## DONUT DELIGHT [DAY 2]

### 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 the relationship between multiplication and division through an array model and volume model.

## Intentionalityâ€¦

In this task, students will determine the number of layers of donuts when given the quantity per layer and the total number of donuts in the entire box. This task can be accessed through multiplication and/or division. Students will be encouraged to continue using models as a tool to determine the missing factor and to represent their thinking. Some big ideas that might be explored in todayâ€™s task include:

• Numbers can be composed and decomposed.
• The relationship between rows and columns in an array.
• Quotative division can be accessed through skip counting, repeated addition, multiplication and/or repeated subtraction.
• Multiplication and division are related.

## Math Talk

Revisit the context from Day One, the box of donuts with dimensions of 25 donuts by 32 donuts. Use the same context to work through the following string. Encourage students to use a concrete, grid or open array in order to represent the different boxes of donuts below and to determine the total number of donuts in each box. In todayâ€™s math talk, you are hoping that students will use efficient strategies shared in yesterdayâ€™s consolidation, including partial products and doubling and halving. The first three are designed to encourage doubling and halving while the next three support the use of partial products.

50 donuts by 12 donuts

25 donuts by 20 donuts

25 donuts by 24 donuts

16 donuts by 28 donuts

14 donuts by 31 donuts

22 donuts by 27 donuts

## Crafting A Productive Struggle: Prompt

Yesterday, we saw the top view of a giant box of donuts. But all that could be seen from that image was the top layer.

Show students the image below:

Today, challenge students to determine how many layers of donuts there must be in the entire box based on what they have done so far. Students already know that one layer is 800, so now they must determine how many layers there are.

## While Students Are Productively Struggling…

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## Student Approach #1: Skip Counting

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## Student Approach #2: Area Model and Repeated Addition

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## Student Approach #3: Scaling in Tandem with a Double Number Line

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## Student Approach #4: Repeated Subtraction Symbolically With Flexible Division

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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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