PSSA Math Review

PSSA Math ReviewPSSA Math Review

Lesson 33 Making PredictionsLesson 33 Making Predictions

StandardsStandards

E.4.1.2E.4.1.2

Make predictions based on survey Make predictions based on survey results or graphs (bar, line, circle, results or graphs (bar, line, circle, scatter plots, etc.)scatter plots, etc.)

Example 1Example 1

Last year, a store manager found Last year, a store manager found that 3 of every 10 T-shirts she sold that 3 of every 10 T-shirts she sold were black. If she expects to sell 500 were black. If she expects to sell 500 T-shirts this year, how many can she T-shirts this year, how many can she predict will be black?predict will be black?

Example 1 - StrategyExample 1 - Strategy

Use a proportion to predict the Use a proportion to predict the result.result.• Step 1: Set up a proportion.Step 1: Set up a proportion.

Let t – the predicted number of black T-Let t – the predicted number of black T-shirts.shirts.

3/10 = t/5003/10 = t/500

• Step 2: Solve for t.Step 2: Solve for t. 3/10 = t/5003/10 = t/500 3 x 500 = 10 x t3 x 500 = 10 x t 1,500/ 10 = t1,500/ 10 = t

Example 1 - AnswerExample 1 - Answer

150 = t150 = t The store manager can predict that The store manager can predict that

she will sell 150 black T-shirts. she will sell 150 black T-shirts.

Example 3Example 3

Rodney surveys students at Lincoln Middle Rodney surveys students at Lincoln Middle School to determine if they support going School to determine if they support going to school in the summer. This circle graph to school in the summer. This circle graph shows the results.shows the results.

Do You Support Going to School in Summer?Do You Support Going to School in Summer?

40% Yes50%

No

10% Not Sure

Example 3 – Cont.Example 3 – Cont.

There are 750 students at Lincoln There are 750 students at Lincoln Middle School. How many are likely Middle School. How many are likely to support going to school in the to support going to school in the summer?summer?

50 %No

40% Yes

10% Not Sure

Example 2 - StrategyExample 2 - Strategy

Use the graph to make a prediction.Use the graph to make a prediction.• Step 1: Identify the percent that voted Step 1: Identify the percent that voted

“Yes”. The graph shows that 40% of the “Yes”. The graph shows that 40% of the students voted “yes”.students voted “yes”.

• Step 2: Find 40% of the total number of Step 2: Find 40% of the total number of students. There are 750 students. Find students. There are 750 students. Find 40% of 750. 40% of 750. 40% x 750 = 0.4 x 750 = 30040% x 750 = 0.4 x 750 = 300

Example 2 – SolutionExample 2 – Solution

Rodney can expect 300 students to Rodney can expect 300 students to support going to school in the support going to school in the summer. summer.

Example 3Example 3

For a science experiment, Deanna For a science experiment, Deanna counts the number of fruit flies living in a counts the number of fruit flies living in a container each day. This graph shows container each day. This graph shows the results.the results.

Fruit Fly Population

05

10152025303540

1 2 3 4 5 6 7 8 9

Day

Po

pu

lati

on

Example 3 – Cont.Example 3 – Cont.

How many fruit flies can she expect on the How many fruit flies can she expect on the 1010thth day? day?

Fruit Fly Population

05

10152025303540

1 2 3 4 5 6 7 8 9

Day

Po

pu

lati

on

Example 3 - StrategyExample 3 - Strategy

Use the graph to make a prediction.Use the graph to make a prediction.• Step 1: Identify the pattern of the graph.Step 1: Identify the pattern of the graph.

The line is increasing from left to right. The line is increasing from left to right. The rate of increase is slowing down as the The rate of increase is slowing down as the

line ”rolls over”. line ”rolls over”.

• Step 2: Extend the line.Step 2: Extend the line.• Step 3: Use the extended line to predict Step 3: Use the extended line to predict

the number for the tenth day. the number for the tenth day. The number for the tenth day is about 40. The number for the tenth day is about 40.

Example 3 - SolutionExample 3 - Solution

Deanna should predict a population Deanna should predict a population of 40 fruit flies on the tenth day. of 40 fruit flies on the tenth day.

Sample Test QuestionSample Test Question

Question 1Question 1

There are 425 people living in Willie’s There are 425 people living in Willie’s apartment building. He asks 30 people about apartment building. He asks 30 people about their preferences in the election for building their preferences in the election for building president. Eighteen say they will vote for Mrs. president. Eighteen say they will vote for Mrs. Adams. If everyone votes, how many votes can Adams. If everyone votes, how many votes can Mrs. Adams expect in the election? Mrs. Adams expect in the election?

A.A. 255255B.B. 295295C.C. 345345D.D. 395395

Question 1 - SolutionQuestion 1 - Solution

Set up a proportion:Set up a proportion:18/30 = x/42518/30 = x/42518 x 425 = 30x18 x 425 = 30x7650/30 = x7650/30 = x255 = x255 = x

Mrs. Adams can expect to receive Mrs. Adams can expect to receive 255 votes in the election.255 votes in the election.

