Success criteria
- I can distinguish “groups of a fraction” from “a fraction of a fraction.”
- I can model numerator-by-numerator and denominator-by-denominator multiplication.
- I can predict when multiplying by a proper fraction makes a positive number smaller.
Explain
4 × 3/8 means four groups of three eighths. 2/3 × 3/5 means two thirds of three fifths. Use an area model for the second and explain why the overlap represents the product.
Independent practice
For 4 × 3/8, enter the numerator of the simplified answer.
The complete simplified result is 3/2.
For 2/3 × 3/5, enter the numerator of the simplified answer.
The product is 2/5. Why is it less than 3/5?
A proper fraction is a scaling factor between zero and one.
Transfer
A model wall is 3/5 m wide. A panel covers 2/3 of that width. Draw the whole, shade the panel, and calculate its width. Label which factor describes the original and which describes the scale.
Delayed check
One week later, solve 5 × 2/7 and 3/4 × 2/5. Predict whether each result is greater or smaller than each factor before calculating.
Evidence and next step
Save the labelled area model at jeremy/portfolio/math/unit-3/fraction-products.md.
- Model, calculation, prediction, and delayed check agree → continue.
- Procedure works but model does not → rebuild one product on grid paper.
- Size prediction fails → compare multiplying by whole numbers versus proper fractions.