · checked against the act

    recognize and describe geometric transformations in the environment or in patterns (e.g. in frieze patterns)

    our translation · original wording (DE): erkennen und beschreiben geometrische Abbildungen in der Umwelt oder in Mustern (z. B. in Bandornamenten)

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Abbildungen erkennen, benennen und darstellen”, Spiegelstrich 3

    Number range: szlaki i ornamenty

    Continuing number sequences and rhythms (we teach in grade 1-4)

  54. KMK.RF.2.4 (our numbering) · Teaching content · checked against the act

    investigate and compare plane figures and solids (plane figures also with regard to perimeter and area, solids also with regard to volume)

    our translation · original wording (DE): untersuchen und vergleichen ebene Figuren und Körper (ebene Figuren auch hinsichtlich des Umfangs und Flächeninhalts, Körper auch hinsichtlich des Rauminhalts)

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Figuren erkennen, benennen und darstellen”, Spiegelstrich 4

    Number range: obwod z dlugosci bokow; pole przez wykladanie

  55. KMK.RF.2.5 (our numbering) · Teaching content · checked against the act

    make drawings of geometric figures with and without aids, also using digital tools

    our translation · original wording (DE): fertigen Zeichnungen geometrischer Figuren mit und ohne Hilfsmittel an, auch unter Nutzung digitaler Werkzeuge

    KMK Bildungsstandards (23.06.2022), Leitidee Raum und Form, Bereich „Geometrische Figuren erkennen, benennen und darstellen”, Spiegelstrich 5

    Number range: rysunek z linijka i na sieci kwadratowej

    Drawing Line Segments and Shapes with a Ruler (we teach in grade 1-4)

  56. KMK.DZ (our numbering) · Teaching content · checked against the act

    Data and chance

    our translation · original wording (DE): Daten und Zufall

    KMK Bildungsstandards Mathematik Primarbereich (23.06.2022), Leitidee Daten und Zufall

  57. KMK.DZ.1 (our numbering) · Teaching content · checked against the act

    Handle data

    our translation · original wording (DE): Mit Daten umgehen

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Mit Daten umgehen”

  58. KMK.DZ.2 (our numbering) · Teaching content · checked against the act

    Investigate events in random experiments

    our translation · original wording (DE): Ereignisse bei Zufallsexperimenten untersuchen

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Ereignisse bei Zufallsexperimenten untersuchen”

  59. KMK.DZ.1.1 (our numbering) · Teaching content · checked against the act

    plan simple surveys and collect and structure data during observations, investigations, and simple experiments

    our translation · original wording (DE): planen einfache Befragungen und erfassen und strukturieren bei Beobachtungen, Untersuchungen und einfachen Experimenten Daten

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Mit Daten umgehen”, Spiegelstrich 1

    Number range: proste badanie i lista kreskowa

  60. KMK.DZ.2.1 (our numbering) · Teaching content · checked against the act

    know and use basic terms to describe random events (certain, possible, impossible)

    our translation · original wording (DE): kennen und nutzen Grundbegriffe zur Beschreibung von Zufallsereignissen (sicher, möglich, unmöglich)

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Ereignisse bei Zufallsexperimenten untersuchen”, Spiegelstrich 1

    Number range: pewne, mozliwe, niemozliwe

    Chance: certain, possible, or impossible (we teach in grade 2-4)

  61. KMK.DZ.1.2 (our numbering) · Teaching content · checked against the act

    represent data in tables, charts and diagrams, also using digital tools, and extract information from tables, charts and diagrams

    our translation · original wording (DE): stellen Daten in Tabellen, Schaubildern und Diagrammen dar, auch unter Nutzung digitaler Werkzeuge, und entnehmen Informationen aus Tabellen, Schaubildern und Diagrammen

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Mit Daten umgehen”, Spiegelstrich 2

    Number range: tabela, diagram slupkowy

    Representing data in tables and charts (we teach in grade 2-4)

