Exploring Types of Data

4.1 3.3 Exploring Types of Data Student Book pp. 120 121 Teacher s Resource pp. 13 15 GOAL Tell the difference between first-hand data and second-hand data. Preparation and Planning Masters Explore BLM-A 4.1 p. 122 Explore BLM-B 4.1 p. 123 Key Entire exploration Assessment Question About the Math This exploration introduces students to first-hand data (data they collect) and second-hand data (data collected by other people). Students need to suggest first-hand data to collect, collect the data, and organize their findings. Some students may have difficulty asking a reasonable question and/or organizing the data they collect. Offer some suggestions of what data students might collect. For example, for figure A in the Student Book, count the number of students who see the rabbit first and the number who see the duck first. For figure D, compare how long it takes before someone sees the seal and how long before they see the bear. Differentiating Instruction You may need to review the organization of collecting data. Ask: What question would you ask to collect first-hand data on the months of birthdays in the class? (What month is your birthday?) How would you organize the data? Would you just ask What month is your birthday? and then write down the month randomly on a piece of paper? (No, I would create a chart with all the birthdays listed in order and use tallies to keep track.) How would you present the information you found? (I would add up all the months and present the month with the most birthdays, the month with the least birthdays, how many students were asked, etc.) For students who need scaffolding during independent practice, provide Explore BLM-A 4.1. For students who need scaffolding to help create a game, provide Explore BLM-B 4.1. Answers to Explore BLM-B 4.1 Answers will vary depending on which 2 optical illusions the students choose. Copyright 2009 by Nelson Education Ltd. Overview 4.1: Exploring Types of Data 121

E-A Name: Date: 4.1 Exploring Types of Data Student Book pages 120 121 What first-hand data can you collect about optical illusions? Step 1: Look at the optical illusions on Student Book p. 121. Step 2: Pick 1 optical illusion for which you can collect first-hand data. Figure Step 3: Who will you collect your data from? Step 4: What might you ask about the optical illusion? Step 5: How are you going to organize your data? Step 6: Collect your first-hand data about the optical illusion. Step 7: What did you learn from the data you collected? Step 8: How will you present your findings to the class? 122 Explore BLM-A 4.1: Exploring Types of Data Copyright 2009 by Nelson Education Ltd.

E-B Name: Date: 4.1 Exploring Types of Data Student Book pages 120 121 GOAL Tell the difference between first-hand data and second-hand data. What first-hand data can you collect about optical illusions? Step 1: Choose an optical illusion from Student Book p. 121. Figure first-hand data Information that you collect second-hand data Information that others have collected Step 2: What 2 figures can you see in the picture? and Step 3: Think of a question that you could ask your classmates about the optical illusion. Step 4: Organize your first-hand data in the table below. Do not forget to label the columns. Hint: The column headings are the names of the figures in the picture. Step 5: What did you find out about this data? For example, did someone see one figure more than the other? Copyright 2009 by Nelson Education Ltd. Explore BLM-B 4.1: Exploring Types of Data 123

