In this lesson, students use all representations they have learned in this unit—double number lines, tables, and tape diagrams—to solve ratio problems that involve the sum of the quantities in the ratio. They consider when each tool might be useful and preferable in a given situation and why (MP5). In so doing, they make sense of situations and representations, and are strategic in their choice of solution method (MP1).
- Choose and create diagrams to help solve problems involving ratios and the total amount.
- Compare and contrast (orally) different representations of and solution methods for the same problem.
Let’s compare all our strategies for solving ratio problems.
You will need the Solving More Ratio Problems Info Gap Blackline Master for this activity. Make one copy for every 6 students, and cut them up ahead of time. It is recommended to use a different color paper for each of the four pages, to make them easier to organize. A class set could be reused if you have more than one class.
- I can choose and create diagrams to help think through my solution.
- I can solve all kinds of problems about equivalent ratios.
- I can use diagrams to help someone else understand why my solution makes sense.
A tape diagram is a group of rectangles put together to represent a relationship between quantities.
For example, this tape diagram shows a ratio of 30 gallons of yellow paint to 50 gallons of blue paint.
If each rectangle were labeled 5, instead of 10, then the same picture could represent the equivalent ratio of 15 gallons of yellow paint to 25 gallons of blue paint.