Grade 6 maths: practise fractions, proportion and percentages

Grade 6 connects fractions and decimals with shares and proportional relationships. This path builds on Grade 5 foundations and moves from reliable calculations to practical applications.

Reference: existing NRW curriculum mapping in Germany. Topics and sequence may vary by federal state, school type and classroom. This selection is not a complete curriculum.

If fractions are difficult, revisit simplifying and expanding in Grade 5 first. Check whether word problems describe a proportional relationship. In the German percentages PDF, questions 1–6 practise foundations and 7–10 are extensions.

1. Calculate with fractions and decimals

Use divisibility rules to simplify fractions. Addition needs a common denominator; multiplication does not. Express the same share as both a fraction and a decimal.

2. Apply shares and proportional relationships

Check the relationship between quantities first. For direct proportion, calculate via the value for one unit. Percent means per hundred; a discount amount differs from the new price.

3. Extend numbers, geometry and data

Order integers including negative values. Distinguish a circle’s circumference from its area. Describe data using frequencies and suitable summary measures.