1. CONNECTING THE DATA: READING AND INTERPRETING GRAPHS AND TABLES

2. Presented by Kenneth Fahndrick CONNECTING THE DATA: READING AND INTERPRETING GRAPHS AND TABLES

3. Developing Data & Graph Literacy Agenda

4. Introductions and Ice Breakers

5. Developing Data & Graph Literacy Agenda Introductions and Ice Breakers Why Develop Data & Graph Literacy? Approximately 50% of GED math test questions involve some kind of visual/graph, from which students must extract some information necessary for using to solving the math problem!

6. Developing Data & Graph Literacy Agenda Introductions and Ice Breakers Why Develop Data & Graph Literacy? Approximately 50% of GED math test questions involve some kind of visual/graph, from which students must extract some information necessary for using to solving the math problem! Construct, Interpret & Compare Graphs of Statistical Data

7. Objectives Broaden Instructional Strategies Incorporate Real-World Materials Recognize and Understand Math Misconceptions of Today’s GED Student –Concepts, Rules, and Principles Provide Tools and Games for GED Math Teachers –Actively Engage Students –Provide Large and small Group Instruction –Provide Hands On Learning Activities

8. Math Themes – Most Missed Questions Theme 1: Geometry and Measurement Theme 2: Applying Basic Math Principles to Calculation Theme 3:Reading and Interpreting Graphs and Tables

9. Why are Graphics Important? Graphic aids are really designed to make the information easier to read and understand. Visuals such as tables, charts, and graphs summarize information in a way that allows us to see it differently. Graphs and Data tables condense information from the text. Reading the graphics will actually save you time!

10. Words to Remember Charts—a graphically representation of numbers. Graphs—represent data visually to compare data from different sources, show change over time, and make projection about the future. Tables—organize information or data in columns and rows. (Specific information is found where the column and row) intersect

11. Types of Graphs and Charts Bar graphs are often used to compare 2 or more items of data or show change over time.

12. Types of Graphs and Charts Line Graphs show change over time.

13. Types of Graphs and Charts Circle graphs/Pie charts show how part of an amount is related to the whole amount; the entire circle equals 100%

14. Types of Graphs and Charts Tables organize data in columns and rows. Specific data is found where columns and rows intersect.

15. Types of Graphs and Charts

16. Pictogram

17. Types of Graphs and Charts Pictogram Frequency table

18. Types of Graphs and Charts Pictogram Frequency table Scatter plots

19. Types of Graphs and Charts Pictogram Frequency table Scatter plots Line of best fit

20. “Scanning the Graph” Helpful Tips to Graphic Interpretation  Look for the Graphic Title  Connect the legend to the graph  Look for both the horizontal and vertical axis labels  Check for both the horizontal and vertical axis scales What does each increment represent? Are the increments spaced evenly on each axis?  Check the graphic for a misleading format.

21. Chart Challenge Daily Graphing Questions: What is the color of your car? red, green, black, white How many hours of TV did you watch last night? How many children do you have? What is your favorite restaurant? How many pets do you have? How many bathrooms do you have in your home? How many siblings do you have? What is your favorite color?

22. Housing Prices What is misleading about this bar graph? How would you change it?

23. Hospital admittance for 2007

24. 11% car Family Budget Income $3000

25. The Price of Gold 700 600 500 400 300 200 100 0 JulyAugSeptOctNov Price on the Last Day of the Month THE PRICE OF GOLD

26. Most Missed Questions: Reading and Interpreting Graphs and Tables Areas of Weakness: –Comparing graphs –Transitioning between text and graphics –Interpreting values on a graph –Interpreting table data for computation –Selecting table data for computation

27. House A cost $100,000 and increased in value as shown in the graph. House B cost less than house A and increased in value at a greater rate. Sketch a graph that might show the changing value of house B. Initial Cost Increasing House Value 0 48 $0 $100,000 $200,000House A Time (years) Most Missed Questions: Reading and Interpreting Graphs and Tables

28. Which One? (3) B A (2) Most Missed Questions: Reading and Interpreting Graphs and Tables (1) 0 48 Time (years) 0 48 $0 $100,000 $200,000 (4) (5) B A Time (years) $0 $100,000 $200,000 A B 0 48 $0 $100,000 $200,000 Time (years) $100,000 8 0 4 $0 $200,000 B A Time (years) 0 48 $0 $100,000 $200,000 B A

29. The changing values of two investments are shown in the graph below. Most Missed Questions: Reading and Interpreting Graphs and Tables Amount of Investment 0 4812 $0 $1000 $2000 Investment A Investment B Time (years)

30. How does the amount initially invested and the rate of increase for investment A compare with those of investment B? Most Missed Questions: Reading and Interpreting Graphs and Tables Amount of Investment 0 4812 $0 $1000 $2000 Investment A Investment B Time (years)

31. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

32. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

33. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

34. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

35. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

36. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

37. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

38. Compared to investment B, investment A had a (1)lesser initial investment and a lesser rate of increase. (2)lesser initial investment and the same rate of increase. (3)lesser initial investment and a greater rate of increase. (4)greater initial investment and a lesser rate of increase. (5)greater initial investment and a greater rate of increase. 0 4812 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years)

39. Most Missed Questions: Reading and Interpreting Graphs and Tables LOGIC STATEMENT: (First Criteria) AND (Next Criteria) ALL criteria must be true, for answer to be true. (First Criteria) OR (Next Criteria) ONE or more criteria must be true, for answer to be true.

