## Task Teacher Guide

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### In This Purposeful Practice…

Students will explore modelling and solving one-step algebraic equations involving multiplication.

### Intentionality…

The purpose of the Day 2 activities is to reinforce key concepts from Day 1. Students will engage in a string of related problems through 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 division;
- Partitive division is when the total quota is known (the dividend), and the number of parts or groups (the divisor) is known;
- Partitive division reveals a rate;
- In partitive division, the dividend and the divisor often have different units;
- The dividend from any division sentence can be decomposed into smaller parts to allow for friendlier division by the divisor. This strategy is known as partial quotients. (i.e.: 85 ÷ 5 = 45 ÷ 5 + 40 ÷ 5 = 9 + 8 = 17);
- Division is the inverse operation of multiplication;
- Variables are used to represent changing or unknown quantities;

When solving an equation where the coefficient of the unknown variable is not equal to 1, division is required to determine the value of the unknown variable and the context of the problem determines which type of division is required.

**Math Talk**

Present the following multiplication and division equations one at a time. Encourage students to describe a partitive context that could be represented by each of the division sentences such as seeds (dividend) and planting pots (divisor) like we did in the last lesson.

Students should use a model of their choice to solve and/or represent their thinking.

48 4 = r4(r) = 48

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Consider leveraging the silent solution animations below to help you prepare to facilitate this math talk. The purpose of this math talk is to reveal that both the division and one-step algebraic equation can be solved using the same strategy and model.

### Problem #1

Show the following visual math talk prompt and be ready to pause the video once prompted:

In this first prompt, we begin with a low floor partitive division problem asking students:

48 candies are to be shared amongst four children.

How many candies would each child receive?

A natural strategy that suits this context and type of division is fair sharing. The candies can be partitioned into four bags equally by fair sharing one-by-one, two-by-two, ten-by-ten or however students choose to unitize for sharing across the bags.

From here, we can ask students what operation they utilized for this problem. While the context is sending a clear call for partitive division, some students might think to the strategy they leveraged (i.e.: skip counting) and believe it was addition or even subtraction as they “removed” candies from the total to distribute to the bags. It is helpful to highlight that while this is a partitive division problem, multiplication can be used as a strategy to solve the problem.

To highlight how division and multiplication are intrinsically related, we can also leverage an area model to highlight how a single model can be used to solve multiplication and division problems.

### Problem #2

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### Problem #3

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**Purposeful Practice**

### While Students Are Practicing…

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### Questions: One-Step Algebraic Equations

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## Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.

Click the links at the top of this task to head to the other related lessons created for this unit of study.

### Problem #1

### Problem #2

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*to access additional Math Talk Prompts as well as the Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.*### 1. For each of the…

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### 2. Lola has 5 baskets…

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### 3. Consider the…

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### 4. Rashmi has…

### 5. One-step algebraic…

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