GED Test Mathematics New information from GEDTS

GED Test Mathematics New information from GEDTS
Most frequently missed math test items Students need both content and strategies Tips for success Reflections In a presentation at the GED Administrators’ Conference in 2005, Kenn Pendleton shared data from a statistical report entitled Who Passed the GED Tests? Analyses of GED test statistics reveal that candidates unable to pass the math exam often experience difficulty when they encounter particular types of problems. In August 2006, USDOE hosted the GED Mathematics Training Institute in Washington, D.C. A CCAE representative was privileged to be a part of the CA delegation along with representatives of most other U.S. states. The information from this presentation comes directly from that training. CCAE gratefully acknowledges USDOE, GEDTS, the contract holder, MPR Associates, Inc., CA Department of Education, and CALPRO for the opportunity to disseminate this current information to the field through the GED Teacher Academy.

Who are GED Candidates? Average Age – 24.7 years
Gender – 55.1% male; 44.9% female Ethnicity 52.3% White 18.1% Hispanic Origin 21.5% African American 2.7% American Indian or Alaska Native 1.7% Asian 0.6% Pacific Islander/Hawaiian Average Grade Completed – 10.0 The 2004 statistical report included information about the candidates who were taking the GED Test.

Standard Score Statistics for Mathematics
Statistics from GEDTS Standard Score Statistics for Mathematics Median Mean Mathematics Score for All U.S. GED Completers 460 469 Mathematics Score for All U.S. GED Passers 490 501 Emphasize that mathematics continues to be the MOST difficult content area for GED candidates. Passing the math test requires candidates to have a set of mathematical abilities, which include Procedural Understanding, Conceptual Knowledge, and Application/Modeling/Problem Solving Skills. Mathematics continues to be the most difficult content area for GED candidates.

GEDTS Statistical Study
Studied three operational test forms Analyzed the 40 most frequently missed items These were 40% of the total items data; released July 2005 The Statistical Study used data from the fiscal year, and the results were released in July of The study analyzed the 40 most frequently missed questions and placed them in three broad themes: Geometry and Measurement, Applying Basic Math Principles to Calculation, and Reading and Interpreting Graphs and Tables.

Most Missed Questions How are the questions distributed between the two halves of the test? Total number of questions examined: 48 Total from Part I (calculator): 24 Total from Part II (no calculator): 24 The Statistical Study found that the frequently missed questions were evenly distributed on the two parts of the GED Math Test.

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 Discuss that three primary themes that were identified by the study as being the areas in which the GED candidates had the most difficulty. The first section will deal specifically with the areas of geometry and measurement.

Puzzler: Exploring Patterns
What curious property do each of the following figures share? 10 8 6 3 6 Each of these figures has the same perimeter and area. Debrief this activity by having participants discuss the pattern they discovered in the figures. Ask if this is true for all triangles, circles, and rectangles. Reinforce that finding patterns is very useful in mathematics and on the GED Test. Ask the instructors if they knew to explore area because the figures were shaded. On the GED Math Test shaded figures mean that the problem is asking for area. 4 2

Most Missed Questions: Geometry and Measurement
Pythagorean Theorem Area, perimeter, volume Visualizing type of formula to be used Comparing area, perimeter, and volume of figures Partitioning of figures Using variables in a formula Parallel lines and angles The Pythagorean Theorem was the most difficult area for all candidates but not the only area of difficulty for students on the GED Math Test. Students also found area, perimeter, and volume questions to be difficult, as well as questions that dealt with parallel lines and angles.

