Expression trees: the structure of terms
An expression drawn as a tree: whatever hangs lowest is calculated first. The order of operations stops being a rule and becomes visible.
Mathematics – grade 7
Unit 1Terms with variables
1.1Setting up and interpreting terms
Describing relationships with variables, evaluating terms with tables and spreadsheets, naming term structures.
1.2Manipulating terms
Laws of exponents, collecting like terms, expanding, factorising and the binomial formulas.
Binomial formulas with squares
The three binomial formulas as areas: a square splits into smaller squares and rectangles.
Unit 2Geometric figures: symmetry and angles
2.1Figures with line and point symmetry
Constructing symmetric figures with compass and ruler, perpendicular bisectors and angle bisectors; ordering quadrilaterals by their symmetries.
Reflections in a line and in a point
In a line or in a point: the shape flips over, and every construction step with the set square stays visible.
Perpendicular bisector and angle bisector
A point equally far from A and B never lies there by chance: the perpendicular bisector appears before you draw it with compasses.
The family of quadrilaterals
Move one corner and the square becomes a kite. When does a quadrilateral get which name?
2.2Angles in figures
Vertical, adjacent, corresponding and alternate angles; proving the angle sum of a triangle and extending it to polygons.
Angles at intersecting lines
Two lines cross and one of them turns. Which angles stay equal? At parallel lines they are called corresponding and alternate angles.
Angle sum in triangles and polygons
Tear off three corners, put them side by side, and you get a straight line: 180°, for every triangle. A quadrilateral gives 360°.
Unit 3Linear equations and further percentages
Setting up equations and solving them by equivalent transformations; more demanding percentage problems.
Linear equations with a balance model
Solve linear equations on a balance: whatever you do to both sides keeps the scale balanced.
Percentage bar
Discounts, VAT, surveys: one single bar holds the base value, the percentage and the part, one above the other.
Unit 4Summary statistics
Comparing median and mean, range and quartiles, drawing and interpreting box plots.
Mean, median and box plots
One outlier pulls the mean away while the median barely moves. Dragging single data points shows which value is how robust.
Unit 5Congruence, special triangles and constructions
Congruence criteria, isosceles and equilateral triangles, theorems and their converses, circumcircle and incircle, Thales’s theorem, constructing tangents.
Congruence and constructing triangles
Construct triangles from three given parts with ruler and compass, step by step as in your exercise book. Sometimes there are no, one or two solutions.
Circumcircle, incircle and special lines in a triangle
Construct the special lines in a triangle. Each set of three always meets in one point, for example at the centre of the circumcircle or the incircle.
Thales’s theorem
Drag a point along the semicircle: the angle there is always a right angle.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): LehrplanPLUS, Gymnasium, Mathematics, grade 7