Spring 2013 Student Performance AnalysisGrade 5 MathematicsStandards of LearningPresentation may be paused and resumed using the arrow keys or the mouse.

This is the spring 2013 student performance analysis for the Grade 5 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 5 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 5.3The student willidentify and describe the characteristics of prime and composite numbers; and identify and describe the characteristics of even and odd numbers.

Identifying Prime and Composite Numbers

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The first Standard of Learning being highlighted is SOL 5.3, which reads: The student will, bullet A, identify and describe the characteristics of prime and composite numbers; and, bullet B, identify and describe the characteristics of even and odd numbers. Student performance was inconsistent across all of the content included within this standard.2Students need additional practice distinguishing betweennumbers that are prime and numbers that are composite.

Select all of the numbers that are prime.

12213749517797

How many of the numbers listed below are composite?

1127335261738191

Suggested Practice for SOL 5.3a

3Five of the numbers are composite.2

SOL 5.3A states that the student will identify and describe the characteristics of prime and composite numbers. This standard includes identifying prime and composite numbers less than or equal to 100.

Students would benefit from additional opportunities to differentiate between prime and composite numbers within a given set of numbers. The answers to the examples are shown on the screen. For question number 2, students must recognize each of the five composite numbers in the list to answer the question correctly.3Suggested Practice for SOL 5.3bStudents need additional practice describing the characteristics of even numbers and odd numbers.

Which statements are true?

A number that is divisible by two is odd.The sum of an even number and an odd number is odd.An even number is a multiple of two.Odd numbers have an odd number or a zero in the ones place.The sum of two odd numbers is even.4

SOL 5.3B requires students to identify and describe the characteristics of even and odd numbers. Student performance was inconsistent with items similar to the example provided. The correct answers are shown on the screen.

As an extension to this question, teachers could ask students to give an example of a number that disproves a statement and explain how that number shows that statement is false. For example, a number that disproves the fourth statement, Odd numbers have an odd number or a zero in the ones place could be the number 10, which has a zero in the ones place but is even and not odd. 4SOL 5.4The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Solving Multistep Problems with Whole Numbers

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The next standard being highlighted is SOL 5.4. This standard reads: The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers. In particular, students had difficulty when solving multistep practical problems that involve more than one operation.5Students need additional practice solving multistep practical problems involving more than one operation with whole numbers.

1. Mrs. Smith is buying pencils for the fifth-graders at her school. The number of students in each class is shown in the table.

Mrs. Smith will give one pencil to each student. There are 12 pencils in each package. How many of these packages of pencils should Mrs. Smith buy?

Suggested Practice for SOL 5.4

6Fifth-Grade ClassesClassWXYZNumber of Students26232524Mrs. Smith needs to buy 9 packages of pencils.

For SOL 5.4, students need additional practice solving multistep practical problems involving more than one operation with whole numbers. Students would benefit from additional experiences that require them to consider how the remainder in a practical division situation impacts the answer.

In this example, Mrs. Smith needs a total of 98 pencils. When 98 is divided by 12, the number of pencils in each package, the quotient is 8 remainder 2. The student must recognize that the quotient represents 8 complete packages of pencils and two additional pencils that will be needed from another package. Mrs. Smith should therefore buy a ninth package of pencils. If she buys 8 packages, she will not have enough pencils for each student. 6Samuels family bought some supplies for their new game room.They bought four game controllers that each cost the same amount for a total of $96.They bought four bean-bag chairs that each cost the same amount for a total of $156.

What was the combined cost of one controller and one bean-bag chair?

Suggested Practice for SOL 5.4

7$63

This suggested practice example for SOL 5.4 also involves division. Student performance on multistep practical problems was lower when division was one of the operations involved. The answer to this example is shown on the screen.

Teachers are encouraged to include experiences with problems for which multiple problem-solving methods are valid. While there are multiple ways to solve this example, an efficient strategy is adding the two subtotals and dividing that total by four. This strategy can be used since both subtotals represent the cost of four items.7SOL 5.5The student willfind the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and create and solve single-step and multistep practical problems involving decimals.

