## REESES PEANUT BUTTER CUPS [DAY 5]

### Multiplication with partial products

Decompose an array to reveal partial products in order to estimate a large quantity.

## Intentionality & Unit Overview

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Students will determine the total cups of sugar in 14 full size Reese’s Peanut Cup packages through counting, additive and multiplicative thinking. Students will explore rate and ratio reasoning though this composed unit or Peanut Butter Cups and cups of sugar.

In this task, students will have an opportunity to determine the total cups of sugar in 14 full size Reese’s packages through ratio reasoning and/or rate reasoning. As was the case in Day 3 and 4, students might use counting, repeated addition or multiplication to scale the composed unit in tandem through ratio reasoning or use rate reasoning and multiply by the rate.

However today, they are working with a fractional amount. Students will continue developing big ideas in proportional reasoning, but will also have an opportunity to explore big ideas related to fractions. Some of the big ideas that might emerge today include:

• Unitizing;
• Ratio reasoning through scaling in tandem;
• The relationship between repeated addition and multiplication;
• 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.
• For equivalence, the ratio must remain constant.
• Fractions may represent a rate.

## Math Talk

Engage students in the following math talk to the big idea of multiplication over addition and over subtraction. The following string of related problems will encourage the use of partial products.

12 x 1.00

12 x 1.10

12 x 1.06

14 x 1.00

14 x 0.99

14 x 0.97

## Crafting A Productive Struggle: Prompt

Share the following prompt with students to craft a productive struggle:

At a party, guests ate 14 full size packages of  Reese’s Peanut Butter Cups.

There is 1 sixth cups of sugar in each package.

How many cups of sugar are in 14 packages of full size Reese’s?

This problem has students using fractional thinking and can be accessed through counting, additive, or multiplicative thinking. While some students may come up with an improper fraction by simply counting or repeatedly adding the 1 sixth unit fraction for a total of 14 sixths, others may on their own, or possibly through teacher questioning, decide to make a mixed fraction. The key here is to ensure students are defending their thinking without simply relying on rules or algorithms they may have picked up along their mathematical journey.

## While Students Are Productively Struggling…

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## Student Approach #1: Pattern Blocks Using Counting and Additive Thinking

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## Student Approach #2: Concrete Materials Using Unitizing To Count Wholes

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## Student Approach #3: Double Number Line Using Counting On

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## Student Approach #4: Ratio Table Using Ratio Reasoning

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## Student Approach #5: Symbolic Representation Using Rate Reasoning

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## Consolidation

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## Reflect and Consolidation Prompts

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

### Consolidation Prompt #1:

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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.