Mutually Exclusive Exhaustive Categories

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1 Activity Mutually Exclusive Exhaustive Categories As a small group, write a question and 4 to 6 mutually exclusive answers that encompass all possible responses. Make sure that everyone who is asked your question can find his or her response on your list of answers, and that it is not possible for someone to select more than one of your answers. Ask each classmate to answer your question. Tally the responses and make a pie chart that illustrates your data, either by hand or with Excel, as instructed. Question: Answers (4 to 6): A. B. C. D. E. F. Have each student in the class record the letter of his or her answer in the cell below that corresponds to his or her card name. Clovers Diamonds Hearts Spades Ace

2 Activity Review of Percents Fill in each blank with the correct answer. You may use a calculator, but show your computation. If the decimal terminates, record the entire answer. If a decimal has a repeating sequence of digits, use a bar above the first sequence of those digits and drop the rest. 1. 3% of 360 is 2. 12% of 72 is 3. What percent of 150 is 25? out of 96 is percent? 5. Express as a decimal: and as a percent: Use the result above to complete the sentence: 40 is % of Express as a decimal: and as a percent: Use the result above to complete the sentence: 38 is % of 20. 3

3 Activity Rounding Decimals and Percents Round each value to the indicated number of decimal places. Value 2 decimal places 3 decimal places Round each value as indicated. Value Nearest whole percent Nearest tenth of one percent 38.71% 1.73% 0.25% % Convert each value to its decimal form. Do not round. Value Decimal form Value Decimal form 38.71% 0.12% 48.62% 1.73% 76.09% 0.025% % % Round each value to three decimal places, then convert the rounded value to percent form. Value To 3 decimal places Percent

4 Activity Rounding Calculated Values Use a calculator to find the decimal form of each value. Record all digits, up to and including the digits in the first four decimal places, exactly as they appear. Then, round each value to three decimal places. Value Digits through first 4 decimals places Round to 3 decimal places * *Explore the need to keep zeros in the last two decimal places in Activities and Compute each value and round to three decimal places. Then convert to percent form, rounded to the nearest tenth of one percent. Value Digits through first 4 decimals places 13 women 15 women 1253 in 377 in $12,980 $10, lbs 293 lbs Round to 3 decimal places Percent, rounded to nearest tenth Compute the numerical expression in each equation to find the value of the variable. Round as indicated. 1. $ $ $ (to nearest tenth of one percent) (to three decimal places) 3. $28.49/$26.32 (to the nearest whole percent) 5

5 Activity Precise Price Circle the numbers below which round to 10 when rounded to the nearest ten Circle the numbers below which round to 10 when rounded to the nearest whole number A hungry student called a local eatery and asked the price of a steak sandwich with a side of fries. The employee who answered the phone said, Around $10. If the employee rounded the price to the nearest ten (dollars), then we know the exact cost of the meal is at least and less than but not equal to. If the price was rounded to the nearest whole (dollar), then we know the exact cost of the meal is at least and less than but not equal to. Given two rounded values of the same number, the one that represents the narrower interval is the more precise value. Which gives the more precise estimate of the exact cost of the meal: rounding to the nearest ten (dollars) or whole (dollar)? If a rounded value is given as 7, we can assume the exact value was rounded to the nearest and that the exact number is at least and less than but not equal to. If a rounded value is given as 7.8, we can assume the exact value was rounded to the nearest and that the exact number is at least and less than but not equal to. Round to the nearest thousandth:, the nearest hundredth:, the nearest tenth:, then circle the most precise rounded value. 6

6 Activity Rounding, Version 6.0 When rounding 5.98 to the nearest tenth, 5.98 rounds to 6.0. Since 6.0 = 6, should the rounded value of 5.98 be simplified to 6? Circle the numbers below which round to 6 when rounded to the nearest whole number Circle the numbers below which round to 6 when rounded to the nearest tenth If 6 is the rounded value, you can conclude that the actual value is at least and less than. If 6.0 is the rounded value, you can conclude that the actual value is at least and less than. Which is the more precise way to round 5.98: 6 or 6.0? Explain. If a rounded value is given as 12, the actual value is at least and less than. If a rounded value is given as 12.0, the actual value is at least and less than. Round to the nearest tenth. Round to the nearest hundredth. 7

