## Task Teacher Guide

Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.

### In This Task…

Students will determine how many chairs can fit in a gym for Grade 8 Graduation.

### Intentionality…

As is true for **any task**, the intentionality or learning objective can vary depending on what mathematical thinking you are hoping to elicit. The purpose of this Make Math Moments problem based lesson is to give students an opportunity to develop algebraic reasoning while applying number sense skills including multiplication, perimeter and area.

In particular, we will explore **equivalence** and **substitution **through big ideas including:

- Each side of an equation can be thought of as a single unit, where both sides are equivalent.
- A multiple of one quantity can be equivalent to a multiple of another quantity which can be used to substitute.
- The algebraic strategy of substitution can assist in solving for unknown quantities in an equation.

## Math Talk

### String of Related Problems

In today’s math talk number string of related problems, students will build on yesterday’s context involving determining the number of chairs you can fit in a gym for a grade 8 graduation. Remind students of the context:

Remember from last day how we were trying to determine the number of chairs we could fit in a gym for grade 8 graduation?

Who can recall how many chairs we calculated to fit in the gym?

Remember that based on the calculations from the images we saw, 360 should have fit. However, in the reveal video, we saw that there were only 286. Be sure to honour students who say 360 and 286 as both are “correct” depending on whether they are referencing what happened in reality or what we had calculated. From there, say:

Can anyone recall how many rows and how many chairs were in each row according to the images we looked at?

Yes! You’re right ! The image suggested that there would be 18 rows and 20 chairs in each row.

Today, we’re going to do a math talk with a string of problems to find the number of chairs we’d expect for different row and chair combinations.

How many chairs would you expect to fit in a gym that has…

**Problem #1:**

… 20 rows with 10 chairs in each?

**Problem #2:**

…20 rows with 20 chairs in each?

**Problem #3:**

…20 rows with 19 chairs in each?

**Problem #4:**

…21 rows with 20 chairs in each?

**Problem #5:**

…19 rows with 19 chairs in each?

**Problem #6:**

…19 rows with 38 chairs in each?

Consider modelling student thinking using an **area model**.

### Facilitator Notes

In today’s math talk, we will provide students with the opportunity to reinforce the multiplication strategy of * partial products* along with opportunities for

*and*

**doubling***as revealed through some of the student approaches you may have observed on day 1. Today, students will build on the context of determining the number of chairs that could fit in rows and columns in different sized gymnasiums.*

**compensation****Big Idea:**

The big idea we hope to reveal explicitly and build on is the idea that factors in a multiplication sentence can be decomposed and recomposed in a variety of ways to make calculating the product more efficient and manageable.

### Walk Through Video

Watch this walk through video of the Math Talk to ensure you maximize the intentionality behind this string of related problems.

## Spark

### Prompt & Estimate

Show students this image:

The prompt we will give our students to think on is:

If 360 chairs can fit in the smaller gym, how many do you think you could fit in this larger gym?

Make an estimate.

Have students make estimates, share and justify with their neighbours using only their spatial and proportional reasoning skills.

## Sense Making

### Craft a Productive Struggle

Then, show this image.

State verbally:

The perimeter of the gym is 3 times its length.

Ask students to use this information to update their estimates. Some focusing questions you might consider asking are:

- About how many chairs long do you think a bench might be?
- About how many chairs do you think you could fit in a square bench of area?
- Can you make some assumptions to update your estimate?

Give students an opportunity to turn and talk with their neighbours to share their assumptions and updated estimates.

Then, show this image revealing that a square “bench” unit of area can fit approximately 9 chairs:

Give students the time and space to productively struggle together.

## During Moves

### While Students Are Productively Struggling…

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### Walk Through Video

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### Sample Student Response #1: Using Toothpicks and Drawing Area Models

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### Sample Student Response #2: Using Number Lines and Algebraic Reasoning Symbolically

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### Sample Student Response #3: Using Algebraic Reasoning Symbolically

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### Consolidation

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### Reveal

After consolidating learning using student generated solution strategies and by extending their thinking intentionally, we can share what really happened with this video.

**Answer: 450 seats**

Here is an optional supporting image:

Revisit the student responses. Have students discuss their thinking and what they would change if they did the task again.

### Reflect

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

**Consolidation Prompt #1:**

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**Consolidation Prompt #2:**

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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.

**Download Editable/Printable Handout**

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### What You Could Do If…

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### Assessment for Learning

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## Resources and Downloads

## Lesson Tip Sheet

Download the lesson plan in PDF format so you can keep it handy and share with colleagues.

## Videos & Images

Download the videos, images, and related media files to your computer to avoid streaming.

## Keynote Slides

Download in Apple Keynote format to avoid streaming video and run the lesson smoothly.

## PowerPoint Slides

Download in Microsoft PowerPoint format to avoid streaming video and run the lesson smoothly.

## Printable Handout

Download/edit the handout so you can keep it handy and share with colleagues.

## 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.

### How many chairs can fit in a gym that has…

*…20 rows with 10 chairs in each?*

### …

*…20 rows with 20 chairs in each?*

### …

*…20 rows with 19 chairs in each?*

### …

*…21 rows with 20 chairs in each?*

### …

*…19 rows with 19 chairs in each?*

### …

*…19 rows with 38 chairs in each?*

### Consolidation Prompt #1

*Login/Join*

### Consolidation Prompt #2

*Login/Join*

**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