Over the course of this unit, students learn to work with ratios using different representations. They began by using discrete diagrams to represent ratios and to identify equivalent ratios. Later, they reasoned more efficiently about ratios using double number lines. Here, they encounter situations in which using a double number line poses challenges and for which a different representation would be helpful. Students learn to organize a set of equivalent ratios in a table, which is a more abstract but also a more flexible tool for solving problems.
Although different representations are encouraged at different points in the unit, allowing students to use any representation that accurately represents a situation and encouraging them to compare the efficiency of different methods will develop their ability to make strategic choices about representations (MP5). Whatever choices they make, they should be encouraged to explain how their method works in solving a problem.
- Comprehend the words “row” and “column” (in written and spoken language) as they are used to describe a table of equivalent ratios.
- Explain (orally and in writing) how to find a missing value in a table of equivalent ratios.
- Interpret a table of equivalent ratios that represents different sized batches of a recipe.
Let’s use tables to represent equivalent ratios.
- If I am looking at a table of values, I know where the rows are and where the columns are.
- When I see a table representing a set of equivalent ratios, I can come up with numbers to make a new row.
- When I see a table representing a set of equivalent ratios, I can explain what the numbers mean.
A table organizes information into horizontal rows and vertical columns. The first row or column usually tells what the numbers represent.
For example, here is a table showing the tail lengths of three different pets. This table has four rows and two columns.
pet tail length (inches) dog 22 cat 12 mouse 2