Comparing the Results of a Survey

Comparing the Results of a Survey Objectives To guide the organization and tabulation of survey data; and to introduce the use of percents to compare quantities expressed as fractions with unlike denominators. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Use a calculator to convert fractions to percents. [Number and Numeration Goal 5] Compare fractions with unlike denominators. [Number and Numeration Goal 6] Create a table and tally chart. [Data and Chance Goal 1] Analyze survey results and make predictions based on collected data. [Data and Chance Goal 2] Key Activities Students tabulate the results from the trivia survey distributed in Lesson 9 1. For each survey question, they write a fraction to express the number of answers as a part of the total number of answers. Then they convert each fraction to a percent. Materials Math Journal 2, p. 261 Study Links 9 1 (Math Masters, p. 280) and 9 5 transparency of Math Masters, p. 290 (optional) calculator slate Solving Number Stories with Multiplication and Division Math Journal 2, pp. 261A and 261B Students solve multiplication and division number stories about gardening. Math Boxes 9 6 Math Journal 2, p. 262 Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 4. [Operations and Computation Goal 7] Study Link 9 6 Math Masters, p. 291 Students practice and maintain skills through Study Link activities. READINESS Comparing Estimates for the Fraction-of a Collection Math Masters, p. 292 pattern blocks large, clear container Students estimate the number of trapezoids in a collection of pattern blocks and compare estimates. ENRICHMENT Graphing Survey Results Math Journal 2, p. 261 Math Masters, p. 403 markers or colored pencils Students make a side-by-side (double) bar graph of the class survey results. EXTRA PRACTICE Taking a 50-Facts Test Math Masters, pp. 410 and 414; p. 416 (optional) pen or colored pencil Students take a 50-facts test. They use a line graph to record individual and optional class scores. Advance Preparation For the optional Readiness activity in Part 3, gather a large collection of pattern blocks and place them in a clear container. Teacher s Reference Manual, Grades 4 6 pp. 69 71, 160 169 750 Unit 9 Fractions, Decimals, and Percents

Getting Started Mental Math and Reflexes Write fraction addition problems on the board where tenths are added to tenths, hundredths to hundredths, and tenths to hundredths. Ask students to share their strategies for solving the problems. Suggestions: 6_ 10 + 3_ 10 = _ 9 10 2_ 10 + 5_ 10 = 7_ 10 7_ 10 + 1_ 10 = 8_ 10 4_ 10 + 5_ 10 = 9_ 10 40_ 100 + 50_ 100 = _ 90 100 32_ 100 + 20_ 100 = 52_ 100 25_ 100 + 25_ 100 = 50_ 100 15_ 100 + 75_ 100 = 90_ 100 6_ 10 + 20_ 100 = 80_ 100, or _ 8 10 10_ 100 + 8_ 10 = 90_ 100, or 9_ 10 9_ 100 + 9_ 10 = 99_ 100 5_ 100 + 5_ 10 = 55_ 100 Math Message Use your calculator to rename the following fractions as percents to the nearest whole percent: 18_ 63, 57_ 78, _ 42 59, 2_ 47 Study Link 9 5 Follow-Up Have partners compare answers. Ask if the percents in the table add up to 100%. yes Students should note that sometimes because of rounding, percents might not add up to 100%. 1 Teaching the Lesson Math Message Follow-Up DISCUSSION Go over the answers. 29%, 73%, 71%, 4% Ask volunteers to show what they did to rename the fractions as percents. Make sure that both methods are presented: Using the percent key on a calculator Dividing the numerator by the denominator and multiplying by 100 Tell students that in this lesson they will rename the fractions from the Trivia Survey as percents. Making a Prediction Based on Individual Survey Data (Math Masters, p. 280) DISCUSSION Have students make some rough guesses about people s behavior based on their survey results. Ask: Do you think it is more likely that a person will read a book or go to a movie? eat breakfast or eat at a fast-food restaurant? like liver or like Mondays? Take a vote and record the results on the board. Name Date STUDY LINK 9 1 Trivia Survey Study Link Master Conduct the survey below. The results will be used in Lesson 9-6. Find at least five people to answer the following survey questions. You can ask family members, relatives, neighbors, and friends. BE CAREFUL! You will not ask every person every question. Pay attention to the instructions that go with each question. Record each answer with a tally mark in the or No column. Answers vary. Question No 1. Is Monday your favorite day? (Ask everyone younger than 20.) 2. Have you gone to the movies in the last month? (Ask everyone older than 8.) 3. Did you eat breakfast today? (Ask everyone over 25.) 4. Do you keep a map in your car? (Ask everyone who owns a car.) 5. Did you eat at a fast-food restaurant yesterday? (Ask everyone.) 6. Did you read a book during the last month? (Ask everyone over 20.) 7. Are you more than 1 meter tall? (Ask everyone over 20.) 8. Do you like liver? (Ask everyone.) 70 py g g p Math Masters, p. 280 Lesson 9 6 751

