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**Spring 2014 Student Performance Analysis**

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 5 Mathematics 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. Presentation may be paused and resumed using the arrow keys or the mouse.

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**Comparing and Ordering Fractions**

SOL 5.2 The student will recognize and name fractions in their equivalent decimal form and vice versa; and compare and order fractions and decimals in a given set from least to greatest and greatest to least. The first standard being highlighted is SOL 5.2, with an emphasis on bullet b: The student will compare and order fractions and decimals in a given set from least to greatest and greatest to least.

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**Suggested Practice for SOL 5.2b**

Students need additional practice comparing and ordering a set of fractions. Which list shows these fractions ordered from greatest to least? A C B D For SOL 5.2b, students need additional practice comparing and ordering fractions. When given a multiple-choice question the most common errors are to order the fractions by their numerators (as in option A) or to order them by their denominators (as in option D). The correct answer is shown on the screen.

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**Suggested Practice for SOL 5.2b**

Students need additional practice comparing and ordering a set of decimals and fractions. Order these numbers from least to greatest. 𝟑 𝟑 𝟒 , 𝟑.𝟑𝟒 , 𝟑 𝟓 𝟖 , 𝟑.𝟓 𝟑.𝟑𝟒 , 𝟑.𝟓 , 𝟑 𝟓 𝟖 , 𝟑 𝟑 𝟒 Students also need additional practice comparing and ordering a set of decimals and fractions. The correct answer is shown on the screen. Common mistakes include incorrectly converting when finding equivalent fractions and decimals (for instance, converting 3 3/4 to 3.34), incorrectly applying whole number understanding when comparing decimals (for instance, stating 3.34 is greater than 3.5 because 34 is greater than 5), and incorrectly comparing the fractions (stating 3 3/4 is less than 3 5/8 because the numerator of 3 is less than the numerator of 5 and the denominator of 4 is less than the denominator of 8).

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**Solving Practical Problems Involving Operations with Whole Numbers**

SOL 5.4 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. The next standard being highlighted is SOL Student performance indicates that students continue to have difficulty solving multistep practical problems with whole numbers, particularly when more than one operation is required.

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**Suggested Practice for SOL 5.4**

Students need additional practice solving multistep problems involving addition, subtraction, multiplication, and division of whole numbers. Paul needs to buy 4 new tires for his car. This table shows the cost of a tire at two different stores. What is the total amount of money Paul will save if he buys 4 tires at Store Y rather than Store X? Store Cost X $115 Y $88 Students need additional practice solving multistep problems with whole numbers that involve the use of more than one operation. In this example students need to use the information in the table and the information in the text. Many students will compute the answer to be $27, which is the amount of money Paul will save on one tire. The correct answer is shown on the screen. $108

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**Suggested Practice for SOL 5.4**

Maria has three boxes of pictures to display on posters. Box A has 96 pictures. Box B has 39 pictures. Box C has 87 pictures. Each poster can hold 10 pictures. What is the minimum number of posters Maria will need to display all of these pictures? Here is another example for SOL 5.4 that requires students to use more than one operation when solving the problem. Students would benefit from experiences that require them to consider how the remainder of a division situation impacts the outcome, as in the example provided. In this example students need to add to find the total number of pictures (222) and then divide by 10 to decide how many posters are needed. Since the result is 22 R2 Maria will need a total of 23 posters in order to display all of the pictures. The correct answer is shown on the screen. Maria will need 23 posters.

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**Finding the Product of Decimals**

SOL 5.5 The student will find 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. The next standard being highlighted is SOL The part of bullet a highlighted is: The student will find the product of two numbers expressed as decimals through thousandths. The highlighted portion of bullet b states: The student will solve multistep practical problems involving decimals.

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**Suggested Practice for SOL 5.5a**

Students need additional practice multiplying decimals. 20.5 x 0.4 = ? 0.55 x 0.5 = ? x 2.5 = ? 8.2 0.275 6.25 For SOL 5.5a, students need additional practice multiplying decimals. Statewide results indicate that the most frequent error made by students on both multiple-choice and technology-enhanced items occurs when placing the decimal into the answer. The correct answers are shown on the screen. Using estimation strategies to verify the reasonableness of a product may be helpful. For example in #3, since 2 times 2 equals 4 and 3 times 3 equals 9, it is reasonable to decide that 2.5 times 2.5 should be between 4 and 9. Therefore, 6.25 is a reasonable answer. If the student incorrectly placed the decimal and got 62.5 as an answer to #3, the student’s estimation should indicate that this is not a reasonable solution.