. One end of a 50-ft cable is attached to the top of a 48-ft tower. The other end of the cable is attached to the ground perpendicular to the base of the tower at a distance x feet from the base. What is the measure, in feet, of x? cable 50 ft tower48 ft  x  Ask the instructors what types of skills this question assesses. Instructors will share that the question assesses a student’s knowledge of the Pythagorean Theorem. Walk the instructors through which of the incorrect alternatives that the GED candidates were most likely to have selected. Note: Although instructors and texts teach the Pythagorean Theorem, it appears that students have difficulty in applying the formula to different types of situations. Students who missed this question selected the distracter #1. From the analysis, it was noted that students generally use addition or subtraction as their first method of solving a problem. Because the answer for subtracting 48 from 50 was one of the options, many students automatically selected this as the correct answer. (1) 2 (2) 4 (3) 7 (4) 12 (5) 14 Which incorrect alternative would these candidates most likely have chosen? (1) 2 Why? The correct answer is (5): 14

height 12 ft  5 ft  side x The height of an A-frame storage shed is 12 ft. The distance from the center of the floor to a side of the shed is 5 ft. What is the measure, in feet, of x? (1) 13 (2) 14 (3) 15 (4) 16 (5) 17 Which incorrect alternative would these candidates most likely have chosen? Although this is also a question regarding the Pythagorean Theorem, the height is indicated by a dotted line. Again, students seem to select addition or subtraction as their choice for computation. In this problem, students selected the distracter that resulted in adding the two numbers indicated on the graphic. Note: This problem is one of the commonly used Pythagorean Triples: 5,12,13. Another Pythagorean Triple (3,4,5) is very commonly used on the GED Math Test. Advise instructors to teach these two triples and to work with examples using these triples and other sets of numbers that are in direct proportion to the triples. Repetitive practice with these triples will be extremely helpful to students. (5) 17 Why? The correct answer is (1): 13

Were either of the incorrect alternatives in the last two questions even possible if triangles were formed? Theorem: The measure of any side of a triangle must be LESS THAN the sum of the measures of the other two sides. (This same concept forms the basis for other questions in the domain of Geometry.) Comprehending whether or not a triangle is possible is an important skill for students to internalize. Although many students may know the rule that the measure of any one side of a triangle must be less than the sum of the measures of the other two sides, they need experiences with creating possible triangles and analyzing why other triangles are impossible.

Below are rectangles A and B with no text. For each, do you think that a question would be asked about area or perimeter? A B Visualizing what math terminology means is important in order for students to identify the correct formula to use. Discuss with instructors the need for students to have real-life experiences with area and perimeter in order to understand what the formulas really mean. One cue for students when taking the test is to identify which figures indicate area versus perimeter. On the GED Math Test, area is always represented by a shaded figure; whereas, perimeter figures are not shaded. A: Area Perimeter Either/both Perimeter B: Area Perimeter Either/both Area

Area by Partitioning An L-shaped flower garden is shown by the shaded area in the diagram. All intersecting segments are perpendicular. house 6 ft 20 ft 32 ft Have instructors partition (“cut”) the L-shaped area into shapes that are areas GED candidates could likely find. Have them label the dimensions appropriate for finding area and compare their partitioning with someone near them. Many students look at this type of question and give up. They don’t believe that they have enough information because they don’t know the dimensions of the house. Instructors should have students practice actually cutting figures in order to understand the concept of partitioning. The shaded area indicates that, on the GED Math Test, students would be calculating the area of the shaded portion.

house 6 ft 20 ft 32 ft 32 ft 6 ft 14 ft 32 × 6 = × 6 = 84 276 ft2 6 ft 26 ft 14 ft 26 × 6 = × 6 = × 6 = 36 276 ft2 6 ft 26 ft 20 ft 26 × 6 = × 6 = 120 276 ft2 Have instructors share with the group what types of partitioning they used in order to solve the problem. See whether or not different methods were used from the possibilities above. Ask whether or not there are other possible ways to solve the problem. Note: Sharing different solutions expands students’ problem solving abilities.

x + 2 x – 2 Which expression represents the area of the rectangle? (1) 2x (2) x2 (3) x2 – 4 (4) x2 + 4 (5) x2 – 4x – 4 Is this an area or perimeter problem? How would you teach students to solve this problem if their algebra skills are not strong? Have you ever used substitution? For some candidates, the presence of variables in a question can cause significant concern. A test-taker with algebra skills will be about to answer some questions more quickly than someone who does not have or cannot recall these concepts. However, there are other ways to determine the correct solution for a multiple-choice question. Substitution is one method. Note: When any number can be chosen, avoid selecting 0 or1. Each of these numbers can lead to a solution that appears to be correct by may not be.

