Binomial formulas with squares
The three binomial formulas as areas: a square splits into smaller squares and rectangles.
Mathematics – grade 8
The curriculum assigns these units to exactly this grade (Saxony, Gymnasium up to grade 12). The unit numbers are the curriculum’s; optional areas (“Wahlbereiche”) are labelled W1–W3 here.
Unit 1Working with terms and equations
Recognising the structure of terms, transforming terms and linear equations by hand, binomial formulas and an introduction to inequalities.
Unit 2Random experiments
Outcomes, events and relative frequencies, Laplace probability, multi-stage experiments with urn models, tree diagrams and path rules, and the product rule for counting.
Law of large numbers
Toss a coin, a die or a drawing pin a thousand times: the more often you throw, the closer the relative frequency gets to the probability.
Multi-stage experiments and path rules
Draw balls from an urn, with or without replacement. The tree diagram and the path rules show how to calculate probabilities.
Counting principle and tree diagrams
How many outfits or ice cream combinations are there? A tree diagram grows step by step and shows why you multiply the options.
Simulating the birthday problem
How likely is it that two people in a class share a birthday? From just 23 people on, it is more likely than not.
Unit 3Functions and linear systems
The concept and properties of functions, linear functions with slope and zero, linear regression, and solving systems with two unknowns graphically and algebraically.
Function or not? Relations and their graphs
Exactly one y for every x? The arrow diagram, table and graph tell you straight away whether a relation is a function.
Linear function
Change the slope and the y-intercept of a line and read off the slope triangle and the zero.
Function plotter with custom terms
Up to three of your own functions at once, with a table of values, zeros and intersections. The tool for anything that can be a graph.
Solving linear systems graphically
Two equations are two lines. Their point of intersection is the solution, which you can read off and check.
Unit 4Similarity
Enlargement, the main similarity theorem and calculating lengths, areas and volumes of similar figures.
Intercept theorems
How tall is the tree without climbing it? Two rays and a parallel line are enough, because the ratios stay the same.
Similar figures: how do area and volume grow?
Enlarge lengths, areas and solids. Doubling the length makes the area four times and the volume eight times as large.
Unit 5Connections: problem-solving strategies
Working forwards and backwards, making solution plans and presenting solutions.
No separate simulation is planned for this.
Unit W1Programming mathematical algorithms (optional)
Describing algorithms and implementing them with sequence, branching and loops.
No separate simulation is planned for this.
Unit W2Linear optimisation (optional)
Solving optimisation problems graphically with an objective function.
No separate simulation is planned for this.
Unit W3Simulation with random numbers (optional)
The Monte Carlo method: generating random numbers and simulating random experiments on the computer.
Monte Carlo method: estimating π by chance
Random points fall on a square with a circle inside. From the share inside the circle you can estimate π.
Law of large numbers
Toss a coin, a die or a drawing pin a thousand times: the more often you throw, the closer the relative frequency gets to the probability.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): Lehrplan, Gymnasium, Mathematics, grade 8