4.2 3.3 Using First-Hand Data Student Book pp. 122 125 Teacher s Resource pp. 16 20 GOAL Create and answer questions using first-hand data. Preparation and Planning Masters Key Question 6 Assessment Question Checking and Practising BLM 4.2 pp. 125 126 Learning BLM 4.2 pp. 127 128 About the Math This lesson discusses the 4 ways to collect first-hand data: interviews, surveys, experiments, and observations. The lesson focuses on the types of survey questions asked and how these questions can affect a conclusion that might be drawn. Students may have difficulty writing a question that yields useful data. Have these students work in small groups to generate a series of related questions for collecting data. Then instruct them to choose which is the most suitable, and test the questions by collecting a small amount of data to see if they are on track. Differentiating Instruction Write this survey question on the board: What is your favourite television show? Tell students that you are conducting a survey to see what television shows all Grade 5 students in your city like to watch. Ask them if they think this is a good question. Inform students that to see if this is a good question, you are going to sample it by asking the class. Ask students to state their favourite television show, and record all the shows on the board or on chart paper. Ask: Was this an effective question? (No, there are too many possible answers and only 28 students were surveyed. If you surveyed all the Grade 5 students in the city, it would be difficult to organize all the data.) How would you narrow the question to have fewer possible answers? (What is your favourite type of television show [e.g., sports, comedy, news, mystery, other]?) Survey students with the revised question and discuss how this question was a better choice. For students who need scaffolding during independent practice, provide Checking and Practising BLM 4.2. For students who need extra learning support, provide Learning BLM 4.2. Answers to Learning BLM 4.2 Step 3: There are only 8 choices so you can use a table to organize the responses. Step 4: A tally chart lets you keep track of all the choices. When complete, you can easily see which snacks are the most popular. Step 5: They should sell pretzels, pudding, cereal bars, and apples because they are the 4 most popular snacks; pretzels 38, pudding 33, cereal bars 31, apples 20 Reflecting: I think she should definitely not buy oranges or yogurt because they were chosen by the fewest number of students; She would use first-hand data because the question was about what students in her school would buy, and it is easy to ask them in a survey. 124 Overview 4.2: Using First-Hand Data Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 4.2 Using First-Hand Data Page 1 Student Book pages 122 125 Checking 1. Matthew asked this question. Which 2 snacks would you buy most often at morning break? apple pretzels cereal bar yogurt orange sunflower seeds raisins pudding a) Do you think Matthew got the same data that Cara got? Look at Cara s question on Student Book p. 123. What is the same about Cara and Matthew s survey question? What is different about Cara and Matthew s survey question? Does the difference change the data that Cara and Matthew collect? How? b) Should Cara s class use Cara s data or Matthew s data to figure out which snacks to sell? Explain your thinking. Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 4.2: Using First-Hand Data 125

C&P Name: Date: 4.2 Using First-Hand Data Page 2 Practising 6. a) Write a question that you can answer using first-hand data. Remember that it has to be a question for which you can collect the data. b) Explain why your question can be answered using first-hand data. c) Which method would you use to collect the data? Circle one. do interviews do a survey do an experiment observe Give a reason for your choice. d) Collect the data using the method you chose in part c). Remember to organize your data. What did you find out about your question? 126 Checking & Practising BLM 4.2: Using First-Hand Data Copyright 2009 by Nelson Education Ltd.

L Name: Date: 4.2 Using First-Hand Data Page 1 Student Book pages 122 125 GOAL Create and answer questions using first-hand data. The students in Cara s class plan to raise money by selling snacks. Cara wants to figure out which 4 snacks they should sell. Which snacks should they sell? Step 1: You need first-hand data to find out which snacks to sell. There are 4 ways to collect first-hand data. Step 2: Determine which ways of collecting first-hand data you 1. Observe. can or cannot do. 2. Do an experiment. 1. You cannot observe because there have not been any sales. 3. Do interviews. 2. You cannot do an experiment. 4. Do a survey. 3. You can do interviews, but they would take too long and be too much work. 4. You can do a survey because it will give you the information you need. Step 3: Write a survey question and then improve it. 1st version: Which type of snack do you prefer? 2nd version: Which snack would you buy at morning break? 3rd version: Which one of these snacks would you buy at morning break? apple pretzels cereal bar yogurt orange sunflower seeds raisins pudding Why is the 3rd version the best question? Copyright 2009 by Nelson Education Ltd. Learning BLM 4.2: Using First-Hand Data 127

L Name: Date: 4.2 Using First-Hand Data Page 2 Step 4: Collect the data in a tally chart. Students Snack Choices Snack apple orange pretzels sunflower seeds cereal bar raisins yogurt pudding Tally Total 20 4 38 12 31 15 8 33 Why is the data organized in a tally chart? Step 5: Determine the answer. Based on the tally chart, what 4 snacks should they sell? How many students chose each of the 4 most popular snacks? Reflecting Which snacks do you think Cara should not buy? Explain your thinking. Why would Cara use first-hand data instead of second-hand data? 128 Learning BLM 4.2: Using First-Hand Data Copyright 2009 by Nelson Education Ltd.

