| Category | Details |
|---|---|
| Module | Variation-co-variation:
|
| Teaching Hours | 3x 1 hour |
| Grade Level/Age Range | 4-6 (9-12 years old) |
| Brief Description | In Module 1, students first explore the number line (Lesson 1). Students walk on the number line to find so-called secret rules (functions). By developing strategies to find these secret rules and by representing their reasoning, students gain understanding about functions. They work with different kinds of relations (additive, multiplicative, single operation, multiple operations). Students then move to the double number line (Lesson 2). Thus, they first engage with physically enacted co-variation on one number line and then with co-variation of quantities on two number lines in a tablet application. They are asked to explore how quantities vary, how the variation of one quantity affects variation in the other quantity, and to identify and express the relation that shows how one quantity corresponds to the other. Students then proceed with exploring function machines (Lesson 3). Function machines can help students understand the input-output aspect of functional thinking and explore relationships between pairs of numbers. Students identify the rule that links the input with the output values, create their own function machines to produce given tables, and examine function composition. Thus, also working on correspondence relations and first steps towards the object view of functions. |
| Design Principles |
|
| Functional Thinking | |
| Learning Goals |
Quantitative reasoning:
- Students experience covarying quantities
- Students discover relationships between numbers based on a ‘secret’ function
- Students identify, generalize and express additive and multiplicative linear relations
Representations of functions:
- Students conceptualize intuitive the idea of functions
- Students identify, generalize and represent additive and multiplicative, linear relations
- Students use functions to represent input-output relationships
- Students represent (verbally, symbolically and graphically) relations between quantities and move between representations (table, graphs, story, numbers)
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