Name Date 9 6 Trivia Survey Data Chart Class Results for the Trivia Survey Question No Total Total % 1. Monday Teaching Master Tabulating Survey Results for the Whole Class (Math Journal 2, p. 261; Math Masters, pp. 280 and 290 ) PROBLEM SOLVING 2. movies 3. breakfast 4. map 5. fast food 6. read 7. meter 8. liver Math Masters, p. 290 Tell students that they will use the results of all the surveys to check their guesses. The first step is to combine the results from all the surveys. The goal is to create a chart that shows the total number of and No answers to each question for the whole class. Ask for suggestions on how to do this most efficiently. One possibility is to divide the class into small groups of four or five. For each question on the survey, have the students in each group find the total number of answers and the total number of No answers for their group. Each group can then report its totals. You or a student volunteer can add these as they are reported. Finally, record the total number of and the total number of No answers to each question on the transparency of Math Masters, page 290. Students copy the results in the and No columns on page 261 in their journals. They add the and No results and record the sums in the Total column. These are the total numbers of people who answered the survey questions. Next, students record the answers as a fraction of the total number of answers in the T otal column. If necessary, help them complete the T otal column for the first two rows of the chart. At this point, the classroom chart might look as follows: Date 9 6 Trivia Survey Results 1. The chart below will show the results of the trivia survey for the whole class. Wait for your teacher to explain how to fill in the chart. Question No Total % 1. Monday 18 45 63 2. movies 57 21 78 Total 18_ 63 57_ 78 Class Results for the Trivia Survey Question No Total T otal % 1. Is Monday your favorite day? 2. Have you gone to the movies in the last month? 3. Did you eat breakfast today? 4. Do you keep a map in your car? 5. Did you eat at a fast-food restaurant yesterday? 6. Did you read a book during the last month? 7. Are you more than 1 meter tall? 8. Do you like liver? 2. On the basis of the survey results, is it more likely that a person will a. read a book or go to a movie? Answers vary. Analyzing the Survey Results (Math Journal 2, p. 261) Have students analyze the survey results so far. Ask: Do you think it is more likely that a person will read a book or go to a movie? eat breakfast or eat at a fast-food restaurant? like liver or like Mondays? b. eat breakfast or eat at a fast-food restaurant? c. like liver or like Mondays? Math Journal 2, p. 261 752 Unit 9 Fractions, Decimals, and Percents

Some students might argue that you need to simply compare the answers. Example: Suppose that 45 out of 50 people interviewed read a book and that 57 out of 78 people saw a movie last month. Is it correct to conclude that because more people saw a movie than read a book, people are more likely to go to the movies than to read a book? Does the total number of people interviewed need to be taken into account? This discussion is crucial to understanding why percents are useful. Students should see that it is difficult to compare quantities that are expressed as fractions with unlike denominators. Explain that this is why we rename fractions with unlike denominators as fractions that have the same denominator. The denominator 100 used in percents is especially useful, because in our base-ten system, it is easy to rename such fractions as decimals and percents. Once students understand why it is helpful to rename the fraction of answers as percents, have them use their calculators to fill in the % column. Ask them to round the answers to the nearest whole percent. Students completed charts should resemble your classroom chart, which might look like this: Date 9 6 Planting a Vegetable Garden Kim and Carl decide to plant a vegetable garden. Solve the following problems about their garden. Sample number models are given. 