4.3 3.3 Using Second-Hand Data Student Book pp. 126 128 Teacher s Resource pp. 21 24 GOAL Create questions that can be answered using second-hand data. Preparation and Planning Masters Key Question 5 Assessment Question Checking and Practising BLM 4.3 pp. 130 131 Learning BLM 4.3 pp. 132 133 About the Math This lesson focuses on creating appropriate questions that can be answered using second-hand data. The Internet is cited as a resource for collecting second-hand data, but magazines, newspapers, and reference books can also be used. It is important to guide students to the most appropriate questions that will help them find the answers. For example, if a student was going to visit Saskatchewan and wanted to know which city has the best summer (Moose Jaw or Regina), their question to search should not be which city has the best summer. Instead, they should ask which city has the highest average temperatures in July and August, or which city has the least average amount of rainfall. Differentiating Instruction Highest Recorded Temperature in Calgary, Alberta Month J F M A M J J A S O N D Temp ( C) 16 22 19 27 31 33 33 33 32 28 22 17 Write the above chart on the board, on chart paper, or on an overhead. Ask students to define second-hand data. (information that others have collected) Tell students that this chart is an example of second-hand data. Ask who could have collected the data and where this information came from. (meteorologists, the Weather Network website) Ask students how they know you did not collect this data first-hand. (because you don t have the equipment to measure the temperature in Calgary, and even if you received the information for every day in each month and found the average, you got the data from someone else) For students who need scaffolding during independent practice, provide Checking and Practising BLM 4.3. For students who need extra learning support, provide Learning BLM 4.3. Answers to Learning BLM 4.3 Step 2: Because it tells you all the recorded information about the weather across Canada Newspaper clippings, reference books, weather station Step 3: Answers will vary depending on what website or resource students use. Reflecting: Answers will vary; For example, temperature; He would have to go to these cities to collect first-hand data, and that would not be practical. It is easier to get second-hand data that experts have collected. Copyright 2009 by Nelson Education Ltd. Overview 4.3: Using Second-Hand Data 129

C&P Name: Date: 4.3 Using Second-Hand Data Page 1 Student Book pages 126 128 Checking 1. Marina is interested in Olympic skiing. a) Write 2 questions about Olympic skiing that Marina can answer using second-hand data. You will need Internet access newspapers, magazines, and reference books Hint: Think about interesting facts and records involved in Olympic skiing. Question 1: Question 2: b) Where might you find second-hand data to answer your questions? Practising 3. Think about the following question: How many students are in each grade in your school? a) Why might it be easier to answer this question using second-hand data rather than first-hand data? Remember: First-hand data must be collected by you. b) Where might you find second-hand data to answer this question? 130 Checking & Practising BLM 4.3: Using Second-Hand Data Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 4.3 Using Second-Hand Data Page 2 4. Write 2 questions about the data in this chart. Suggested words in your questions: Canadian city, temperatures, month, highest, lowest Question 1: City July Aug. Sept. Yellowknife 16.5 14.1 6.7 Winnipeg 19.5 18.5 12.3 Fort McMurray 16.8 15.3 9.4 Regina 18.8 18.0 11.7 Question 2: Penticton 20.4 20.1 14.9 5. There are many waterfalls in the world, including Della Falls on Vancouver Island. a) Write a question about waterfalls that you can answer using second-hand data. Hint: Think about what information people have compared about different waterfalls. b) Explain how you know your question can be answered using second-hand data. c) Where can you find second-hand data to answer your question? Give a reason for your choice. d) Collect the data (using books, the Internet, magazines, etc.). Answer your question. Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 4.3: Using Second-Hand Data 131

