Lernziele:

1. Calculate final prices with discounts, markups, taxes, tips, and commissions, clearly labeling each intermediate step.

2. Compute percent increase/decrease and percent error in quality-control or estimation scenarios and interpret the results.

3. Select and convert between fraction, decimal, and percent representations to streamline calculations and justify the choice.

4. Model simple interest (I = Prt) for savings or loans and compare options over different time periods.

5. Build a mini-budget or shopping plan in a calculator or spreadsheet and run what-if percent changes (e.g., an extra 10% coupon).

Module

Lernziele:

1. Combine like terms and factor out common factors to model bundle pricing or rectangular areas.

2. Expand expressions using the distributive property and justify equivalence in context (e.g., a + 0.08a = 1.08a for sales tax).

3. Translate written fee structures (base fee plus per-use) into expressions and simplify to a single equivalent form.

4. Represent expressions with algebra tiles or area models and explain why two forms are equivalent.

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Lernziele:

1. Solve equations of the form px + q = r and p(x + q) = r with rational numbers, check by substitution, and interpret solutions in context.

2. Solve equations with variables on both sides and identify when there is no solution or infinitely many solutions; explain what that means in the scenario.

3. Model constraints with inequalities (e.g., budget caps, minimum requirements), solve, and graph solution sets on a number line.

4. Compare algebraic and arithmetic methods for the same problem and evaluate which is more efficient or transparent.

Module

Lernziele:

1. Compute actual lengths and areas from a map or blueprint scale and determine the scale given real measurements.

2. Redraw a room, floor plan, or map at a new scale and label corresponding parts, specifying the scale factor.

3. Construct triangles from given sides or angles (using ruler/protractor or GeoGebra) and determine whether the conditions yield a unique triangle, many, or none.

4. Use complementary, supplementary, vertical, and adjacent angle relationships to write and solve equations for unknown angles in street-intersection or layout diagrams.

5. Describe and identify 2D cross-sections formed by slicing right prisms and pyramids and connect them to real objects (e.g., loaf of bread, shipping box).

Module

Lernziele:

1. Compute circumference and area of circles and decide which measure answers questions about wheels, tracks, or circular gardens.

2. Decompose composite shapes made of rectangles, triangles, and circle parts to find total area and justify the decomposition.

3. Calculate the volume of cubes and right prisms and solve packing or storage problems with correct units.

4. Build or sketch nets for prisms and pyramids and compute surface area to estimate material needs or paint coverage.

5. Predict how changing a dimension affects volume or surface area in a packaging redesign and verify with calculations.

Module

Lernziele:

1. Plan and critique sampling methods, explain why random sampling reduces bias, and identify invalid sampling procedures.

2. Summarize and compare groups using dot plots, box plots, or histograms and compute mean, median, and MAD to support claims.

3. Approximate probabilities by collecting data from repeated trials and use relative frequency to predict future outcomes.

4. Represent compound events with organized lists, two-way tables, or tree diagrams and compute associated probabilities.

5. Design and run simulations with dice, spinners, or a random-number generator to estimate probabilities for compound events and compare simulated to theoretical results.

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