Grade 7 maths: directed numbers, equations and functions

Grade 7 extends the number system to negative numbers and introduces systematic work with variables. Equations and functions appear here and stay with you until you leave school.

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.

Write the sign in every step when calculating with negative numbers; most errors happen here. For equations, check the solution by substituting it back. A quick revision of terms before equations pays off.

1. Calculate with negative numbers and percentages

Order directed numbers and keep track of the sign. In percentage and interest problems, distinguish the base value, the percentage value and the rate; an interest rate always refers to one year.

2. Terms, equations and functions

Collect like terms and expand brackets using the distributive law. A linear function describes steady growth: the factor in front of x is the slope, the number after it is the starting value.

3. Geometry and probability

Triangles and quadrilaterals need area formulas and angle sums. Thales’ theorem places the right angle on a semicircle. In random experiments, count favourable outcomes and multiply along the branches of a tree diagram.