Solving Problems with Decimals

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The next standard being highlighted is SOL 5.5. This SOL states: the student will bullet A, find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and bullet B, create and solve single-step and multistep practical problems involving decimals.

In particular, student performance was inconsistent on questions involving multiplication of decimals, which is included in bullet A, and on multistep practical problems involving decimals, which is content included in bullet B.8Students need additional practice finding the product of two decimals.

What is the product of 0.38 and 0.05?0.4300.1900.0430.019

0.82 x 0.045 = ____________

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

Suggested Practice for SOL 5.5a

90.0369

For SOL 5.5A, students would benefit from additional practice involving multiplication of decimals and should understand the associated vocabulary, as in the first example provided. Practice with both multiple-choice and open response formats is encouraged. The answers are shown on the screen.

Please refer to the Practice Item Guide that accompanies the Practice Items on the Virginia Department of Education Web site (http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml#math)for additional information regarding the scoring of fill-in-the-blank technology-enhanced items on the Standards of Learning assessments.9Students need additional practice solving multistep practical problems involving decimals.

Tom has a goal of running 50 miles this week in preparation for a marathon. He recorded the miles run each day in the table.

Tom plans to finish his 50 miles when he runs on Saturday. Based on the number of miles in the table, how many miles must Tom run on Saturday to meet his goal?

Suggested Practice for SOL 5.5b

10DayMilesMonday12.3Wednesday13.4Friday11.812.5 miles

SOL 5.5B requires students to create and solve single-step and multistep practical problems involving decimals. Students performance when solving multistep practical problems involving decimals was inconsistent. Teachers are encouraged to provide opportunities to practice with information presented in a variety of formats. While this example uses a table to organize the information students must use to solve the problem, the information could also be presented in paragraph form or within a bulleted list. The answer to this example is shown on the screen.

10SOL 5.6The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.

Solving Multistep Problems with Fractions

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The next standard being highlighted is SOL 5.6, which states: The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form. Statewide performance indicates that solving multistep problems involving fractions and/or mixed numbers continues to challenge students.11Students need additional practice solving multistep practical problems involving fractions and mixed numbers.

Mrs. Jones had a total of 8 cartons of vanilla ice cream to sell in the concession stand. She sold: cartons on Friday cartons on Saturday

How many cartons of ice cream does Mrs. Jones have left to sell?

Suggested Practice for SOL 5.6

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cartons sold}

cartons left to sell

For SOL 5.6, student performance was lower on questions that required regrouping; this was true whether the denominators of the given fractions were the same or different.

One strategy for solving this problem is shown on the screen. Students might choose to break the addition that is shown as one step into multiple steps, or they might choose to use addition to determine the number of cartons left to sell (i.e., think about how much must be added to 4 1/12 to make a total of 8 cartons). 12

cupscups

Joseph needs several cups of flour for the baking he will do this weekend. The table shows the amounts needed for each recipe.

What is the total number of cups of flour needed for these three recipes?

Joseph used cups of flour last weekend. What is the difference in the amount of flour he used last weekend and the total amount he will use this weekend?

Suggested Practice for SOL 5.6

13Recipe123Amount of Flour, in Cups

Here is another example for SOL 5.6. In this example, students are given information within a table to use when solving two different problems that require regrouping. The first problem involves addition of mixed numbers with unlike denominators. The second problem requires students to find the difference of two mixed numbers that have unlike denominators. The answers to the problems are shown on the screen.13SOL 5.7The student will evaluate whole number numerical expressions, using the order of operations limited to parentheses, addition, subtraction, multiplication, and division.

Applying the Order of Operations

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The next standard being highlighted is SOL 5.7. This standard states: The student will evaluate whole number numerical expressions, using the order of operations limited to parentheses, addition, subtraction, multiplication, and division. 14Students need additional practice applying the order of operations.

What is the value of ? 12334245

Based on the order of operations, what should be the first calculation in simplifying ?

________

Suggested Practice for SOL 5.7

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For this standard, students would benefit from experiences that include multiple-choice as well as open-ended response formats. The answers to these examples are shown on the screen.

Since the answer for example two is open-ended, students might identify the expression within the parentheses as the first portion of the larger expression that needs simplification. Based on the order of operations, this is accurate. However, since the question asks students to identify the first calculation, ask what calculation within the parenthesis should be done first, and that would be 3X2.

