## DONUT DELIGHT [DAY 4]

### MULTIPLICATION AND DIVISION

Use arrays to develop and understanding of the relationship between multiplication and division.

## Intentionality & Unit Overview

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Students will explore models and strategies to support conceptual understanding of the product that results from multiplying a 4 digit number by a 3-digit number through an extension of the donut task.

## Intentionalityâ€¦

In this task, students tackle a new scenario related to the box of donuts. Today, they will be multiplying the 2 400 donuts by a rate, the number of calories per donut. Students will be encouraged to use models and leverage big ideas previously explored in this unit to solve this multiplication problem using an efficient strategy. Some of the big ideas that we will continue to develop or that may emerge through todayâ€™s task include:

• Numbers can be composed and decomposed;
• The distributive property of multiplication over addition/over subtraction;
• The associative property of multiplication;
• The result of multiplying by the base.

Because students will be working with a ratio as a composed unit (in this case, number of calories and number of donuts), big ideas in proportional reasoning are also likely to emerge, including the following:

• Ratio reasoning through scaling in tandem;
• A composed unit is one way of defining the relationship that exists in a ratio;
• There is a constant multiplicative comparison that exists between two quantities in any ratio that is derived from the same rate.

## Math Talk

Revisit the context from Day 3, where the box of donuts was being shared equally by 8 classes. Present the following scenarios and encourage students to determine the quotient through the use of models as tools. Remind them of some strategies that we applied to solve yesterdayâ€™s problem, including decomposing and fair sharing new units of donuts, partitioning and using fractional thinking.

1 600 donuts : 8 classes

750 donuts : 6 classes

840 donuts : 7 classes

600 donuts : 8 classes

## Crafting A Productive Struggle: Prompt

If your school purchased the box of 2 400 donuts, how many calories were consumed if the entire box is eaten?

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.

## While Students Are Productively Struggling…

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## Student Approach #1: Distributive Property With An Open Array

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## Student Approach #2: Associative Property Using Symbolic Notation

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## Student Approach #3: Scaling in Tandem with a Ratio Table

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## Consolidation

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## Reflect and Consolidation Prompts

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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## Educator Discussion Area

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## Explore Our 60+ Problem Based Units

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