## HOT CHOCOLATE [DAY 3]

### MULTIPLICATION & PROPORTIONAL REASONING

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

## Intentionality & Unit Overview

### Access each lesson from this unit using the navigation links below

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 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.

Todayâ€™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.

## 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

## 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.

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…

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

## Student Approach #1: Repeated Addition

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

## Student Approach #4: Doubling and Addition

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

## Extend: Prompts to Extend Learning

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

## Consolidation

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

## Reflect and Consolidation Prompts

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

## Consolidation Prompt:

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

## Educator Discussion Area

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

## Explore Our 60+ Problem Based Units

This Make Math Moments Lesson was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, number talks and extensions to elicit and emerge strategies and mathematical models.

Dig into our other units of study and view by concept continuum, grade or topic!