7 Activity People, Percents and Politics The following chart shows the breakdown of registered voters in a small Mid western town. Fill in the empty cells with the correct values. Show your computation in each cell, as well. Political Party Percent of Registered Voters Number of Registered Voters Republican 38 Democrat Other Total How many registered voters are in this town? 8

8 Activity Male and Female Moviegoers A study is to be conducted in which people s reactions to certain genres of movies are observed. The study will consist of 1360 people. Twenty five percent of all the men and 25% of all the women in the study will watch an action movie. Ten percent of all the men and 10% of all the women in the study will watch a drama. Fill in the empty cells with the correct values. Show your computations in each cell or in the margins. Genre Percent Number of Males Number of Females Action 25 Drama 10 Comedy 500 Thriller 18 Documentary Total

9 Activity Data for Pie Charts Complete the tables. Number the cells and record the work on the back or on separate paper. First Vehicle Ever Owned, by Type Number Percent Degrees in Pie Chart Sedan 120 Coupe 20 Truck 54 SUV 24 Motorcycle 5 Total Party Affiliations of Registered Voters Number Percent Degrees in Pie Chart Republican 126 Democrat 40 Independent 144 Other 18 Total 720 Classes offered by Division at Palomar College, Summer Number Percent Round to nearest whole percent Degrees in Pie Chart Round to nearest whole degree Arts, Media Business, CompSci 168 Career, Technical, Extended Ed 8 Counseling Services 18 Languages and Literature 90 Math, Natural & Health Sciences 40 Sociology & Behavioral Sciences 140 Total

10 Activity At Least, At Most, Less Than, More Than Twelve thousand 25 year olds were asked how many college units they had successfully completed. The results are summarized in the following table. Number of Units None or more 8 Percent of Respondents Answer each question and show all computations. 1. In a pie chart, how many degrees would be in the central angle of the sector representing units? Round to the nearest whole degree. 2. How many of the 25 year olds surveyed have earned at least one unit? 3. How many have earned less than 60 units? 4. How many have earned at least 60 units? 5. It is not possible to determine the number of 25 year old students who have earned more than 60 units. Explain why it cannot be determined. 11

11 Activity Page 1 of 2 Bar Graph Analysis: Average Annual Earnings by Undergraduate Major and Gender A bar graph, Average Annual Earnings One Year after College Graduation by Undergraduate Major and Gender, was published in AAUW s 2012 publication, Graduating to a Pay Gap, written by Corbett and Hill. Use Figure 5, found on p. 26 out of 64 of the PDF file (p. 14 of the printed booklet) at the following link, to answer the questions. to a pay gap the earnings of women andmen one year after college graduation.pdf 1. Which major shows the greatest discrepancy in salary between men and women? 2. Give two different ways the graph can be used to answer question Which majors show no discrepancy? 4. Of computer and information sciences graduates, what percent of men s earnings do women make? (continued on p. 2) 12

12 Activity Page 2 of 2 5. Summarize the information displayed in this graph, as though explaining it to someone who has not seen it. Explain what information is displayed and what observations can be made from the graph. 6. Watch the video at the following link: pay day ivankatrump christine romans.cnnmoney Based on the video and your own ideas, offer possible explanations for the findings in the bar graph. Do not state what the data shows (that men make more than women in many fields), but provide two possible reasons why the data might be the way it is. 13

13 Activity Comparing with Difference and Ratio Sixteen people surveyed indicated their preference of cell phone type, and the results of the survey are illustrated in the bar graph below. One way to compare the number of those who prefer iphone to the number who prefer Android is to ask the question, How many more prefer iphone than Android? To answer this question, calculate the difference between the two numbers: number who prefer iphone minus number who prefer Android. Another way to compare is to ask the question, The number who prefer iphone is how many times as large as the number who prefer Android? To answer this question, calculate the ratio between the two numbers: number who prefer iphone divided by number who prefer Android. Answer each question and show the computation. Pay attention to order. 1. How many more prefer iphone than Android? 2. The number who prefer iphone is how many times as large as the number who prefer Android? 3. How many fewer prefer Android than iphone? (Hint: Android iphone, then interpret the negative) 4. The number who prefer Android is what percent as large as the number who prefer iphone? (Hint: Compute a ratio then convert to percent. Round to the nearest tenth of a percent.) 14

Activity 1 2.3 Working Students College students were asked whether or not they were also employed. Results are shown in the bar graph below. Answer each question and show each computation.