x + 2 Choose a number for x. I choose 8. Do you see any restrictions? Determine the answer numerically. x – 2 (8 + 2 = 10; 8 – 2 = 6; 10  6 = 60) Which alternative yields that value? Discuss that substitution is a strategy that can be used in calculation problems as well. Provide instructors with different examples of how students can use substitution to solve a problem. Identify different conditions that should exist when identifying a number to substitute for x, such as should it be larger than 2, easy to calculate such as a single digit whole number. Don’t use a fraction or a decimal. The example uses the number 8 to substitute for x. The process of substituting values for variables is not the most time-efficient way to find the correct answer. However, it is an approach that should be considered if the GED candidate cannot recall the necessary algebra skills. Candidates should consider working on these problems last so that they will have enough time to also work on other questions. Note: Inform participants that the extra (1) in the slide is a mistake. 2  8 = 16; not correct (60). 2x (2) x (3) x2 – (4) x (5) x2 – 4x – 4 82 = 64; not correct. 82 – 4 = 64 – 4 = 60; correct! = = 68. 82 – 4(8) – 4 = 64 – 32 – 4 = 28

b 8 7 6 5 4 3 2 1 Parallel Lines If a || b, ANY pair of angles above will satisfy one of these two equations: x = y x + y = 180 Which one would you pick? If the angles look equal (and the lines are parallel), they are! If they don’t appear to be equal, they’re not! Have instructors identify which expression they would select and why. Note: Reinforce with instructors that if the angles look equal and the lines look parallel, they are. If they don’t appear to be equal and the lines don’t look parallel, they are not. The GED Math Test makes a clear distinction with equal versus non-equal angles and lines.

8 7 6 5 trapezoids These are not parallel. parallelograms 4 3 2 1 Where else are students likely to use relationships among angles related to parallel lines? Have instructors brainstorm different types of scenarios where their students would use relationships regarding angles related to parallel lines. Where else are candidates likely to use the relationships among angles related to parallel lines?

Comparing Areas/Perimeters/Volumes A rectangular garden had a length of 20 feet and a width of 10 feet. The length was increased by 50%, and the width was decreased by 50% to form a new garden. How does the area of the new garden compare to the area of the original garden? The area of the new garden is 50% less 25% less the same 25% greater 50% greater Another most missed question deals with comparing areas, perimeters, and volumes. Which distracter do you think students selected most often? What strategy would you teach so that students would more likely select the correct answer?

original garden 20 ft (length) 10 ft (width) Area: x 10 = 200 ft2 new garden 5 ft 30 ft Area: x 5 = 150 ft2 Many students are not visual learners. By drawing a picture of what the question is asking, students are more likely to set up the equation correctly. The new area is 50 ft2 less; 50/200 = 1/4 = 25% less.

original garden 20 ft (length) 10 ft (width) Area: x 10 = 200 ft2 new garden 5 ft 30 ft Area: x 5 = 150 ft2 Assess what would occur if the length of the figure were decreased by 50% and the width increased by 50%. Compare this answer to the original. Have instructors brainstorm how they could use this activity in class to help students develop a deeper understanding of this concept. How do the perimeters of the above two figures compare? What would happen if you decreased the length by 50% and increased the width by 50%

