Spring 2013 Student Performance AnalysisGrade 8 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 8 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 8 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 8.1The student willsimplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers; andcompare and order decimals, fractions, percents, and numbers written in scientific notation.

Compare and Order Decimals, Fractions, Percents, and Numbers Written in Scientific Notation

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The first Standard of Learning highlighted is SOL 8.1. In particular, student performance was inconsistent on questions that assessed bullet b, which states: The student will compare and order decimals, fractions, percents, and numbers written in scientific notation.2

Suggested Practice for SOL 8.1b

Students need additional practice comparing and ordering percents,decimals, mixed numbers, and numbers written in scientific notation.

Select each number that is between

Identify the number with the smallest value.

3For this standard, students need additional practice comparing and ordering percents, decimals, mixed numbers, and numbers written in scientific notation. Student performance data indicates that students find it difficult to compare and order numbers when the number is a percent greater than 100 and when the number written in scientific notation has a negative or zero power of 10.

The answers to the examples are shown on the screen.3SOL 8.2The student will describe orally and in writing the relationships between the subsets of the real number system.

Recognizing Subsets of the Real Number System

4The next standard being highlighted is SOL 8.2, which states: The student will describe orally and in writing the relationships between the subsets of the real number system. Statewide, students found all of the content within this standard challenging.

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Students need additional practice identifying natural numbers from a list of numbers.

Identify each natural number from the list of numbers.

Suggested Practice for SOL 8.2

a)b)

5For SOL 8.2, students need additional practice selecting natural numbers from a list that includes fractions, square roots, decimals, and integers.

The answers to the examples are shown on the screen.5SOL 8.3The student willsolve practical problems involving rational numbers, percents, ratios, and proportions; anddetermine the percent increase or decrease for a given situation.

Solving Practical Problems Involving Decimals, Information Presented as Graphs, and Percent Increase and Decrease

6The next standard being highlighted is SOL 8.3. The standard reads: The student will, bullet a, solve practical problems involving rational numbers, percents, ratios, and proportions; and bullet b, determine the percent increase or decrease for a given situation. Student performance data indicate students found all of the content within this standard challenging.

6Students need additional practice solving practical problemsinvolving computation procedures with decimals.

Kimberly wants to buy a new television for her mother.The cost of the television is $276.45, including tax.She has $90 saved.She will babysit for three months to save the remaining amount of money needed to buy the television.She will earn the same amount of money each month.How much money must Kimberly earn each month to save the exact remaining amount needed?

Suggested Practice for SOL 8.3a

$ 62.15

7For SOL 8.3a, students need additional practice with multistep practical problems involving decimal numbers. Specifically, students struggle on problems that require more than one operation, as in the example shown.

The answer to the example is shown on the screen.7Students need additional practice solving practical problems when information is represented as percentages in a graph.

Dedra polled people at the mall to determine which types of movies they preferred to watch. She displayed the results in a circle graph.

Suggested Practice for SOL 8.3a

Of the people polled, 84 preferred to watch comedies. Use this information and the graph to answer these questions.

What is the total number of people Dedra polled?

What is the total number of people that preferred:Horror Drama

2401248

8Students need additional practice with practical problems that require them to interpret a circle graph to answer questions. When percentages were part of the information provided in the graph, students had difficulty determining the total number represented by a graph, and the total number represented by sections of the graph.

The answers to the examples provided are shown on the screen.

8Suggested Practice for SOL 8.3b

Students need additional practice solving practical problems involving percent increase and decrease.

Cayleys mom made a graph to represent Cayleys weight in March and in December. Cayley weighed a total of 6 pounds in March. Her weight increased by 175% from March to December. Complete the graph to show Cayleys weight in December.

MonthWeight(Pounds)9

For SOL 8.3b, students need additional practice determining a value of increase or decrease when given the percentage. Teachers are encouraged to provide experiences that require students to find the percent increase or decrease as well as the resulting value after the increase or decrease is applied to the original value. In addition, students would benefit from opportunities that require them to represent these values on a graph.

The answer to this example is provided on the screen.9Suggested Practice for SOL 8.3b

The price of a video gaming system was $259. The price decreased to $199. What is the percent decrease inthe price of this system? Round your answer to the nearest whole percentage.

23%

10This example for SOL 8.3b requires students to find the percent decrease in a practical problem. Students are challenged when they are required to find the percent of change when given an initial value and an ending value.

The answer to the example is shown on the screen.10SOL 8.6The student willverify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; andmeasure angles of less than 360.

Identifying Angle Relationships

11The next standard being highlighted is SOL 8.6. In particular, student performance was inconsistent on questions that assessed bullet a, which states: The student will verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles.

