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

2. © 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?

3. © 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 RodrigoRachel Words per min # of pages

4. © A Very Good Teacher 2007 Percent of a Percent … Change percents to decimals Remember: “of” means multiply 9, 8.3B 75% =.75175% = 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

5. © 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

6. © 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% =.09 G=600+.09x S 708 708 = 600 +.09S -600 108 =.09S 1200 = S

7. © 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 wins Total games played

8. © 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 3. Set 1300 = 16x 16 x = 81.25%

9. © 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 Probability

10. © 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

11. © 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 = ∙ 9, 8.11A

12. © 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 18x = 450 18 x = 25

13. © 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 Car16 Truck22 SUV10 Van2 50x = 37950 50 x = 759

14. © A Very Good Teacher 2007 Measures of Central Tendency There are 4 measures that fit this description: –Mean: –Median: –Mode: –Range: 9, 8.12A NumbersMiddleLikelihood Average Middle … put numbers in order 1 st Most … not all data sets have a mode *you may have to average the 2 in the middle* Biggest - Smallest

15. © 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) = Median (Middle)56, 72, 81, 94 Mode (Most) None Range (Biggest – Smallest) 94 - 56= 38

16. © 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 Pizza3 Mexican7 Burgers5 Chinese2 Total # of Restaurants = 17 Pizza 63.5˚ Mexican 148.2˚ Pizza 63.5˚ Mexican 148.2˚ Burgers 105.9˚ Pizza 63.5˚ Mexican 148.2˚ Burgers 105.9˚ Chinese 42.4˚

17. © 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 others B. Its speed is much faster than others C. Its speed is about the same as others D. Its speed is somewhat slower than others