7th Grade Math

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PART A B C

Main Idea

Determine how

changes in dimensions

affect area and

volume.

Multi-Part

Lesson 2

GLE 0706.4.3

Understand and use scale

factor to describe the

relationships between

length, area, and volume.

SPI 0706.4.3 Apply scale

factor to solve problems

involving area and volume.

Also addresses GLE 0706.1.3.

652 Measurement and Proportional Reasoning

Changes in Scale

CAKE DECORATING A cake decorator is making a cake in the shape of a

children’s board game. The original game is 12 inches by 16 inches. The

cake’s dimensions will be half as long and half as wide. How does the

cake’s perimeter and area compare to the game’s perimeter and area?

What do you need to find? the change in scale for perimeter

and area of the cake

Draw a model of

6 in.

8 in.

the cake on grid paper

where each centimeter

represents 1 inch.

Find the perimeter

of the cake using

the grid paper.

8 in. + 8 in. + 6 in. + 6 in. = 28 inches

Compare this to the game’s perimeter, 56 inches.

Since _^2856 = _ 21 , the perimeter of the cake is _ 21 of the

perimeter of the board game.

Find the area of the cake.

8 × 6 = 48 square inches

Compare this to the game’s area, 192 square inches.

Since _ 19248 = _^14 , the area of the cake is _^14 the area of the

board game.

the Results

1. Suppose another cake’s dimensions are twice as long and wide
   as the board game. How do the perimeter and area of the cake
   compare to the perimeter and area of the game?


2. MAKE A CONJECTURE How does changing the dimensions of a
   figure affect its perimeter? area?

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