1. CONFIDENTIAL1 Good Afternoon! Today we will be learning about Double Bar Graphs Let’s warm up : 1) Judy has made 7 T-shirts. Each day she makes another 4 T-shirts. Harry has made 11 T-shirts and makes another 3 T-shirts everyday. How many T-shirts total will Judy and Harry have made after six days? 2) Steve has read 5 books. Each week he reads 3 more books. Emily has read 6 books. Each week she 2 more. How many books will each have read when they have read a total of 41 books? 1) 60 T-shirts 9) Steve 23 books; Emily 18 books

2. CONFIDENTIAL2 Let’s review what we did in the last session Survey: A survey is one way to collect information or data. When you conduct a survey, you ask a question and record the answers. The question for one class survey was, “What do you like to eat?” The answer choices were Chicken nuggets, corn, French fries, salad and tuna sandwich. What do you like to eat? AnswerTallyNumber Chicken nuggets13 Corn7 French fries6 salad0 tuna sandwich4 The answer choice nuggets was given more often.

3. CONFIDENTIAL3 Review To conduct a survey and organize your data keep in mind the following things.  Choose a topic for your survey to tell what the data shows.  Choose the questions that you will ask.  Show the answers on the table.  Organize the chart by making a tally mark for each answer.  Choose how many answers you will allow each person to give.  Keep track of the number of people you survey.

4. CONFIDENTIAL4 Review So, in general you should do the following steps : STEP 1: Write a question that has 3 or 4 possible answers. List the possible answers in a tally chart like the one shown. STEP 2: Survey 20 people. Allow each person to give only one answer. Make a tally mark for each answer. Then add the tally marks for each answer. STEP 3: Analyze your data, i.e. how would describe the results of your survey. Question: AnswerTallyNumber

5. CONFIDENTIAL5 Review Tally: A tally chart is a way to show the information or data you have collected. Use the tally chart to answer the questions. How many children are in your family? AnswerTallyNumber 12 213 38 42 More than 40 1) What is the survey question? [How many children are in your family?] 2) Which answer was given most often? Least often? [2 children; More than 4 children]

6. CONFIDENTIAL6 Review Mike has 4 baseball cards. Each week he gets 2 more cards. Fredrick has 3 baseball cards and gets 1 more card each week. How many baseball cards will each have when they have a total of 19 baseball cards? Here is the table of information about the problem. Mike’s cardsFredrick’s cardsTotal cards 437 6410 8513 10616 12719 Week1 Week2 Week3 Week4 How many cards each boy had when the total card is 19. Mike has 4 cards and Fredrick has 3 cards.

7. CONFIDENTIAL7 Review Make a table Read each sentence and then paraphrase, which says the same thing in a different way. Original sentenceParaphrase Art is twice bob’s age.Art’s age ÷ 2 = Bob’s age OR, Bob’s age × 2 = Art’s age Cal is half Dee’s age.Cal’s age × 2 = Dee’s age OR, Dee’s age ÷ 2 = Cal’s age Each person is 3 inches taller than the next tallest person. First person’s height + 3’ = Second person’s height Second person’s height + 3’ = Third person’s height

8. CONFIDENTIAL8 Together, Herman’s age and his sister’s age equal 27. Herman’s sister’s age is twice Herman’s age? How old is Herman? How old is his sister? Herman’s ageSister’s ageTotal age 123 246 369 4812 51015 61218 71421 81624 91827 Here is the table of information about the problem. Herman is 9 years old and his sister is 18 years old. Review

9. CONFIDENTIAL9 Let’s start with Double Bar Graphs Bar graphs are one of the many techniques used to present data in a visual form so that the reader may readily recognize patterns or trends. In the bar graphs, the objects or categories are listed along the horizontal axis and the associated numerical value is indicated by the length of a bar above the category. Bar graphs usually present categorical and numeric variables grouped in class intervals. The important point to note about bar graphs is their bar length or height—the greater their length or height, the greater their value.

