Proportional Relationships: From Ratio Tables to Graphs and Equations
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Students will use ratio tables, double number lines, and coordinate graphs to identify, represent, and reason about proportional relationships, connecting unit rate to the constant of proportionality and to the equation y = kx.
Lesson Overview
Students progress from identifying equivalent ratios in tables to writing equations and interpreting unit rates as slopes on graphs, using ratio reasoning throughout. The lesson builds from concrete ratio tables to abstract equation writing and graph interpretation.
Materials
- Vertical whiteboards or large chart paper
- Dry-erase markers (multiple colors)
- Pencils and scratch paper
Scaffolded Task Progression
| Oats (cups) | Flour (cups) |
|---|---|
| 2 | 3 |
| 4 | ? |
| 6 | ? |
| 10 | ? |
| ? | 15 |
What do you notice about the relationship between oats and flour?
Oats: 0 ——— 2 ——— 4 ——— 6 ——— 7 ——— 8
Flour: 0 ——— 3 ——— ? ——— ? ——— ? ——— ?
Explain how you located 7 on the oats line and found the matching flour value.
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