L Name: Date: 4.3 Using Second-Hand Data Page 1 Student Book pages 126 128 GOAL Create questions that can be answered using second-hand data. René is from Calgary and his cousin is from Winnipeg. They both love winter. What question can René ask and answer to compare winter in Calgary with winter in Winnipeg? Step 1: You need to know how much snow each city gets in the winter. So, you need to write a clear question. Question: Does Calgary or Winnipeg receive more snow in the winter? Step 2: Answer the question using second-hand data. You can get information about snowfall from Environment Canada. Why is Environment Canada a good place to find this second-hand data? 132 Learning BLM 4.3: Using Second-Hand Data Copyright 2009 by Nelson Education Ltd.

L Name: Date: 4.3 Using Second-Hand Data Page 2 Can you think of any other places where you can find information about the snowfall in Calgary and Winnipeg? Step 3: Use the Environment Canada website or another source to answer the question. Which city had the most snowfall in the winter? How many centimetres? Where did you find the answer? Reflecting What other questions could René have asked about winter climate? Why do you think René decided to use second-hand data instead of first-hand data? Remember: You collect first-hand data. So you would measure the amount of snowfall. Copyright 2009 by Nelson Education Ltd. Learning BLM 4.3: Using Second-Hand Data 133

4.4 3.3 Interpreting Double-Bar Graphs Student Book pp. 132 135 Teacher s Resource pp. 30 34 GOAL Interpret and compare double-bar graphs. Preparation and Planning Masters Key Question 5 Assessment Question Checking and Practising BLM 4.4 pp. 135 136 Learning BLM 4.4 pp. 137 138 About the Math This lesson uses double-bar graphs to compare 2 sets of data. Students need to have a good understanding of the importance of the title, scale, and legend in order to interpret the data. Review with students why there is a legend, what the colours represent, and why the colours are important. Have students look at the bar graph in the Communication Tip box on Student Book p. 133. Discuss what the blue and red bars represent and why the 2 colours are needed to represent the data. Differentiating Instruction Place the double-bar graph from the Communication Tip box from Student Book p. 133 on the board, on an overhead, or on chart paper. Beside it, construct the same information from that double-bar graph, only with a scale of 5. Ask: What is the same about both of these graphs? (title, legend, labelling, information) What is the difference? (scale) Does the scale affect the way the information is presented? (Yes, the graph with a scale of 1 is stretched out so I can see the accurate reading of the information. When I look at it, I can tell which type of music is most popular and least popular by the height of the bars. In the graph with the scale of 5, the bars are close in height and I can t tell what the exact amount is.) For students who need scaffolding during independent practice, provide Checking and Practising BLM 4.4. For students who need extra learning support, provide Learning BLM 4.4. Answers to Learning BLM 4.4 Step 1: Step 2: Province Population for 2001 BC 170 000 AB 157 000 SK 130 000 MB 150 000 Total 607 000 Province Population for 2001 BC 170 000 AB 157 000 SK 130 000 MB 150 000 Total 607 000 Step 3: yes; yes; 10 000; 25 000 They are different scales because they count by different numbers. Reflecting: Yes, the graphs show the same data. They both sum to the same amounts. 134 Overview 4.4: Interpreting Double-Bar Graphs Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 4.4 Interpreting Double-Bar Graphs Page 1 Student Book pages 132 135 Checking 1. Angus and Esther asked 40 students from Grade 5 and 40 students from Grade 6 a question. They graphed their results. a) What question do you think they asked? Hint: Look at the title and labels. b) How are the 2 graphs the same? Angus s Graph Favourite Winter Olympic Sport Number of students 20 16 12 8 4 0 speed skating snowboarding bobsledding Winter Olympic sport Esther s Graph downhill skiing Favourite Winter Olympic Sport Winter Olympic sport cross-country skiing downhill skiing bobsledding snowboarding speed skating Grade 5 Grade 6 0 4 8 121620 Grade 5 Grade 6 cross-country skiing Number of students How are they different? c) Which winter Olympic sport is the most popular? Do both classes agree? How do you know? d) Why did Angus and Esther use double-bar graphs? Why did they need pairs of bars representing 2 different sets of data? Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 4.4: Interpreting Double-Bar Graphs 135

