Spring 2014 Student Performance AnalysisPresentation may be paused and resumed using the arrow keys or the mouse.

Grade 7 MathematicsStandards of LearningPresentation may be paused and resumed using the arrow keys or the mouse.Statewide results for the spring 2014 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 Standards of Learning test, this PowerPoint presentation has been developed to provide examples of SOL content identified by this analysis. It should be noted that 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 keep the content of this statewide analysis in perspective. The information provided here should be used as supplemental information. Instructional focus should remain on the standards as a whole, with school or division level data being used as the focal guiding resource to help improve instruction.

12Comparing and Ordering Fractions, Decimals, Percents, and Numbers Written inScientific NotationSOL 7.1The student will investigate and describe the concept of negative exponents for powers of ten;determine scientific notation for numbers greater than zero;compare and order fractions, decimals, percents and numbers written in scientific notation;determine square roots; andidentify and describe absolute value for rational numbers.

The first standard highlighted is SOL 7.1, in particular bullet c. Bullet c reads: The student will compare and order fractions, decimals, percents, and numbers written in scientific notation.

2Students need additional practice comparing numbers written in scientific notation.

Identify two numbers that have a value less than 3.3Suggested Practice for SOL 7.1c

For SOL 7.1c, students need additional practice comparing numbers written in scientific notation. Students would benefit from additional practice comparing numbers written in scientific notation that have a power of ten that is zero or one. It appears that some students erroneously believe ten raised to the first power is one. Student performance also indicates that some students erroneously evaluate ten raised to the zero power as ten or zero.

The correct answer is shown on the screen.3Students need additional practice comparing fractions, decimals, percents, and numbers written in scientific notation.

Which number would make the sentence true?

A

B

C

D4Suggested Practice for SOL 7.1c

For SOL 7.1c, students need additional practice comparing fractions, percents, decimals, and numbers written in scientific notation.

The correct answer is shown on the screen.45Using Proportional ReasoningSOL 7.4The student will solve single-step and multistep practical problems, using proportional reasoning.

The next standard highlighted is SOL 7.4. This standard reads: The student will solve single-step and multistep practical problems, using proportional reasoning.5Students need additional practice finding the discounted price of an item.

The original price of a chair was $545.00. A store discounted the price of this chair by 25%. What is the exact price of the chair, not including tax, with this discount? A $136.25

B $408.75

C $520.00

D $681.25

6Suggested Practice for SOL 7.4Most common error

For SOL 7.4, students need additional practice finding the discounted price of an item. The problem on the screen can be considered single-step or multistep depending upon the method used to solve the problem. The most common student error is to select answer option a, which is the amount to be discounted from the original price of $545.00.

Students would benefit from a discussion on the different ways this problem could be solved. For instance, instead of finding 25% of $545.00 and subtracting the amount of the discount, they could find 75% of $545.00.

The correct answer is shown on the screen. 6Students need additional using proportional reasoning to solve a problem.

Max ran 5 miles on Thursday. One mile is equal to 5,280 feet. Which proportion can be used to determine how many feet, x, Max ran on Thursday?

A B

C D

7Suggested Practice for SOL 7.4

For SOL 7.4, students need additional practice using proportional reasoning to solve a problem. Note that this item provides the number of feet in one mile, and then asks which proportion could be used to determine how many feet are in five miles. The correct answer is shown on the screen.

As an extension, teachers could ask students other proportions that could be used to solve this problem.78Describing Surface Area and VolumeSOL 7.5The student will describe 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.

