## Task Teacher Guide

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### In This Purposeful Practice…

Students will explore equivalent ratios, reveal rates through partitive division and scale factors through quotative division.

### Intentionality…

The purpose of the Day 4 activities is to reinforce key concepts from Days 1 to 3. Students will engage in a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.

- There are two types of ratios; composed unit and multiplicative comparison;
- A composed unit is often (not always) a ratio with two distinct units;
- A composed unit can be scaled in tandem;
- Equivalent ratios are derived from the same rate;
- When you divide a composed unit through partitive division, you reveal a rate.
- Quotative division is applied when trying to determine a scale factor between two quantities/measures of the same unit (i.e. rice and rice, water and water);
- When you invert the dividend and the divisor in a quotative division sentence, the quotient (the revealed scale) has a reciprocal relationship (i.e., 4 1 = 4 ,1 4 = ¼ ).

## Math Talk

### Overview of the Problem String

In today’s visual math talk, we will be presenting the following quotative division sentences one at a time. Since we are dividing quantities of the same unit, the type of division is quotative and the resulting quotient will represent a scale factor. Encourage the use of an area, volume or linear model to justify each equation.

**$60 ÷ $30**

**$30 ÷ $60**

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Consider leveraging the following visual math talk prompt videos to understand how to facilitate this math talk using a stacked bar model as well as to provide students with an engaging set of visual prompts.

### Problem #1

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### Problem #2

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### Problem #3

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## Purposeful Practice

### While Students Are Practicing…

### Questions: Ratios and Rates

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## Printable Handout

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### Problem #1

### Problem #2

### Problem #3

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### Problem #6

### 1. Model and solve…

### 2. Calista is baking…

### 3. Consider the…

### 4. Complete the…

### 5. Logan says that…

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