Spring 2013 Student Performance AnalysisGrade 7 MathematicsStandards of Learning1Presentation may be paused and resumed using the arrow keys or the mouse.

This is the spring 2013 student performance analysis for the Grade 7 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 7 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 7.3 The student willmodel addition, subtraction, multiplication, and division of integers; andadd, subtract, multiply, and divide integers.

Simplifying Integer Expressions2

The first standard being highlighted is SOL 7.3. For this standard, students had difficulty with bullet B. Bullet B reads: The student will add, subtract, multiply, and divide integers.2Suggested Practice for SOL 7.3bStudents need additional practice evaluating expressions, particularly when expressions contain negative numbers.

What is the value of the expression?

1)

2)

3)

3

For SOL 7.3b students need additional practice evaluating expressions, particularly when expressions contain negative numbers. The three examples shown contain negative integers and require students to use the order of operations in order to correctly evaluate the expression. The answers are shown on the screen.3SOL 7.5 The student willdescribe volume and surface area of cylinders;solve practical problems involving the volume and surface area of rectangular prisms and cylinders; anddescribe how changing one measured attribute of a rectangular prism affects its volume and surface area.

Determining the Effect Changing One Dimension Has on Volume or Surface Area4

The next standard being highlighted is SOL 7.5. In particular, students had difficulty with bullet C. Bullet C reads: The student will describe how changing one measured attribute of a rectangular prism affects its volume and surface area.4Students need additional practice determining the effect ofchanging an attribute of a rectangular prism on its volume.

Which method would result in tripling the volume of this rectangular prism?

Add three to each dimension of the prismAdd three to the height of the prism and keep the other dimensions the sameMultiply each dimension of the prism by threeMultiply the width of the prism by three and keep the other dimensions the same

Suggested Practice for SOL 7.5c5height=5 cmwidth=2 cmlength=10 cm

For SOL 7.5c, students need additional practice determining the effect of changing an attribute of a rectangular prism on its volume. The example on the screen asks: Which method would result in tripling the volume of this rectangular prism? Student performance on questions requiring this type of analysis was lower than on questions in which students were given the attribute change and asked to determine the effect on the volume. The answer to the question is shown on the screen.

5SOL 7.6The student will determine whether plane figuresquadrilaterals and trianglesare similar and write proportions to express the relationships between corresponding sides of similar figures.

Write Proportions to DetermineSide Lengths of Similar Figures6

The next standard being highlighted is SOL 7.6. This standard requires students to determine whether quadrilaterals and triangles are similar and to write proportions to express the relationships between corresponding sides of similar figures. In particular, students had difficulty identifying the proportions that could be used to find missing side lengths.6Students need additional practice identifying a proportion that can be used to determine the missing side length of a triangle, when given similar triangles.

Triangle JKL is similar to triangle PQR.

Which three proportions can be used to find the value of x?

Suggested Practice for SOL 7.67JKLPQR81065x3

For SOL 7.6, students need additional practice identifying a proportion that can be used to determine the missing side length of a triangle, when given similar triangles. It is important for students to recognize that many different proportions can be written to solve for a missing side. Students must be able to recognize any one of the correct proportions among the answer options in a multiple choice item. Questions such as the example provided will give students practice identifying multiple correct proportions that can be used to solve for a missing side. The answers are shown on the screen.7SOL 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.

Comparing and Contrasting Quadrilaterals8

The next standard being highlighted is SOL 7.7. This standard reads: The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. In particular, students had difficulty comparing and contrasting the properties of rhombi with the properties of parallelograms and squares.8Suggested Practice for SOL 7.7Students need additional practice classifying an image of a rhombus.

Which classifications describe this figure?

Parallelogram Trapezoid Quadrilateral Square Rhombus Rectangle

9

For SOL 7.7, students need additional practice classifying an image of a rhombus. A common student error is to identify the image of a rhombus as a square. The answers are shown on the screen.9Suggested Practice for SOL 7.7Students need additional practice differentiating between an image of a rhombus and a parallelogram.