C&P Name: Date: 4.4 Interpreting Double-Bar Graphs Page 2 Practising 2. Meredith keeps track of the number of telephone calls she makes and e-mail messages she writes each month. Does Meredith make more telephone calls or send more e-mails? Meredith s Communications Number of communications 350 300 250 200 150 100 50 0 telephone calls e-mails Jan. Feb. Mar. Apr. May June July Month Aug. Sept. Oct. Nov. Dec. Look at the number of telephone calls every month. Find the sum. Look at the number of e-mails each month. Find the sum. Which sum is greater: telephone calls or e-mails? 5. Susan found these 2 graphs. 100 people were interviewed to obtain the data for each graph. a) Do the graphs show the same data? Explain. Hint: Compare the titles, labels, scales, legends, and bars. b) Which graph would you use to display the data? Think: Which graph displays the data the best? People s Bathing Habits Number of people 60 40 20 0 shower bath wash Bathing habit People s Bathing Habits Number of people 60 55 morning 50 evening 45 40 35 30 25 20 15 10 5 0 shower bath wash Bathing habit morning evening 136 Checking & Practising BLM 4.4: Interpreting Double-Bar Graphs Copyright 2009 by Nelson Education Ltd.

L Name: Date: 4.4 Interpreting Double-Bar Graphs Page 1 Student Book pages 132 135 GOAL Interpret and compare double-bar graphs. For a social studies project, Desmond compares the Aboriginal populations in 4 provinces. He found the information in double-bar graphs like these. double-bar graph A graph with pairs of bars; each pair of bars represents 2 different sets of data Do these double-bar graphs show the same data? Aboriginal Populations in Western Provinces Number of people 180 000 160 000 140 000 120 000 100 000 80 000 60 000 40 000 20 000 0 1996 2001 BC AB SK MB Province Aboriginal Populations in Western Provinces Number of people 200 000 150 000 100 000 50 000 0 1996 2001 BC AB SK MB Province Step 1: Look at the bars for 2001 on the first graph. Fill in the estimated populations for 2001 in the chart for each province. The first one is done for you. Population Province for 2001 BC 170 000 AB SK MB Total Add up the populations to find the estimated total number of Aboriginal people. You may use a calculator. Copyright 2009 by Nelson Education Ltd. Learning BLM 4.4: Interpreting Double-Bar Graphs 137

L Name: Date: 4.4 Interpreting Double-Bar Graphs Page 2 Step 2: Look at the bars for 2001 on the second graph. Fill in the estimated populations for 2001 in the chart for each province. The first one is done for you. Add up the populations to find the estimated total number of Aboriginal people. You may use a calculator. Step 3: Compare the 2 graphs. Are the titles the same in both graphs? Are the legends the same in both graphs? Population Province for 2001 BC 170 000 AB SK MB Total legend An explanation of the symbols or colours on a graph Look at the scales. The graph on the left counts by. The graph on the right counts by. Are the scales the same or different? Explain. Reflecting Do you think the 2 graphs show the same data? Look at your answers above to help you explain how you know. 138 Learning BLM 4.4: Interpreting Double-Bar Graphs Copyright 2009 by Nelson Education Ltd.