Question 2Question 2

This bar graph shows This bar graph shows the number of cell the number of cell phones owed by phones owed by students in each students in each grade at Booker T. grade at Booker T. Washington School. Washington School. What is the best What is the best prediction for the prediction for the number of cell number of cell phones owned by 9phones owned by 9thth graders? graders?

Cell Phone Ownership

0

50

100

150

200

250

300

Grade

Num

ber

of C

ell P

hone

s

5th

6th 7th8th

Question 2 – Cont.Question 2 – Cont.

What is the best prediction for the What is the best prediction for the number of cell phones owned by 9number of cell phones owned by 9thth graders?graders?

A.A. 240240

B.B. 250250

C.C. 270270

D.D. 300300

Cell Phone Ownership

0

50

100

150

200

250

300

Grade

Nu

mb

er o

f C

ell

Ph

on

es

5th

6th 7th8th

Question 2 - SolutionQuestion 2 - Solution

The best prediction is C. 270. The best prediction is C. 270.

Question 3Question 3

Which term best describes the Which term best describes the correlation between cost and the number correlation between cost and the number of radios sold?of radios sold?

A.A. Strong positiveStrong positive

B.B. Strong negativeStrong negative

C.C. Weak negativeWeak negative

D.D. No correlation No correlation

Radio Sales

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Radio Prices (in dollars)

Nu

mb

ers

So

ld

Question 3 – SolutionQuestion 3 – Solution

Strong negative correlation. Strong negative correlation.

Question 4Question 4

How many radios are likely to be sold if How many radios are likely to be sold if the price is set at $34?the price is set at $34?

A.A. 2424

B.B. 2828

C.C. 3232

D.D. 3838

Radio Sales

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60

Radio Prices (in dollars)

Nu

mb

ers

So

ld

Question 4 - SolutionQuestion 4 - Solution

32 radios will likely be sold. 32 radios will likely be sold. C. C.

Question 5Question 5

T.J. surveyed 60 students in his T.J. surveyed 60 students in his school about their after-school school about their after-school activities. The results are shown in activities. The results are shown in this graph. this graph.

50% Sports

25% Clubs15% Band

10% Yearbook

Question 5 – Cont.Question 5 – Cont.

If there are 800 students in the If there are 800 students in the school, how many can T.J. expect to school, how many can T.J. expect to be in the band? be in the band?

A.A. 99

B.B. 6060

C.C. 8080

D.D. 120120

50% Sports

25%

Clubs

15% Band

10%

Yearbook

Question 5 - SolutionQuestion 5 - Solution

First find 15% of 60.First find 15% of 60..15 x 60 = 9.15 x 60 = 9

9 students out of 60 are in the band.9 students out of 60 are in the band.

Next, set up a proportion.Next, set up a proportion.9/60 = x/8009/60 = x/800

Cross multiply:Cross multiply:9 x 800 = 60x9 x 800 = 60x

Solve for x:Solve for x:7200/60 = x7200/60 = x120 = x120 = x

Question 6Question 6

This graph shows the speed of a race car This graph shows the speed of a race car during its first few seconds off the during its first few seconds off the starting line. If the pattern continues, starting line. If the pattern continues, how fast can you expect the car to go in how fast can you expect the car to go in the tenth second?the tenth second?

A.A. 170 miles per hour170 miles per hourB.B. 190 miles per hour190 miles per hourC.C. 210 miles per hour210 miles per hourD.D. 230 miles per hour230 miles per hour

Racecar Speeds

020406080

100120140160180200

1 2 3 4 5 6 7 8 9

Time (sec)

Sp

eed

(m

i/h

r)

Question 6 - SolutionQuestion 6 - Solution

B. 190 mphB. 190 mph

Open Ended QuestionOpen Ended Question

Felicia buys a box of 200 filled chocolates. Felicia buys a box of 200 filled chocolates. She eats 8 of them and finds that 3 are She eats 8 of them and finds that 3 are caramel-filled.caramel-filled.

A.A. How many chocolates in the box can she How many chocolates in the box can she expect to be caramel-filled?expect to be caramel-filled?

B.B. Use what you know about making Use what you know about making predictions to explain why your answer is predictions to explain why your answer is correct. Use words and/or numbers in correct. Use words and/or numbers in your explanation.your explanation.

Open EndedOpen Ended A. She can expect 75 of the chocolates to be A. She can expect 75 of the chocolates to be

caramel-filled.caramel-filled. B. First you set up a proportion to help estimate B. First you set up a proportion to help estimate

the total amount that could possibly be caramel-the total amount that could possibly be caramel-filled. filled. 3/8 = x/2003/8 = x/200Next you cross multiply to solve for x. Next you cross multiply to solve for x. 3 x 200 = 8x3 x 200 = 8xThen you divide both sides by 8 to get x by itself.Then you divide both sides by 8 to get x by itself.600/8 = x 600/8 = x Finally you solve for x and this will tell you an Finally you solve for x and this will tell you an approximate prediction for the number of approximate prediction for the number of chocolates that will be caramel-filled. chocolates that will be caramel-filled. 75 = x75 = x