## Task Teacher Guide

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### In This Purposeful Practice…

Students will continue exploring the relationship between the area of rectangles and the array model. The array replaces the need to count individual units and makes it possible to calculate an area.

### Intentionality…

The purpose of the Day 2 activities is to reinforce key concepts from Day 1. Students will engage in a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.

- To measure the area of a rectangle, it must be completely covered by units of area (square units), without gaps or overlaps;
- The alignment of square units produces the rows and columns of an array, with the same number of units in each row;
- The array replaces the need to count individual units and makes it possible to calculate an area;
- Both the number of units in each row and the number of units in a column can be determined from the length of the rectangle’s sides.

## Math Talk

### Overview of This Visual Math Talk

Present the following rectangles one at a time. Students are asked to calculate the area of each rectangle in square units. Represent the student thinking symbolically. For example, if a student uses repeated addition, write the addition sentence on the board. If a student uses multiplication, write the multiplication sentence.

### Visual Math Talk Prompt #1

Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Then ask students:

**What is the area of the rectangle?**

**Convince your neighbour.**

The goal with the first visual number talk prompt in this string of problems is to ensure that students are understanding that determining a quantity of area involves counting 2-dimensional units. In this case, they are squares.

Although some students may choose to count each square 1-to-1, some students may recognize the pattern of rows and columns (an array) and use them to help make counting easier by skip counting.

At this point, we want to ensure we highlight student strategies such as one-to-one counting and skip counting and explicitly connect the skip counting strategies by rows and/or columns as a multiplication sentence.

For students that counted by rows, we can see that there were 5 rows of 8 units per row.

For students counting by columns, we can highlight that there are 8 columns of 5 units per column.

Regardless of the strategy or strategies used by students, we hope all students are able to articulate that the area of this rectangle is 40 square units or 40 units-squared.

### Visual Math Talk Prompt #2

Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Then ask students:

What is the area of the rectangle?Convince your neighbour.

Although all of the strategies leveraged in visual number talk prompt #1 are valid and helpful here, we will focus our attention on some more advanced strategies that students may bring forward or that we hope to help emerge through our facilitation of this math talk.

After our consolidation of the previous number talk prompt, some students may quickly identify the number of rows and columns noticing that we have the same number of columns, but 1 less row. That student might choose to simply remove 1 group of 8 square units from the previous result.

Other students might recognize that 2 rows of 8 square units is 16 square units and therefore, they can double that result to land on the same total of 32 square units.

It is helpful to write down this strategy both visually over the array (or area model) and symbolically so students can make connections between representations.

Of course open the floor to other students who are interested in sharing other strategies that can be helpful to determine the area of the rectangle.

### Visual Math Talk Prompt #3

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### Visual Math Talk Prompt #4

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## Purposeful Practice

### While Students Are Practicing…

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### Questions: Area of a Triangle

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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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## 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.

### Visual Math Talk Prompt #1

### Visual Math Talk Prompt #2

### Visual Math Talk Prompt #3

### Visual Math Talk Prompt #4

### Question #1

### Question #2

### Question #3

### Question #4

**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