10. CONFIDENTIAL10 A bar graph can be used to display data that can be counted. There are many characteristics of bar graphs that make them useful. Some of these are that:  They make comparisons between different variables very easy to see.  They clearly show trends in data, meaning that they show how one variable is affected as the other rises or falls.  Given one variable, the value of the other can be easily determined.

11. CONFIDENTIAL11 Number of nights below freezing point NovemberDecemberJanuary Seattle, WA277 Helena, MT162729 Table Look at the table below. It has rows and columns of numbers. The table shows the number of nights of two cities having temperature below freezing point. With the help of the data we formulate a bar graph comparing the two sets of data. NEXT PAGE

12. CONFIDENTIAL12 Seattle, WA Helena, MT 35 30 25 20 15 10 5 0 NovemberDecember Number of nights below freezing point Double Bar Graph Labels Title Key Interval January Seattle Helena

13. CONFIDENTIAL13 Double bar graph On a vertical bar graph, objects or categories are listed along a horizontal axis and the associated numerical value is indicated by the length of a bar above each category. The double (or group) vertical bar graph is an effective means of comparing sets of data about the same places or items. This type of vertical bar graph gives two or more pieces of information for each item on the x-axis instead of just one.

14. CONFIDENTIAL14 Susan saw many types of birds at her bird feeder. Mitch also saw many types of birds at his bird feeder. Susan Mitch 20 15 10 5 0 Number of birds Birds at Susan's and Mitch’s feeders Robin Sparrow Cardinal By reading the graph, you can see:  Susan saw five more robins than Mitch.  Mitch saw five more Sparrow than Susan.  Mitch and Susan both saw five cardinals. Types of birds

15. CONFIDENTIAL15 Mike Jen 35 30 25 20 15 10 5 0 Number of plants Mike's and Jen’s garden CarrotsLettuceBeans Types of plants Peas Use the bar graph to answer the questions. 1) How many carrot plants did Mike have in his garden? 2) Did Mike or Jen have more bean plants? NEXT PAGE 1) 5 plants 2) Mike

16. CONFIDENTIAL16 Mike Jen 35 30 25 20 15 10 5 0 Number of plants Mike's and Jen’s garden CarrotsLettuceBeans Types of plants Peas Use the bar graph to answer the questions. 3) How many pea plants did Mike and Jen have altogether? 4) All of Jen’s plants are shown on the graph. How many plants does Jen have in her garden altogether? 3) 30 pea plants 4) 60 plants

17. CONFIDENTIAL17 A double bar graph can be used to compare two sets of data. The steps for making and interpreting double bar graph are: STEP 1: Choose a title and labels for the graph. Then choose colors for the key. The key shows what each bar stands for. Next, choose an interval. The difference between the two numbers on the scale is the interval. STEP 2: Use the data from the table to make the graph. STEP 3: Use the completed graph to compare the data.

18. CONFIDENTIAL18 The table below shows the rainfall of two towns in three months. Rainfall of two towns (in cm) JuneJulyAugust Seattle, WA608595 Helena, MT304760 Use the table to draw a double bar graph. STEP 1: Title of the graph : “Rainfall of two towns (in cm)”. Labels for the graph : “June”, “July” and “August”. key: “Red” for Seattle and Blue for “Helena”. Interval : 0 - 15, 15 - 30,...................

19. CONFIDENTIAL19 Seattle, WA Helena, MT STEP 2: Seattle Helena 105 90 75 60 45 30 15 0 June July Rainfall of two towns (in cm) August Rainfall (in cm) Months Using the data from the table to make the graph.

20. CONFIDENTIAL20 Assessment Arnold made a chart to show his sales for the two most popular items at his painting studio. The table below shows the sales for each item. Use the table to make a double bar graph. Then use the graph to answer the questions. Number of items sold Item200220032004 Portraits6070 Landscapes606575 1) What interval did you choose for graph? Explain your choice. 2) In which year were there more landscapes sold than portrait? 1) 10; all of the data is divisible by 10 or 5. 2) 2004.

