CONNECTING THE DATA: READING AND INTERPRETING GRAPHS AND TABLES.

CONNECTING THE DATA: READING AND INTERPRETING GRAPHS AND TABLES

Presented by

Kenneth Fahndrick

CONNECTING THE DATA: READING AND INTERPRETING GRAPHS AND TABLES

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!



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

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

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

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!

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

Types of Graphs and Charts

Bar graphs are often used to compare 2 or more items of data or show change over time.


• Line Graphs show change over time.


• Circle graphs/Pie charts show how part of an amount is related to the whole amount; the entire circle equals 100%

Types of Graphs and Charts Tables organize data in columns and rows.

Specific data is found where columns and rows intersect.



• Pictogram


• Pictogram

• Frequency table


• Pictogram

• Frequency table

• Scatter plots


• Pictogram

• Frequency table

• Scatter plots

• Line of best fit

“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.

Chart ChallengeDaily 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?

Housing PricesWhat is misleading about this bar graph? How would you change it?

Hospital admittance for 2007

0

10

20

30

40

50

60

70

1st Qtr 2ndQtr

3rd Qtr4th Qtr

emergency

pediatrics

surgery

11%car

Family Budget Income $3000

The Price of Gold

700600500

400300200100

0July Aug Sept Oct Nov

Price on the Last Day of the Month

THE PRICE OF GOLD

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

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

4 8$0

$100,000

$200,000

House A

Time (years)


Which One?

(3)

BA

(2)


(1)

0

4 8

Time (years)

0

4 8$0

$100,000

$200,000

(4)

(5)

BA

Time (years)$0

$100,000

$200,000

AB

0

4 8$0

$100,000

$200,000

Time (years)

$100,000

8

0

4$0

$200,000 B

A

Time (years)

Time (years)

0

4 8$0

$100,000

$200,000 B

A

The changing values of two investments are shown in the graph below.


Amount of Investment

0

4 8 12

$0

$1000

$2000

Investment A

Investment B

Time (years)

How does the amount initially invested and the rate of increase for investment A compare with those of investment B?


Amount of Investment

0

4 8 12

$0

$1000

$2000

Investment A

Investment B

Time (years)

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.

04 8 12

$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)







0

4 8 12$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)







0

4 8 12$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)







0

4 8 12$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)

0

4 8 12$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)

0

4 8 12$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)

0

4 8 12$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)







0

4 8 12$0

$1000

$2000Amount of

Investment

Investment A

Investment B

Time (years)


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.

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.


0

4,000 8,000 12,000$0

$200

$400

Profit/Loss in Thousands of

Dollars

Video Games Sold -$200

What is the expected profit/loss before any video games are sold?

(1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000


0

4,000 8,000 12,000

$0

$200

$400


Dollars



(1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000


0

4,000 8,000 12,000$0

$200

$400


Dollars



(1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000


0

4,000 8,000 12,000$0

$200

$400


Dollars



(1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000


0

4,000 8,000 12,000

$0

$200

$400


Dollars


Results of Internet Purchase SurveyNumber of Purchases

Number of Respondents

0 14

1 22

2 39

3 25

What was the total number of internet purchases made by the survey respondents?

(1) 86 (2) 100 (3) 106 (4) 175 (5) 189


Results of Internet Purchase SurveyNumber of Purchases Number of

Respondents

0 14

1 22

2 39

3 25


(1) 86 (2) 100 (3) 106 (4) 175 (5) 189


0 x 14 = 0

1 x 22 = 22

2 x 39 = 78

3 x 25 = 75

Results of Internet Purchase SurveyNumber of Purchases Number of

Respondents

0 14

1 22

2 39

3 25


(1) 86 (2) 100 (3) 106 (4) 175 (5) 189


0 x 14 = 0

1 x 22 = 22

2 x 39 = 78

3 x 25 + 75

175

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


Dress Size 10 12 14 16

Style A Yards of Fabric Needed

35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5

Style B Yards of Fabric Needed

35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information




Fabric

Width 54 in

2.5 2.875 3 3

What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14?

Yardage Information


Dress Size+ 10 12 14 16


35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information


Dress Size+ 10 12 14 16


35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information


Dress Size+ 10 12 14 16


35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information


Dress Size+ 10 12 14 16


Fabric

Width 54 in

2.5 2.875 3 3


Yardage Information


Dress Size+ 10 12 14


Fabric

Width 54 in

2.5 2.875 3


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75

2.500


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75

2.500

2.875


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75

2.500

2.875

3.000


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75

2.500

2.875

+ 3.000


Yardage Information




35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5


35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75

2.500

2.875

+ 3.000

8.375

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

Graph website

• http://nces.ed.gov/nceskids/createagraph/default.aspx

CONNECTING THE DATA: READING AND INTERPRETING GRAPHS AND TABLES.

Documents

interpreting graphs

chartspictogramtypes

chartsline graphs

chartstypes of graphs

data tables

specific data

items of data

graphsrepresent data