40. The profit, in thousands of dollars, that a company expects to make from the sale of a new video game is shown in the graph. Most Missed Questions: Reading and Interpreting Graphs and Tables 0 4,0008,00012,000 $0 $200 $400 Profit/Loss in Thousands of Dollars Video Games Sold -$200

41. What is the expected profit/loss before any video games are sold? (1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000 Most Missed Questions: Reading and Interpreting Graphs and Tables 0 4,0008,00012,000 $0 $200 $400 Profit/Loss in Thousands of Dollars Video Games Sold -$200

42. What is the expected profit/loss before any video games are sold? (1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000 Most Missed Questions: Reading and Interpreting Graphs and Tables 0 4,0008,00012,000 $0 $200 $400 Profit/Loss in Thousands of Dollars Video Games Sold -$200

43. What is the expected profit/loss before any video games are sold? (1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000 Most Missed Questions: Reading and Interpreting Graphs and Tables 0 4,0008,00012,000 $0 $200 $400 Profit/Loss in Thousands of Dollars Video Games Sold -$200

44. What is the expected profit/loss before any video games are sold? (1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000 Most Missed Questions: Reading and Interpreting Graphs and Tables 0 4,0008,00012,000 $0 $200 $400 Profit/Loss in Thousands of Dollars Video Games Sold -$200

45. Results of Internet Purchase Survey Number of PurchasesNumber of Respondents 014 122 239 325 What was the total number of internet purchases made by the survey respondents? (1) 86 (2) 100 (3) 106 (4) 175 (5) 189 Most Missed Questions: Reading and Interpreting Graphs and Tables

46. Results of Internet Purchase Survey Number of PurchasesNumber of Respondents 014 122 239 325 What was the total number of internet purchases made by the survey respondents? (1) 86 (2) 100 (3) 106 (4) 175 (5) 189 Most Missed Questions: Reading and Interpreting Graphs and Tables 0 x 14 = 0 1 x 22 = 22 2 x 39 = 78 3 x 25 = 75

47. Results of Internet Purchase Survey Number of PurchasesNumber of Respondents 014 122 239 325 What was the total number of internet purchases made by the survey respondents? (1) 86 (2) 100 (3) 106 (4) 175 (5) 189 Most Missed Questions: Reading and Interpreting Graphs and Tables 0 x 14 = 0 1 x 22 = 22 2 x 39 = 78 3 x 25 + 75 175

48. Claude is sewing 3 dresses in style B using fabric that is 54 inches wide. The table below contains information for determining the yards of fabric needed. Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

49. Claude is sewing 3 dresses in style B using fabric that is 54 inches wide. The table below contains information for determining the yards of fabric needed. Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

50. Claude is sewing 3 dresses in style B using fabric that is 54 inches wide. The table below contains information for determining the yards of fabric needed. Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

51. Claude is sewing 3 dresses in style B using fabric that is 54 inches wide. The table below contains information for determining the yards of fabric needed. Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

52. Claude is sewing 3 dresses in style B using fabric that is 54 inches wide. The table below contains information for determining the yards of fabric needed. Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style B Yards of Fabric Needed Fabric Width 54 in 2.52.87533

53. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size+10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

54. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size+10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

55. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size+10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

56. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size+10121416 Style B Yards of Fabric Needed Fabric Width 54 in 2.52.87533

57. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size+101214 Style B Yards of Fabric Needed Fabric Width 54 in 2.52.8753

58. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75

59. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75 2.500

60. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75 2.500 2.875

61. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75 2.500 2.875 3.000

62. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75 2.500 2.875 + 3.000

63. What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Yardage Information Most Missed Questions: Reading and Interpreting Graphs and Tables Dress Size10121416 Style A Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.253.875 333.25 2.3752.52.75 2.25 2.5 Style B Yards of Fabric Needed 35 in Fabric 45 in Width 54 in 60 in 3.87544.1254.625 3.1253.25 3.625 2.52.87533 2.252.3752.52.75 2.500 2.875 + 3.000 8.375

64. Tips from GEDTS: Reading and Interpreting Graphs and Tables Have candidates find examples of different types of graphs. Have candidates create questions for their graphics and/or those of others. Develop the capacity to translate from graphics to text as well as text to graphics. Develop the capacity to select pertinent information from the information presented. Reinforce the need to read and interpret scales, present graphs without scales or without units. Kenn Pendleton, GEDTS Math Specialist

65. Graph website http://nces.ed.gov/nceskids/cr eateagraph/default.aspx