  62. KMK.DZ.2.2 (our numbering) · Teaching content · checked against the act

    estimate chances for the occurrence of events in everyday phenomena or simple random experiments and compare (e.g., "is more likely than", "has greater chances than") these based on data

    our translation · original wording (DE): schätzen Chancen für das Eintreten von Ereignissen bei alltäglichen Phänomenen oder einfachen Zufallsexperimenten ein und vergleichen (z. B. "ist wahrscheinlicher als", „hat größere Chancen als“) diese datenbasiert

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Ereignisse bei Zufallsexperimenten untersuchen”, Spiegelstrich 2

    Number range: porownanie szans dwoch zdarzen

  63. KMK.DZ.1.3 (our numbering) · Teaching content · checked against the act

    interpret representations of data and reflect on them critically

    our translation · original wording (DE): interpretieren Darstellungen von Daten und reflektieren diese kritisch

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Mit Daten umgehen”, Spiegelstrich 3

    Number range: wniosek z zestawienia: najwiecej, najmniej, o ile wiecej

    Reading and comparing data from tables (we teach in grade 2-4)

  64. KMK.DZ.1.4 (our numbering) · Teaching content · checked against the act

    solve simple combinatorial problems through a systematic approach (e.g. systematic trial and error) or with the help of heuristic aids (e.g. sketch, tree diagram, table)

    our translation · original wording (DE): lösen einfache kombinatorische Fragestellungen durch systematisches Vorgehen (z. B. systematisches Probieren) oder mit Hilfe von heuristischen Hilfsmitteln (z. B. Skizze, Baumdiagramm, Tabelle)

    KMK Bildungsstandards (23.06.2022), Leitidee Daten und Zufall, Bereich „Mit Daten umgehen”, Spiegelstrich 4

    Number range: systematyczne wypisanie mozliwosci

Skills step by step

Addition up to 100 with regrouping

Children learn to reliably add two-digit numbers up to 100 with regrouping, mentally or using intermediate steps.

Curriculum point KMK.ZO.2.4 (our numbering) understand mental and semi-written calculation strategies for the four basic operations and use them flexibly (our translation)

In 2nd grade, children solve addition problems within 100 where the ones digit crosses the tens boundary. They use mental and informal written calculation strategies by breaking problems down flexibly—such as first bridging to the next ten and then adding the remainder. Column addition is not yet introduced at this grade level.

Children often forget the newly formed ten when calculating and only add the ones to the original tens place (for example, 38 + 7 = 35 instead of 45). Skipping the next ten with two-digit addends also easily leads to calculation errors if intermediate steps are not clearly tracked.

Typical tasks challenge children in various ways:

  • Basic exercises such as Addition within 100 with regrouping or Making ten: how much is missing,
  • Comparative formats such as Balancing both sides or Which sum is greater,
  • Word problems, including Word problem — addition (change) and Word problem with extraneous information,
  • Spotting errors and checking work, such as Check the answer and find the mistake or True or false.
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)

Multiplication tables up to 100

Children learn to master basic multiplication facts within the number range up to 100 by heart, to find calculation errors, and to reliably determine missing factors.

Curriculum point KMK.MS.2.1 (our numbering) recognize and describe functional relationships in real-world situations (e.g. quantity - price) (our translation)
Curriculum point KMK.ZO.2.1 (our numbering) have an understanding of operations for the four basic arithmetic operations and recognize and use the relationships between the operations (our translation)
Curriculum point KMK.ZO.2.2 (our numbering) master the basic facts of mental arithmetic (among others, number bonds, addition facts, multiplication tables) from memory and reliably derive their inverses (our translation)

In 2nd grade, children build an initial understanding of multiplication and work through the multiplication tables up to 100. They learn to recall core facts from memory and understand what multiplication means: a number is repeatedly added together or describes practical relationships, such as the connection between quantity and price.

Children often find it difficult to solve fill-in-the-blank problems—such as when the goal is not to find the product, but rather the missing factor (e.g., _ · 4 = 24). Another typical mistake occurs when multiplication and addition are confused, or when a number is skipped while counting up step by step in a sequence.