14 Activity Working Students College students were asked whether or not they were also employed. Results are shown in the bar graph below. Answer each question and show each computation. Round percents to the nearest tenth. 1. Are the categories, Student, and Employed, mutually exclusive? Why or why not? 2. How many students were surveyed altogether? 3. What percent of all students surveyed were also employed? 4. The number of employed female students is what percent as large as the number of employed male students? 5. What percent of the female students surveyed were employed? 6. If one of the students surveyed is randomly selected, is that student more likely to also be employed if she is female or if he is male? Explain. (Hint: Use the result of 5 and compute a similar percent for male students.) 15

15 Activity High School Grads and Summer School Thirty two Math 54 students were asked to select the best answer to the following multiplechoice question: Did you graduate from high school this spring, and/or did you attend summer school this summer? A. I graduated from high school this spring. B. I attended summer school this summer. C. Both D. Neither Fifteen chose A, nine chose B, seven chose C. Complete the Venn diagram below by inserting numbers in the appropriate regions. Math 54 Students Spring and Summer HS Grad Summer School A different class of thirty two Math 54 students was asked to raise their hands to signify, Yes, to the following questions, asked one at a time: 1. Did you graduate high school this spring? 2. Did you attend summer school this summer? Ten students raised their hand in answer to question (1) and twenty three raised their hand in answer to question (2). These questions are not mutually exclusive. In fact, seven students raised their hands in answer to both questions. Complete the Venn diagram to illustrate this. 16

16 Activity Pie Charts, Bar Graphs and Venn Diagrams Using the counting numbers 15 through 30, determine how many and/or which ones are divisible by 2, which are divisible by 3 and which are divisible by 5. Then, make the indicated graph to illustrate this information, if possible. If not possible, explain. 1. Pie Chart 2. Bar Graph 3. Venn Diagram 17

17 Activity Spreadsheet Basics Drag Down Enter the number 10 in cell A1. In A2, use a formula to add 1 to the cell above. Drag down to fill the cells through A25 in the same manner. Three Ways to Compute a Sum In Cell A30, record the sum of A3, A10 and A16 by entering =A3+A10+A16 In Cell A31, record the sum of A3, A10 and A16 by entering =SUM(A3,A10,A16) In Cell A32, record the sum of A1 through A25 by entering =SUM(A1:A25) Multiplication and Exponents Enter the number 1000 in B1. In B2, use a formula to add 50 to the line above. Drag down to fill the cells through B25 in the same manner. Enter the number 1000 in C1. In C2, use a formula to multiply the line above by Drag down to fill the cells through C25 in the same manner. In Cell D1, compute the product of B4 times A3. In Cell D2, compute A2 raised to the 3 rd power. Division, Percents and Rounding In Cell D4, compute the quotient of A2 and A3. Use the % icon to express the quotient as a percent, and use the increase/decrease decimal icon to round to the nearest tenth of a percent. Charts Make a pie chart from the data you collected in Activity Make a bar graph from the same data. 18

18 Activity DOLLARS and percents Sense Combine the terms in each expression, if possible. If not possible, explain why not. 1. $5 $ % of 3% of 2. 7% 9% % of $500 25% of $ % 12% 7. 15% of 4. $10 3% % of 12 3% of 30 Three students computed the total of a $124 textbook and 8% tax. Tell whether each is correct and explain what the student was thinking. Student A: $ $124 Student B: 108% $124 Student C: $

