## Task Teacher Guide

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### In This Task…

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

### Intentionality…

In this task, students will have an opportunity to reason through an activity involving the ratio between two quantities; a package of hot chocolate mix and the cost for one package. 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 1 and 2 including the following:

- Unitizing;
- Ratio reasoning through scaling in tandem;
- The relationship between repeated addition and multiplication; and,
- A composed unit is one way of defining the relationship that exists in a ratio.

Today’s task will potentially also emerge the following big ideas:

- Numbers can be composed and decomposed;
- The distributive property of multiplication over addition; and,
- There is a constant multiplicative comparison that exists between two quantities in any ratio that is derived from the same rate.

## Math Talk

### String of Related Problems

Introduce the context through a **notice and wonder** by showing students the following image:

After students share anything they notice and wonder, let them know that you are now considering purchasing individual packages of hot chocolate rather than the large can.

Tell students that you opened up one package and counted the number of scoops. There are 6 scoops in one package. Engage in the following math talk by asking students to determine the number of scoops or the number of packages. You might consider recording student thinking in a ratio table.

1 package

2 packages

4 packages

5 packages

42 scoops

11 packages

## Sense Making

### Crafting A Productive Struggle: Prompt

Build on the context of the packages of hot chocolate used in the math talk.

Explain to students that packages of hot chocolate are sold individually at Bulk Barn for $1.10 per package.

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

Students will have an opportunity to work through determining the price for different quantities of hot chocolate packages in the ratio table below.

Click here to view full size image.

Download this Sense Making Prompt (and Extension Questions) BLM [ OPEN PDF IN NEW TAB | DOWNLOAD PDF ]

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.

## During Moves

### While Students Are Productively Struggling…

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### Student Approach #1: Repeated Addition

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### Student Approach #2: Manipulatives For Skip Counting & Addition

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### Student Approach #3: Skip Counting By 1s and 10s

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### Student Approach #4: Doubling and Addition

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### Student Approach #5: Multiplying With Rate and Partial Products

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### Extend: Prompts to Extend Learning

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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

## Printable PDF Handout

## 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.

### Extend Prompt #1

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### Extend Prompt #2

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### Extend Prompt #3

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### Extend Prompt #4

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**Download Editable/Printable Handout**

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### Consolidation Prompt

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**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