Typical exercise formats reinforce calculations through varied practice:

  • Solving classic multiplication problems up to 100 and comparing products with each other (which result is greater and by how much).
  • Working on fill-in-the-blank problems where the missing factor must be inserted or where it must be determined how many times a number was taken.
  • Independently checking given calculations for correctness, spotting calculation errors, or solving problems containing an unnecessary number.
Create a worksheet for this skill

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

Subtraction problems within 100

Children learn to reliably subtract two-digit numbers within the number range up to 100 mentally or using informal written methods.

Curriculum point KMK.ZO.2.4 (our numbering) understand mental and semi-written calculation strategies for the four basic operations and use them flexibly (our translation)

In 2nd grade, children solve subtraction problems within the number range up to 100, including regrouping across tens. To do this, they use flexible mental and semi-written calculation strategies, such as subtracting in steps. Column subtraction is not yet taught at this grade level.

Common errors occur when crossing the ten: in a problem like 52 minus 7, children often subtract the 2 first, but then forget to subtract the remaining amount from 50. In word problems, it can also be difficult to determine the original starting value when having to think backwards.

Typical exercises challenge understanding in different ways:

  • Solving two consecutive subtractions or determining the starting value (How many there were at the beginning).
  • Working through word problems where conditions change (Left and arrived) or where an unnecessary number must deliberately be ignored.
  • Checking given calculations and specifically identifying calculation errors.
Create a worksheet for this skill

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)

Calculating with money in everyday life

Children learn to determine amounts of money, calculate purchases, and find the correct change within the number range up to 100.

Curriculum point KMK.GM.3.3 (our numbering) solve word problems with measurements (our translation)
Curriculum point KMK.MS.2.1 (our numbering) recognize and describe functional relationships in real-world situations (e.g. quantity - price) (our translation)

In 2nd grade, children calculate with amounts of money in the number range up to 100. They apply addition and subtraction to typical everyday situations: they determine how much money is still needed for a desired item, check whether their savings are sufficient, and calculate simple functional relationships such as the total price for multiple items of an article.

Typical difficulties often arise when determining change or when crossing tens with different coin values. Children then count individual coins or mix up cent and euro amounts instead of counting up step by step to the amount paid or properly subtracting the purchase price.

In the exercises, children work on realistic word problems related to shopping:

  • Paying with which coins: Laying out exact amounts of money with matching coins.
  • Is the money enough: Comparing their own budget with the prices.
  • Shopping and change: Calculating the change to receive after a purchase.
  • How much do multiple items cost: Determining the price for several identical items.
Create a worksheet for this skill

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)

Addition within 100

Children learn to reliably add two or three numbers within the number range up to 100 and to represent calculation strategies on the number line.

Curriculum point KMK.ZO.2.1 (our numbering) have an understanding of operations for the four basic arithmetic operations and recognize and use the relationships between the operations (our translation)

In 2nd grade, children solve addition problems within the number range up to 100. They consolidate their understanding of addition by not only adding two numbers together, but also skillfully adding three addends at once or entering results into tables.

Common mistakes occur when bridging the tens: children often forget the newly formed ten or miscount during larger single steps. Confusing tens and ones also quickly leads to incorrect results when adding step by step.

Typical tasks use different representations to support calculating:

  • Addition on the number line: The calculation steps are visualized as jumps.
  • Three addends at once: Children practice advantageous calculation strategies up to 100.
  • Result tables and comparison tasks: Sums are systematically calculated in tables, or incorrect calculations with differing results are tracked down.

Create a worksheet for this skill

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

Children learn to understand short, everyday word problems within the number range up to 100 and to match them with the appropriate addition or subtraction equation.

Curriculum point KMK.GM.3.3 (our numbering) solve word problems with measurements (our translation)
Curriculum point KMK.ZO.3.1 (our numbering) apply arithmetic operations in word problems and describe the relationships between the real-world context and the individual solution steps (our translation)

In 2nd grade, children understand short everyday situations and translate them into a mathematical equation. Within the number range up to 100, they determine which arithmetic operation fits the described situation, perform the addition or subtraction, and relate the result back to the original question.

Children often jump to the given numbers too quickly and start calculating without carefully examining the sequence of events. Typically, in "working backward" questions ("How many were there at the beginning?"), they mistakenly subtract instead of adding because a cue word such as take away or lose is hastily associated with minus.