1. Kim and Carl plan to make their garden in the shape of a rectangle that is 8 feet long. They have 36 feet of fencing. How wide should their garden be if they want to use all the fencing? (36 2) - 8 = w (36 2) - 8 = 10 Answer: 10 feet wide 2. Pepper plants are on sale. The original price for 6 plants was $14.95. The sale price for 6 plants is $9.72. If they purchase 12 plants on sale, how much will they spend? $9.72 2 = c Answer: $19.44 $9.72 2 = $19.44 3. Some small vegetable seeds come attached to a 15-foot tape instead of in a seed packet. Kim purchased lettuce, carrot, and radish seed tapes, each costing $4.95. What is the cost per foot for a seed tape? $4.95 15 = f $4.95 15 = $0.33 Answer: 33 cents 4. Carl told Kim that a radish takes about 600 hours to grow after the seed is planted. About how long, in weeks and days, does Kim have to wait to eat a radish after she plants the seeds? (600 24) 7 = w Answer: 3 weeks 4 days (600 24) 7 3 R4 Math Journal 2, p. 261A 178A 178B Question No Total % 1. Monday 18 45 63 2. movies 57 21 78 Total 18_ 63 57_ 78 29% 73% Have partners use their completed table to answer Problem 2 at the bottom of journal page 261. Date Adjusting the Activity Have students combine the trivia survey data from all of the fourthgrade classes in the school. Discuss why % estimates based on the combined data are more reliable than estimates based on the data collected by any single classroom. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L 9 6 Planting a Vegetable Garden continued 5. The tomatoes take about 77 days to grow. The leaf lettuce takes 45 days to grow. How many hours longer does it take the tomatoes to grow than the leaf lettuce? (77-45) 24 = h Answer: 768 hours (77-45) 24 = 768 6. Carl and Kim s garden was a great success. Kim and Carl picked 132 tomatoes from their garden. They put aside a third of the tomatoes to make spaghetti sauce. If each batch of spaghetti sauce uses 10 tomatoes, how many full batches of sauce will they be able to make? (132 3) 10 = b (132 3) 10 4 R4 Answer: 4 batches 178A 178B 7. They sold most of the carrots at farmer s markets. They tied the carrots into bundles of 6. Then they placed 8 bundles into each basket. If they sold 15 baskets of carrots during the season, how many carrots did they sell in all? 6 8 15 = c Answer: 720 carrots Try This 6 8 15 = 720 8. They picked about 23 pounds of green beans over the summer. The family ate about 12 pounds of green beans. Their mother froze the rest in plastic bags weighing about 22 ounces each. About how many bags of green beans did their mother freeze? (Hint: There are 16 ounces in a pound.) (23-12) 16 = 176; 176 22 = b Answer: 8 bags (23-12) 16 = 176; 176 22 = 8 Math Journal 2, p. 261B Lesson 9 6 753

Date 9 6 Math Boxes 1. If you threw a 6-sided die 54 times, about how many times would you expect it to land on a number less than 3? Choose the best answer. 9 times 12 times 18 times 36 times Store Y Sample answer: Show how you solved the problem. Store X: $35 / 10 = $3.50, 2 $3.50 = $7.00, and $35 - $7 = $28. Store Y: $32 / 4 = $8, and $32 - $8 = $24. 5. What is the area of the triangle? Include the correct unit. 1_ Number model: 2 (8 6) = 24 Area = 24 in 2 6" 8" 81 2. Name a percent value Sample answers: a. greater than 1_ 4 and less than 2_ 3. 50% b. less than 4_ 5 and greater than 5_ 8. 75% 3. Store X is selling bathing suits at 20% off 4. If 1 inch on a map represents 200 miles, then the regular price of $35. Store Y is selling the same suits for 1_ off the regular price of a. 5 inches represent 1,000 miles. 4 $32. Which store is offering the better buy? b. 8 inches represent 1,600 miles. 38 39 59 Math Journal 2, p. 262 6. a. Which is warmer, -15 C or -3 C? 3 C How many degrees warmer? 12 C b. Which is colder, -15 C or -20 C? 20 C How many degrees colder? 5 C 61 62 c. 4 inches represent 800 miles. d. 3 1_ 4 inches represent 650 miles. 1 3_ 4 e. inches represent 350 miles. 