The next standard highlighted is SOL 7.5. In particular, students had difficulty with part of bullet a, describing the surface area of cylinders; part of bullet b, solving practical problems involving volume, and part of bullet c, describing how changing one measured attribute of a rectangular prism affects its volume.8Students need additional practice describing the surface area of a cylinder.One way to determine the surface area of this cylinder is to

A add the areas of both bases to the rectangular area around the cylinderB add the areas of both basesC multiply the area of the base by the heightD multiply the rectangular area around the cylinder by pi

9Suggested Practice for SOL 7.5a

For SOL 7.5a, students need additional practice describing the surface area of a cylinder. The most common errors for an item similar to the one shown are for students to choose answer choices c and d. This may be because students recognize that area involves multiplication and they select an option with the key word multiply without making sense of the entire answer choice. Conceptually, students may not recognize that the shape around the cylinder can be a rectangle. Working with a net of a cylinder may help students understand the shapes that are involved. Working with nets, in conjunction with a discussion about what each term in the surface area formula represents, may help students connect the parts of the net and the surface area formula.

The correct answer is shown on the screen.9Students need additional finding the volume of a cube, given its edge length.

A container in the shape of a cube will be completely filled with sand. The container has an edge length of 8 inches. What is the exact number of cubic inches of sand needed to completely fill the container?

10Suggested Practice for SOL 7.5bcubic inches

For SOL 7.5b, students need additional practice finding the volume of a cube, given its edge length. There are several misconceptions on items similar to the one shown on the screen. The most common misconception is to square the edge length. In this example, that error would result in an answer of 64 cubic inches. Another common error is to multiply the edge length by 6, which is the number of sides of a cube. Still, other students will multiply the edge length by three, rather than finding the value of the edge length to the third power.

The correct answer is shown on the screen.10Students need additional practice describing how a change in one measured attribute of a rectangular prism impacts volume.Rectangular Prism A is shown.

Rectangular Prism B has the same height and width as rectangular Prism A but its length is 8 inches. The volume of Prism B is A twice the volume of Prism AB one-half the volume of Prism AC one-fourth the volume of Prism AD four times the volume of Prism A

11Suggested Practice for SOL 7.5c

Most common error

h = 5 cm w = 3 cm l = 4 cm For SOL 7.5c, students need additional practice describing how a change in a measured attribute of a rectangular prism impacts volume. The most common error for an item similar to the one shown on the screen is the selection of option B.

The correct answer is shown on the screen.1112Classifying QuadrilateralsSOL 7.7The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.

The next standard 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.12Students need additional practice classifying a given figure.

Which classifications must describe the figure shown?

A square and parallelogramB trapezoid and parallelogramC square and quadrilateralD trapezoid and quadrilateral

13Suggested Practice for SOL 7.7

For SOL 7.7, students need additional practice classifying a given figure. Student data indicate that there are many misconceptions about the classifications of a figure similar to the one shown on the screen. Incorrect classifications include classifying this figure as a square, rectangle, parallelogram, and rhombus. This indicates that many students do not understand the characteristics of the sides and angles of quadrilaterals which distinguish them from one another.

The correct answer is shown on the screen.13Select each classification that does NOT describe this figure.

Parallelogram Rhombus Rectangle Trapezoid Square Quadrilateral

14Suggested Practice for SOL 7.7

Here is another example for SOL 7.7.

Teachers are encouraged to reason through this question with students and discuss why this figure does or does not meet the criteria of each classification.

First, ask students to look at the figure and explain what is given and what can be inferred. This diagram shows a figure with four sides of equal measure. From this diagram, students can see that both pairs of opposite angles are of equal measure. However, all four angles are not the same measure, nor are any of the angles ninety degrees.

Next, use this information to determine which classifications describe this figure. This figure can be classified as a quadrilateral because it has four sides; it can be classified as a rhombus because it is a quadrilateral with four sides of equal length; because it is a rhombus, it can be classified as a parallelogram.

Since the figure is classified as a parallelogram, it can be stated that the figure must have two pairs of parallel opposite sides. This figure would therefore NOT be a trapezoid, because a trapezoid has only one pair of parallel sides; it would NOT be a rectangle or square because all four angles are not congruent, nor are the angles right angles.

1415Representing Transformations on the Coordinate PlaneSOL 7.8The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane.