Which classifications appear to describe both of these figures?

Parallelogram Trapezoid Quadrilateral Square Rhombus Rectangle

10

For this SOL, students also need additional practice differentiating between an image of a rhombus and a parallelogram. A common student error is for students to identify both of these figures as rhombi. The answers are shown on the screen.10Suggested Practice for SOL 7.7Students need additional practice identifying the properties of a rhombus.

Select each property that is true for any rhombus.There is exactly one pair of parallel sides.There are exactly two pairs of parallel sides.There are exactly four congruent sides.There are exactly four right angles.There are exactly two pairs of congruent opposite angles.There are exactly four congruent angles.

11

For SOL 7.7, students also need additional practice identifying the properties of a rhombus. Common misconceptions are that a rhombus must have four right angles and/or four congruent angles. The answers to the example are shown on the screen.11SOL 7.8 The student, given a polygon in the coordinate plane, willrepresent transformations (reflections, dilations, rotations, andtranslations) by graphing in the coordinate plane.

Graphing Transformations in the Coordinate Plane12

The next standard being highlighted is SOL 7.8. This standard reads: The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane.

12

yxStudents need additional practice applying transformations to a given figure on a coordinate plane.

Suggested Practice for SOL 7.8Identify the coordinates of the image of triangle ABC after a dilation about the origin by a factor of 2.

Identify the coordinates of the image of triangle ABC after a rotation of 180 degrees clockwise about the origin.

Identify the coordinates of the image of triangle ABC after a reflection over the y-axis.

13A (-2,4) B (-2,-3) C (-4,-3)ABC

For this standard, students need additional practice applying transformations to a given figure on a coordinate plane. Students need additional practice identifying the image of a figure when given the pre-image on the coordinate plane, and they also need additional practice identifying the vertices of the image of a figure, as in the examples on the screen. Students did better on multiple choice items that required identification of a vertex of the image, but did not do as well on a technology enhanced item when asked to plot the points on the coordinate plane. The answers to these questions are shown on the screen.13SOL 7.9 The student will investigate and describe the difference between the experimental probability and theoretical probability of an event.

Determining Experimental and Theoretical Probability of Events14

The next standard being highlighted is SOL 7.9. This standard reads: The student will investigate and describe the difference between the experimental probability and theoretical probability of an event.

14Students need additional practice determining the theoretical and/or experimental probability of an event.These cards are the same size and shape. They are placed inside a bag.

A card is randomly selected and then placed back inside the bag. This is done 30 times. The card with an A is selected 3 times. What is the theoretical probability of selecting a card with an A?What was the experimental probability of selecting a card with an A?Compare and contrast the theoretical and experimental probabilities of selecting a card with an A after a card is randomly selected 1,000 times.

Suggested Practice for SOL 7.915

BACDEFSample Answer: The theoretical probability of selecting a card with an A stays the same. The experimental probability should get closer to the theoretical probability.

For this standard students need additional practice determining the theoretical and/or experimental probability of an event. It is important for students to understand that the experimental probability of an event approaches the theoretical probability of an event as the number of trials increases. The answers to the three questions are shown on the screen.

15SOL 7.10 The student will determine the probability of compoundevents, using the Fundamental (Basic) Counting Principle.

Determining the Probability ofCompound Events16

The next standard being highlighted is SOL 7.10. This standard reads: The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle. 16Students need additional practice using the FundamentalCounting Principle to determine the number of possibleoutcomes.The letters A, B, C, and D can be used to create a code for a lock. Each letter can be repeated. What is the total number of four-letter codes that can be made using these letters?

Each letter can be repeated. What is the total number of three-letter codes that can be made using these letters?

Extension: No letter can be repeated. What is the total number of three-letter codes that can be made using these letters?

Suggested Practice for SOL 7.1017

For SOL 7.10, students need additional practice using the Fundamental Counting Principle to determine the number of possible outcomes. Students performed well on many of the items that assessed the use of the Fundamental Counting Principle but did not perform as well on the application of the Fundamental Counting Principle as illustrated by the first two examples on the screen. The answers are provided.