19 Activity Must I Repeat Myself? 1. Rewrite each expression using the number 4 to indicate the number repetitions. a c b d Rewrite each expression using the variable to indicate the number of repetitions. a , where 50 is added times b , where 50 is multiplied times c , where 50 is added times d , where 50 is multiplied times 3. Rewrite each expression without repetition. Use to represent the number of repetitions if the number of repetitions is not known. a b c

20 Activity What Goes Up: Percent Increase Value Find 5% of the value Add 5% of the value to the value $100 Find the decimal form of 105% Multiply the value by the decimal form of 105% $250 $18 $75 To increase a value by 5%, multiply that value by the decimal form of %. To increase a value by 3%, multiply that value by the decimal form of %. To increase a value by r%, multiply that value by the decimal form of ( )%. 21

21 Activity Must Come Down: Percent Decrease Value Find 5% of the value Subtract 5% of the value from the value $100 Find the decimal form of 95% Multiply the value by the decimal form of 95% $250 $18 $75 To decrease a value by 5%, multiply that value by the decimal form of %. To decrease a value by 3%, multiply that value by the decimal form of %. To decrease a value by r%, multiply that value by the decimal form of ( )%. 22

22 Activity Ups and Downs Complete each empty cell in the tables below. Base Percent Increase One step Calculation Result $40 3% $325 6% $ % Base Percent Decrease One step Calculation Result $40 3% $325 6% $ % Use the 1 step method to perform the percent increase or decrease described in each situation. Show the calculation and result. If the result is not a whole number, round to two decimal places. 1. The tuition of $50 per unit will be increased next year by 6%. 2. Sam, who weighed 192 lbs, decreased his weight by 3% when he started an exercise program. 3. An 18% tip is added to the cost of $42.39 for food and beverage. 4. An investment account was originally $100,538, but decreased in value by 2% due to fluctuating market conditions. 23

23 Activity Two Types of Interest SIMPLE INTEREST: Deposit $2500 in an account that pays interest in the amount of 4% of the initial deposit every year. Complete the table to illustrate simple interest. Year # 1 Beginning Balance $ Expression for interest earned Interest $ Ending Balance $ Expression for End Balance Involving the Initial Deposit x Simple Interest: The balance at the end of year x is computed by ADDING (to the initial deposit) 4% of the initial deposit x times. COMPOUND INTEREST: Deposit $2500 in an account that pays, at the end of each year, interest in the amount of 4% of the balance at the beginning of that year. Year # 1 Beginning Balance $ Expression for interest earned Interest $ Ending Balance $ Expression for End Balance Involving the Initial Deposit x Compound Interest: The balance at the end of year x is computed by MULTIPLYING (the initial deposit) by 104%, or 1.04, x times. The phrase, An account grows at 4% per year, refers to compound interest. Even though not explicitly stated, the implication is that the 4% is computed on the balance at the beginning of each year, not always the initial deposit at the beginning of the first year. 24

24 Activity Creating Expressions Involving Repetitions Jay makes an initial deposit of $3000 in an account. Each year, the account earns interest in the amount of 4% of the initial deposit. The amount of interest added each year is: (Show the calculation as well as the result.) Complete the table. Year Beginning Balance $ Complete the Expression, Involving the Initial Deposit, for Ending Balance (Show all repetitions) Condensed Expression Ending Balance $ 1 $ $ $ $3000 x Jazmyne deposits $3000 in an account. The ending balance in her account each year is computed by increasing the balance at the beginning of that year by 4%. A 4% increase of the beginning balance can be computed in one step by multiplying it by the decimal form of %, which is. Complete the table, and where necessary, round to the nearest cent. Year Beginning Balance $ Complete the Expression, Involving the Initial Deposit, for Ending Balance (Show all repetitions) Condensed Expression Ending Balance $ 1 $ $ $ $3000 x 25

25 Activity Simple vs Compound Interest Suppose you deposit $1200 in each of two accounts that each earns 6% annual interest, but one account pays simple interest and the other pays compound interest. 1. Complete the table: Initial Deposit Amount after 1 year after 2 years after 3 years after 10 years Simple Interest Account Compound Interest Account 2. Find an expression for the amount in each account after 35 years, but do not compute. a. Simple Interest Account: b. Compound Interest Account: 26