Tips from GEDTS: Geometry and Measurement
Any side of a triangle CANNOT be the sum or difference of the other two sides (Pythagorean Theorem). If a geometric figure is shaded, the question will ask for area; if only the outline is shown, the question will ask for perimeter (circumference). To find the area of a shape that is not a common geometric figure, partition the area into non-overlapping areas that are common geometric figures. If lines are parallel, any pair of angles will either be equal or have a sum of 180°. The interior angles within all triangles have a sum of 180°. The interior angles within a square or rectangle have a sum of 360°. Kenn Pendleton, GEDTS Math Specialist THESE HINTS ARE GOLD FOR GED TEACHERS. DESIGN LESSONS AROUND THEM. Geometry is the development of spatial sense and the actual measuring and the concepts related to units of measure. As with all areas of mathematics, instructors should actively involve students in activities in order to build their understanding of geometric ideas, to see the power and usefulness of geometry in their lives, and to feel confident in their own capabilities as problem solvers. When students can be engaged in using and applying geometric knowledge to investigate and/or think about situations that relate to geometry, true problem solving occurs.

Reflections What are the geometric concepts that you feel are necessary in order to provide a full range of math instruction in the GED classroom? How will you incorporate the areas of geometry identified by GEDTS as most problematic into the math curriculum? If your students have little background knowledge in geometry, how could you help them develop and use such skills in your classroom?

Theme 1: Geometry and Measurement Theme 2: Applying Basic Math Principles to Calculation Theme 3: Reading and Interpreting Graphs and Tables Review the three primary themes that were identified by the study as being the areas in which the GED candidates had the most difficulty. The second section will deal specifically with the areas of applying basic math principles to calculation. Principles and Standards for School Mathematics (NCTM 2000) encourages instructors to move away from giving students just the typical array of drill and skill problems and instead to challenge them with experiences that improve their problem solving and transference skills. This idea is mirrored in the Adult Numeracy Network (ANN) Teaching and Learning Principles (2004).

Investigate an Unusual Phenomenon Investigate an Unusual Phenomenon
Select a four-digit number (except one that has all digits the same). Rearrange the digits of the number so they form the largest number possible. Now rearrange the digits of the number so that they form the smallest number possible. Subtract the smaller of the two numbers from the larger. Take the difference and continue the process over and over until something unusual happens. Select a four-digit number (except one that has all digits the same). Rearrange the digits of the number so they form the largest number possible. Now rearrange the digits of the number so that they form the smallest number possible. Subtract the smaller of the two numbers from the larger. Take the difference and continue the process over and over until something unusual happens. Have instructors explain their findings. Ask them if this works with all numbers and why or why not. Note: This is a sample activity called the endless loop. You may wish to include a different math starter activity to open the theme of calculation. If this activity is used, encourage instructors to use the calculator. This type of brainteaser activity provides students with meaningful practice in using the Casio fx-260 calculator.

Most Missed Questions: Applying Basic Math Principles to Calculation
Visualizing reasonable answers, including those with fractional parts Determining reasonable answers with percentages Calculating with square roots Interpreting exponent as a multiplier Selecting the correct equation to answer a conceptual problem Review the types of questions that were most missed by the students. Note: Share with instructors that, according to the statistical study, use of the calculator does not appear to assist students in their ability to apply basic math principles to calculation and obtain the correct answer.The statistical study shows that students miss as many problems in Part I as they do in Part II in the area of applying basic math principles to calculation. Eleven of the 20 identified questions appeared on Part I where the calculator is available. The calculator can provide an alternate means of determining the correct response for certain questions. Candidates should have practice with this strategy so that they can use the technique on the test. For both halves of the test, having a sense of what is reasonable will go a long way towards selecting the appropriate alternative.

When Harold began his word-processing job, he could type only 40 words per minute. After he had been on the job for one month, his typing speed had increased to 50 words per minute. By what percent did Harold’s typing speed increase? (1) 10% (2) 15% (3) 20% (4) 25% (5) 50% We will take a look at some of the different types of questions that were missed by the GED candidates and what distracters were most often selected and why. This questions was intended for Part II. Any percentages found on Part II will involve only simple calculation. Candidates who can estimate/calculate 10% of any number and 25% of a whole number will have an advantage on this type of problem.

