© A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 9

© A Very Good Teacher 2007

Exit Level

TAKS Preparation UnitObjective 9


Percent % of Change

9, 8.3B

• When asked to determine % of change (What percent did Ernesto save?) …

• Example: The original cost of a pair of jeans is $75. Heather purchases the jeans during a sale and pays only $37.50. What percent did Heather save?

/

100

increase decrease x

original

75 37.50

75 100

x 75 3750x

37.5

75 100

x

50%x 75 75


Problems with Proportions• Arrange your proportions specifically!

• Example: Rodrigo types 50 words per minute and completes 12 pages each time Rachel completes 11.2 pages. Which is a reasonable estimate of Rachel’s typing speed?

9, 8.3B

Rodrigo RachelWords per min

# of pages50

12

wpm

pages?

11.2

wpm

pages

50

12 11.2

x 46.67x

121212 560x


Percent of a Percent …• Change percents to decimals

• Remember: “of” means multiply

9, 8.3B

75% = .75 175% = 1.757.5% = .075

5% of 200 = .05 x 200 = 10

5% of 20% = .05 x .20 = .01 Or 1%

5% of 20% of 80 = .05 x .20 x 80 = .8


Percent of a Percent cont…

• Example: Jermaine has a photo measuring 8 inches by 10 inches that he is reducing to fit into a smaller frame. He reduces the photo by 80%, but it is not small enough. He reduces the photo again by 80%. What are the dimensions of the new image?

9, 8.3B

8 x .80 x .80 = 5.12 inches

10 x .80 x .80 = 6.4 inches


Writing Equations with Percents

• Change percents to decimals

• Convert sentences to equations

• Example: Gary earns $600 per week plus a 9% commission of his sales. How much must his total weekly sales be in order for him to earn exactly $708 per week?

9, 8.3B

9%

=.09G = 600 + .09 x S

708

708 = 600 + .09S-600 -600

108 = .09S.09 .09

1200 = S


Converting Ratios to Percents

• A ratio compares quantities like wins:losses

• A percent compares a quantity to a total like

• To convert a ratio to percent:1. Determine the total

2. Put specific quantity over total

3. Set

9, 8.3B

winsTotal games played 100

x

100

x


Converting Ratios to Percents cont…

• Example: The Green Bay Packers have a regular season record of 13:3. What percentage of games did they win?

9, 8.3B

13 wins, 3 losses, Total Games Played = 16

1. Determine the total

2. Put specific quantity over total

100

x

13

163. Set

100

x

13

161300 = 16x

16 16x = 81.25%


Simple Probability

• Probability =

• Example: A geometric pattern is made up of 2 squares and 1 circle grouped randomly together. What is the probability that the 2 squares are placed together?

9, 8.11A

Favorable outcomes

Possible outcomes

Favorable outcomes

Possible outcomes

2 squares together

Probability2

3


Com∙pound Probability• Com∙pound Probability is just several

Simple Probabilities multiplied together

• Watch out for the words – “Replacement”

– “Without Replacement”

9, 8.11A

Favorable outcomes

Possible outcomes

Favorable outcomes

Possible outcomes

Com∙pound Probability = ∙

Means you choose an object and then put it back before you choose again

Means you choose an object and hold on to it while you choose again


Com∙pound Probability cont…• Example: Jordan has a box containing 12 strips of

paper. 5 of the strips contain the first 5 numbers greater than zero. Another 7 strips contain the first 7 letters of the alphabet. If Jordan draws 2 strips of paper without replacement, what is the probability that he will draw an even number and a vowel?

Favorable outcomes

Possible outcomes

Favorable outcomes

Possible outcomes

Com∙pound Probability = ∙

2

12

2

11

1

334

132

9, 8.11A


Making Predictions from Data• There are 2 types of questions in this

section:1. Questions where the data are stated

2. Questions with tables of data

• On all questions use proportions• Example from Type 1: Steve made 15 of his last

18 field goal attempts from 35 yards. How many field goals can he be expected to make if he attempts 30?

9, 8.11B

30

x

15

18

part

total

18x = 45018 18

x = 25


Making Predictions from Data, cont…

• Example from Type 2: Josia surveyed 50 of his classmates to determine their choice in automobile types. The results are shown in the table below. If there are 1725 students at Josia’s school, how many can be expected to prefer trucks?

9, 8.11B

Auto Type

# of Students

Car 16

Truck 22

SUV 10

Van 2

part

total50x = 37950

50 50

x = 759

22

50 1725

x


Measures of Central Tendency

• There are 4 measures that fit this description:

– Mean:

– Median:

– Mode:

– Range:

9, 8.12A

Numbers Middle Likelihood

Average sum

quantity

Middle … put numbers in order 1st

Most … not all data sets have a mode*you may have to average the 2 in the middle*

Biggest - Smallest


Measures of Central Tendency, cont…

• Example: Hulan earned the following grades on his tests in Geometry this six weeks: 94, 72, 56, 81. Which measure of central tendency will give him the highest score?

9, 8.12A

Mean (Average) =94 72 56 81

4

303

4 75.75

Median (Middle) 56, 72, 81, 9472 81 153

2 2

76.5

Mode (Most) None

Range (Biggest – Smallest) 94 - 56 = 38


Making Circle Graphs

• To create a circle graph you must know how much of the circle to designate for each category

• Example: Create a circle graph for the following data.

9, 8.12C

Food Type # of Restarurants

Pizza 3

Mexican 7

Burgers 5

Chinese 2

Total # of Restaurants = 17

2

17

5

17

7

17

3

17

3

17 360

x

63.5x 17 1080x

Pizza 63.5˚

148.2x 17 2520x

7

17 360

x

105.9x 17 1800x

5

17 360

x

Pizza 63.5˚

Mexican 148.2˚

Pizza 63.5˚

Mexican 148.2˚

Burgers 105.9˚

2

17 360

x

17 720x 42.4x

Pizza 63.5˚

Mexican 148.2˚

Burgers 105.9˚

Chinese 42.4˚


Making Conclusions from Data• PROCESS OF ELIMINATION!• Example: An internet service provider claims that

its connection speed is faster than its competitors. The company uses the graph shown below to demonstrate this point. According to the graph, which statement best describes the company’s product?

9, 8.13B

A. Its speed is faster than some, but much slower than othersB. Its speed is much faster than othersC. Its speed is about the same as othersD. Its speed is somewhat slower than others

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© A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 9