As an extension for this type of item, have students determine the number of three letter codes that can be made if no letter can repeat. First students must determine the number of possible choices for each letter of the code, and find the product of those numbers to determine the total number of three-letter codes. The answer to the extension example is shown on the screen.17Students need additional practice determining the probabilityof compound events.

A fair coin has faces labeled heads and tails. A fair cube hasfaces labeled 1, 2, 3, 4, 5, and 6. Adam will flip this coin and roll the cube one time each.

What is the probability that the coin will land with heads facing up and the top side of the cube will be a number that is composite?

What is the probability that the coin will land with tails facing up and the top side of the cube will be a number that is a multiple of 2?

Suggested Practice for SOL 7.1018

For SOL 7.10, students also need additional practice determining the probability of compound events. These two examples demonstrate how prior knowledge may be used in an item. For example, students would need to know what the word composite means in order to correctly answer question one. Similarly, students need to understand the concept of a multiple to answer question two. When prime numbers are mentioned in probability items, a common error is to include the number one as a prime number, and another error is NOT including the number two as a prime number. The answers to these two questions are shown on the screen.18SOL 7.11 The student, given data in a practical situation, will a) construct and analyze histograms; and b) compare and contrast histograms with other types of graphs presenting information from the same data set.

Analyzing Histograms19

The next standard being highlighted is SOL 7.11. In particular, students had difficulty with bullet A, analyzing histograms, and bullet B, comparing and contrasting histograms with other types of graphs presenting information from the same data set.19Students need additional practice analyzing histograms.

Suggested Practice for SOL 7.11a20Number of Students By Classroom in First BlockNumber of StudentsNumber of ClassroomsThe graph describes the number of students in each classroom during first block at a high school.

What percent of the classrooms have at least 21 students during first block?

48242482

For SOL 7.11a, students need additional practice analyzing histograms. This example demonstrates one skill with which students are having difficulty: identifying a percent of the data that meets certain criteria. In this example, the question asks for the percent of classrooms that have at least 21 students during first block. In order to solve this problem, students need to add the heights of each of the bars to find the total number of classrooms, which is 20, and then add the heights of bars three, four, and five to find the number of classrooms that have at least 21 students. There are 14 classrooms that have at least 21 students. The answer to the question is shown on the screen.20Students need additional practice determining which graphical representation is the best to use for a given analysis.

Jamie recorded the time it took 25 students to complete a mathematics test. She created a histogram and a stem-and-leaf plot to represent the data. To determine the median of the data set, Jamie analyzed the

a) histogram because it showed each value in the set of datab) stem-and-leaf-plot because it showed each value in the set of datac) histogram because the median is always the bar with the greatest heightd) stem-and-leaf-plot because the median is always the leaf that appears most often

Suggested Practice for SOL 7.11b21

For SOL 7.11b, students need additional practice determining which graphical representation is best used for a given analysis and what makes that type of graph the most appropriate choice. An example and its answer are shown on the screen.

21SOL 7.12 The student will represent relationships with tables, graphs,rules, and words.

Representing Relations in Different Forms22

The next standard being highlighted is SOL 7.12. In particular, students need more practice representing the same relation using tables, graphs and/or rules.22

Students need additional practice representing a relation on the coordinate plane when the relation is given as a rule.

Plot three points on the coordinate plane that lie on the relation represented by . The coordinates of the points must be integers.

Suggested Practice for SOL 7.12Sample Answers23

For SOL 7.12, students need additional practice representing a relation on the coordinate plane when the relation is given as a rule. An example of this skill is shown on the screen. Sample answers that will plot on an 8 by 8 grid are shown.

23Students need additional practice matching a rule to a table of values.Which number sentence represents the relation shown in this table?

a)

b)

c)

d)

Suggested Practice for SOL 7.1224xy-2-1121613

For this SOL, students also need additional practice matching a rule to a table of values. An example of this skill is shown on the screen. The answer is provided.24SOL 7.15 The student will solve one-step inequalities in one variable; and graph solutions to inequalities on the number line.

