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Curriculum (Germany)

Mathematics — Grade 6

Grade 6 Mathematics: The first topic ready is fractions — fractions as parts of a whole, expanding and simplifying, mixed numbers, comparing fractions, and the basic arithmetic operations with simple fractions. Further 6th grade topics will follow. Ready-to-print worksheet templates are available for each topic.

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What does a child learn in 6th grade mathematics?

In the 6th grade, a fraction turns from a proportion into a number you calculate with: expanding and reducing fractions, finding a common denominator, comparing, adding, and subtracting — at the Gymnasium, multiplying and dividing are also covered, whereas at the Realschule, this usually happens in grade 7.

Important note on educational standards: The KMK educational standards for the first and intermediate secondary school qualifications describe what is achieved by the end of lower secondary education (Sekundarstufe I) — not year by year. The assignment to the 6th grade is our choice based on the core curricula of the federal states (initially North Rhine-Westphalia).

Status of this page: Fraction arithmetic is complete; further topics for the 6th grade will follow.

Curriculum scope

  1. KMKS1.ZO (our numbering) · Teaching content · checked against the act

    Number and Operations

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

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation

  2. KMKS1.ZO.1 (our numbering) · Teaching content · checked against the act

    use meaningful concepts of rational numbers, especially natural numbers, integers, and fractions, according to the need for application

    our translation · original wording (DE): nutzen sinntragende Vorstellungen von rationalen Zahlen, insbesondere von natürlichen, ganzen und gebrochenen Zahlen entsprechend der Verwendungsnotwendigkeit

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 1 (obie kolumny)

  3. KMKS1.ZO.3 (our numbering) · Teaching content · checked against the act

    nutzen sinntragende Vorstellungen von Operationen rationaler Zahlen (z. B. schrittweiser, halbschriftlicher Verfahren)

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 3 (obie kolumny)

  4. KMKS1.ZO.4 (our numbering) · Teaching content · checked against the act

    investigate numbers for their factors, in simple cases without digital mathematics tools

    our translation · original wording (DE): untersuchen Zahlen nach ihren Faktoren, in einfachen Fällen ohne digitale Mathematikwerkzeuge

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 4 (obie kolumny)

  5. KMKS1.ZO.5 (our numbering) · Teaching content · checked against the act

    stellen Zahlen der Situation angemessen dar, z.B. unter anderem in Zehnerpotenzschreibweise

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 5 (obie kolumny)

  6. KMKS1.ZO.6 (our numbering) · Teaching content · checked against the act

    calculate with natural numbers, integers, and rational numbers that occur in daily life, both for verification and mentally, and explain the meaning of the arithmetic operations

    our translation · original wording (DE): rechnen mit natürlichen, ganzen und rationalen Zahlen, die im täglichen Leben vorkommen, sowohl zur Kontrolle als auch im Kopf und erklären die Bedeutung der Rechenoperationen

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 6 (obie kolumny)

  7. KMKS1.ZO.9 (our numbering) · Teaching content · checked against the act

    explain using examples the different concepts of fractions (in particular parts of one or more wholes, relative parts)

    our translation · original wording (DE): erläutern an Beispielen die verschiedenen Vorstellungen zum Bruchbegriff (insbesondere Teile eines oder mehrerer Ganzer, relative Anteile)

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 9 (obie kolumny)

  8. KMKS1.ZO.10 (our numbering) · Teaching content · checked against the act

    use arithmetic laws (e.g. commutative, associative, distributive laws), also for mental calculation strategies

    our translation · original wording (DE): nutzen Rechengesetze (z. B. Kommutativ-, Assoziativ -, Distributivgesetz), auch zum vorteilhaften Rechnen

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 10 (obie kolumny)

  9. KMKS1.ZO.11 (our numbering) · Teaching content · checked against the act

    nutzen Überschlagsrechnungen zur Orientierung und zur Kontrolle

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 11 (obie kolumny)

  10. KMKS1.ZO.12 (our numbering) · Teaching content · checked against the act

    round numbers sensibly according to the context

    our translation · original wording (DE): runden Zahlen dem Sachverhalt entsprechend sinnvoll

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 12 (obie kolumny)

  11. KMKS1.ZO.13 (our numbering) · Teaching content · checked against the act

    check and interpret results, also in real-world situations

    our translation · original wording (DE): prüfen und interpretieren Ergebnisse, auch in Sachsituationen

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 13 (obie kolumny)

  12. KMKS1.ZO.14 (our numbering) · Teaching content · checked against the act

    explain using examples the relationship between arithmetic operations and their inverses and use these relationships

    our translation · original wording (DE): erläutern an Beispielen den Zusammenhang zwischen Rechenoperationen und deren Umkehrungen und nutzen diese Zusammenhänge

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 14 (obie kolumny)

  13. KMKS1.ZO.15 (our numbering) · Teaching content · checked against the act

    use percentage and interest calculations based on mental models (e.g., percentage strips) and appropriately

    our translation · original wording (DE): verwenden Prozent - und Zinsrechnung vorstellungsbasiert (z. B. Prozentstreifen) und sachgerecht

    KMK Bildungsstandards Mathematik ESA/MSA (23.06.2022), Leitidee Zahl und Operation, Spiegelstrich 15 (obie kolumny)

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