## Objective

Solve real-world and mathematical problems involving area of polygons.

## Common Core Standards

### Core Standards

The core standards covered in this lesson

6.G.A.1— Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

### Geometry

6.G.A.1— Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

### Foundational Standards

The foundational standards covered in this lesson

3.MD.C.7.D

### Measurement and Data

3.MD.C.7.D— Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

4.MD.A.3

### Measurement and Data

4.MD.A.3— Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

*For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.*

## Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

- Apply strategies to find area of polygons to solve real-world problems.
- Find the area of figures with space missing inside the figure by subtracting the missing area.

## Tips for Teachers

Suggestions for teachers to help them teach this lesson

- Students will have additional opportunities to engage with real-world contexts in Lesson 9 when they look at polygons on and off the coordinate plane.
- Note: The Target Task is longer than usual and may require additional time.
- In these problems, students analyze the diagrams to make sense of them in context and determine what math strategies they can use in their solution. They determine any missing measurements they may need and add labels or markings to the diagrams as needed, organizing their work along the way. Finally, students should ask themselves at the end if their answer makes sense for the context (MP.1).

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## Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

### Problem 1

A carpenter is building a new wall for a house that he is renovating. He knows that there will be a door and a window in the wall. Around the door and window, he uses wooden board to create the wall. A blueprint of the wall is shown below.

How much wooden board, in square feet, does the carpenter need to build the wall?

#### Guiding Questions

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### Problem 2

Jamie is planning to cover a wall with red wallpaper. The dimensions of the wall are shown below.

a.How many square feet of wallpaper are required to cover the wall?

b.Wallpaper comes in long rectangular strips that are 24 inches wide. If Jamie lays the strips of wallpaper vertically, how many strips will she use and how long will each strip be? Explain.

c.If Jamie lays the strips of wallpaper horizontally, can she cover the wall without wasting any wallpaper? Explain.

#### Guiding Questions

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#### References

Illustrative Mathematics *Wallpaper Descomposition*

*Wallpaper Descomposition*, accessed on March 20, 2018, 9:38 a.m., is licensed by Illustrative Mathematics under either theCC BY 4.0orCC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

### Problem 3

Find the area of the shaded region in square units. Show your reasoning.

#### Guiding Questions

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#### References

Open Up Resources *Grade 6 Unit 1 Lesson 11*—Lesson 11.4 Pinwheel (See the teacher version for a pdf and further commentary)

*Grade 6 Unit 1 Lesson 11* is made available by Open Up Resourcesunder theCC BY 4.0license.Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 20, 2018, 9:42 a.m..

## Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

15-20 minutes

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## Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

The diagram below shows one wall in an attic. The shape of the wall is a trapezoid, and there is a rectangular window in the wall.

Not including the window, what is the area of the wall’s surface?

### Student Response

An example response to the Target Task at the level of detail expected of the students.

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## Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

- Engage students in experimenting with area around the classroom. Have them find the area of a wall after accounting for a door or window. Or find the area of all of the classrooms, based on the area of their classroom. Or the area of their desks. You can have students measure lengths, you can provide them with lengths, or you can have students make reasonable estimates.

- EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic A > Lesson 6—Problem Set
- Dan Meyer's Three-Act Math
*Bubble Wrap*

Lesson 5

Lesson 7