4.5 3.3 Constructing Double-Bar Graphs Student Book pp. 136 139 Teacher s Resource pp. 35 39 GOAL Construct and interpret double-bar graphs. Preparation and Planning Masters Key Question 3 Assessment Question Checking and Practising BLM 4.5 pp. 140 141 Learning BLM 4.5 pp. 142 143 1 cm Grid Paper, MB p. 22 About the Math In this lesson, students construct double-bar graphs to compare 2 sets of data. Students may have difficulty remembering that they need to include a correct scale, legend, labels, and title. Having an example of a double-bar graph on your math wall will help students. Providing a checklist for reference will also be useful. For example: Do you have a title that describes your graph? Did you choose a good scale? Did you label the side with your scale? Did you label the items? Did you include a legend? Did you choose 2 different colours for the bars? Differentiating Instruction Students may have difficulty choosing an appropriate scale. List numbers of possible data on the board (e.g., 82, 95, 23, 45, 52). Ask: Would a scale of 1 be appropriate? (No, because the scale would have to be too tall to reach 95.) What scale would you use for this data? (Count by 10s until 100. That will leave enough room to find the numbers that fall in between the 10s.) Repeat this activity with different sets of numbers, such as 4, 5, 6, 8, 12, 16 (scale of 2) and 2, 3, 3.5, 5, 6.5, 8.5 (scale of 1). For students who need scaffolding during independent practice, provide Checking and Practising BLM 4.5. For students who need extra learning support, provide Learning BLM 4.5. Answers to Learning BLM 4.5 Step 2: 95; 10 Step 3: Favourite racquet sport; tennis, badminton, squash, none/other Step 4: Number of students Step 5: Favourite Racquet Sports Step 6: Maple School; Pine School Answers will vary depending on the class results of the tally. Reflecting: Answers will vary based on the tallies. Copyright 2009 by Nelson Education Ltd. Overview 4.5: Constructing Double-Bar Graphs 139

C&P Name: Date: 4.5 Constructing Double-Bar Graphs Page 1 Student Book pages 136 139 Checking 1. The following chart shows the hours of sunlight in 6 northern locations on the longest day (summer solstice) and the shortest day (winter solstice) of the year. a) Display the data in a double-bar graph. b) What is the title? Hint: Look at the title of the chart. Location You will need 1 cm grid paper pencil crayons a ruler Hours of Sunlight in Six Northern Locations Hours of sunlight on summer solstice Hours of sunlight on winter solstice Ketchikan 17.5 7.0 Anchorage 19.5 5.5 Fort Smith 18.0 9.0 Yellowknife 20.0 6.5 Norman Wells 22.0 4.0 Arctic Circle 24.0 0.0 What 2 colours did you choose for the 30 28 legend? Remember that one bar represents 26 24 Hours of sunlight on summer solstice and the other Hours of sunlight on winter solstice. Hours of sunlight 22 20 18 16 14 12 10 8 6 4 What is the scale? 2 0 Ketchikan Anchorage Fort Smith Yellowknife Norman Wells Arctic Circle Location c) How many bars did you draw for hours of sunlight at the Arctic Circle? Why? 140 Checking & Practising BLM 4.5: Constructing Double-Bar Graphs Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 4.5 Constructing Double-Bar Graphs Page 2 Practising 3. A travel company surveyed customers about the types of holidays they prefer. a) Display the second-hand data in a double-bar graph. b) Step 1: Ask your classmates the following questions: Favourite Holiday in Summer and Winter Season Visiting another country Which type of holiday would you like to take in summer and in winter? visiting another country visiting family or friends/attending festivals camping, hiking, or skiing seeing Canada by car Step 2: Record their answers in the following tally charts. Camping, hiking, or skiing Visiting family or friends/ attending festivals Seeing Canada by car summer 34 26 22 18 winter 53 18 26 3 Summer Holiday Tallies Winter Holiday Tallies visiting another country camping, hiking, or skiing visiting family or friends/ attending festivals seeing Canada by car visiting another country camping, hiking, or skiing visiting family or friends/ attending festivals seeing Canada by car Step 3: Make a double-bar graph with your first-hand data. c) Were the same numbers of people surveyed in both graphs? How do you know? Was there an activity or activities that showed the same results on both graphs? Why do you think that happened? Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 4.5: Constructing Double-Bar Graphs 141

