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Lesson 3: Creating Diagrams to Represent Ratios

Kate and Christopher create a diagram to explain why the distance and times values for two cars make them go the same speed. In the process, they form a ratio by joining the distance and time values for one car into a unit or “little trip,” which can be repeated (iterated) or split apart (partitioned) to solve proportional reasoning problems.

Episode 1: Making Sense

Kate and Christopher notice two patterns in the distance and time values for cars that are going the same speed.

Episode 2: Making Sense

The students continue to suggest and test patterns. They are surprised that some patterns do not work.

Episode 3: Exploring

Christopher and Kate create a diagram to explain why a car traveling 20 miles in 8 minutes goes the same speed as a car traveling 10 miles in 4 minutes.

Episode 4: Repeating Your Reasoning

Kate and Christopher draw a diagram to show why traveling 15 miles in 6 minutes is the same speed as going 10 miles in 4 minutes.