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**Suggested Practice for SOL 5.5b**

Students need additional practice solving practical problems that involve multiplication of decimals. Emily bought 1.5 pounds of grapes at a cost of $2.26 per pound and 0.4 pounds of potatoes at a cost of $1.10 per pound. What is the total cost of these grapes and potatoes? A $3.36 B $3.83 C $6.38 D $7.79 For SOL 5.5b, students need additional practice solving practical problems involving multiplication of decimals. The answer is shown on the screen.

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**Solving Practical Problems Involving Addition and Subtraction of Fractions**

SOL 5.6 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. 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.

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**Suggested Practice for SOL 5.6**

Students need additional practice solving practical problems involving addition and subtraction with fractions and mixed numbers. At the end of May, George’s height was inches. At the end of August, George’s height was inches. Exactly how much did George grow between the end of May and the end of August? A inches C inch B inch D inches Statewide results indicate that students have difficulty when adding and subtracting fractions that require regrouping. The answer to the problem is shown on the screen. When mixed numbers are included in the problem, students frequently subtract the smaller fraction from the larger fraction and subtract the smaller whole number from the larger whole number. For example, in this question many students would subtract one-eighth from three-fourths to get five-eighths and also subtract 54 from 55 to get 1, resulting in the incorrect selection of option A. Most common error

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**Suggested Practice for SOL 5.6**

Jill has a bag containing cups of flour. She will use cups of flour to make cookies and cup of flour to make candy. How many cups of flour will Jill have left after she has made these cookies and candy? cups This is another multistep problem involving fractions and mixed numbers. There are several strategies that could be used to solve this problem. One strategy that could be used is to subtract 1¼ from 3½ to get 2¼ and then subtract 1/3 to get the answer. Another strategy would be to add 1¼ to 1/3 to get 1 7/12 and then subtract 1 7/12 from 3½ to arrive at the same answer. Students would benefit from a discussion of different approaches to arrive at the solution. The answer is shown on the screen.

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**Solving Practical Problems Involving Area, Perimeter, Volume, and Measurement**

The student will find 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; and choose an appropriate unit of measure for a given situation involving measurement using U.S. Customary and metric units. The next standard being highlighted is SOL 5.8, with an emphasis on bullets a and c. The highlighted portion of bullet a reads, the student will find the perimeter and area in standard units of measure; and bullet c reads, the student will identify equivalent measurements within the metric system.

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**Suggested Practice for SOL 5.8a**

Students need additional practice finding area of squares and rectangles. A square has a side length of 12 centimeters. What is the area of the square? A 24 square centimeters C square centimeters B 48 square centimeters D square centimeters For SOL 5.8a, students need additional practice finding the area of a figure, particularly when the figure is not provided. The example on the screen asks students to find the area of a square. The answer is shown on the screen (animation 1). In problems similar to the one shown, the most common error occurs when students confuse area and perimeter (animation 2). Most common error

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**Suggested Practice for SOL 5.8a**

Students need additional practice finding perimeter and area of a right triangle. Select a number and a unit to indicate the area and perimeter of the right triangle. Area = Perimeter = 3 inches 4 inches 5 inches For SOL 5.8a, students also need additional practice finding the area and/or perimeter of a right triangle. In this example, all three side lengths are given. Students have to decide which measures to use to calculate area and which to use to calculate perimeter. In addition, they should be able to select the appropriate unit of measure to label their answers. The answers are shown on the screen. 6 12 square inches inches 6 inches square inches 10 12 15 20

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**Suggested Practice for SOL 5.8c**

Students need additional practice identifying equivalent measurements within the metric system. Match each measurement in Column A with an equivalent measurement in Column B. Column A Column B 4.35 meters 435 grams kilograms centimeters 43.5 milliliters liters 435 centimeters 43,500 grams liters For SOL 5.8c, students need additional practice identifying equivalent measurements within the metric system, particularly when the numbers involve decimals. The correct answers are shown on the screen (animation).

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**Developing Definitions of Plane Figures**

SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will develop definitions of these plane figures; and investigate and describe the results of combining and subdividing plane figures. The next standard being highlighted is SOL 5.13 with an emphasis on bullet a. Bullet a reads: the student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will develop definitions of these plane figures.

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**Suggested Practice for SOL 5.13a**

Students need additional practice identifying the similarities among and differences between squares, rectangles, parallelograms, rhombi, and trapezoids. Which statement is true for all rectangles? A The diagonals bisect each other. B Exactly one pair of opposite sides is parallel. C Exactly one pair of opposite angles is congruent. D All four sides are congruent. Students need additional practice identifying the similarities among and differences between squares, rectangles, parallelograms, rhombi, and trapezoids. Through constructing, drawing, measuring, comparing, and classifying geometric figures, students develop definitions for quadrilaterals. These activities will help definitions become meaningful and help students understand the relationships among figures. The answer to the question is shown on the screen. Answer option B is not correct because both pairs of opposite sides are parallel. Answer option C is not correct because a rectangle has four right angles. Answer option D is not correct because this option describes a square.