The next standard highlighted is SOL 7.8. In particular, students had difficulty representing dilations and rotations on the coordinate plane.15Students need additional practice dilating a figure on a coordinate plane. Polygon ABCD is dilated by a scalefactor of using the origin as thecenter of dilation. What coordinatepair best represents the image of B ?A BCD16Suggested Practice for SOL 7.8

B'

For SOL 7.8, students need additional practice dilating a figure on a coordinate plane. Students should be familiar with how a fractional scale factor of one fourth or one half, as well as a whole number scale factor of two, three, or four, impacts the coordinates of the vertices of an image.

The answer to the question in shown on the screen. Students should also recognize that B prime is a way to denote the image of B.16A rectangle is plotted on the coordinate plane as shown.

Which graph shows the rectangle rotated 90 degrees counterclockwise about the origin? (Answer choices are on the next screen.)

17Suggested Practice for SOL 7.8

Here is the beginning of another example for SOL 7.8. The answer choices that go along with this image and question are on the next screen.17Which graph shows the rectangle rotated 90 degrees counterclockwise about the origin?

AC

BD

18Suggested Practice for SOL 7.8

Students must find the image of a rectangle that has been rotated around the origin. The most common error on an item similar to the one shown on the screen is the selection of answer option A, which is the figure rotated 90 degrees clockwise, rather than counterclockwise as indicated in the problem. Another common error would be the selection of option D. A student choosing this option recognizes the correct direction of the rotation, but does not realize that the figure changes orientation when rotated.

The correct answer is shown on the screen.1819Using the Fundamental Counting PrincipleSOL 7.10The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle.

The next standard highlighted is SOL 7.10. This standard reads: The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle.19Students need additional practice determining probability of compound events.This table shows the types of pizza and drink selections at a party.

Maya will randomly select one type of pizza and one drink from these choices. What is the probability that Maya will select pepperoni pizza and cola?A B C D

20Suggested Practice for SOL 7.10Type of PizzaDrinkPepperoniApple JuiceVegetableOrange JuicePlain CheeseColaWaterMost common error

Here is an example for SOL 7.10. The most common student error in a question like the one on the screen is to surmise that the sample space is seven rather than twelve and erroneously determine that the probability of the event is two-sevenths. Students should understand that there are twelve possible ways in which Maya can select one type of pizza and one drink, and the pepperoni pizza and cola selection is one out of the twelve possible pizza/drink selections. Alternately, students can also multiply the probabilities of these two independent events, one-third and one-fourth, to get one-twelfth.

2021Representing RelationshipsSOL 7.12The student will represent relationships with tables, graphs, rules, and words.

The next standard highlighted is SOL 7.12. This standard reads, the student will represent relationships with tables, graphs, rules, and words.21Students need additional practice representing an equation with a table of values.Which table of values represents the same relationship asthe rule ?

A C

B D

22Suggested Practice for SOL 7.12xy-3-306521xy-3-3-2-12524xy-3-15-20521xy-2-1206524

For SOL 7.12, students need additional practice representing the relationship expressed by an equation with a table of values. For examples similar to the one shown, students did well when all of the domain values were positive. Students find the question more challenging when one or more domain values are negative.

The answer to the question is shown on the screen.22 Students need additional practice representing a relationship shown on a coordinate plane as an equation. Which rule is best represented by this graph?

23Suggested Practice for SOL 7.12A

B

C

D

For SOL 7.12, students also need additional practice representing a relationship shown on a coordinate plane as an equation. There is not a common error on an item similar to the one shown on the screen. It would be beneficial to discuss problem solving strategies with students. For instance, one method would be to create a table of values and then match that table of values to one of the equations shown. To support that strategy, ask students: Are they making a table of values from points on the graph? How many points must they use in the table of values? Which points are they using? Are some points easier to use than others? What should they do once they select the points; meaning, how do they determine which rule matches the table of values they created?

The answer to the question is shown on the screen.23Students need additional practice representing a relationship given in words with a table of values.Larry charges a customer a one-time fee of $15 plus $40 each week. Which table has values that represent this situation?

