Illustrative Mathematics | v.360 Curriculum

Problem 1

Find the area of each shaded region. Show your reasoning.

Figure A is composed of 3 rectangles. rectangle 1, height = 5 units, base = 2 units, rectangle 2, height = 4 units, base = 2 units, rectangle 3, height = 2 units, base = 2 units. — A

Figure B, square, side lenght = 6 units. 2 white square inside of square, side length of each square = 2 units. Area outside of squares is shaded. — B

Figure C, pentagon. composed of a rectangle, base = 6 units, height = 2 units, and two triangles, each with base = 3 units, height = 2 units. — C

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Problem 2

Find the area of each shaded region. Show or explain your reasoning.

Figure A composed of rectangle with base = 6 centimeters, height = 4 centimeters, and a square with side length = 2 centimeters. — A

Figure B, rectangle with base = 8 centimeters, height = 5 centimeters. Unshaded slanted rectangle inside of rectangle with base = 3 centimeters, height = 2 centimeters. — B

Figure C, rectangle with smaller rectangle inside of it. region outside of inner rectangle is shaded. Outer rectangle, base = 10 centimeters, height = 15 centimeters. — C

Figure D, triangle, base = 16 centimeters, height = 5 centimeters. Triangle is symmetric. — D

Problem 3

Two plots of land have very different shapes. Noah said that both plots of land have the same area. Do you agree with Noah? Explain your reasoning.

Two shapes labeled “plot A” and “plot B”.

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Problem 4

ForLesson 2: Finding Area by Decomposing and Rearranging

A homeowner is deciding on one size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches.

Tell whether or not you agree with each statement about the tiles. Explain your reasoning.

Regardless of the size she chooses, she will need the same number of tiles.
Regardless of the size she chooses, the area of the wall that is being tiled is the same.
She will need two 2-inch tiles to cover the same area as one 4-inch tile.
She will need four 4-inch tiles to cover the same area as one 8-inch tile.
If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles.

Problem 5

from an earlier course

Find the area of the rectangle with each set of side lengths.

5 in and \(\frac13\) in
5 in and \(\frac 43\) in
\(\frac 52\) in and \(\frac 43\) in
\(\frac 7 6\) in and \(\frac 67\) in

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Reasoning to Find Area

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Lesson 3 Resources