presented by cheryl sanders kenneth fahndrick october 15-16, 2010 u.s. department of education ♦...
TRANSCRIPT
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Presented by
Cheryl Sanders
Kenneth Fahndrick
October 15-16, 2010U.S. Department of Education ♦ Office of
Vocational and Adult Education Division of Adult Education and Literacy ♦ Texas Education Agency
♦ Texas LEARNS ♦ Texas A&M Kingsville
CONNECTING THE DATA: READING AND INTERPRETING GRAPHS AND TABLES
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Slide 22
Developing Data & Graph Literacy Agenda
Introductions and Ice Breakers
Why Develop Data & Graph Literacy
Construct, Interpret & Compare Graphs of Statistical Data
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Slide 33
Objectives
• Broaden Instructional Strategies
• Incorporate Real-World Materials
• Recognize and Understand Math Misconceptions of Today’s GED Student
– Mathematical Concepts
– Mathematical Rules
– Mathematical Principle
• Provide Tools and Games for GED Math Teachers
– Actively Engage Students
– Provide Large and small Group Instruction
– Provide Hands On Learning Activities
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Slide 44
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
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Slide 55
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 as you read the text will actually save you time!
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Slide 66
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 .
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Slide 77
Types of Graphs and Charts
Bar graphs are often use to compare 2 or more items of data or show change over time.
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Slide 88
Types of Graphs and Charts
• Line Graphs show change over time.
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Slide 99
Types of Graphs and Charts
• Circle graphs/Pie charts show how part of an amount are related to the whole amount; the entire circle equals 100%
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Slide 1010
Types of Graphs and Charts
Tables organize data in columns and rows. Specific data is found where columns and rows intersect.
Miles Driven Gas (gal) Cost
287 17.5 $32.85
310
289
16.8
15.7
$32.60
$29.89
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Slide 1111
Types of Graphs and Charts
• Pictogram
• Frequency table
• Scatter plots
• Line of best fit
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Slide 1212
“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 horizontal and vertical scales
What does each increment represent?
Are the increments even on each axis?
Check the graphic for a misleading format.
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Slide 1313
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 beds do you have in your home?
• How many siblings do you have?
• What is your favorite color?
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Slide 1414
Housing Prices
What is misleading about this bar graph? How would you change it?
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Slide 1515
Hospital admittance for 2007
0
10
20
30
40
50
60
70
1st Qtr 2ndQtr
3rd Qtr4th Qtr
emergency
pediatrics
surgery
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Slide 1616
11%car
Family Budget Income $3000
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Slide 1717
The Price of Gold
$700
$600
$500
$400
$300
$200
$100
$0
July Aug Sept Oct Nov
Price on the Last Day of the Month
THE PRICE OF GOLD
(Dollars per ounce)
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Slide 1818
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
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Slide 1919
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)
Most Missed Questions: Reading and Interpreting Graphs and Tables
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Slide 2020
Which One?
(3)
BA
(2)
Most Missed Questions: Reading and Interpreting Graphs and Tables
(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
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Slide 2121
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
4 8 12
$0
$1000
$2000
Investment A
Investment B
Time (years)
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Slide 2222
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
4 8 12
$0
$1000
$2000
Investment A
Investment B
Time (years)
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Slide 2323
Most Missed Questions: Reading and Interpreting Graphs and Tables
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
4 8 12$0
$1000
$2000
Amount of Investment
Investment A
Investment B
Time (years)
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Slide 2424
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
4,000 8,000 12,000$0
$200
$400
Profit/Loss in
Thousands of Dollars
Video Games Sold
-$200
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Slide 2525
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
4,000 8,000 12,000$0
$200
$400
Profit/Loss in
Thousands of Dollars
Video Games Sold
-$200
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Slide 2626
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
(0 14) + 1 22 + 2 39 + 3 25 = 22 + 78 + 75 = 175
Most Missed Questions: Reading and Interpreting Graphs and Tables
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Slide 2727
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 Informatio
n
Most Missed Questions: Reading and Interpreting Graphs and Tables
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
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Slide 2828
What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14?
Yardage Informatio
n
Most Missed Questions: Reading and Interpreting Graphs and Tables
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
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Slide 2929
What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14?
Yardage Informatio
n
Most Missed Questions: Reading and Interpreting Graphs and Tables
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
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Slide 3030
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Slide 3131
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Slide 3232
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Slide 3333
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Slide 3434
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Slide 3535
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Slide 3636
Graph website
•http://nces.ed.gov/nceskids/createagraph/default.aspx
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Slide 3737
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
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Slide 3838
Final Tips
• Candidates do not all learn in the same manner.
– Present alternate ways of approaching the solution
• After the full range of instruction has been covered, consider revisiting the area of graphics once again before the candidates take the test.
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Slide 3939
39
Thank you
• Wrap-up, evaluations
• Training based on instructional materials from the Math Institute Program
• Presenters–Kenneth Fahndrick & Cheryl Sanders
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Slide 4040
Texas Education Agency
• Copyright © 2008 Texas Education Agency
• Copyright © Notice. The materials are copyrighted © and trademarked ™ as the property of the Texas Education Agency (TEA) and may not be reproduced without the express written permission of TEA, except under the following conditions:
• Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts’ and schools’ educational use without obtaining permission from TEA.
• Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of TEA.
• Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way.
• No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged.
• Private entities or persons located in Texas that are not Texas public school districts, Texas Education Service Centers, or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from TEA and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty.
• For information contact
• Richard JarrellOffice of Copyrights, Trademarks, License Agreements, and RoyaltiesTexas Education Agency1701 N. Congress Ave.Austin, TX 78701-1494(512) 463-9270 or (512) 936-6060