Solving and Graphing Inequalities25

The next standard being highlighted is SOL 7.15. This standard reads: The student will, bullet A, solve one-step inequalities in one variable; and bullet B, graph solutions to inequalities on the number line.

Students need additional practice with the skills associated with both bullets of this standard.25Students need additional practice solving inequalities and identifying values that are part of the solution set.

What is the solution to ?

a)

b)

c)

d)

Suggested Practice for SOL 7.15a26

For SOL 7.15a, students need additional practice solving inequalities and identifying values that are part of the solution set. An example and its answer are shown on the screen. The most common error is not changing the sign of the inequality when dividing or multiplying both sides of the inequality by a negative number.

26What is the solution to ?

a)

b)

c)

d)

Suggested Practice for SOL 7.15a27

This second example has the variable on the right and requires computing with negative numbers to solve the inequality. Inequalities with these attributes are more difficult for students. The answer is shown on the screen.27Which is a value of x that will make true?

a)

b)

c)

d)

Suggested Practice for SOL 7.15a28

Here is another example for SOL 7.15a. This example asks for one value that is part of the solution set of the inequality. Students had difficulty with this type of question. The answer is shown on the screen.28Students need additional practice graphing solutions to inequalities.Graph the solution to the inequality on the number line.1)

2)

Suggested Practice for SOL 7.15b 2 3 45 1 0 -1 -2 -3-4 2 3 45 1 0 -1 -2 -3-429

Here is an example for SOL 7.15b. Students would benefit from additional practice graphing solutions to inequalities. One common misconception is that the shading on the graph needs to match the direction in which the inequality symbol points. Another common error is incorrectly identifying whether the circle on the graph needs to be open or closed. Two examples and their answers are shown on the screen. 29SOL 7.16The student will apply the following properties of operations with real numbers:the commutative and associative properties for addition and multiplication;the distributive property;the additive and multiplicative identity properties;the additive and multiplicative inverse properties; andthe multiplicative property of zero.

Identifying Properties30

The next standard being highlighted is SOL 7.16. This standard pertains to applying the properties of operations with real numbers. Students struggled with all bullets of this standard.30Students need additional practice identifying propertiesof operations with real numbers.

Which property is illustrated by this number sentence?

Identity Property of AdditionInverse Property of MultiplicationCommutative Property of AdditionAssociative Property of Multiplication

Suggested Practice for SOL 7.1631

For SOL 7.16, students need additional practice identifying properties of operations with real numbers. Notice in this example of the Commutative Property of Addition, students have to identify the quantity negative one times five as one addend and the number six as the other addend. The answer to the question is shown on the screen.31Identify the property illustrated by each equation.

1)

2)

3)

4)

Choose from this list of properties:Inverse Propertyof Addition Commutative Property of AdditionIdentity Property of Addition Commutative Property of MultiplicationIdentity Property of Multiplication Associative Property of AdditionDistributive Property Associative Property of Multiplication

Suggested Practice for SOL 7.1632

Distributive PropertyIdentity Property of MultiplicationCommutative Property of MultiplicationInverse Property of Addition

Here are other examples that require students to identify the property that is being illustrated by the equation. The list of properties to choose from is not exhaustive, but it contains the properties that would most likely be strong distractors for students. The answers to the questions are shown on the screen.32This concludes the student performance information for the spring 2013 Grade 7 Mathematics SOL test.

Additionally, test preparation practice items forGrade 7 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

Practice Items

33

This concludes the student performance information for the spring 2013 Grade 7 Mathematics SOL test.

Additionally, test preparation practice items for Grade 7 Mathematics can be found on the Virginia Department of Education Web site at the URL shown on the screen.

33For questions regarding assessment, please contactStudent_assessment@doe.virginia.gov

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

Contact Information

34For questions regarding assessment, please contact Student_assessment@doe.virginia.gov.

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

34