Spring 2013 Student Performance AnalysisGrade 6 MathematicsStandards of Learning1Presentation may be paused and resumed using the arrow keys or the mouse.

1This is the spring 2013 student performance analysis for the Grade 6 Mathematics Standards of Learning test. Statewide results for the spring 2013 mathematics SOL tests have been analyzed to determine specific content that may have challenged students. In order to support preparation of students for the Grade 6 Mathematics test, this PowerPoint presentation has been developed to provide examples of SOL content identified by this analysis.

While some of this content was first introduced in the 2009 mathematics SOL, other content is included in both the 2001 and 2009 mathematics SOL. There are also many similarities between the content identified during this analysis and the content identified during the spring 2012 student performance analysis.

This PowerPoint presentation contains concrete examples of the content for which student performance was weak or inconsistent. These items are not SOL test questions and are not meant to mimic SOL test questions. Instead, they are intended to provide mathematics educators with further insight into the concepts that challenged students statewide.

It is important to note that the SOL and examples highlighted in this presentation should not be the sole focus of instruction, nor should these suggestions replace the data that teachers or school divisions have collected on student performance. Rather, this information provides supplemental instructional information based on student performance across the Commonwealth of Virginia.

1SOL 6.1The student will describe and compare data, using ratios, and will use appropriate notations, such as , a to b, and a:b.

Using Ratios to Describe and Compare Data

2

The first standard being highlighted is SOL 6.1. This standard reads: The student will describe and compare data, using ratios, and will use appropriate notations, such as a over b (a/b), a to b, and a colon b (a:b). In particular, students need improvement describing and comparing data using ratios.2Students need additional practice identifying a practical situation that corresponds to a given ratio.

A box contains red marbles and blue marbles. The ratio of red marbles to blue marbles in the box is 8 to 3. Select each statement that could represent the number of red marbles and blue marbles in this box.

There are exactly 3 red marbles and 8 blue marbles in the box. There are exactly 64 red marbles and 24 blue marbles in the box. There are exactly 18 red marbles and 13 blue marbles in the box. There are exactly 48 red marbles and 18 blue marbles in the box.

Suggested Practice for SOL 6.1

3For SOL 6.1, students need additional practice identifying a practical situation that corresponds to a given ratio, such as the example provided on the screen.

The answers to the example are shown.

3Students need additional practice identifying a practical situation that corresponds to a given ratio.

A board contains stars and triangles. The ratio of triangles to stars is 3 to 1. Select each picture that could represent the number of stars and triangles on this board.

Suggested Practice for SOL 6.1

4Student performance for this standard also indicated that students need additional practice identifying pictorial representations of a given ratio in a non-multiple choice format. In this example, it is important for students to recognize that the given ratio compares triangles to stars and not stars to triangles.

The answers are shown on the screen.4SOL 6.2The student will investigate and describe fractions, decimals and percents as ratios;identify a given fraction, decimal or percent from a representation; demonstrate equivalent relationships among fractions, decimals, and percents; and compare and order fractions, decimals, and percents.

Demonstrating Equivalent Relationships Among Fractions, Decimals, and Percents

5The next standard being highlighted is SOL 6.2. Student performance was inconsistent for bullets b and c within this standard. These bullets read: the student will, bullet b, identify a given fraction, decimal or percent from a representation; and, bullet c, demonstrate equivalent relationships among fractions, decimals, and percents. 5Students need additional practice identifying fractions, decimals, and percents from representations.

This model is shaded toWrite a fraction, decimal, andrepresent one whole.percent to represent the shaded part of each model.

Suggested Practice for SOL 6.2b

Possible answers:

Possible answers:

6For bullet b of this standard, students should be able to describe a given representation using a fraction, decimal, and percent.

The answers to this question are shown on the screen.

An extension of this question could be to ask students to represent these models on a number line or a grid. 6Students need additional practice demonstrating equivalent relationships among fractions, decimals, and percents.

Identify each statement that is true.

