© a very good teacher 2007 exit level taks preparation unit objective 9
TRANSCRIPT
© A Very Good Teacher 2007
Exit Level
TAKS Preparation UnitObjective 9
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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%
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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˚
© A Very Good Teacher 2007
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