11Students need additional practice identifying angle relationships among multiple angles.

Name pairs of vertical, adjacent, supplementary, andcomplementary angles.Suggested Practice for SOL 8.6a

Vertical AnglesAdjacent AnglesSupplementary AnglesComplementary Anglesa and c e and da and b b and c a and c

a and b b and c c and dd and ea and e

aebdc

12For SOL 8.6a, students need additional practice identifying angle relationships among multiple angles. Students can benefit from practice recognizing all angle relationships, however, students had particular difficulty recognizing adjacent angles. Performance data also show that students are challenged when items have more than one correct answer.

The answers to the examples provided are shown on the screen.12SOL 8.7The student willinvestigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and describe how changing one measured attribute of a figure affects the volume and surface area.

Solving Practical Problems Involving Surface Area

13The next standard being highlighted is SOL 8.7. Student performance indicates that students need additional practice with bullet a in this standard. Specifically, finding the surface area of pyramids.

13Suggested Practice for SOL 8.7a

Students need additional practice determining surface area of a square-based pyramid.

Timothy built a wooden square-based pyramid for a history classproject on Egypt. He needs to buy enough gold paper to cover theentire surface. The base length is 2.5 ft and the slant height is 1.5 ft.

What is the minimum amount of gold paper he needs to purchase?

13.75 sq ft2.5 ft1.5 ft

14Students need additional practice determining the surface area of a square-based pyramid. Teachers are encouraged to provide practice with both multiple-choice and open-response formats and to include measurements that are decimals.

The answer to the example is shown on the screen.14SOL 8.8The student willapply transformations to plane figures; andidentify applications of transformations.

Determining the Coordinates of a Figure After a Transformation

15The next Standard of Learning being highlighted is SOL 8.8. In particular, student performance was inconsistent on questions that assessed bullet a, which states: The student will apply transformations to plane figures.

15This polygon is rotated 270 counterclockwise about the origin. Plot theimage of point D (-4,5) and name the coordinates.

Suggested Practice for SOL 8.8a

Students need additional practice determining the coordinatesof a figure after it is rotated about the origin in the counterclockwise direction.

D(5, 4) D

16Students need to focus on understanding how a figure is affected when it is rotated in the counterclockwise direction. Teachers are encouraged to include opportunities for students to plot the resulting image of one or more vertices on a coordinate plane.

The answer to this example is shown on the screen.16SOL 8.9The student will construct a three-dimensional model, given the top or bottom, side, and front views.

Identifying a Figure When Given Three Views

17The next standard being highlighted is SOL 8.9. It states: The student will construct a three-dimensional model, given the top or bottom, side, and front views. Statewide student performance indicates that students need additional practice on identifying a figure when given three views.

17Suggested Practice for SOL 8.9

Students need additional practice using the top or bottom, side, and front views to determine which figure is represented.

A three-dimensional figure was constructed using identical cubes. The top-, front-, and left-side views of this figure are shown. Which could be this figure?

FrontTopLeft Side

18For SOL 8.9, students are challenged when they must select the 3-D figure that matches three given views. Students perform better when selecting the views that represent a given figure.

The answer to this example is shown on the screen.18SOL 8.11The student will solve practical area and perimeter problems involving composite plane figures.

Finding the Area and Perimeter of Composite Figures

19The next Standard of Learning being highlighted is SOL 8.11. Student performance data indicate that students need additional practice solving practical area and perimeter problems involving composite plane figures.193ft 10 ft 8 ft5ftBobby is painting a figure on a banner for a homecoming parade. The figure he is painting consists of an isosceles triangle, a rectangle, and a semicircle, as shown.

What is the total area of the figure, rounded to the nearest tenth?

What is the total perimeter of the figure, rounded to the nearest tenth?

Suggested Practice for SOL 8.11

Students need additional practice finding the area and perimeter of composite figures.

117.1 sq ft42.6 ft

20Students find items that involve finding the area and/or perimeter of composite figures challenging.

The answers to the examples are shown on the screen.20SOL 8.12The student will determine the probability of independent and dependent events with and without replacement.

Determining the Probability of Independent and Dependent Events

21The next standard being highlighted is SOL 8.12. It reads: The student will determine the probability of independent and dependent events with and without replacement.

21Suggested Practice for SOL 8.12

Students need additional practice finding the probability of events, with and without replacement.

Ms. Wright has a box of markers that are all the same shape and size that she uses to write on the board. There are 4 red markers, 3 green markers, and 8 black markers.

What is the probability that Ms. Wright will select a red marker, put it back in the box, and then select a green marker?