Suggested Practice for SOL 6.2c

7For bullet c of this standard, which appears in the non-calculator section of the test, students showed inconsistent performance identifying and demonstrating equivalent relationships among fractions, decimals, and percents. Students would benefit from additional practice with items similar to the one shown. Students will need to evaluate each statement to decide how many correct answers there are. Note that this item uses numbers with similar digits.

The answers to this question are shown on the screen.

It is important to note that if this question were on an SOL test, students would have to select all three correct answers, and only those answers, to get this item correct.7SOL 6.6The student will multiply and divide fractions and mixed numbers; andestimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions.

Solving Practical Problems Involving Fractions

8The next standard being highlighted is SOL 6.6. In particular, students had difficulty with bullet b, which reads, the student will estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions.8Students need additional practice solving single-step and multistep practical problems involving fractions.

Jill had 3 full pans of brownies.Each pan was the same size.She gave of the original amount of brownies to her friends. She gave of the original amount of brownies to her teacher. Exactly how many pans of brownies does Jill have left over?

Suggested Practice for SOL 6.6b

pans

9Students need opportunities to solve practical problems involving fractions using different strategies. The example shown on the screen is a multistep practical problem involving fractions. Teachers are encouraged to ask students to solve this problem in more than one way.

The answer to the question is shown on the screen.9Students need additional practice adding and subtracting fractions with regrouping.

Kendra recorded the amount of water she used in one week for four activities. 1. What is the total amount of water, in gallons, recorded for these activities?

2. How much more water was used doing laundry than cooking?Suggested Practice for SOL 6.6bActivityAmount of Water (in gallons)BathingDoing LaundryWashing CarCooking

gallons

gallons10For this standard, students also need additional practice adding and subtracting fractions with regrouping.

The answers to these questions are shown on the screen.

As an extension, the information in the table can be used to ask questions such as, What is the total amount of water Kendra would use for these activities if she cut the amount of water used for cooking in half?10SOL 6.10The student will define pi as the ratio of the circumference of a circle to its diameter;solve practical problems involving circumference and area of a circle, given the diameter or radius;solve practical problems involving area and perimeter; anddescribe and determine the volume and surface area of a rectangular prism.

Solving Problems Involving Perimeter, Circumference, Area, Surface Area, and Volume

11The next standard being highlighted is SOL 6.10. Student performance was inconsistent for bullets b and c of this standard. These bullets read, the student will, bullet b, solve practical problems involving circumference and area of a circle, given the diameter or radius; and, bullet c, solve practical problems involving area and perimeter.11Students need additional practice solving practical problems involving circumference and area, particularly when a figure is not provided.

Leo is designing a circular table top with a diameter of 10 feet.

1. Which is closest to the 2. Which is closest to circumference of this table the area of this table top? top?

314.2 feet a) 314.2 feet78.5 square feet b) 78.5 square feet31.4 feet c) 31.4 feet15.7 square feet d) 15.7 square feet

Suggested Practice for SOL 6.10b

12For SOL 6.10b, students need additional practice solving practical problems involving circumference and area, particularly when a figure is not provided. Student performance also indicates that students do not know whether the diameter or radius should be used in a calculation, and whether the resulting units are linear or square units. Questions like the ones on the screen give students practice finding circumference and area when given a diameter, as well as deciding the appropriate unit of measure for their answers.

The answers are shown on the screen.12Students need additional practice solving practical problems involving area and perimeter.

This triangle represents a section of a garden. (Figure is not drawn to scale.)

What are the area and perimeter of the garden?

Suggested Practice for SOL 6.10c

Area = 25.5 mPerimeter = 35.3 m5 m4 m3 m13 m13.3 m

13For SOL 6.10c, students need additional practice solving practical problems involving area and perimeter. Student performance was inconsistent when students had to determine which information to use to answer the question. For instance, in this example, students need to determine which measurements to use to find the area, and which measurements to use to find the perimeter. As in the previous example, students also need practice determining the correct unit of measure to use when labeling the answers.