AC

BD

24Suggested Practice for SOL 7.12Number of WeeksTotal Amount of Charges1$553$135Number of WeeksTotal Amount of Charges1$153$45Number of WeeksTotal Amount of Charges1$553$165Number of WeeksTotal Amount of Charges1$153$95

For SOL 7.12, students need additional practice representing a relationship given in words with a table of values.

The correct answer is shown on the screen.2425Identifying Algebraic ExpressionsSOL 7.13The student will write verbal expressions as algebraic expressions and sentences as equations and vice versa; and evaluate algebraic expressions for given replacement values of the variables.

The next standard highlighted is SOL 7.13. Students did well on most aspects of this standard. They did well when translating expressions and evaluating algebraic expressions for given replacement values; however, student performance indicated that students have misconceptions about the defining characteristics of an expression.25Students need additional practice identifying expressions.

Select each of the following that is an expression. 26Suggested Practice for SOL 7.13

The example on the screen asks students to identify expressions. Data indicate that there are many misconceptions. When asked a question similar to the one shown on the screen, some students confused the definition of an expression with an equation and erroneously selected the equations. Some students knew that an expression did not have an equal sign but thought that an expression had to have more than one term. This error would result in the selection of 2x-7 and 2+7, but not -14 or 3x. Others thought an expression had to include a variable. This error would result in the selection of all options that have a variable, regardless of whether it is an expression or an equation. A related error is that some students knew that an expression does not have an equal sign but thought it had to include a variable. This error would result in the selection of only 2x-7 and 3x. Students should recognize that an expression does not have an equal sign and can contain one or more numbers, variables, and/or operations. The correct answer to the question is shown on the screen.2627Solving InequalitiesSOL 7.15The student will solve one-step inequalities in one variable; andgraph solutions to inequalities on the number line.

The next standard 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.27Students need additional practice solving one-step inequalities in one variable.Complete the solution set for the inequalities using one of the symbols and one of the numbers from the choices shown.

28Suggested Practice for SOL 7.15a

For SOL 7.15a, students need additional practice solving one-step inequalities in one variable.

A common error in an item similar to the example shown on the left would be not reversing the inequality sign when dividing both sides by negative four. Students may also incorrectly compute; the incorrect answer options represent mistakes that students make when computing a number on the right side of the inequality.

For the example on the right, students are again computing with integers, but this inequality does not require that students reverse the inequality sign. It would be beneficial to discuss with students why the inequality sign is reversed in the question on the left, but not in the question on the right.

The correct answers are shown on the screen.28Students need additional practice graphing solutions to one-step inequalities on a number line.

Graph the solution set to the inequality shown.

29Suggested Practice for SOL 7.15b

For SOL 7.15b, students would benefit from additional practice graphing solutions to one-step inequalities on a number line. Statewide data show that students have more difficulty with inequalities similar to this example, which has the variable on the right side of the inequality and requires computation with negative integers.

The answer to the example is shown on the screen.

2930Applying PropertiesSOL 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.

The last standard highlighted is SOL 7.16. Students had difficulty applying the properties of operations, as highlighted in green on the screen.30Students need additional practice applying the properties of operations with real numbers.

Which expression completes this equation using only the multiplicative property of zero?

A B C D

31Suggested Practice for SOL 7.16

Uses the Identity Property of AdditionUses the Inverse Property of AdditionUses the Commutative Property of Addition

?

For SOL 7.16, students need additional practice applying the properties of operations with real numbers. The answer to the question is shown on the screen. As an extension, teachers might ask students which property is being applied in the other answer choices. The answers to this extension question are shown on the screen.31Which equation illustrates the multiplicative identity property?

A

B C D

32Suggested Practice for SOL 7.16

Uses the Multiplicative Property of ZeroUses the Identity Property of AdditionUses the Inverse Property of Multiplication

Here is another example for SOL 7.16. The correct answer is shown on the screen, along with the properties that are illustrated in each of the other answer options.32This concludes the student performance information for the spring 2014 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

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This concludes the student performance information for the spring 2014 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

34

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