WELCOME BACK!TUESDAY

Please write your homework in your agenda book for the week.

Please have your journal on your desk and be ready to start Investigation 44.1 Using Similarity to Solve a Mystery

AssignmentWorksheet 4.1

INVESTIGATION 4

Using Similarity

SUMMARIZE WHAT YOU KNOW ABOUT SIMILARITY 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

Enlarged ImageSimilar Figure

Area is four times as large.

Original

OriginalOriginal

Original

Side Lengths and Perimeter double.

Using a two-band stretcher:

RECALL FROM INVESTIGATION 3:

How do we know if two figures are similar?Corresponding angles are equalRatio of all corresponding sides are the same

How do we find the scale factor between two similar figures?

How can we use the scale factor to find area of larger image?Scale factor^2(area of original) = area of

enlarged

2

4

6

?

)(2 inalareaoforigrscalefacto

NOW YOU TRY! LET’S REVIEW… 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

4

10

?

USING SIMILARITY TO SOLVE A MYSTERY 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?

DID YOU KNOW? 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.

PROBLEM 4.1 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?

WARM-UP: 12/3/13 The rectangles below are similar.

1. What is the value of x?

2. What is the scale factor from C to D?

Quarter 2: Week 6

C Dx

4

1

8

Welcome to Pre-algebraWednesday:

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

PROBLEM 4.1 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?

PROBLEM 4.1 FOLLOW-UP1. 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?

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

PROBLEM 4.2 Raphael is closing his bookstore. He

wants to place a full-page advertisement in the newspaper to announce his going-out-of-business 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.

PROBLEM 4.2 FOLLOW-UP

What would you suggest Raphael say to the ad department about making a full-page, similar ad from his model?

WARM-UP: 12/4/13 The rectangles below are similar.

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?

Quarter 2: Week 6

C Dx

4

1

8

Welcome to Pre-Algebra HonorsFriday

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

Relating Fractions, Decimals, and Percents

Percents are ratios that compare a number to 100.

Ratio Decimal Percent

     

   

   

30%

50%

75%

310

30100=

12

50100=

34

75100=

0.30

0.50

0.75

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

Reading Math

To convert a fraction to a decimal, divide the numerator by the denominator.

18 = 1 ÷ 8 = 0.125

To convert a decimal to a percent, multiply by 100 and insert the percent symbol.

0.125 100 12.5%

• Change the decimal to a percent1. 7.622. 85.73223. 8.7574. .255. .024

Quarter 2: Week 6