Harold’s typing speed, in words per minute, increased from 40 to 50. Increase of 10% = 4 words per minute; = 44; not enough (50). Increase of 20 % (10% + 10%); = 48; not enough. Increase of 30% (10% + 10%+ 10%); = 52; too much. Answer is more than 20%, but less than 50%; answer is (4) 25%. Think about how it would assist a student in solving this type of problem if he/she could find 25% of any whole number. However, some students have difficulty in figuring 25% even if the instructors show them how they can first take half of the number and then take half of that number. For some students, being able to multiply any number by 10% can provide a good estimate from which to base a correct answer. Review the thinking process to solve this most missed question type by using a simple calculation of 10%.

A positive number less than or equal to 1/2 is represented by x. Three expressions involving x are given: (A) x (B) 1/x (C) 1 + x2 Which of the following series lists the expressions from least to greatest? A, B, C B, A, C B, C, A C, A, B C, B, A What strategy can be used to solve this type of problem by students who feel that they do not understand algebra? Substitution of a number for the letter x is a method that students can easily use if provided with multiple experiences in the classroom. Note: Model this process with the instructors. Have them identify the conditions of the number: a positive number less than or equal to 1/2. Discuss whether or not the number can be a decimal. Why or why not? Select a number for x that agrees with the information in the first sentence and have the group solve the problem. Use different numbers to show transference of the concept of substitution.

A positive number less than or equal to 1/2 is represented by x. Three expressions involving x are given: (A) x + 1 (B) 1/x (C) 1 + x2 Which of the following series lists the expressions from least to greatest? A, B, C B, A, C B, C, A C, A, B C, B, A Select a fraction and decimal and try each. ½ Evaluate A, B, and C using ½ and then 0.1. A: 1 ½ A: 1.1 B: 2 B: 10 C: 1 ¼ C: 1.01 Arrange (Least Greatest) 1 ¼, 1 ½, 2 (C, A, B) 1.01, 1.1, 10 (C, A, B) Note: This is an example of the problem being solved using a fraction and then a decimal number.

A survey asked 300 people which of the three primary colors, red, yellow, or blue was their favorite. Blue was selected by 1/2 of the people, red by 1/3 of the people, and the remainder selected yellow. How many of the 300 people selected YELLOW? (1) 50 (2) 100 (3) 150 (4) 200 (5) 250 This question was designed for Part II. As it is true with any percents on the GED Math Test, any calculation with fractions on Part II is relatively easy. Note: For many of these questions, you may wish to have the instructors assess the question and what they think the students did incorrectly and what type of strategy would have helped students in improved problem-solving skills.

Visualizing a Reasonable Answer When Calculating With Fractions
Most Missed Questions: Applying Basic Math Principles to Calculation Visualizing a Reasonable Answer When Calculating With Fractions Of all the items produced at a manufacturing plant on Tuesday, 5/6 passed inspection. If 360 items passed inspection on Tuesday, how many were PRODUCED that day? Which of the following diagrams correctly represents the relationship between items produced and those that passed inspection? Does this make sense? produced passed A produced passed B

Of all the items produced at a manufacturing plant on Tuesday, 5/6 passed inspection. If 360 items passed inspection on Tuesday, how many were PRODUCED that day? 300 432 492 504 (5) 3000 Hint: The items produced must be greater than the number passing inspection. Which incorrect alternative do you think was selected most often? 300! Students did not visualize that the number of items produced could not be less than those that passed inspection. They set up the problem to multiply 360 x 5/6 and got the answer 300. Point out to instructors that this question has a hint - a few GED questions have hints, and it is important that students realize that paying attention to the hint is important. Visualization is a very important skill in mathematical problem solving. Build in curriculum that gives students repeated practice with visualization. Some practice for students to check their own visualization skills would be to ask them to draw: circles the size of a penny, nickel, dime, and quarter circle the size of the bottom of a soda can rectangle the size of a dollar bill line the length of your foot rectangle the size of a credit card rectangle the size of a business card any other plane figure that you think may be part of their daily lives

