OLD VERSION: IM 6.1.2 Lesson

This GeoGebra activity has been created from [url=https://curriculum.illustrativemathematics.org/MS/students/1/1/2/index.html]this original lesson[/url] authored by [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url].

[size=200]LESSON[/size]

You may recall the term [b][i]area[/i][/b] tells us something about the number of squares inside a two-dimensional shape.[br][br]Below are four drawings that each show squares inside a shape. Select all drawings whose squares could be used to find the area of the shape. Be prepared to explain your reasoning.[br][br][img width=431,height=313]https://lh4.googleusercontent.com/1UhaVnHuYtbj1FOqlyaePp4LOzPaKOS14Js4bmqwYzn_1s1ccCRBue-FVAF8uiLuQX0YSKBp1n2It1kxBjKojMq2XpWM8wU5_RxlmSz6T89V18XFGuVWZbJy-W42G0RAeSTY5DWs[/img]

D A B C

Write a definition of area that includes all the information that you think is important:

This app has one square and some small, medium, and large right triangles. Click on a shape and drag to move it. Grab the point at the vertex and drag to turn it.The area of the square is 1 square unit.

[color=#0c0300]Notice that you can put together [/color][b][color=#1e84cc]two small triangles[/color][/b][color=#0c0300] to make a [/color][b][color=#bf9000]square[/color][/b][color=#0c0300]. What is the area of the [/color][b][color=#bf9000]square[/color][/b][color=#0c0300] composed of [/color][b][color=#1e84cc]two small triangles[/color][/b][color=#0c0300]? Explain your reasoning.[/color]

Use these shapes to create a new shape with an area of 1 square unit that is not a square. Place this shape near the bottom of this app.

Use your shapes to create a new shape with an area of 2 square units. Place this shape near the bottom of this app.

Use your shapes to create a DIFFERENT SHAPE with an area of 2 square units. Place this shape near the bottom of this app.

Use your shapes to create a new shape with an area of 4 square units. Place this shape near the bottom of this app.

Are you ready for more? Find a way to use all of your pieces to compose a single large square.

What is the area of the large square you created in the app above?

Recall that the area of the square is 1 square unit. Use this app to help illustrate your answers to your questions below.

[color=#0c0300]The area of the [/color][b][color=#1e84cc]small triangle[/color][/b][color=#0c0300] is ____________ square units. I know this because____________________. [/color]

[color=#0c0300]The area of the [/color][b][color=#cc0000]medium triangle[/color][/b][color=#0c0300] is ____________ square units. I know this because____________________. [/color]

[color=#0c0300]The area of the [/color][b][color=#38761d]large triangle[/color][/b][color=#0c0300] is ____________ square units. I know this because____________________. [/color]

[size=200]PRACTICE[/size]

This rectangle has been decomposed along its diagonal. Recompose the two pieces to make a different shape.

How does the area of this new shape compare to the area of the original rectangle? Explain how you know.

Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of original square to make a new figure.[br][br][img width=463,height=253]https://lh4.googleusercontent.com/XVjiTkoIAKI6UCmozsT_i4uGAp4BGfc4o-hLPYzrYUSoR64wPh3ZFJK4S1_wLuP2Yd80kDpX37f3eCi8L0F9003dtWBKCQjdlhqvwcFWDvtr8Un7QNWfiSMizEs0Itl8HfrkgJjb[/img][br][br]How does the area of her new figure compare with that of the original square?

The two figures have the same area. The area of the original square is greater. We don’t know because neither the side length nor the area of the original square is known. The area of the new figure is greater.

The area of the square is 1 square unit. Two small triangles can be put together to make a square or to make a medium triangle.[br][br][img width=526,height=108]https://lh6.googleusercontent.com/3li3Hmimr9ugeVuaSbohYk9Wel-ZT1q2veCobmrx2qCN0iVDaqm0GIY3YKZZWoGX12JJSjyXDoJL_3rCnBpQcaMoe5A-kzrXGgoaQ7IlRsPID8Jz84NlaxQUP4fL8YanWKqi8Qc8[/img][br][br][br]Refer to figures A - D to answer the question below. [br][br][img width=526,height=263]https://lh4.googleusercontent.com/9boYYTlrNHXfGlayfoRfekl6lzFzezT6KKxHyQ9lSkBlLURodIi8VLPzyL4KO4thKZ7lawKDK4s9YBfvBYGnKjx6m00SFMPDdbOuAaRZujr8RvCp8uitfMuzlRS1P23zs3r4XIy0[/img][br][br]Which figure also has an area of [math]1\frac{1}{2}[/math] square units? Select all that apply.

Figure B Figure A Figure C Figure D

A student said, “We can’t find the area of the shaded region because the shape has many different measurements, instead of just a length and a width that we could multiply.”[br][br][img width=503,height=282]https://lh4.googleusercontent.com/Qy2VMqJY1-bQaLw0DnNac6214myOPGbZiCb14M-LB5kPlPp2HVnOKel5i53fzmulmwIdlU9WETuTEJNdwn8MMQsf4Iykx4GAqm6G2qZEx-sHniE8jVcRKBUm-A0OaakLJmj9f9SF[/img][br][br][br]Explain why the student’s statement about area is incorrect. You can use the pen tool in the app below to provide a sketch that helps support your explanation.

Use this app to help illustrate your typed explanation above.

The area of a rectangular playground is 78 square meters. If the length of the playground is 13 meters, what is its width?