Curriculum (Germany)

Mathematics — Grade 1 of Primary School

1st grade math curriculum: Counting and arithmetic within 20, addition and subtraction without regrouping, comparing numbers, plane shapes, telling time, and introductory word problems. Ready-made exercise templates are available for each topic, from which you can generate a printable PDF worksheet.

Create a worksheet for this curriculum

What does a child learn in 1st grade math?

In 1st grade, children count within the number range up to 20, add and subtract mentally, compare numbers, and recognize the most important plane figures. They learn about the clock and the calendar, and solve their first word problems — usually involving a single calculation step and supported by a drawing.

Important note on educational standards: The KMK educational standards for primary education describe what a child can do at the end of grade 4 — rather than year by year. Therefore, the section on curriculum alignment below lists the competency expectations for grades 1 to 4 along with quotes from the resolution. Which of these we cover in grade 1 is our didactic decision and not part of the official resolution.

Curriculum scope

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
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”
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”
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”
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
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

Addition within the number range up to 100 (we teach in grade 1-4)
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 first word problems (we teach in grade 1-4)
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
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 bridging ten (we teach in grade 1-4)
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
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)
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
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)
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
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 Arithmetic Strategies and Commutative Problems (we teach in grade 1-4)
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)
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
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
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”
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”
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”
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 lengths and weights (we teach in grade 1-4)
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
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
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
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

Learning to tell time (we teach in grade 1-4)
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
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
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
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

Solving first word problems (we teach in grade 1-4)
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
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
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”
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”
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 Patterns (we teach in grade 1-4)
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
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 Patterns (we teach in grade 1-4)
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
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 Arithmetic Strategies and Commutative Problems (we teach in grade 1-4)
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
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
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”
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”
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”
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
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) · Recognizing and naming geometric solids (we teach in grade 1-4)
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
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
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) · Recognizing and naming geometric solids (we teach in grade 1-4)
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
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
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
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 Patterns (we teach in grade 1-4)
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
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)
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
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”
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”
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
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
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
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
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
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 within the number range up to 100

Children learn to solve addition problems up to 100, use calculation strategies on the number line, and add multiple numbers together.

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)

Children develop a fundamental understanding of addition operations and calculate within the number range up to 100. They learn to combine numbers reliably, follow calculation steps, and add multiple summands in a single problem.

Typical mistakes often occur when children lose track of intermediate steps with multiple summands. Also, when reading or jumping along the number line, steps are occasionally miscounted because starting points and distances are confused.

In the exercises, children solve problems such as addition on the number line to visualize the calculation steps. In addition, they add three summands at once, fill in result tables, or compare different calculations in the task Which problem has a different result.

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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 first word problems

Children learn to understand short word problems within the number range up to 20 and to write down the corresponding addition or subtraction problem.

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 1st grade, children translate everyday situations into mathematical calculations. Within the number range up to 20, they extract the important numbers from short texts and decide whether something is being added or taken away. They connect the action with a matching addition or subtraction and thus find the correct result.

Typically, schoolchildren initially just pick out all the mentioned numbers and add them together, without paying attention to the meaning of the story. Words like remain or questions about an initial state are often overlooked, leading to incorrect calculations instead of thinking about which arithmetic operation describes the situation.

Typical task formats show short everyday stories:

Simple word problem — how many remain: A subtraction problem is formed from an initial situation.
Which calculation solves the problem: Children choose the appropriate calculation from given options.
How many were there at the beginning: Working backward, it is determined how many items were present at the start.

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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

Using Arithmetic Strategies and Commutative Problems

Children learn to cleverly simplify calculation methods and to compare sums by rearranging numbers.

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 the first grade, children use basic arithmetic properties when adding within the number range up to 20. They realize that the result of an addition problem does not change when the numbers are swapped (turnaround facts). They also learn to arrange three numbers in a way that makes calculating easier—such as by first adding two numbers that make a ten.

A typical stumbling block is that children stubbornly calculate from left to right instead of first taking a calm look at the numbers. In problems with multiple addends, they often overlook simple partial calculations or calculate in a roundabout way, which leads to avoidable counting errors.

On the worksheets, children practice this using clear, illustrative task formats:

Choose the convenient order: Children rearrange three addends so they can take advantage of a mental math strategy.
Compare the two sums: Children compare two addition expressions and recognize from the numbers whether both sides are equal.

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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

Comparing lengths and weights

Children compare lengths and weights directly with one another and order objects without calculating based on properties such as lighter or longer.

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

In 1st grade, children learn to compare objects based on measurable attributes such as length or weight. This is initially done purely visually and without formal units of measurement or calculation: they determine what is longer or heavier, and order things sequentially.

A typical stumbling block when comparing lengths is that objects are pictured side by side but do not share a common starting point. Children then often look only at the end that seems to extend further, overlooking that both ribbons or pencils must start at the same line. With weight, appearance often tempts them to automatically consider larger objects heavier than smaller ones.