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**Suggested Practice for SOL 5.13a**

Which statement is true for all trapezoids? A The diagonals bisect each other. B Exactly one pair of opposite sides is parallel. C All four angles are right angles. D All four sides are congruent. Here is another example for SOL 5.13a. The answer is shown on the screen. Students would benefit from opportunities to compare and contrast properties of quadrilaterals. Additionally, having students draw figures that disprove the incorrect answer options may help them develop a better understanding of the characteristics of quadrilaterals.

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**Using a Sample Space to Make Predictions and Determine Probability**

SOL 5.14 The student will make predictions and determine the probability of an outcome by constructing a sample space. The next standard being highlighted is The SOL reads, the student will make predictions and determine the probability of an outcome by constructing a sample space. Statewide student performance indicates that students have difficulty constructing a sample space and interpreting a sample space that has already been constructed for them.

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**Suggested Practice for SOL 5.14**

Students need additional practice constructing a sample space and interpreting a sample space to determine a probability. Hilda has 4 shirts and 3 skirts in her closet. The table shows the colors of the shirts and skirts. Construct a sample space to represent all of the possible combinations of one shirt color and one skirt color that Hilda could choose from her closet. Red, Brown Red, Black Red, White Green, Brown Green, Black Green, White Blue, Brown Blue, Black Blue, White Yellow, Brown Yellow, Black Yellow, White Shirts Skirts Red Brown Green Black Blue White Yellow Students need additional practice constructing a sample space from given information and interpreting a sample space to determine a probability. The first part of this question requires students to use the information in the table to construct a sample space. One way the sample space could be represented is shown on the screen (animation 1). There are other correct representations of this sample space. The second part of the question requires students to use the sample space to determine a probability. This answer is also shown on the screen (animation 2). What is the probability Hilda will randomly choose a yellow shirt and a black skirt? 𝟏 𝟏𝟐

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**Suggested Practice for SOL 5.14**

A bakery sells cakes. Each cake is either chocolate or vanilla. Each cake can be either round or square in shape. Each cake can have yellow, pink, or blue icing. The tree diagram shows all the possible combinations of cake types, cake shapes, and icing colors. Yellow Round Pink Chocolate Blue Square Pink Blue Vanilla Blue How many combinations are shown on this tree diagram? A 3 B 6 C 12 D 18 Students also need additional practice interpreting a sample space that has been constructed for them. In this question students have been given information and a tree diagram has been constructed to display the information. The students must determine the number of possible outcomes. The correct answer is shown on the screen (animation 1). The most common error made by students is to count each word in the tree diagram (animation 2). Most common error

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**Modeling One-Step Linear Equations and Creating Problem Situations Based on an Open Sentence**

SOL 5.18 The student will investigate and describe the concept of variable; write an open sentence to represent a given mathematical relationship, using a variable; model one-step linear equations in one variable, using addition and subtraction; and create a problem situation based on a given open sentence, using a single variable. The next standard being highlighted is In particular, students need additional practice with bullets c and d. Bullet c reads, the student will model one-step linear equations in one variable, using addition and subtraction; and bullet d reads, the student will create a problem situation based on a given open sentence, using a single variable.

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**Suggested Practice for SOL 5.18c**

Students need additional practice modeling one-step linear equations. Create a model to represent this equation. m + 4 = 10 = For SOL 5.18c, students need additional practice creating the model to represent a given one-step linear equation. The answer is shown on the screen. It is important to note that the answer is also correct if the student places ten triangles on the left side of the equation mat and the star and four triangles on the right side. Key: = m = 1

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**Suggested Practice for SOL 5.18d**

Students need additional practice creating a problem situation based on a given open sentence. Which situation could be represented by m + 4 = 16? A Rocco had 16 marbles. James gave him 4 more marbles. How many marbles does Rocco have now? B Rocco had 16 more marbles than James. James has 4 marbles. How many marbles does Rocco have? C Rocco had 4 marbles. He bought some more marbles for a total of 16. How many marbles did he buy? D Rocco had 16 marbles. He separated them into 4 equal piles. How many marbles are in each pile? For SOL 5.18d, students need additional practice creating or identifying a problem situation that is represented by a given open sentence. The answer is shown on the screen. In addition to multiple choice answer options, students would benefit from opportunities to create their own situations that could be represented by the same open sentence.

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Practice Items This concludes the student performance information for the spring 2014 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: This concludes the student performance information for the spring 2014 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.

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