L Name: Date: 4.5 Constructing Double-Bar Graphs Page 1 Student Book pages 136 139 GOAL Construct and interpret double-bar graphs. Lauren is planning after-school activities at a community centre. She asked students from 2 schools which racquet sport they preferred to play. The chart shows her results. You will need 1 cm grid paper pencil crayons a ruler Favourite Racquet Sport School Maple School Pine School Tennis 69 95 Badminton 56 45 Squash 10 17 None/ other 8 10 How can you create and interpret a double-bar graph to describe students racquet-sport preferences? Step 1: Use a double-bar graph to compare the preferences of students in 2 schools, using the same categories. Step 2: Create a scale for the double-bar graph. The greatest number is close to 100. Which number in the chart is close to 100? What is the scale? Favourite Racquet Sport 100 90 80 70 60 50 40 30 20 10 0 tennis badminton squash none/ other Favourite racquet sport Number of students Step 3: Label the horizontal axis. What is the label on the horizontal axis? What are the categories on the horizontal axis? Step 4: Label the vertical axis. What is the label on the vertical axis? Step 5: Create a title for the double-bar graph. What is the title? 142 Learning BLM 4.5: Constructing Double-Bar Graphs Copyright 2009 by Nelson Education Ltd.

L Name: Date: 4.5 Constructing Double-Bar Graphs Page 2 Step 6: Create a legend for the double-bar graph. Which school do the dark grey bars represent? Which school do the light grey bars represent? Fill in the names of the schools for the legend. Ask 2 groups of classmates this question. Which racquet sports do you prefer: tennis, badminton, squash, none/other? Record your results in the tally chart below: Group 1 Group 2 Racquet Sport Tallies Racquet Sport Tallies tennis badminton squash none/other tennis badminton squash none/other Display your results in a double-bar graph. Make sure that the colour of the bars for the first group is different from the colour of the bars for the second group. Reflecting 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 tennis badminton squash none/other What does the graph tell you about your classmates racquet sport preferences? Which sport do they like the most? Which sport do they like the least? Remember to look at the data from both bars. Copyright 2009 by Nelson Education Ltd. Learning BLM 4.5: Constructing Double-Bar Graphs 143

4.6 3.3 Solving Problems by Creating Diagrams Student Book pp. 140 142 Teacher s Resource pp. 40 43 GOAL Use diagrams, charts, or graphs to solve problems. Preparation and Planning Masters Key Question 4 Assessment Question Checking and Practising BLM 4.6 pp. 145 146 Learning BLM 4.6 pp. 147 148 1 cm Grid Paper, MB p. 22 About the Math In this lesson, students use problem-solving strategies to organize data. It would be useful to have a problem-solving chart on your Math Wall for students to reference. Make sure they understand each step. Step 1: Understand the Problem. What information has been given in the problem? What do I need to find? Step 2: Make a Plan. How can I solve this problem? Is there more than one way? Which way is the most efficient? Step 3: Carry Out the Plan. Follow the steps in your plan. Did you show all the steps? Would someone be able to follow these steps to solve the problem? Step 4: Look Back. Did you make any errors? Was there a more efficient way to solve the problem? Would you add anything? Differentiating Instruction Some students may not be able to organize data in a tally chart (e.g., knowing how many columns, rows). Write the following question on the board: Last night and the night before, how many of you had 30 minutes of homework, less than 30 minutes of homework, or more than 30 minutes of homework? Ask: How would you organize the information and answers to the question? (tally chart) How can you organize the tally chart? (2 rows 1 for last night and the other for the night before. 3 columns 1 for less than 30 minutes, 1 for 30 minutes, and 1 for more than 30 minutes. Add 1 more row and 1 more column for headings.) Draw this on the board. Have students answer the question and keep track on the tally chart. Ask: How would you graph this information? Why? (double-bar graph because we can compare the 2 nights of homework side-by-side) How would you label the double bar graph? (2 bars would be last night and the night before. The horizontal axis would have less than 30 minutes, 30 minutes, and more than 30 minutes. The vertical axis would be the number of students, and the scale would be counting by 2s.) For students who need scaffolding during independent practice, provide Checking and Practising BLM 4.6. For students who need extra learning support, provide Learning BLM 4.6. Answers to Learning BLM 4.6 Step 3: You are going to check traffic for 5 days, so you need 5 rows, 1 for each day. There are 2 intersections, so you need 2 columns. You also need 1 more row and 1 more column for headings; Intersection 2 was the busiest. All the bars for intersection 2 were taller than the bars for intersection 1; Intersection 2 because there was more traffic. Reflecting: I would use a double-bar graph because it is easier to see which intersection has more traffic by seeing which bar is higher. 144 Overview 4.6: Solving Problems by Creating Diagrams Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 4.6 Solving Problems by Creating Diagrams Page 1 Student Book pages 140 142 Checking 1. The Grade 1 students are planning a field trip. They will have to cross a busy road, so they want to cross when the traffic is lightest. You will need 1 cm grid paper pencil crayons a ruler Should they go on the field trip in the morning or the afternoon? a) Describe how you would make your decision. Understand What is the problem that you need to solve? Make a Plan What would be a good way to find and organize the data? b) Would putting the data in a bar graph make the results easier to see? Explain your thinking. Hint: Remember the bar graph from the problem on Student Book p. 141. Was it easier to see the results? Why? Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 4.6: Solving Problems by Creating Diagrams 145