Typical task formats support precise understanding through targeted questions:

  • Which equation solves the problem: Children choose the appropriate addition or subtraction equation for a story from several given options.
  • How many are left: A classic word problem where a remaining quantity is calculated after a deduction.
  • How many were there at the beginning: A word problem story where the original starting quantity must be determined using an inverse operation.
Create a worksheet for this skill

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

Using calculation strategies and comparing sums

Children learn to use arithmetic properties in the number range up to 100 to cleverly commute and associate terms in sums, and to identify equivalences.

Curriculum point KMK.MS.1.3 (our numbering) recognize, represent equality of mathematical expressions and use this (e.g. expressing numbers through different expressions, comparing expressions) (our translation)
Curriculum point KMK.ZO.2.6 (our numbering) recognize, explain and use laws of arithmetic (e.g. commutative law: turnaround facts) (our translation)

In 2nd grade, children use properties of addition within the number range up to 100 to make calculating easier. They realize that the result of an addition problem does not change when numbers are swapped or grouped cleverly. Instead of rigidly adding three or more numbers from left to right, they specifically look for pairs of numbers that make, for example, a multiple of ten.

A typical mistake occurs when children blindly apply these rules to other operations. Some thoughtlessly swap numbers in subtraction as well, or completely overlook a number when adding multiple terms in a new order. Many also find it difficult at first to recognize that two arithmetic expressions written differently can have the same value without calculating both completely.

In the exercises, children encounter typical task formats:

  • Choose the convenient order: In problems with multiple terms, children rearrange the numbers so that intermediate steps are easier to do mentally.
  • Compare the two sums: Children compare two expressions directly with each other and use the arithmetic laws to decide whether both sides are equal.
Create a worksheet for this skill

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

Comparing and ordering quantities

Children learn to compare lengths and weights directly with each other, to order them by size, and to determine length differences in the number range up to 100.

Curriculum point KMK.GM.1.1 (our numbering) compare and order quantities (monetary values, lengths, time spans, masses, areas and volumes) (our translation)

In 2nd grade, children compare properties such as lengths or masses. In doing so, they first compare directly without any calculation: they determine which object is lighter, heavier, or longer. In addition, they determine differences between lengths mathematically within the number range up to 100 using subtraction.

A typical error when comparing occurs when children are misled solely by appearance—such as assuming that a larger object must automatically be heavier than a smaller one. When measuring differences in length, they also often forget to align both objects to the same baseline, resulting in reading incorrect differences.

In typical tasks, children arrange several depicted objects in order, such as in the template Order from lightest. In tasks such as How much longer is the ribbon, they compare two strips and calculate the exact difference in length.

Create a worksheet for this skill

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

Reading and comparing data from tables

Children learn to read simple tables within the number range up to 100 and to reliably determine differences between values.

Curriculum point KMK.DZ.1.3 (our numbering) interpret representations of data and reflect on them critically (our translation)

In 2nd grade, children record and analyze data from simple tables. They identify at a glance which category has the most or the least, and calculate within the number range up to 100 how much greater one value is than another.

Children often still struggle with specific questions about the difference: when asked "How many more?", they frequently give only the larger total value instead of finding the difference through subtraction. Sometimes children also lose their place when reading the rows and columns in the table.

Typical exercise formats focus specifically on these interpretations: in Which category has the most, children find the top value from an overview, while formats like How many more according to the table require a precise comparison of two entries using the calculated difference.

Create a worksheet for this skill

Task types: Bar chart: how many more · How many more, from the table · Which category has the most · Difference between two rows: choose the correct answer · Difference between two rows: true or false · How many groups are above the given number · The gap between the largest and the smallest

Recognizing and naming plane figures

Children learn to name flat geometric shapes such as triangles, squares, or rectangles and recognize them in pictures.

