# Proportions Lesson 6

### Solving Proportions Using Multiplication and Division

Kate and Christopher make connections between their speed diagrams and the operations of multiplication and division.  This helps give meaning to number sentences used to solve proportion problems.

##### Episode 1: Making Sense

Kate and Christopher use number sentences to determine the number of minutes it should take the red car to travel 200 miles so that it goes at the same speed as a car traveling 10 miles in 4 minutes.

##### Episode 2: Exploring

Christopher and Kate draw a diagram to solve the problem from Episode 1. Then they connect each number and operation in their number sentences to their meaning in the speed diagram.

##### Episode 3: Exploring

The students consider a proportional reasoning problem by first anticipating how many groups of a one car’s journey fit into another car’s journey.

##### Episode 4: Repeating Your Reasoning

Kate and Christopher anticipate how many groups of the blue car’s journey (10 miles in 4 minutes) will fit in the red car’s journey, when the red car travels 65 miles in some unknown number of minutes.  Then they use this information to figure out how long the red car should take so that it goes the same speed as the blue car.