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.
Kate and Christopher notice two patterns in the distance and time values for cars that are going the same speed.
The students continue to suggest and test patterns. They are surprised that some patterns do not work.
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.
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.