##
* *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 knowledge**¹

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

Lesson 7 of 21

## Objective: SWBAT use unit rate and ratio tables to find proportionate values.

#### Do Now

*10 min*

Students enter silently according to the Daily Entrance Routine. “Do Now” assignments include problems requiring rational number operations. Students are to enter their answers into clickers with achievements and paycheck points awarded to those who finish on time.

Reviewing the work for these problems is key. Students must be practicing a neat way to show calculations and work for rational number operations. A great way to foster neat work is through neatness competitions. I select the top 5 neatest work shown on students’ papers and display it on the board for teachers to vote on, without knowing the students’ names. The winner earns a free lunch on me with a friend.

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#### Practice

*40 min*

In the first ten minutes of this section I will model three different strategies for solving ratio problems on this sheet and ask students to take notes. Questions are to be asked at the end of each example. For the first example I use equivalent ratios to reduce and identify the unit rate, for the second example I use a ratio table to arrive at the value of the whole wall, and for example #3, I use proportions to find the number of teaspoons.

For each example it is important to calculate the unit rate and discuss its important and helpfulness in calculating the answers to the questions.

**#1**

**#2**

**#3**

In the next 10 minutes, students work for with partners to complete the next three examples included in the classwork. As students complete each problem I ask different groups to go up to the board to display their work.

When we review the answers in this section I use the opportunity to get kids talking about math and describing the reasoning behind their solutions. This is also a good time to encourage the use of vocabulary words: ratio, rate, equivalent, in proportion, proportionate, etc.

In the last ten minutes of this section students will work independently to solve 2 additional problems along with an exit ticket.

There is a large cushion of time in this section because I want to feel free to allow the time for students to communicate about math and to get most to talk about the solutions for today’s problems.

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#### Closing

*10 min*

Students will use the remaining time to complete the independent practice problems and exit ticket at the end of class and turn them in for me to check. I will be using this data to determine if I need to reteach or remediate any skills with targeted groups of students.

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- UNIT 1: Integers
- UNIT 2: Operations with Rational Numbers
- UNIT 3: Expressions and Equations - The Basics
- UNIT 4: Multi-step Equations, Inequalities, and Factoring
- UNIT 5: Ratios and Proportional Relationships
- UNIT 6: Percent Applications
- UNIT 7: Statistics and Probability
- UNIT 8: Test Prep
- UNIT 9: Geometry

- LESSON 1: Mastering Rational Numbers
- LESSON 2: Introducing Ratios and Rates in Word Problems
- LESSON 3: Best Buy
- LESSON 4: Ratio Tables
- LESSON 5: Quiz + Graphing Proportional Relationships
- LESSON 6: Bar Models and Ratios
- LESSON 7: Unit Rates and Ratio Tables
- LESSON 8: The Constant of Proportionality
- LESSON 9: Quiz + The Constant of Proportionality in Equations and Tables
- LESSON 10: Put it Together - Equations y = kx
- LESSON 11: Equations and Bar Models + The Constant of Proportionality
- LESSON 12: Identifying the Constant of Proportionality
- LESSON 13: Determine and Interpret Proportionality through Table and Graphs - Day 95
- LESSON 14: Quiz + Similar Figures
- LESSON 15: Scale Drawings
- LESSON 16: Map Scales
- LESSON 17: Let's Dream About a Different Place...
- LESSON 18: Practice Test
- LESSON 19: Unit 5 Test
- LESSON 20: Unit 5 Test Debrief
- LESSON 21: MAP it Out: Part 2