## Task Teacher Guide

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### In This Task…

Students will explore the relationship between partitive and quotative division.

### Intentionality…

In this task, students will begin making generalizations about the relationship between quotative and partitive division. Using the same box of 2 400 donuts, students will be tasked with a partitive division problem today.

Some of the big ideas that will emerge in today’s task include:

- Numbers can be composed and decomposed.
- Multiplication and division are related.
- Quotative division can be accessed through skip counting, repeated addition, multiplication and/or repeated subtraction.
- Partitive division can be assessed through fair sharing (or equal distribution), partitioning and multiplying by a fraction.

### Math Talk

Revisit the context from Day 2, the box of 2 400 donuts partitioned into layers of 800 donuts. Use the following information to practice similar quotative division problems. Students are encouraged to use models as tools and to represent their thinking. The question for each of the following scenarios is, how many layers of donuts are in the box?

400 donuts per layer, 1 200 donuts altogether

700 donuts per layers, 2 800 donuts altogether

450 donuts per layer, 2 250 donuts altogether

325 donuts per layer, 1 300 donuts altogether

## Sense Making

### Craft A Productive Struggle:

If your school bought this box of doughnuts to split between 8 classes, how many would each class get?

Students are encouraged to work through this problem with partners or in small groups. Students should use models to defend their thinking and convince their community that their answer is correct.

## During Moves

### While Students Are Productively Struggling:

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### Student Approach #1: Decomposing Dividend and Fair Sharing

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### Student Approach #2: Repeatedly Halving a Bar Model

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### Student Approach #3: Repeatedly Halving With A Double Number Line

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## Next Moves

### Consolidation

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### Reflect

Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently.

**Consolidation Prompt:**

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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## Resources and Downloads

## Lesson Tip Sheet

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## PowerPoint Slides

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## Printable Handout

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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.

### How many layers if…

*400 donuts per layer, 1 200 donuts altogether*

### …

*700 donuts per layers, 2 800 donuts altogether*

### …

*450 donuts per layer, 2 250 donuts altogether*

### …

*325 donuts per layer, 1 300 donuts altogether*

### Consolidation Prompt:

*Login/Join*

**Download Editable/Printable Handout**

Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy