Ratios and Proportions / Ratio Tables

Understanding

In addition to solving problems by finding the sum/ difference of the columns in a ratio table, they use the notion of unit rate as a strategy to find solutions to problems involving proportions.

What to look for

Be sure that students pay attention to the units or labels in setting up and working the problems. Ratios only make sense in context and the units involved in the context are important in setting up a ratio and interpreting any equivalent ratio.

Sample Assessment

A car can travel 250 miles on 6 gallons of gasoline. How far can it travel on 9 gallons?

Answer: 375 miles.

The Big Idea

The sum of two equivalent ratios is another equivalent ratio. This “additive” property of equivalent ratios can be used to solve both multiplication and division problems by creating appropriate and “easy” equivalent ratios.

What are the students doing?

Students generate a table of equivalent ratios in any order and that are any fraction or whole number multiple of the original ratio.

What is the teacher doing?

Monitor the student work and select student groups to explain each strategy for building their ratio table. Have them show their beginning ratio and describe how they used that strategy to complete a column in their table.