C&P Name: Date: 4.6 Solving Problems by Creating Diagrams Page 2 Practising 4. Star wants to know whether the population of the Prairie provinces is growing more quickly than the population of the Atlantic provinces. a) What data does she need to collect? From both Prairie and Atlantic provinces, Star needs. b) Collect the data and organize it in the chart. Where can you go to find the populations of each province? Fill in the chart below. Year Atlantic provinces Prairie provinces c) Construct a double-bar graph on graph paper. Which provinces populations are growing more quickly? How do you know? 146 Checking & Practising BLM 4.6: Solving Problems by Creating Diagrams Copyright 2009 by Nelson Education Ltd.

L Name: Date: 4.6 Solving Problems by Creating Diagrams Page 1 Student Book pages 140 142 GOAL Use diagrams, charts, or graphs to solve problems. There are 2 intersections near Matthew s school. The city council wants to install traffic lights at the busier intersection. You will need 1 cm grid paper pencil crayons a ruler At which intersection should the traffic lights be installed? Step 1: Understand You need to know which intersection has more traffic. Step 2: Make a Plan 1. Count the number of vehicles that go through the 2 intersections for 15 minutes before school and 15 minutes after school. 2. Record the data in a tally chart. 3. Make a double-bar graph. 4. Analyze the data. Step 3: Carry Out the Plan 1. Count the number of vehicles that go through the 2 intersections. 2. Record the data in a tally chart. How do know how many columns and rows you need for the tally chart? Traffic at Two Intersections Number of vehicles at Intersection 1 Day Mon. Tues. Wed. Thu. Fri. Number of vehicles at Intersection 2 Copyright 2009 by Nelson Education Ltd. Learning BLM 4.6: Solving Problems by Creating Diagrams 147

L Name: Date: 4.6 Solving Problems by Creating Diagrams Page 2 3. Use the data to make a double-bar graph. Traffic at Two Intersections Fri. Thurs. Day Wed. Tues. Mon. 0 10 20 30 40 Number of vehicles Intersection 1 Intersection 2 4. Analyze the data. Look at the bars. Which intersection was the busiest every day? How do you know? Where do you think the stop light should go? Why? Reflecting Would you use Matthew s tally chart or his double-bar graph to show where to install the traffic lights? Explain your choice. 148 Learning BLM 4.6: Solving Problems by Creating Diagrams Copyright 2009 by Nelson Education Ltd.