## Task Teacher Guide

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### In This Task…

Students will determine the volume of 8 boxes of Girl Guide cookies organized in a 2 x 2 x 2 rectangular prism. Students will measure the volume of the prism using cookies as their non-standard unit of measure.

### Intentionality…

In this task, students will learn that one box of Girl Guide Cookies contains 24 cookies. They will observe 8 boxes being stacked together to form a rectangular prism (2 boxes x 2 boxes x 2 boxes). Students will be asked to draw the top and side view of the prism and to show the cookies that would be visible from both sides (if they had x-ray vision).

They will be asked to calculate the total number of cookies inside the rectangular prism, and to describe the dimensions of the rectangular prism using cookies as their unit of measure. This unit will support the development of the following ** big ideas**:

- Volume and capacity can be measured using non-standard and standard units;
- A rectangular prism has three views. It can be viewed from the top, front and side. Each of these three faces are two dimensional, with a length and a width;
- A rectangular prism has three dimensions, which can be described using three linear measurements; the length, the width and the height;
- The measurements of length, width, and height are used to determine volume;
- Volume can be determined by multiplying the area of the base by the height of the prism;
- Volume is related to the operations of multiplication and addition;
- A solid figure which can be packed without gaps or overlaps using a
is said to have a volume of that**quantity of unit cubes**.**same quantity of cubic units**

## Spark

### What Do You Notice? What Do You Wonder?

**Part 1**

Show students the **following video**:

Then, ask students:

What do you notice?

What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Replaying the video and/or leaving a screenshot from the video up can be helpful here.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other means to ensure students know that their voice is acknowledged and appreciated.

Some of the noticing and wondering that may come up includes:

- I notice a box.
- I notice the name is Sweet Shop.
- I notice cookies.
- I notice 2 rows of cookies.
- It looks like about 8 cookies are showing.
- I wonder how many cookies there are in the whole box?
- I wonder what kinds of cookies they are?
- I wonder if they are Girl Guide Cookies?

At this point, you can answer any wonders that you can cross off the list right away. For example:

- This is one box of cookies that are being sold for a school fundraiser.
- They are shortbread cookies.

You might consider adding other details that you feel will be helpful to build an understanding of the context.

**Part 2 **

Show students the * following video*:

Then, ask students:

What do you notice?

What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Replaying the video and/or leaving a screenshot from the video up can be helpful here.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other means to ensure students know that their voice is acknowledged and appreciated.

Some of the noticing and wondering that may come up includes:

- I notice there are eight boxes.
- I notice the eight boxes make one big rectangle.
- I wonder how many cookies there are.
- I wonder if all of the boxes are full.
- I wonder if it is the same type of cookie.

At this point, you can answer any wonders that you can cross off the list right away. For example:

- These are the same boxes of Shortbread Cookies.
- There are 8 boxes.

### Estimation: Prompt

After we have heard students and demonstrated that we value their voice, we can land on the first questions we will challenge them with:

If you could look down on this arrangement of boxes from above with x-ray vision, how many cookies do you think you would see on the top layer? Draw a diagram of how the cookies would be arranged.

We can now ask students to draw a diagram of the cookies viewed from the top of this arrangement of boxes. Encourage them to actually identify the cookies pictorially or concretely and represent how they would be arranged in their columns and rows. Encourage students to engage in a conversation about how many cookies they would see from the top of the boxes, and how they know.

### Estimation: Partial Reveal

Share the following image:

Engage students in a conversation around the dimensions and the total area of the top view using cookies as your unit of measure.

## Sense Making

### Crafting A Productive Struggle: Prompt

Prompt students with the following:

**Prompt #1:**

Draw a diagram of the side view of this arrangement.

Make sure that your diagrams show how the first layer of cookies would be organized in their rows and columns if you could see through the boxes with your x-ray vision.

After giving students some time to estimate how many layers are in each box, you can prompt them with the following:

**Prompt #2:**

How many cookies are in this arrangement of boxes altogether? How do you know?

Students should reason through this prompt without the use of a calculator. Visual or concrete representations are expected of all learners.

## During Moves

### While Students Are Productively Struggling:

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### Student Approach #1: Linking Cubes with Addition Using Compensation

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### Student Approach #2: Pictorial Representation with Addition Using Partial Sums

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### Student Approach #3: Open Array with Multiplication Using Partial Products

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## Next Moves

### Consolidation: Making Connections

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### Reveal

Show students the following * reveal video*:

Here is a screenshot of the final frame that you may choose to leave up on the screen:

### Reflect

Students will complete the following task and reflection independently without the use of a calculator.

**Consolidation Prompt:**

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## Resources and Downloads

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## Lesson Tip Sheet

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## Videos & Images

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## Keynote Slides

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## PowerPoint Slides

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## 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.

### Struggle Prompt #1

*Draw a diagram of the side view of this arrangement.*

*Make sure that your diagrams show how the first layer of cookies would be organized in their rows and columns if you could see through the boxes with your x-ray vision.*

### Struggle Prompt #2

*How many cookies are in this arrangement of boxes altogether? How do you know?*

### Struggle Prompt #2: Image

### Consolidation Prompt #1

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