26 Activity Compounding Really Adds Up! Suppose that every five years, you transfer the amount you have been able to accumulate in your savings account to an investment account that pays 7% per year, compounded annually. You do this every five years beginning in the year Due to changing circumstances, the amount you are able to save over each five year period is different. Complete the table to find the value of each deposit in the year Then, find the total value of all the deposits in the year 2045, the year you plan to retire. Complete the table: Year Deposit Made Amount of Deposit Expression for the value of the deposit in $6000 $6000 Value of the deposit in $ $ $11, $12,500 Total Value in 2045: 27

27 Activity See the Difference Create a spreadsheet in Excel as follows: 1. In the first column, use a formula to generate the balance at the beginning of each year for thirty years if the initial deposit in A1 is $5000 and the account pays simple interest of 6% per year. 2. In the second column, use a formula to generate the balance at the beginning of each year for thirty years if the initial deposit in B1 is $5000 and the account pays compound interest of 6% per year (compounded annually). 3. Create a double bar graph using the data described above. Title your graph and label your axes. To replace Series 1 and Series 2 with Simple Interest and Compound Interest, hover the cursor over the bar graph and right click. Choose, Select Data. Series 1 should be highlighted, then click Edit, type in the desired title, then OK. Select Series 2, and proceed. 4. Print your graph. 5. With a pen or pencil, connect the tops of the bars from the simple interest account. Next, connect the tops of the bars from the compound interest account. 6. At the bottom of your printed graph, copy and complete the following sentences: The simple interest account shows growth. The compound interest account shows growth. 28

28 Activity Measure Up 1. Indicate which type of quantity is being measured by the following expression: length, area, volume or neither. Expression Length, Area, Volume or Neither Expression Length, Area, Volume or Neither 3 ft 13 in 12 m 3mi 4 mi 5 mi 7 yd 2in 2 5 in 1 5 cm 3 cm 2 3 in 5 ft 5 3 in 3 in 2 2 in 2. Use the Multiplication Property of Equality to form an equivalent equation below each given equation by multiplying or dividing both sides of the first equation by the same number. If applicable, round to two decimal places ft = 1 mi 24 hr = 1 day 1.61 km = 1 mi = 3 mi 100 hr = 10 km = 29

29 Activity Over and Under 1. Consider the set of 8 numbers: 42, 53, 58, 60, 62, 78, 90, 93 Verify that the mean is 67. Fill in each blank with a number to make a true statement: 42 is under the mean by. 78 is over the mean by. 53 is under the mean by. 90 is over the mean by. 58 is under the mean by. 93 is over the mean by. 60 is under the mean by. 62 is under the mean by. The total of the amounts by which the five numbers that are less than the mean are under the mean is. The total of the amounts by which the three numbers that are greater than the mean are over the mean is. Add to each number the amount by which it is under the mean: Subtract from each number the amount by which it is over the mean: What can be said of all the results? 2. The mean of a set of nine numbers is 14. The first eight numbers are listed in order, but the largest number is missing. 3, 6, 7, 8, 13, 18, 19, 25, Subtract the mean from each of the nine numbers listed. Some results will be negative and others will be positive. Find the sum of the results, then complete the sentence by circling one of the boldfaced words and filling in the blanks: The missing number must be over or under mean by, so the number must be. 30

30 Activity 1 R Review 1. Create a pie chart, a bar graph and a Venn diagram, if possible, to illustrate the set of whole numbers 1 through 20 with respect to these three categories: Less than 12, At least 8, and Odd. If it is not possible to create a particular graph for this set, explain why it is not possible. 2. A group of 2400 college students was polled and the results are in the table below. Number of hours worked in a Percent of respondents particular week More than 16 a. Complete the empty cell in the table above. b. How many students worked at least 9 hours? c. How many students worked fewer than 5 hours? d. Why is it not possible to determine the number of students who worked fewer than 4 hours? 31

Before How can lines on a graph show the effect of interest rates on savings accounts?

Compound Interest LAUNCH (7 MIN) Before How can lines on a graph show the effect of interest rates on savings accounts? During How can you tell what the graph of simple interest looks like? After What