A cross-section of a uniformly thick piece of tubing is shown at the right. The width of the tubing is represented by x. What is the measure, in inches, of x? 0.032 0.064 0.718 0.750 2.936 inside diameter in outside diameter in x Which was the distracter most selected by the students? Why? Have instructors brainstorm how this question can be answered by subtracting and dividing, or it can also be answered only by adding. Learning different ways to solve problems increases the students’ ability to be successful. Note: This questions was designed for Part I of the GED Math Test. However, it can be easily solved without a calculator. = 1.500

Exponents The most common calculation error appears to be interpreting the exponent as a multiplier rather than a power. On Part I, students should be able to use the calculator to raise numbers to a power several ways. On Part II, exponents are found in two situations: simple calculations and scientific notation. When numbers are written in scientific notation, candidates should recognize that positive exponents represent large numbers and negative exponents represent small decimal numbers; they must be able to convert from one expression to another.

If a = 2 and b = -3, what is the value of 4a  ab? -96 -64 -48 2 (5) 1 This question was designed for Part I, so the calculator could be used to find the correct answer. Negative exponents mean that instead of multiplying that many of the base number together, you divide by the indicated number of factors. In this example: 42 = 16 and 2-3 = 1/8. The way most people think of negative exponents is “put it in the bottom of the fraction.” A negative exponent is often thought of as a reciprocal so that 2-3 = 1/2 x 1/2 x 1/2 = 1/8. Note: According to the statistical analysis, only one operational form of the GED Math Test was found to have had negative exponents. However, a significant number of students missed this question.

Calculation with Square Roots Any question for which the candidate must find a decimal approximation of the square root of a non-perfect square will only be found on Part I. Questions involving the Pythagorean Theorem may require the candidate to find a square root. Other questions also contain square roots. Review the types of square roots that are generally found on Part I (calculator) versus Part II (paper and pencil). Square roots found on Part II are those that are generally those represented by whole numbers, such as the square root of 100 or 16 or 9 or 4. Square roots found on Part I, where the calculator can be used, may result in a decimal, such as the square root of 10 or 7 or 5.

Tips from GEDTS: Applying Basic Math Principles to Calculation
Replace a variable with a REASONABLE number, then test the alternatives. Be able to find 10% of ANY number. Try to think of reasonable (or unreasonable) answers for questions, particularly those involving fractions. Try alternate means of calculation, particularly testing the alternatives. Remember that exponents are powers, and that a negative exponent in scientific notation indicates a small decimal number. Be able to access the square root on the calculator; alternately, have a sense of the size of the answer. Kenn Pendleton, GEDTS Math Specialist THESE HINTS ARE GOLD FOR GED TEACHERS. DESIGN LESSONS AROUND THEM. Students need a strong focus on what strategies are required to solve a problem, detect errors quickly, and develop a common-sense approach to numbers. However, being able to calculate numbers competently and accurately is only the first step. Students must also be able to make decisions regarding the best method use for a particular situation and then to transfer those skills to other situations. Note: GEDTS recommends that, after the full range of instruction has been covered, that these specific areas of learning be reviewed prior to the test.

Reflections What are the mathematical concepts that you feel are necessary in order to provide a full range of math instruction in the GED classroom? What naturally occurring classroom activities could serve as a context for teaching these skills? How do students’ representations help them communicate their mathematical understandings? How can teachers use these various representations and the resulting conversations to assess students’ understanding and plan worthwhile instructional tasks? How will you incorporate the area of applying basic math principles to calculation, as identified by GEDTS as a problem area, into the math curriculum?

Theme 1: Geometry and Measurement Theme 2: Applying Basic Math Principles to Calculation Theme 3: Reading and Interpreting Graphs and Tables Review the three primary themes were identified by the study as being the areas in which the GED candidates had the most difficulty. The third section will deal specifically with the areas of reading and interpreting graphs and tables. One of the key components of learning is to be able to apply what you have seen and heard. This skill is particularly useful in the area of reading and interpreting graphs and tables. Students must not only be able to see what is meant, but also to translate that information themselves into the creation of a graphic that makes sense. Graphics are an integral part of both the workplace and daily life. Charts, tables, and diagrams provide necessary information for the completion of job-related and academic tasks. Competent interpretation of graphs requires that students develop skills in both decoding graphs and then applying the information to a specific task.