Ms. Wright is passing out markers to her students. What is the probability that she first selects a black marker, does not replace it, and then selects a red marker?

22Slide Revised March 5, 2014For standard 8.12, students need additional experiences that require them to determine the probability of dependent and independent events. In example a, the red marker is replaced, which indicates that the two events (selecting a red marker and then a green marker) are independent. In example b, the black marker is NOT replaced, which indicates that the two events (selecting a black marker and then a red marker) are dependent.

The answers are shown on the screen.22Suggested Practice for SOL 8.12

Students need additional practice finding the probability of two independent events.

Clinton has two spinners. Spinner A has 4 congruent sections and Spinner B has 3 congruent sections as shown.

Clinton will spin these two spinners at the same time.What is the probability that both spinners will land on a color that is NOT pink?

What is the probability that Spinner A will land on orange and spinner B will land on green?

GreenPinkOrangeBluePinkGreenGreenSpinner ASpinner B

23For this standard, students are challenged by items requiring them to determine the probability of two independent events, such as flipping two coins at the same time or spinning two spinners at the same time. Additionally, teachers are encouraged to include opportunities for students to consider the probability of events that will NOT occur, as in example a.

The answers to the examples are shown on the screen.23SOL 8.13The student willmake comparisons, predictions, and inferences, using information displayed in graphs; andconstruct and analyze scatterplots.

Using Information Displayed in Graphsand Analyzing Scatterplots

24The next standard being highlighted is SOL 8.13. In particular, student performance was inconsistent on questions that assessed bullet a, which states: The student will make comparisons, predictions, and inferences, using information displayed in graphs. In addition, students can benefit from more practice analyzing scatterplots, which is part of SOL 8.13b.

24Suggested Practice for SOL 8.13a

Students need additional practice using data represented in a graph to make inferences or answer questions.

The numbers and prices of meals sold at a restaurant are represented in the graph.

Number of Meals SoldPrice of a Meal (in dollars)Based on the information in the graph:What is the mean price of all of the meals sold?

What is the median price of all the meals sold?

What is the total number of meals costing more than 7 dollars?$7.249$7.00

25Students have difficulty making inferences when data is represented in a graph and is not represented as a set of numbers. Teachers are encouraged to provide experiences where data is represented in a variety of graphical forms such as bar graphs, circle graphs, and line graphs. The answers are shown on the screen.25Suggested Practice for SOL 8.13b

the graph shows a positive relationship for the average price of a gallon of gas

the graph shows a negative relationship for the average price of a gallon of gas

the graph shows the average price of a gallon of gas remains constant

the graph shows no relationship between the average price of a gallon of gas and the months

This scatterplot shows the average price of a gallon of gas during each month in 2013. Which statement best describes the gas prices as the months progress from January to December?JulyOctoberAugustSeptemberNovember2013 National Average Gas PricesPrice of a Gallon of Gas ( in dollars)MonthsJanuaryFebruaryMarchMayJuneAprilDecember

26For SOL 8.13b, students also have difficulty determining the type of relationship that exists within a data set represented in a scatterplot.

The answer to the example shown is option B.26SOL 8.14The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship.

Making Connections Between Representations of a Relationship

27The next standard being highlighted is SOL 8.14, which states: The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship.

27Suggested Practice for SOL 8.14

Students need additional practice making connections between any two representations of a given relationship.

Use the table to answer questions a, b and c.

Possible answer:y is equal to the product of 2 and a number x decreased by 3a) Plot the ordered pairs in the table on the coordinate plane.b) Use words to describe the relationship found in the table.

c) Write an equation for the relation that includes the ordered pairs in the table.

x-2013y-7-3-13

Possible answer: 28

When given one form of a relation, students must be able to represent that relation in other forms. In the example provided, students are given the relation in a table and are then asked to graph the relation, represent that relation using words, and then write an equation to represent that relation.

The answers to the examples are shown. 28SOL 8.15The student willsolve multistep linear equations in one variable on one and two sides of the equation;solve two-step linear inequalities and graph the results on a number line; andidentify properties of operations used to solve an equation.

Solving Equations and Inequalities

29The next standard being highlighted is SOL 8.15, which states: The student will bullet a, solve multistep linear equations in one variable on one and two sides of the equation; bullet b, solve two-step linear inequalities and graph the results on a number line; and bullet c, identify properties of operations used to solve an equation.29Suggested Practice for SOL 8.15a

Students need additional practice solving multistep equations.

Solve each equation.

a)

b)

c)

30For SOL 8.15a, student performance indicates that students need additional practice solving multistep equations that include fractions, variables with negative coefficients, and variables on both sides of the equation.