The answers are shown on the screen.13SOL 6.14The student will construct circle graphs;draw conclusions and make predictions, using circle graphs; andcompare and contrast graphs that present information from the same data set.Solving Problems Involving Circle Graphs

14The next standard being highlighted is SOL 6.14, bullets b and c. These bullets read, the student will, bullet b, draw conclusions and make predictions, using circle graphs; and, bullet c, compare and contrast graphs that present information from the same data set.14Students need additional practice solving problems involving circle graphs.A car salesman sold 40 cars last month. The circle graph shows the results of his sales by car color.1. Identify the car color that mostlikely represents exactly 10 cars.

2. Identify two car colors that most likely represent a combined total of 25 cars.

Suggested Practice for SOL 6.14bBlueGreenRedPurpleGreenBlue and Purple OR Blue and Red

15For SOL 6.14b, students need additional practice solving problems involving circle graphs.

Take a moment to read the example shown on the screen.

Students are having difficulty making the connection between the percent or fraction represented by a section of the graph and the number of data elements represented by the same section.

In the first example provided, 10 out of 40 cars represents 25%, or of the data. Students must, in turn, recognize that the green section of the graph most closely represents 25% or of the data. Student performance data indicate that a common student misconception is to attribute 25 data elements to the green section because it represents 25% of the data. Therefore, students would NOT correctly name the green section as representative of 10 cars.

Similarly, in example 2, a common student error might be to choose the purple and red sections of the graph as representing 25 cars since those combined pieces represent about 25% of the data.

The answers are shown on the screen.15Students need additional practice comparing data in circle graphs with data in other graphs.Bob asked a group of people to identify their favorite vegetable. The circle graph shows the results. Which graph on the next slide could represent the same data?

Suggested Practice for SOL 6.14c

CornCarrotsBeansBroccoliAsparagus

16For this standard, students need additional practice comparing data in circle graphs with data in other graphs. In particular, students need additional practice using the data in a circle graph when specific numbers are not provided.

Teachers are encouraged to have students discuss the data in the circle graph and what conclusions can be drawn, even though the number of people surveyed is not given. For example, in this graph, asparagus was selected by the fewest people. It also appears that half of the people surveyed selected beans as their favorite vegetable and of the people surveyed selected corn . This means there were twice as many people who selected beans as their favorite vegetable as there were people who selected corn as their favorite vegetable. Another conclusion is that the sum of the number of people who selected carrots, broccoli, and asparagus should equal the number of people who selected corn. Once students have drawn conclusions based on the circle graph, they can proceed to analyze other graphs to determine which one represents the same data. See the next slide for the remainder of this question.16

Suggested Practice for SOL 6.14cCornCarrotsBeansBroccoliAsparagusWhich bar graph could represent the same data?

17When comparing these bar graphs to the circle graph, students need to identify the bar graph that represents the data in the same relationships as shown in the circle graph. Students should reference the conclusions they drew from the circle graph, when selecting the correct answer.

For example, one of the conclusions drawn from the circle graph was that asparagus was selected by the fewest people. In each of the bar graphs, asparagus was selected by the fewest people, so that statement will not help eliminate a choice. Another conclusion drawn from the circle graph was that there were twice as many people who selected beans as there favorite vegetable as there were people who selected corn as their favorite vegetable. This statement will eliminate the first and second graph, because these graphs do not show this relationship. The other conclusion previously drawn, that the sum of the number of people who selected carrots, broccoli, and asparagus should equal the number of people who selected corn, can be checked against the third graph to confirm its selection.

It is important for students to be asked to explain their reasoning for eliminating a graph, and eventually selecting the correct graph.17SOL 6.15The student will describe mean as balance point; anddecide which measure of center is appropriate for a given purpose.Determining and Using Measures of Center

18The next standard being highlighted is SOL 6.15. The standard states, the student will, bullet a, describe mean as balance point; and, bullet b, decide which measure of center is appropriate for a given purpose.18Suggested Practice for SOL 6.15a

Students need additional practice finding the balance point of a set of data represented on a line plot.