21. CONFIDENTIAL21 Number of items sold Item200220032004 Portraits6070 Landscapes606575 3) Which item did Arnold sell the same number of ii 2003 and 2004? 4) Which item showed a steady increase in sales for each year? 5) What is the total number of both items that Arnold sold for all 3 years? 6) In which year did Arnold sold fewer than 65 landscapes? 7) From the graph, would you expect that Arnold to sell more than or fewer than 75 landscapes in 2005? Explain. 3) Portraits 4) Landscapes. 5) 400. 6) 2002 7) more; there is an increase for each of the 3 years shown.

22. CONFIDENTIAL22 8) Which could you show with a double bar graph? A) The height of the world’s 7 tallest mountains. B) The birthdays of all the student’s in a class. C) The number of centimeters a corn plant and a tomato plant grew each week. D) The number of inches of rainfall your hometown received each month. 8) C

23. CONFIDENTIAL23 Double Bar Graphs Bar graphs are one of the many techniques used to present data in a visual form so that the reader may readily recognize patterns or trends. In the bar graphs, the objects or categories are listed along the horizontal axis and the associated numerical value is indicated by the length of a bar above the category. Bar graphs usually present categorical and numeric variables grouped in class intervals. The important point to note about bar graphs is their bar length or height—the greater their length or height, the greater their value. Very Good! Let's Review

24. CONFIDENTIAL24 A bar graph can be used to display data that can be counted. There are many characteristics of bar graphs that make them useful. Some of these are that:  They make comparisons between different variables very easy to see.  They clearly show trends in data, meaning that they show how one variable is affected as the other rises or falls.  Given one variable, the value of the other can be easily determined. Review

25. CONFIDENTIAL25 Number of nights below freezing point NovemberDecemberJanuary Seattle, WA277 Helena, MT162729 Table Look at the table below. It has rows and columns of numbers. The table shows the number of nights of two cities having temperature below freezing point. With the help of the data we formulate a bar graph comparing the two sets of data. NEXT PAGE Review

26. CONFIDENTIAL26 Seattle, WA Helena, MT 35 30 25 20 15 10 5 0 NovemberDecember Number of nights below freezing point Double Bar Graph Labels Title Key Interval January Seattle Helena Review

27. CONFIDENTIAL27 Double bar graph On a vertical bar graph, objects or categories are listed along a horizontal axis and the associated numerical value is indicated by the length of a bar above each category. The double (or group) vertical bar graph is an effective means of comparing sets of data about the same places or items. This type of vertical bar graph gives two or more pieces of information for each item on the x-axis instead of just one. Review

28. CONFIDENTIAL28 Susan saw many types of birds at her bird feeder. Mitch also saw many types of birds at his bird feeder. Susan Mitch 20 15 10 5 0 Number of birds Birds at Susan's and Mitch’s feeders Robin Sparrow Cardinal By reading the graph, you can see:  Susan saw five more robins than Mitch.  Mitch saw five more Sparrow than Susan.  Mitch and Susan both saw five cardinals. Types of birds

29. CONFIDENTIAL29 A double bar graph can be used to compare two sets of data. The steps for making and interpreting double bar graph are: STEP 1: Choose a title and labels for the graph. Then choose colors for the key. The key shows what each bar stands for. Next, choose an interval. The difference between the two numbers on the scale is the interval. STEP 2: Use the data from the table to make the graph. STEP 3: Use the completed graph to compare the data. Review

30. CONFIDENTIAL30 The table below shows the rainfall of two towns in three months. Rainfall of two towns (in cm) JuneJulyAugust Seattle, WA608595 Helena, MT304760 Use the table to draw a double bar graph. STEP 1: Title of the graph : “Rainfall of two towns (in cm)”. Labels for the graph : “June”, “July” and “August”. key: “Red” for Seattle and Blue for “Helena”. Interval : 0 - 15, 15 - 30,................... Review

31. CONFIDENTIAL31 Seattle, WA Helena, MT STEP 2: Seattle Helena 105 90 75 60 45 30 15 0 June July Rainfall of two towns (in cm) August Rainfall (in cm) Months Using the data from the table to make the graph. Review

32. CONFIDENTIAL32 You have done a nice job. See you in the next session.