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.
MathematicsGrade 5–10
Terms and equations
Make the structure of terms visible, interpret algebraic manipulation geometrically and solve equations algebraically and graphically.
Link to the German educational standards (KMK)
- L1Number and operations
- L3Structures and functional relationships
- K5Working with mathematical objects
Terms
Grade 5–9
Binomial formulas with squares
The three binomial formulas as areas: a square splits into smaller squares and rectangles.
Equations and systems of equations
Grade 7–10
Linear equations with a balance model
Solve linear equations on a balance: whatever you do to both sides keeps the scale balanced.
Solving linear systems graphically
Two equations are two lines. Their point of intersection is the solution, which you can read off and check.
Solving equations graphically: intersections of graphs
Draw both sides of an equation as graphs. The solutions are where the graphs cross.