Jill recorded the number of pull-ups each of ten students did on this line plot. What is the balance point for this data? 1 2 3 4 5 6 7 8 9Pull-UpsEach X represents 1 student.Number of Pull-UpsThe balance point for this data is 5.XXXXXXXXXX

19For SOL 6.15a, students need additional practice interpreting data represented on line plots to determine the balance point.

The answer to this question is shown on the screen.

Students should be able to connect the terms balance point and arithmetic mean. As an extension, teachers could ask students to compare the balance point with the median and mode and ask which is a better representation of the average number of pull-ups for these ten students. This will help students with the skills associated with SOL 6.15b, which was also an area where students struggled.19Students need additional practice determining the best measure of center for a given situation.

Andy surveyed his friends to determine the number of books each of them read in February. These are the results of the survey.

3, 2, 3, 19, 2, 1, 2, 2, 2, 2

What is the mean for this data set? What is the median for this data set? Is the mean or median a more appropriate measure of center to use for this data? Why?Suggested Practice for SOL 6.15bSample answer:Since one friend read significantly more books (19), the median provides a more accurate measure. The friend who read 19 books caused the mean to be higher than the number of books read by nine of the ten friends.3.8 books2 books

20For SOL 6.15b, students showed inconsistent performance when determining which measure of center was most appropriate for a data set.

The answers to these questions are shown on the screen.

Teachers are encouraged to have students plot this data on a line plot as it will provide a visual representation that may help them understand why the median is a better measure of center for this data set.20SOL 6.17The student will identify and extend geometric and arithmetic sequences.Identifying and Extending Sequences

21The next standard being highlighted is SOL 6.17. This standard states, the student will identify and extend geometric and arithmetic sequences.21Students need additional practice identifying the common ratio or common difference for a sequence.

1.What is the common ratio of this sequence?

5, 25, 125, 625, 3125, . . .

2.What is the common ratio of this sequence?

3125, 625, 125, 25, 5, . . .

3.What is the common difference of this sequence?

55, 58, 61, 64, 67, . . .

4.What is the common difference of this sequence?

67, 64, 61, 58, 55, . . .Suggested Practice for SOL 6.17

22For SOL 6.17, students showed inconsistent performance in determining the common ratio or common difference.

Students had difficulty determining whether a common ratio is a whole number or a fraction. Questions like number one and number two give students opportunities to determine which has a common ratio of 5 and which has a common ratio of 1/5.

The answers to questions one and two are shown on the screen.

Students also had difficulty determining whether a common difference is positive or negative. In questions three and four, students must determine which has a common difference of 3 and which has a common difference of -3.

The answers to questions three and four are shown on the screen.

22SOL 6.18The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.Solving One-Step Equations and Identifying Parts of an Expression

23The next standard being highlighted is SOL 6.18. This standard reads: The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.

23Students need additional practice solving one-step equations when answer options are NOT presented in multiple-choice format and when the solutions contain a decimal or fraction.

Solve each equation.

1. 4.

2. 5.

3.6.

Suggested Practice for SOL 6.18

24For SOL 6.18, students need additional practice solving one-step equations when answer options are NOT presented in multiple choice format. In addition, students need opportunities to solve equations that result in solutions that have decimals or fractions.

The answers are shown on the screen.24

Practice ItemsThis concludes the student performance information for the spring 2013 Grade 6 Mathematics SOL test.

Additionally, test preparation practice items for Grade 6 Mathematics can be found on the Virginia Department of Education Web site at:

http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml#math

25This concludes the student performance information for the spring 2013 Grade 6 Mathematics SOL test.

Additionally, test preparation practice items for Grade 6 Mathematics can be found on the Virginia Department of Education Web site at the URL shown on the screen.

25For questions regarding assessment, please contactStudent_assessment@doe.virginia.gov

For questions regarding instruction, please contact Michael.Bolling@doe.virginia.gov

Contact Information

26For questions regarding assessment, please contact Student_assessment@doe.virginia.gov.

For questions regarding instruction, please contact Michael.Bolling@doe.virginia.gov.26