Building Rectangles to Compare Ratios and Rates
Objective
Students will analyze ratios and rates by constructing and comparing rectangles with different dimensions
Materials
- Grid paper
- Colored pencils
- Rulers
- Chart paper
- Calculators
Hook
Partners receive two mystery ratio cards and must quickly sketch what they think equal rectangles for ratios 2:3 and 4:6 would look like. After 3 minutes, groups compare their sketches to see if anyone discovered these ratios create the same rectangle shape.
Main Activity
Working in pairs, students build rectangles on grid paper using given width-to-length ratios like 3:4, 6:8, and 9:12. Each pair constructs at least six different rectangles, then calculates the actual measurements and rates. Groups rotate around the classroom to examine other teams' rectangle collections, recording observations about which rectangles have the same shape despite different sizes. Partners collaborate to sort all rectangles into families that share equivalent ratios, then create a visual display showing how ratios and rates connect to geometric relationships.
Discussion Questions
- How did you determine which rectangles belonged in the same ratio family?
- What patterns did you notice when comparing rectangles with equivalent ratios?
- How does doubling both numbers in a ratio affect the rectangle you build?
- When might architects or designers need to use equivalent ratios in real construction projects?
- What strategies helped your team identify rates that produce identical shapes?
Exit Ticket
Draw two rectangles that have equivalent ratios but different dimensions, then explain how you know the ratios are equivalent using both visual and numerical reasoning
Differentiation
Support: Provide pre-drawn rectangle outlines with grid marks so students focus on measuring and comparing rather than construction accuracy
Extension: Challenge pairs to find the simplest form ratio for each rectangle family and create word problems involving rates that would produce rectangles in their collections