Curriculum point KMK.RF.2.1 (our numbering) classify solids and plane figures according to properties, assign technical terms and describe relationships between geometric figures (e.g. square and rectangle) (our translation)
Curriculum point KMK.RF.2.2 (our numbering) recognise solids and plane figures in the environment (our translation)

In 2nd grade, children learn to reliably distinguish basic plane shapes and name them using the correct technical terms. They look at shapes such as triangles or quadrilaterals and identify their properties to recognize which figure it is.

Typical difficulties often arise when a shape is rotated or stretched: a square standing on its corner is then mistakenly no longer recognized as such or confused with another shape. Finding specific shapes in nested or complex pictures also often poses a challenge for children, as they can easily overlook individual lines or count them twice.

In the exercises, children encounter simple task formats:

  • What is the name of the drawn shape: The correct technical term must be matched to a depicted shape.
  • How many triangles are in the picture: The number of triangles contained within a composite drawing must be determined.

Create a worksheet for this skill

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?

Addition up to 20 without regrouping

Children learn to reliably solve addition problems mentally within the number range up to 20, as long as the tens boundary is not crossed.

Curriculum point KMK.ZO.2.2 (our numbering) master the basic facts of mental arithmetic (among others, number bonds, addition facts, multiplication tables) from memory and reliably derive their inverses (our translation)

At the beginning of 2nd grade, children consolidate basic addition facts within the number range up to 20. When adding without crossing the ten, they solve problems like 12 + 5 or 13 + 4 by relying on known basic facts up to 10. The result always remains in the same decade, so no regrouping into the next ten is required yet.

A typical stumbling block is confusing tens and ones. Some children accidentally add the second number to the tens instead of the ones, mistakenly arriving at 53 for 13 + 4, or they laboriously count up one by one on their fingers instead of using number bonds up to 10 to their advantage.

Typical practice formats use two approaches for this:

  • Classic math problems for addition within 20, where pure numbers are added (e.g., 11 + 6 = _).
  • Missing addend problems such as how many to make ten, which reinforce confident number partitioning and lay the foundation for later calculating across the ten.
Create a worksheet for this skill

Task types: Addition within 20 · Count the two frames · How many are missing to make ten · Correct the mistake in adding to 20 · Adding within 20: choose the correct answer · Adding within 20: three numbers · Adding within 20: true or false

Counting forwards and backwards in steps

Children learn to recognize regular intervals in number sequences up to 100 and to continue the sequences forwards or backwards accordingly.

Curriculum point KMK.MS.1.2 (our numbering) recognise and describe structures in geometric and arithmetic patterns (e.g. number sequences, pentominoes) and use these in mathematical contexts (e.g. encryptions) (our translation)
Curriculum point KMK.ZO.1.3 (our numbering) orient themselves in the number range up to 1 000 000 (e.g. order numbers by size, determine neighbouring numbers) (our translation)

In 2nd grade, children identify arithmetic patterns and count forwards and backwards in even steps. Within the number range up to 100, they use fixed step sizes—such as steps of two, five, or ten—to reliably continue number sequences. This strengthens their orientation within the hundred chart and simultaneously prepares them for multiplication tables.

Typical difficulties occur primarily when counting backwards or crossing tens boundaries. Children often fail to maintain the step size consistently and inadvertently switch to simple counting in steps of one, especially when the sequence does not start at a familiar round number.

Typical exercises are titled Continue counting in the same step. Children are given number sequences such as 24, 26, 28 or 65, 60, 55, and must independently determine the step size and fill in the missing numbers accordingly.

Create a worksheet for this skill

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

Reading the time correctly

In Grade 2, children learn to read the time on analog clocks and reliably use them as a measuring tool for time intervals in everyday life.

Curriculum point KMK.GM.2.2 (our numbering) measure lengths, time spans, masses and capacities appropriately using suitable units and different measuring instruments (our translation)

In 2nd grade, children learn how to properly use a clock as a measuring tool for time intervals. The main focus is on telling the time on an analog clock face with hour and minute hands. In doing so, children connect the hand positions with the corresponding times within the number range up to 100.

A typical stumbling block is confusing the hour hand and the minute hand. Children also often find it difficult to read the exact hour when the minute hand is just before the next full hour: for example, if the clock shows 10:50, the hour hand is already close to the 11, leading many children to mistakenly read it as 11:50.