136 60 139 145 2 Ongoing Learning & Practice Solving Number Stories with Multiplication and Division (Math Journal 2, pp. 261A and 261B) INDEPENDENT Students solve multiplication and division number stories about gardening. Some problems involve multistep calculations and interpreting remainders. Students write a number model with an unknown, solve the problem, and then write a summary number model. Math Boxes 9 6 (Math Journal 2, p. 262) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-8. The skill in Problem 6 previews Unit 10 content. Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem 4 Use Math Boxes, Problem 4 to assess students ability to interpret a map scale. Students are making adequate progress if they are able to solve Problems 4a 4c. Some students may be able to solve Problems 4d and 4e, which involve fractions of inches. [Operations and Computation Goal 7] Study Link Master Name Date STUDY LINK 9 6 Use Percents to Compare Fractions 1. The girls varsity basketball team won 8 of the 10 games it played. The junior varsity team won 6 of 8 games. Which team has the better record? Explain your reasoning. The varsity team. They won 8_ 10 = 80% of their games. The junior varsity team won 6_ 8 = 3_ 4 = 75% of their games. 2. Complete the table of shots taken (not including free throws) during a game. Calculate the percent of shots made to the nearest whole percent. 62 207 Study Link 9 6 (Math Masters, p. 291) Home Connection Students use percents to compare quantities expressed as fractions with unlike denominators. INDEPENDENT Player Shots Made Shots Missed Total Shots _ Shots Made Total Shots % of Shots Made 1 5 12 17 5_ 17 29% 2 5 6 11 5_ 11 45% 3 3 0 3 3_ 3 100% 4 9 2 11 9_ 11 82% 5 4 3 7 4_ 7 57% 6 11 5 16 11_ 16 69% 7 6 4 10 6_ 10 60% 8 1 1 2 1_ 2 50% 3. The basketball game is tied. Your team has the ball. There is only enough time for one more shot. Based only on the information in the table, which player would you choose to take the shot? Why? Sample answer: I would choose Player 4, who has taken 11 shots and made 82% of her shots. Player 3 has a higher percent of shots made (100%), but she has only taken 3 shots. Practice 3_ 6, 1_ 4 9_ 10 or 1_ 2 4. 1_ 3 + 1_ 6 = 5. = 3_ 4-1_ 2 6. = 7_ 10 + 1_ 5 7. 5_ 8-1_ 4 = Math Masters, p. 291 3_ 8 291 754 Unit 9 Fractions, Decimals, and Percents

3 Differentiation Options READINESS Comparing Estimates for the Fraction-of a Collection (Math Masters, p. 292) SMALL-GROUP 5 15 Min To explore the comparison of quantities expressed as fractions with unlike denominators using a concrete model, have students compare estimates for the number of red trapezoids in a collection of pattern blocks. Have students share their strategies for making comparisons. Discuss how finding nearby easy fractions or converting to decimals could help them compare their estimates. Ask why estimates with different denominators cannot be compared directly. Name Date 9 6 Fraction-of a Collection Part One 1. Estimate the total number of pattern blocks in the jar given to you by your teacher. pattern blocks 2. Estimate the total number of red trapezoids in the jar. red trapezoids 3. Write your estimates as a fraction. total number of red trapezoids total number of pattern blocks = 4. Record the estimates made by the members of your group. Part Two 5. Count the number of pattern blocks in the jar. pattern blocks 6. Count the number of red trapezoids in the jar. red trapezoids 7. Record the counts as a fraction. total number of red trapezoids total number of pattern blocks = Part Three Teaching Master Answers vary. 8. Which of your group members estimates do you think was closest to the actual fraction of trapezoids in the jar? Explain why you think so. 59 ENRICHMENT Graphing Survey Results (Math Journal 2, p. 261; Math Masters, p. 403) PARTNER 15 30 Min Math Masters, p. 292 To apply students ability to represent data, have them graph the results of the class survey on centimeter grid paper (Math Masters, page 403). You might suggest that students use a side-by-side (double) bar graph. For example: Survey Questions 1. Monday 2. movies 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% No EXTRA PRACTICE Taking a 50-Facts Test (Math Masters, pp. 410, 414, and 416) SMALL-GROUP 5 15 Min See Lesson 3-4 for details regarding the administration of a 50-facts test and the recording and graphing of individual and optional class results. Lesson 9 6 755