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Unit: Proportional Reasoning

Students work with an applet that allows them to run races between two cars by entering values for each car’s distance and time. They explore the effect on the cars’ speeds by first working with one quantity and then changing both distance and time. Through a series of diagram-construction activities, they form a ratio, iterate and split ratios, and create a unit ratio. Students move from reasoning additively to forming multiplicative comparisons.

Who are Kate and Christopher?

Lesson 1: Changing One Quantity at a Time

Lesson 2: Changing Two Quantities

Lesson 3: Creating Diagrams to Represent Ratios

Lesson 4: Using Diagrams to Iterate Ratios

Lesson 5: Forming a Unit Ratio

Lesson 6: Solving Proportions Using Multiplication and Division

Lesson 7: Making Multiplicative Comparisons