As an extension to example two, students could evaluate the given expression, which has a value of 231.15SOL 5.8The student willfind perimeter, area, and volume in standard units of measure;differentiate among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;identify equivalent measurements within the metric system;estimate and then measure to solve problems, using U.S. Customary and metric units; andchoose an appropriate unit of measure for a given situation involving measurement and U.S. Customary and metric units.

Finding Area and Metric Equivalents

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The next standard being highlighted is SOL 5.8. Student performance was inconsistent for bullets A and C within this standard. These bullets read: the student will, bullet A, find perimeter, area, and volume in standard units of measure; and bullet C, identify equivalent measurements within the metric system.16Students need additional practice finding the area of a right triangle when a diagram of the triangle is not provided.

What is the area of a right triangle with a base of 12 inches and a height of 5 inches?17 square inches30 square inches34 square inches60 square inches

A right triangle has a height of 6 centimeters and a base of 8 centimeters. What is the area of this triangle?

Suggested Practice for SOL 5.8a

1724 square centimeters

For this standard, students had difficulty determining the area of a right triangle when a diagram of the triangle was not provided. Students would benefit from additional practice with both multiple-choice and open-ended questions. The answers to these examples are shown on the screen.17Students need additional practice identifying the measurement that is equivalent to a given metric measurement.

1,710 milliliters = _____ liters1,710,000171,0001.710.171

_______ kilograms = 53 grams

1.45 meters = ______ centimeters

Suggested Practice for SOL 5.8c

180.053145

For SOL 5.8 C, students should be able to find equivalent measures between any two units within the metric system. The answers to the examples provided are shown on the screen.18SOL 5.13The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), willdevelop definitions of these plane figures; andinvestigate and describe the results of combining and subdividing plane figures.Defining and Subdividing Plane Figures

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The next standard being highlighted is SOL 5.13. This standard states, the student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will bullet A, develop definitions of these plane figures; and bullet B, investigate and describe the results of combining and subdividing plane figures. Students had difficulty answering questions that assessed content from each of these bullets.19Students need additional practice identifying characteristics of plane figures.

Select each statement that is true.

The opposite sides of a rhombus are congruent.All sides of a rhombus are congruent.Every rhombus is a square.A trapezoid must have two congruent sides.A trapezoid must have one pair of parallel sides.Every trapezoid is a quadrilateral.

Suggested Practice for SOL 5.13a

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For SOL 5.13A, students had difficulty determining which of several statements about plane figures were true. Teachers are encouraged to provide opportunities for students to consider more than one statement for a specific figure.

This example includes three statements about rhombi and three about trapezoids. Additionally, students should have experiences that help them differentiate between characteristics that are always true, characteristics that are sometimes true, and characteristics that are never true for a given figure. The answers to the example provided are shown on the screen.20Students need additional practice determining the figures that result when a polygon is subdivided.

This polygon will be divided into three figures by cutting along the dashed line segments. The dashed line segments are parallel to line segment c.Side a is parallel to side b.

Use the terms from the word bank to label the figures that result from the cuts shown:Triangle ParallelogramRectangleRhombusSquareTrapezoid

Suggested Practice for SOL 5.13b

21TriangleParallelogramTrapezoidabc

For SOL 5.13B, students need additional practice determining the figures that result when a polygon is subdivided. The answers to the examples are shown on the screen.

Students should recognize that information about both pairs of sides being parallel must be given in order to identify the middle figure as a parallelogram. If only information about one pair of sides being parallel was given, the most specific name for the middle figure would be trapezoid.21

Practice ItemsThis concludes the student performance information for the spring 2013 Grade 5 Mathematics SOL test.

Additionally, test preparation practice items for Grade 5 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

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This concludes the student performance information for the spring 2013 Grade 5 Mathematics SOL test.

Additionally, test preparation practice items for Grade 5 Mathematics can be found on the Virginia Department of Education Web site at the URL shown on the screen.

22For questions regarding assessment, please contactStudent_assessment@doe.virginia.gov

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

Contact Information

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For 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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