The answers to the examples are shown on the screen.30Solve and graph the inequality.

a)b)

Suggested Practice for SOL 8.15b

Students need additional practice solving two-step linearinequalities and graphing the solutions on a number line.

31For SOL 8.15b, students need additional practice solving two-step inequalities that include decimals, fractions with the variable in the numerator, and variables that have negative coefficients.

The answers to the examples are provided on the screen.31Suggested Practice for SOL 8.15c

Students need additional practice identifying the properties of operations used to solve an equation.

Select each equation that shows the use of the commutative property of multiplication.

32For SOL 8.15c, students need additional practice identifying the properties of operations used to solve an equation. Although students have had prior experiences recognizing all of the properties of operations used to solve equations, students are having difficulty distinguishing between the application of the commutative and associative properties.

The answers to the example are shown on the screen.32

Suggested Practice for SOL 8.15c

Students need additional practice identifying the properties of operations used to solve an equation.

Joanna was given the equation to solve. The first five steps she used to solve the equation are shown.

Between which two steps is the commutative property of addition applied? Between which two steps is the associative property of addition applied?

Step 1 and Step 2 Step 2 and Step 3 33Slide revised March 7, 2014

Here is another example for SOL 8.15c.

The answers are shown on the screen.33SOL 8.16The student will graph a linear equation in two variables.

Graphing Linear Equations

34The next standard being highlighted is SOL 8.16. It reads: The student will graph a linear equation in two variables.34

Suggested Practice for SOL 8.16

Students need additional practice determining corresponding graphs and equations.

Identify the equation that best represents the graph. Equation A

ABCEquation BEquation C

35For this standard, students need additional practice determining corresponding graphs and equations. Particularly, students need additional practice identifying the linear equation that is represented by a given graph, as in the examples provided.

The answers are shown on the screen.35SOL 8.17The student will identify the domain, range, independentvariable, or dependent variable in a given situation.

Determining the Domain, Range, Independent Variable, or Dependent Variable

36The next standard being highlighted is SOL 8.17, which states: The student will identify the domain, range, independent variable, or dependent variable in a given situation.

36Suggested Practice for SOL 8.17

Students need additional practice determining the domain andrange of a relation from a set of points.

xy-51-38064-9

a)b)Determine the domain and range of each relation.Domain: {-5, -3, 0, 4}Range: {-9, 1, 6, 8}Domain: {-7, -2, 0, 5}Range: {1, 2, 3, 9}

37For this standard, students have difficulty determining the domain and range of a relation. Students would benefit from questions that show relations represented in different formats. Example a presents the relation in a table, while ordered pairs in set notation are given in example b.

The correct answers are shown on the screen.37Suggested Practice for SOL 8.17

c)Identify the domain and range of each relation.

Domain: {-4, 0, 3, 8} Range: {-7, -4, 3}

38Here is another example for SOL 8.17. Students would benefit from experiences with relations represented as points plotted on a coordinate plane, as in this example.

The correct answers are shown on the screen.38Suggested Practice for SOL 8.17

Students need additional practice recognizing a relation with a given range.

Select each relation that has a range of .

39For this standard, students also need additional practice recognizing a relation with a given range. Student performance data show that when given a specific range, students have difficulty identifying sets of ordered pairs with the given range. In particular, students must recognize that values in the range may be used more than once in the relation.

The answers to this example are shown on the screen.39Suggested Practice for SOL 8.17

Students need additional practice identifying the dependentvariable and independent variable in a practical problem.

Determine the dependent variable and independent variable in each situation.Brianna is saving the money she earns babysitting to buy a present for her mother. The more hours she babysits, the more money she earns.

Makayla has a basket of yarn she uses to knit scarves. As she finishes knitting scarves, she has less yarn in her basket.

Dependent Variable: The money she earnsIndependent Variable: The number of hours she babysitsDependent Variable: The amount of yarn in her basketIndependent Variable: The number of scarves she finishes

40Here is the last example for SOL 8.17. These examples ask students to identify the dependent variable and independent variablein a practical problem.

The answers are shown on the screen.40Practice ItemsThis concludes the student performance information for the spring 2013 Grade 8 Mathematics SOL test.

Additionally, test preparation practice items for Grade 8 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

41This concludes the student performance information for the spring 2013 Grade 8 Mathematics SOL test.

Additionally, test preparation practice items for Grade 8 Mathematics can be found on the Virginia Department of Education Web site at the URL shown on the screen.

41For questions regarding assessment, please contactStudent_assessment@doe.virginia.gov

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

Contact Information

42For questions regarding assessment, please contact Student_assessment@doe.virginia.gov.

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

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