##
* *Reflection: Flexibility
Determine Equivalent Ratios - Scale Factor Between Ratios - Section 1: Introduction

The lesson went well for my first class. Two things helped when showing the example problem. The first is that we used the value of the ratio (simplest form) to test all of the other ratios. It can get pretty messy drawing arrows from the value to the other ratios. I noticed some of my students were just putting a multiplier over the column (ex. x2, x3, x5 etc...). I started doing that because it makes the work more clear.

When solving part ii, we put the known value in the table but also modeled the ratio in fraction form. 48/x = 4/3. We did not cross multiply and divide to solve, we looked for a common scale factor of times 12.

In the Independent Problem Solving Section, I labeled the ratio columns as Batch A, Batch B, Batch C, etc. This made it easier for students to the three part ratio and made question i more clear. I could just ask: Which batch is not proportional to the others.

In my second period class today, the fire marshall decided to test our school with a fire drill. Thank you, Mr or Ms Fire Marshall. We skipped GP2 on the guided problem solving and did not get to the last Independent Problem Solving problem. I'll either have to incorporate those problems into tomorrow's lesson or use one of my intervention blocks later in the week.

*Helping Students Read Ratios in a Table & FIRE DRILL!!!*

*Flexibility: Helping Students Read Ratios in a Table & FIRE DRILL!!!*

# Determine Equivalent Ratios - Scale Factor Between Ratios

Lesson 6 of 12

## Objective: SWBAT determine if quantities in a table are in a proportional relationship by finding a scale factor equivalent to 1 between the quantities

## Big Idea: One useful way to determine equivalent ratios is to find a common scale factor between ratios.

*45 minutes*

#### Introduction

*10 min*

The lesson will begin with a discussion of what we know so far about proportional relationships. I will ask the essential question and ask students to discuss it. In order to provide a reference for their thinking I will present a simple problem or ratio. This is to bring out the idea that equivalent ratios can be seen as multiples of each others.

I will then show the example problem. The idea of multiples is here. I will draw them in from column to column as we discuss. This will help us identify the column of values that is not proportional to the others.

For part ii, I will show at least two ways to solve this problem. One will be using a bar model and the other will be using multiplication.

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#### Guided Problem Solving

*10 min*

The first guided practice problem shows a proportional relationship. Part ii of the problem asks students to find out how much the company will contribute based on an employee contribution of $20. Students may struggle a bit in finding the common scale factor. As a hint I may say "How many times greater is 16 than 8? What operation tells me this?". This can then be applied to this problem. I will allow my students to use calculators so that they can spend time focus on proportional relationships and not arithmetic.

The second problem asks students to create two tables based on different pay rates. I will be on the look out for people who think Abe's earnings should be $23 for 1 hour, $46 for 2 hours, $69 for 3 hours, etc.. They will need to be reminded to read the description very carefully.

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#### Independent Problem Solving

*20 min*

Now students work in pairs or independently while solving 3 more problems. Students should be encouraged to use a model to solve. For problem 1, this can be as simple as drawing the multiplier used between columns. A double number line may be especially helpful for problems 2 and 3. I will just need to be making sure students are using these models correctly.

Part i of problem 3 looks tricky but hopefully students will quickly see that Quantity C is the culprit.

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#### Exit Ticket

*5 min*

Each problem will be worth 2 points: 1 for a correct answer and 1 for a valid explanation. A score of 3 out of 4 will be considered a success. Before beginning we will summarize/review what we know about equivalent ratios. Up to this point, we have only discussed the relationship of a common multiple between the ratios. I will accept a student answer that identifies the proportional relationship by using any other valid method.

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##### Similar Lessons

###### End of Grade Review: Tables, Graphs, and Equations of Proportional Relationships

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- LESSON 1: Proportional Relationships of Whole Numbers
- LESSON 2: Proportional Relationships With Decimals
- LESSON 3: Proportional Relationships With Fractions
- LESSON 4: Finding Distances on Maps
- LESSON 5: Scaling a Recipe
- LESSON 6: Determine Equivalent Ratios - Scale Factor Between Ratios
- LESSON 7: Determine Equivalent Ratios - Scale Factor Between Terms
- LESSON 8: Determine The Graph of a Proportional Relationship
- LESSON 9: Determine Equivalent Ratios - Common Unit Rate
- LESSON 10: Writing The Constant of Proportionality Equation
- LESSON 11: Writing Equations for Proportional Relationships
- LESSON 12: The Distance Formula