Reflection: Adjustments to Practice Unit Rates and Ratio Tables - Section 2: Practice

In the third video of this section you seem be describing my students’ favorite strategies for solving problems involving proportional relationships: the proportion. The new standards put a high emphasis on students’ ability to understand proportional relationships, not just to memorize the algorithms that will enable them to find missing pieces. Throughout this unit, students will be asked to deeply analyze relationships in real life situations such as making smart shopping decisions, percent interest, taxes, tip, and other consumer math topics. The progression documents on the commoncoretools.me website suggest that we focus more on students’ understanding of equivalent ratios so that they can discover the process of using proportions on their own. These documents define the difference between these two ideas as follows:

Proportional relationships involve collections of pairs of measurements in equivalent ratios. In contrast, a proportion is an equation stating that two ratios are equivalent…¹

And later, when describing the use of ratio tables to make sense of equivalent ratios, explain that:

This perspective allows students to begin to reason about proportions by starting with their knowledge about multiplication tables and by building on this knowledge¹

It makes sense; prioritizing the understanding that there can be many equivalent ratios is much more useful than teaching a rote memory trick which doesn't explore the meaning of the equivalent values themselves. This is also a great example of the shift on greater focus on fewer topics. These are also some reasons why I have stepped away from teaching students how to use a proportion to solve. Some students bring up this strategy on their own. I do review its use with them, but throughout the review, will ask questions like:

• This proportion is made up of two of these.. what are they called? Equivalent ratio
• What is a ratio? A comparison of two units
• What two units are being compared here? Miles and hours, dollars and pounds
• What does this part of the ratio represent? 3 miles traveled in one hour, 4 oranges cost \$3.50

¹https://commoncoretools.files.wordpress.com/2012/02/ccss_progression_rp_67_2011_11_12_corrected.pdf

Focus on Equivalent Ratios over Proportions
Adjustments to Practice: Focus on Equivalent Ratios over Proportions

Unit Rates and Ratio Tables

Unit 5: Ratios and Proportional Relationships
Lesson 7 of 21

Big Idea: students work with partners to find the unit rates and use them to solve ratio word problems

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60 minutes

Yazmin Chavira MTP

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