## HOT CHOCOLATE [DAY 4]

### MULTIPLICATION & PROPORTIONAL REASONING

Explore proportional relationships through skip counting, repeated addition, multiplication, and more.

## Intentionality & Unit Overview

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Students will explore the idea of scaling in tandem with a ratio as a composed unit.

## Intentionalityâ€¦

In this task, students will have an opportunity to reason through a second activity involving the ratio between two quantities; a package of hot chocolate mix and the cost per pack. Through this task, students will have the opportunity to apply models including the double number line and the ratio table. They will have an opportunity to continue exploring big ideas from Day 3 including the following:

• 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.
• Numbers can be composed and decomposed.
• There is a constant multiplicative comparison that exists between two quantities in any ratio that is derived from the same rate.

A new big idea that may be emerged through this task includes:

• The distributive property of multiplication over subtraction.

## Group Counting

For todayâ€™s Math Talk, students will engage in group counting. Take turns having students share the answer as you count by 9s. In your first time through, start at 9. As students share the next number in the count sequence, record the numbers on the board in vertical columns. After 10-15 numbers in the count sequence have been shared, ask students what they observe.

Students might state the following:

• The numbers are always going up.
• The number in the ones column is always going down one.
• The number in the tens is going up 1.
• Once you get to 0 in the ones, the pattern changes.
• It is like adding ten every time, but then taking away one.
• And many moreâ€¦

If students are still actively listening and participating, engage in a second group count. This time, choose a number between 1 and 10 that is not 9.

Count up to 15 numbers in the sequence and ask students to make observations about the pattern.

### Facilitator Notes

Assuming students are able to count by 10s with automaticity, asking students to count by 9s encourages them to intuitively count by 10s and subtract 1 each time. This is helpful to begin emerging the big idea of the distributive property over subtraction which will be a helpful big idea to use for the Sense Making portion of todayâ€™s lesson.

For example, students who do not yet have automaticity counting by 9s might be using this strategy (often in their mind):

• Thinks: 9, Says: 9
• Thinks: 9 + (10 â€“ 1), or 19 â€“ 1, Says: 18
• Thinks: 18 + (10 â€“ 1) or 28 â€“ 1, Says: 27
• And so onâ€¦

By engaging in this group counting activity, the idea of distributive property over subtraction may begin emerging through the later portion of this lesson.

## Crafting A Productive Struggle: Prompt

Build on the context of the packages of hot chocolate used in the previous lesson.

Explain to students that you have been shopping around to find a better price on the packages of hot chocolate.

You found the packages being sold individually this time at Giant Tiger.

They are only \$0.99 per package.

You want to determine the total cost for different quantities of packages at Giant Tiger.

Students may work with a partner or in a small group, however they will do so without the use of a calculator. They must also be able to convince others of how their answers are true.

## While Students Are Productively Struggling…

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## Student Approach #1: Repeated Addition and Counting

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## Student Approach #2: Doubling, Halving Using Partial Quotients and Addition

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## Student Approach #3: Multiplying by the Rate

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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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