Time Out for a Math Starter!
Let’s get started problem solving with graphics by looking at the following graph. Who is represented by each point? Use this math starter with the participants. Ask them to work with a partner or in a small group. Tell them this is a good example of problem solving and interpreting a graphic. Ask them to look at the graph and the legend and determine who is represented by each point. Once they have located each of the individuals on the graph, discuss whether they think the graph is well constructed. Why or why not? What are the elements of a well constructed graphic? Note: Debrief the activity by having the instructors report on their findings, as well as their evaluation of a well-constructed graph. Discuss how one of the common errors that students make is not reading the text that accompanies the pictorial display. You may wish to have the instructors develop a graph that would be more effective in charting the provided information. This is a simple activity. Finally, point out that this graph is an example of a scatter plot. One form of the GED Official Practice Tests has a scatter plot question on Part II. GED Prep texts do not typically address scatter plots.

Most Missed Questions: Reading and Interpreting Graphs and Tables
Comparing graphs Transitioning between text and graphics Interpreting values on a graph Interpreting table data for computation Selecting table data for computation Approximately 50% of the questions on the GED Math Test use some type of graphic. GED candidates must answer questions based on text, graphics, or a combination of text and graphics. Each of the mathematical content areas (Number Sense/Operations, Measurement/Geometry, Data/Statistics/Probability, and Algebra/Functions/Patterns) includes questions where students must visually construct, read, interpret, or draw inferences from graphs, tables, or charts in order to model or solve a problem. Review the different types of questions that were most missed by students. Note: From the analysis, it was noted that the interpretation of graphic was most problematic for the students at the lowest levels of performance.

Increasing House Value
Most Missed Questions: Reading and Interpreting Graphs and Tables Initial Cost Increasing House Value 4 8 $0 $100,000 $200,000 House A Time (years) Before answering a question, students need to be able to visualize what type of graphic display is being described. One strategy is to have students insert what they comprehend the question is asking. What would the changing value of House B look like graphically. Note: Due to the size of the graphics and the amount of text, many of the questions are developed over several slides. 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.

$100,000 8 4 $0 $200,000 B A Time (years) A B 4 8 $0 $100,000 $200,000 Time (years) (1) (2) B Time (years) 4 8 $0 $100,000 $200,000 B A (3) $0 $100,000 $200,000 A (4) Seldom do texts have examples where students have to select the type of graph that depicts the scenario described. Have instructors brainstorm some ways they can better help students in obtaining this type of skill. Why is this important? Take a look at the next question that asks students to compare data. 4 8 Time (years) $0 $100,000 $200,000 A (5) B Which One? 4 8 Time (years)

The changing values of two investments are shown in the graph below. Amount of Investment 4 8 12 $0 $1000 $2000 Investment A Investment B Time (years) Review what the graph displays.

How does the amount initially invested and the rate of increase for investment A compare with those of investment B? Amount of Investment 4 8 12 $0 $1000 $2000 Investment A Investment B Time (years) What does this question ask?

4 8 12 $0 $1000 $2000 Amount of Investment Investment A Investment B Time (years) What problem would students exhibit when answering this type of question? Note: Instructors may respond that this looks like an organization question from the Language Arts Writing Test, Part I or that the verbiage is too confusing. Remembers that all test items on the GED Test were normed using a norming population of high school graduating seniors. Thus, the questions are determined to be valid and reliable. Also note that the colors used with the PowerPoint are not necessarily the colors used for the graphs on the GED Math Test. Check the GED Official Practice Tests to see a different set of colors. The colors used on the test were identified to be easily viewed in print by all students. The colors used on the PowerPoint are ones more easily viewed from a distance. Compared to investment B, investment A had a lesser initial investment and a lesser rate of increase. lesser initial investment and the same rate of increase. lesser initial investment and a greater rate of increase. greater initial investment and a lesser rate of increase. greater initial investment and a greater rate of increase.