Typical exercises from the topic area Telling the time show analog clock faces for which children write down the correct time in numbers or words. Conversely, given a specific time, children draw in the missing hands correctly on the clock face.

Create a worksheet for this skill

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 the inverse operation

Children learn to independently check addition problems up to 100 using the corresponding subtraction problem.

Curriculum point KMK.ZO.2.1 (our numbering) have an understanding of operations for the four basic arithmetic operations and recognize and use the relationships between the operations (our translation)
Curriculum point KMK.ZO.2.8 (our numbering) check solutions through suitable procedures (e.g. estimation, inverse operation) (our translation)

In 2nd grade, children consolidate their understanding of the number range up to 100 and specifically use the close connection between addition and subtraction. They learn to independently check a completed addition by using the result as the starting point for the corresponding inverse operation (subtraction).

A typical stumbling block lies in the structure of the inverse operation: children often mistakenly subtract one number from the other instead of placing the calculated sum at the beginning. If they accidentally calculate 34 − 28 instead of checking 34 + 28 = 62, they do not notice their own calculation errors because the total result is not being checked at all.

Practical exercises on the topic of checking addition using subtraction usually present an addition problem, for which the child must directly write down and calculate the corresponding subtraction problem. This allows children to see immediately whether they arrive back at the first initial number and whether their calculation is correct.

Create a worksheet for this skill

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

Chance: certain, possible, or impossible

Children learn to assess whether an event is certain, possible, or impossible, and use these terms appropriately.

Curriculum point KMK.DZ.2.1 (our numbering) know and use basic terms to describe random events (certain, possible, impossible) (our translation)

In Grade 2, children are introduced to the first basic concepts of probability. They assess simple everyday situations and random experiments, accurately describing their outcomes using the terms certain, possible, or impossible.

Difficulties often arise when distinguishing between possible and certain. Children frequently confuse a highly likely event with an absolutely certain one, or classify something as impossible simply because it happens very rarely or because they wish for a specific outcome.

Typical tasks from the Certain, possible, or impossible template use visual examples such as drawing marbles from a bag or playing dice games: for instance, if there are only red marbles in the bag, it is certain that a red marble will be drawn and impossible to pick a blue marble. The children match the appropriate term to each given statement.

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

Finding calculation errors within the number range up to 100

Children check given calculations within the number range up to 100, detect calculation errors, and correct the wrong result.

Curriculum point KMK.ZO.2.5 (our numbering) describe, compare and evaluate different calculation methods; find, explain and correct calculation errors (our translation)

In 2nd grade, children consolidate their arithmetic skills within the number range up to 100. With this skill, they do not simply calculate from scratch themselves, but specifically check already solved addition and subtraction problems for mistakes. They identify whether a result is correct and correct a wrong result.

Typical mistakes occur especially when crossing tens: children forget the carry, calculate in the wrong direction with the tens, or swap ones and tens. Often, an incorrect result is accepted uncritically because it is not checked step by step.

In the exercises for the template Correct the wrong result, children see completed calculations with an incorrect result. Their task is to spot the mistake, cross out the incorrect result, and write the correct result next to it.

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Task types: Correct subtraction result: choose the answer · Correct subtraction result: true or false · Correct the wrong multiplication · Correct the wrong subtraction result · Fix the mistake in a two-step calculation · By how much someone was wrong

Drawing Line Segments and Shapes with a Ruler

Children learn to use a ruler to draw straight lines on grid paper and use them to neatly construct given shapes such as rectangles.

Curriculum point KMK.RF.2.5 (our numbering) make drawings of geometric figures with and without aids, also using digital tools (our translation)

In 2nd grade, children practice using a ruler with confidence on a square grid structure. They use the grid lines as a guide to measure segments precisely and to neatly draw geometric shapes with given side lengths.

The ruler often slips while drawing a line because the hand does not press the tool firmly enough against the paper. In addition, many children do not place the pencil precisely on the corners of the grid squares, which makes the vertices inaccurate or causes lines to extend too far.

