CCSS.Math.Content.7.G.A.1

1Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Scale Factor

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7th Grade Geometry

Standard 1

Computing actual lengths and areas

5 cm

4 c

m

? cm?

cmScale

factor =2

Area = 10cm2 Area = ?

10 cm8

cm

Area = 40cm2

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7th Grade Geometry

Standard 1

© 2008 National Council of Teachers of Mathematics http://illuminations.nctm.org

Scale Factor

For similar figures, scale factor is the common ratio between pairs of corresponding sides.

The scale factor for Hot Wheels® Monster Jam® cars is 1:24.

The scale factor for HO scale trains is 1:87.

The scale factor is the number by which each dimension of the original object is multiplied to find the corresponding dimension of the model.

4 inches

What is the length of the real monster truck?

that we have enlarged a picture (by using the “magnification” feature of a xerox ma-

chine or the same feature of geometry software) and then we compare it with the

original picture to isolate some observable characteristics of the enlargement. We are

not saying we already know what “enlargement” means; rather, we try to find out

what it could mean by looking at something we all agree is already enlarged. Then

we turn around and use these observed characteristics to define “magnification”. So

suppose we already have a picture of a house and a tree, to be called S; see the pictureon the right below. Let the left picture (to be denoted by S 0) be an “enlargement”,

in the intuitive sense, of S. Then it is not di�cult to see that, in the process of

enlargement, a point in the right picture S goes to one and only one point in S 0 on

the left. For example, the point A in S goes to the point A0 in S 0, the point B in Sgoes to the point B0 in S 0, etc.

P

.

.

.

.

.

A

B

C

D

E

P

.

.

.

.

.

A

B

C

D

E

Put di↵erently, there is a precise pairing of each point of S on the right to one and

only one point of S 0 on the left, and also of each point of S 0 on the left to one and

only one point of S on the right. Thus we may symbolically represent this pairing as

A $ A0, B $ B0, . . . , E $ E 0, and so on, for every point in either picture. Such

pairing is an example of what is known as a one-to-one correspondence. But we can

go further, it is intuitively clear that the paired points enjoy the property that the

“enlarged distances are proportional to the original distances” in the following sense:

if we use |AB| to denote the distance between A and B as usual, then:

|A0B0||AB| =

|A0C 0||AC| = . . . =

|A0E 0||AE| =

|B0C 0|BC| = · · · = |D0E 0|

|DE| ,

48

A scale drawing is either the reduction or the magnification of a two-dimensional picture.

4

9

16

1 2

3 7

5

86 14

12

10

151311

How many units long is side Z

newold

106

106 ・

4 1

=406

= 6 23

Use graph paper and a ruler

Draw and label 4 rectangles

Rectangle A B C D

Length

Width

3 6 9 15

1 2 4 5

Which are similar?

A

B

C

DA, B, and D

These Rectangles are Similar

Scale Drawing Project

Scale Drawing Project

Instructions:• Select a small picture from the list, or find your

own (must be approved before you start)• Label and number both axes• Get a large piece of paper (11x17)• Identify the scale factor• Reconstruct the image from the original,

including a border• Pay attention to detail

SCALE DRAWING PROJECT Rubric:

NOTE: When you submit your project, you will first score yourself using this rubric. Be honest and thorough in your evaluation. Remember to include the following parts in your presentation:

Include in your project: 1. The original picture2. The enlarged picture (colored to match original)3. Measurements of the original picture4. The scale selected to enlarge the picture5. Self-Completed Evaluation

10 – 9 8 – 7 6 – 5 4 - 0

Scale Scale factor is accurately calculated and properly displayed

Scale is calculated and displayed

Scale factor is inaccurately calculated

Scale factor is not calculated or displayed

Reconstruction All proportions are accurate on the enlarged picture

Most proportions are accurate on the enlarged picture

Few proportions are accurate on the enlarged picture

No proportions are accurate on the enlarged picture

Presentation The enlarged image is colored neatly in the lines and colors match original picture

Most of the enlarged image is colored neatly in the lines and most of the colors match original picture

Some of the enlarged image is colored neatly in the lines and some of the colors match original picture

The enlarged image is not colored neatly in the lines and does not match original picture

Self-Assessment: Teacher-Assessment:

Scale: ____/10 Scale: ____/10

Reconstruction: ____/10 Reconstruction: ____/10

Presentation: ____/10 Presentation: ____/10

Total Points: ____/30 Total Points: ____/30

Comment on your level of effort Teacher Comments:

and accuracy on this project:

Scale Factor Computer Activities

Print screenshots. Label information.

Write a short summary.Add to geometry portfolio.

http://illuminations.nctm.org/ActivityDetail.aspx?ID=176

http://www.mrperezonlinemathtutor.com/CARFILES/Similarity_Triangles_Enlargement_Reduction_by_Scaled_Factor.html