On the worksheets, children encounter concrete visual tasks on these topics:

Order from lightest: Different objects are observed and arranged in the correct order according to their weight.
How much longer is the ribbon: The lengths of two ribbons are directly compared with each other to determine the visible 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

Recognizing and naming plane figures

In 1st grade, children learn to recognize simple two-dimensional shapes such as triangles, name them correctly, and identify them in drawings.

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 1st grade, children get to know basic plane figures. They match drawn shapes with the appropriate terms and identify the figures in their environment as well as in composite pictures.

Children often find it difficult to recognize a shape when it is rotated or shown in an unfamiliar orientation. For example, a square resting on one of its vertices is often mistakenly no longer recognized as a square, or an acute triangle is overlooked because it does not match the familiar standard shape.

On the worksheets, children practice this through specific tasks: In the exercise What is the name of the drawn figure, they match an illustration with the correct name. In How many triangles are in the picture, they count specific shapes in a drawing.

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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?

Addition up to 20 without bridging ten

Children learn to confidently solve addition problems up to 20 mentally, without crossing the ten boundary.

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 first grade, children consolidate their arithmetic skills within the number range up to 20. They solve simple addition problems that do not require crossing the tens boundary. In doing so, they use familiar problems from the range up to 10 and transfer them to the second ten, such as moving from 3 + 4 to 13 + 4. Decomposing the number 10 is also one of the fundamental building blocks in this area of arithmetic.

Children often miscount by exactly one when they laboriously count on their fingers instead of using calculation strategies or number bonds. Another typical mistake occurs when the tens digit and the ones digit get mixed up and children, for example, mistakenly change the tens digit in 12 + 5.

Typical problems on the worksheets directly challenge children to calculate:

Classic calculations such as 11 + 6 or 14 + 3 for addition within the number range up to 20.
Missing-number problems like How much is missing to make ten, which specifically practice number bonds for ten.

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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 identify regular number patterns within the range up to 20 and to count forwards and backwards confidently in fixed steps.

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 1st grade, children explore their first arithmetic patterns within the number range up to 20. They no longer just count in steps of one, but skip numbers according to set rules—such as counting forward in steps of 2 (2, 4, 6 …) or backward. This trains the recognition of structures and forms the foundation for later arithmetic.

Children often lose their rhythm when they unconsciously slip back into the familiar habit of counting by ones. Another typical hurdle is counting backward in steps, as mentally subtracting equal intervals requires more concentration than counting forward.

Typical practice exercises use the format Continue counting in the same step. Children see given number sequences such as 3, 5, 7, … or 12, 10, 8, … and fill in the missing numbers accordingly.

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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

Learning to tell time

In 1st grade, children learn to correctly read and tell the time on an analog clock for the first time.

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 1st grade, children learn about the clock as a tool for measuring intervals of time. As part of early mathematics education, they acquire the ability to understand an analog clock face and read simple times.

A typical stumbling block is confusing the hour hand and the minute hand. Because both hands rotate on the same clock face, many students initially find it difficult to reliably distinguish between the different lengths and functions of the hands at a glance.

Typical exercises in the Telling the Time template usually show an analog clock face with hands. Children determine the time shown and write in the corresponding time as numbers, or match clocks to the appropriate time.

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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

Drawing line segments and shapes with a ruler

In Grade 1, children learn to draw straight lines using a ruler and to draw flat shapes such as rectangles on grid paper.

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

In 1st grade, children learn their first practical use of the ruler as a tool. On a square grid structure (grid paper), they draw precise straight line segments and connect them to form 2D geometric shapes such as rectangles.

Typical difficulties usually arise from fine motor skills: the ruler slips easily when drawing with the pencil if it is not pressed firmly enough onto the paper with the other hand. As a result, edges become crooked or corners do not meet cleanly on the grid lines.

In the exercises, children are usually given the task: Draw a rectangle with the given sides. Based on given lengths or numbers of squares, they draw the sides line by line precisely onto the grid using the ruler.

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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 Patterns

Children recognize the fixed pattern in simple number sequences within the number range up to 20 and continue them independently step by step.

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 1st grade, children discover fixed patterns in number sequences up to 20. For example, they recognize whether numbers always increase or decrease by the same step, and they use this rule to correctly continue the sequence.

Children often simply continue counting the sequence in steps of one as soon as they see a familiar number, instead of carefully checking the difference between the given numbers. With decreasing number sequences, they also easily get confused and inadvertently count forward instead of backward.

Typical exercises use the format Continue the number pattern: A starting sequence is provided, such as 2, 4, 6 or 15, 14, 13. The children find the underlying step size and fill in the missing numbers in the empty boxes.

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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 and naming geometric solids

Children learn to recognize basic geometric solids by their properties, name them correctly, and match them to objects in their environment.

In 1st grade, children learn to distinguish typical geometric solids such as cubes, spheres, or rectangular prisms. They grasp basic features such as round or angular shapes, assign the appropriate terms to the solids, and rediscover these shapes in their everyday environment.

Children often still confuse three-dimensional solids with flat shapes. Thus, a cube is easily referred to as a square or a sphere as a circle, because spatial depth is harder to perceive on flat paper than with real objects.

On the worksheets for the exercise What is the name of this solid, children look at pictures of geometric solids and choose the matching term or write in the correct name.

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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.