This document provides instructions and materials for a math lesson on similarity and scale factors. It includes examples of similar figures with questions about their side lengths, scale factors, and areas. It also discusses how police use measurements and similar figures to determine characteristics like a criminal's height from surveillance photos. Students are asked to use a photo of a teacher holding an object of known size to calculate the teacher's height, and to explain how police may have used a similar technique to determine a robber's height from a store surveillance photo.

1.  Please
write your homework in your
agenda book for the week.
 Please have your journal on your desk
and be ready to start Investigation 4
 4.1 Using Similarity to Solve a Mystery
 Assignment
 Worksheet 4.1

2. Using Similarity

3. Using a two-band stretcher:

By now, you should have a good
understanding of what it means for
two figures to be similar. In the last
investigation, you created similar
figures by putting identical smaller
figures together and by dividing a
figure into identical smaller figures.
You learned that the scale factor is
the number that a figure’s side
lengths must be multiplied by to get
the side lengths of a similar figure.
By finding the number of figures it
took to cover a larger, similar
figure, you discovered the
relationship between the scale
factor and the areas of two similar
figures. In this investigation, you
will use all of your new knowledge to
solve some interesting problems.
Original Figure
Side Lengths
and Perimeter
double.
Enlarged Image
Similar Figure
Area is four times as large.
Original
Original
Original
Original

4.  How


do we know if two figures are similar?
Corresponding angles are equal
Ratio of all corresponding sides are the same
 How
do we find the scale factor between two
similar figures?
6
2
 How
4
?
can we use the scale factor to find area of
larger image?

Scale factor^2(area of original) = area of enlarged

5.  If



these two rectangles are similar:
What is the length of the large rectangle?
What is the scale factor from the small rectangle
to the large rectangle?
How do their areas compare?
2
10
4
?

6.  Many
stores, particularly those that stay
open late into the night, have surveillance
cameras. One night the local Dusk to Dawn
convenience store was robbed. The
surveillance camera had taken several
photographs during the robbery. By
inspecting a picture of the robber standing in
front of the cash register, police were able to
determine the robber’s height.
 How did they do it?

7. Measurement is used in investigatory and police work
all the time. For example, some stores that have
surveillance cameras mark a spot on the wall 6 feet
from the floor so that, when a person is filmed
standing near the wall, it is easier to estimate that
person’s height.
 Investigators take measurements of skid marks at the
scene of auto accidents to help them determine the
speed of the vehicles involved.
 Photographs and molds may be made of footprints at
a crime scene to help determine the type of shoe and
the weight of the person who made the prints.
 And measurements of holes and damage made by
bullets can help investigators determine the type of
gun that shot the bullet and the direction from which
it was shot.


8.  The
teacher’s guides for Connected
Mathematics measure 8 ½ in. by 11 in.
Below is a photograph of a middle school
teacher holding a teacher’s guide.
 A. Use the photograph to figure out how tall
the teacher is. Explain your procedure.
 B.
How do you think the police determined
the robber’s height?

9. Quarter 2: Week 6
 The
x
rectangles below are similar.
C
1
8
D
4
1.
What is the value of x?
2.
What is the scale factor from C to D?

10. Welcome to Pre-algebra
Wednesday:
1.Please have your homework on your desk
and get started on your warm up.
2.Finish and Discuss Follow up 4.1 and
Worksheet 4.1
3.Homework
• Workbook p. 187 # 1 - 5

11.  The
teacher’s guides for Connected
Mathematics measure 8 ½ in. by 11 in.
Below is a photograph of a middle school
teacher holding a teacher’s guide.
 A. Use the photograph to figure out how tall
the teacher is. Explain your procedure.
 B.
How do you think the police determined
the robber’s height?

12. 1.
Estimate the height of the door in the
photograph.
2.
Do you think your estimate in question 1 is
an underestimate or an overestimate?
Why?

13. Welcome to Pre-Algebra
Thursday
1. Please have your homework on your desk
and complete the warm up.
2. Correct Homework
– Workbook p. 187 # 1 - 5
3. Please have your journal ready for 4.2
– 4.2 Scaling up
4. Today’s Assignment
– Finish Follow up 4.2

14.  Raphael
is closing his bookstore. He wants to
place a full-page advertisement in the
newspaper to announce his going-out-ofbusiness sale. A full-page ad is 13" by
22", which allows for a white border around
the ad
 Raphael used his computer to make an 8 ½ "
by 11" model of the advertisement, but he
wants the newspaper ad department to
enlarge it to full-page size. Is this possible?
Explain your reasoning.

15.  What
would you suggest Raphael say to the
ad department about making a fullpage, similar ad from his model?

16. Quarter 2: Week 6
 The
x
rectangles below are similar.
C
8
1
D
4
1.
What is the area of each rectangle?
2.
What is the relationship of the area of
rectangle C to the area of rectangle D?

17. Welcome to Pre-Algebra Honors
Friday
1. Please have your homework on your desk
and complete the warm up.
2. Discuss 4.2
– Problem and Follow up
3. Please have your journal ready for notes
– Changing percents to decimals and decimals to
percents
4. Today’s Assignment
– Facing Math Lesson 16

18. Relating
Fractions, Decimals, and
Percents

20. Percents are ratios that compare a number
to 100.
Ratio
30
3
=
100
10
50
1
= 100
2
3
75
=
4 100
Decimal
Percent
0.30
30%
0.50
50%
0.75
75%

21. Reading Math
Think of the % symbol as meaning per 100
or /100. 75% = 75/100 = 0.75

22. To convert a fraction to a decimal, divide
the numerator by the denominator.
1
= 1 ÷ 8 = 0.125
8
To convert a decimal to a percent, multiply by
100 and insert the percent symbol.
0.125

100  12.5%

23. Quarter 2: Week 6
• Change the decimal to a percent
1. 7.62
2. 85.7322
3. 8.757
4. .25
5. .024