Typical exercises directly prompt children: “Draw a rectangle with the given sides.” On the worksheet, they draw the specified lengths step by step along the grid lines and connect them into a closed figure.

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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

Continuing number sequences and rhythms

Children recognize the underlying rule in a number sequence within the number range up to 100 and continue the pattern independently.

Curriculum point KMK.MS.1.1 (our numbering) understand and use structures in arithmetic and geometric representations (e.g. in number representations, visual aids) (our translation)
Curriculum point KMK.MS.1.2 (our numbering) recognise and describe structures in geometric and arithmetic patterns (e.g. number sequences, pentominoes) and use these in mathematical contexts (e.g. encryptions) (our translation)
Curriculum point KMK.RF.3.3 (our numbering) recognize and describe geometric transformations in the environment or in patterns (e.g. in frieze patterns) (our translation)

In 2nd grade, children explore regularities in arithmetic patterns. They identify constant differences between consecutive numbers within the range up to 100 and use this rule to correctly continue the sequence. Discovering these structures helps them better understand relationships between numbers and basic calculation steps.

Typical mistakes usually occur when children only look at the step between the first two numbers instead of checking the entire sequence for its pattern. With alternating patterns or larger steps, they also sometimes miscount by one, especially when crossing a ten.

Practical tasks from the template Continue the number rhythm show, for example, a given sequence such as 24, 28, 32, .... The child determines the respective difference and fills in the next appropriate numbers in the sequence.

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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

Representing data in tables and charts

Children learn to read and represent data in simple tables and bar charts, and to determine the total within the number range up to 100.

Curriculum point KMK.DZ.1.2 (our numbering) represent data in tables, charts and diagrams, also using digital tools, and extract information from tables, charts and diagrams (our translation)

In 2nd grade, children collect data from their everyday lives and record it clearly in tables or simple bar charts. In doing so, they learn to use rows and columns systematically and to reliably retrieve or add up quantities within the number range up to 100.

Children often lose their place when reading across a row or confuse columns with one another. Accurately counting the units along the axes of a bar chart also often requires effort, leading to values being read as one too high or one too low.

Typical tasks such as “How many in total in the table” ask children to read several given subsets from a table and calculate the total number using addition.

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Task types: How many altogether in the table · Pictogram: one picture stands for several · The missing row when the total is known · Total from a table: choose the correct answer · Total from a table: true or false

Identifying and naming geometric solids

Children learn to distinguish geometric solids such as cubes or spheres based on their characteristics and to name them using the correct technical terms.

Curriculum point KMK.RF.2.1 (our numbering) classify solids and plane figures according to properties, assign technical terms and describe relationships between geometric figures (e.g. square and rectangle) (our translation)
Curriculum point KMK.RF.2.2 (our numbering) recognise solids and plane figures in the environment (our translation)

In 2nd grade, children learn about basic geometric solids and distinguish them based on their properties. They explore shapes such as cubes, rectangular prisms, or spheres, match them with the correct technical terms, and discover these shapes in their everyday environment.

Children often confuse three-dimensional solids with two-dimensional shapes. For example, a cube is often mistakenly called a square, or a sphere is called a circle. The difficulty lies in distinguishing the spatial depth and the boundary faces of a solid from a flat shape.

Typical task formats like What is the name of this solid? show an illustration of a geometric solid that the child must identify precisely. Often, children match given terms to the correct drawing or connect everyday objects with the corresponding geometric shape.

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Task types: What is this solid called · Correct the name of the solid · Find an object shaped like the solid · Which solid is it? Choose · Which solid is it? 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

Multiplication tables up to 100

Subtraction problems within 100

Calculating with money in everyday life

Addition within 100

Solving simple word problems

Using calculation strategies and comparing sums

Comparing and ordering quantities

Reading and comparing data from tables

Recognizing and naming plane figures

Addition up to 20 without regrouping

Counting forwards and backwards in steps

Reading the time correctly

Checking results using the inverse operation

Chance: certain, possible, or impossible

Finding calculation errors within the number range up to 100

Drawing Line Segments and Shapes with a Ruler

Continuing number sequences and rhythms

Representing data in tables and charts

Identifying and naming geometric solids

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