4,000 8,000 12,000 $0 $200 $400 Profit/Loss in Thousands of Dollars Video Games Sold -$200 Interpreting values on a graph is another area that causes GED candidates difficulty. What would be the problem that students would display when interpreting this graph? What real-life scenarios may use this type of display? (Example: Graphs that show trends in earnings where companies may show a profit or loss for the quarter or year) Note: Have instructors identify different types of errors that students may make when interpreting this type of graph. 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.

4,000 8,000 12,000 $0 $200 $400 Profit/Loss in Thousands of Dollars Video Games Sold -$200 Now that instructors can view the answers, what additional problem or problems would students have when interpreting this graph? Note: Most students selected answer (2) $150. They were able to read the graph, but did not interpret the value correctly. This is an example of a graph where students must read all of the text that describes the graph, including the headings for each axis. What is the expected profit/loss before any video games are sold? (1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000

Results of Internet Purchase Survey
Most Missed Questions: Reading and Interpreting Graphs and Tables Results of Internet Purchase Survey Number of Purchases Number of Respondents 14 1 22 2 39 3 25 Select the correct data to use when completing a calculation is another problem for students. Have instructors look at the chart and identify problems that they think students would encounter with this type of question. What was the total number of Internet purchases made by the survey respondents? (1) (2) (3) (4) (5) 189 (0  14) + 1    25 = = 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. Dress Size 10 12 14 16 Style A Yards of Fabric Needed 35 in Fabric in Width in 60 in 3.25 3.875 3 2.375 2.5 2.75 2.25 Style B Yards of Fabric Needed 4 4.125 4.625 3.125 3.625 2.875 Yardage Information Some charts provide more information than is required. This is an example of a type of chart used on the GED Math Test. Note: Due to the size of the graphics and the amount of text, this question is developed over several slides.

What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Dress Size+ 10 12 14 16 Style A Yards of Fabric Needed 35 in Fabric in Width in 60 in 3.25 3.875 3 2.375 2.5 2.75 2.25 Style B Yards of Fabric Needed 4 4.125 4.625 3.125 3.625 2.875 Yardage Information Selecting pertinent data and following the vertical and horizontal lines of a chart to find specific data are both areas with which students have difficulty. In this type of question, GED candidates were asked to use the chart in order to determine how much fabric was needed by Claude. What types of problems do you think students encountered with this type of question? Note: This question required that the GED candidates grid their answers. Although the calculation for the problem is basic addition, they did not have numeric answers from which to choose.

What is the minimum number of yards of fabric recommended for one dress each of size 10, 12, and 14? Dress Size 10 12 14 16 Style A Yards of Fabric Needed 35 in Fabric in Width in 60 in 3.25 3.875 3 2.375 2.5 2.75 2.25 Style B Yards of Fabric Needed 4 4.125 4.625 3.125 3.625 2.875 Yardage Information Have instructors share different techniques that they use in the classroom to help students in selecting the correct data with which to complete a calculation. If no one mentions using the scratch paper to isolate the correct line, point that out as an excellent tool. What types of real-life charts could be used in the classroom to simulate this type of question? (Example: Income tax charts) Note: The boxes on the chart are slightly out of place, and this could not be changed on the slide.

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 THESE HINTS ARE GOLD FOR GED TEACHERS. DESIGN LESSONS AROUND THEM. Graph sense or graph comprehension involves reading and making sense of graphs seen in real-life situations, such as newspapers and the media, as well as constructing graphs that best convey data.

Reflections What are the major concepts that you feel are necessary in order to provide a full range of graphic literacy instruction in the GED classroom? How will you incorporate the areas of graphic literacy identified by GEDTS as most problematic into the math curriculum? If your students have difficulty in interpreting graphics, how could you help them develop and use such skills in your classroom?

GED Test Mathematics New information from GEDTS

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GED Test Mathematics New information from GEDTS

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