Using the Student Performance Analysis

Using the Student Performance Analysis
Grade 3 Mathematics Standards of Learning This is the spring 2013 student performance analysis for the Grade 3 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 3 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.

Practice for SOL 3.2 Circle each number sentence that can be completed by using the basic fact sentence Write four different number sentences that are related to the basic fact sentence Student performance was significantly stronger on questions that required students to identify one related fact sentence when compared to questions that required students to identify all of the related fact sentences in a set. In the first example provided, students must consider several different number sentences and determine which can be completed by using the basic fact 2x8=16. Teachers are encouraged to make connections, when possible, between related number sentences and students’ investigation of the commutative properties of addition and multiplication in SOL The correct answers to these examples are shown on the screen.

Practice for SOL 3.3 This model is shaded to Model 1 is shaded to show a represent one whole. fraction of one whole. Model 1 Which is shaded to show a fraction with a value equal to the fraction shaded in Model 1? For SOL 3.3, students need additional practice comparing fractions with unlike denominators. Students use models when comparing fractions in grade 3, as in the example shown here. The answer to the example is shown on the screen. As a follow-up question, the teacher could ask students to use each of the answer options that is not selected and write an inequality statement that compares that fraction to the fraction shaded in Model 1. For example, for the answer choice that has 7/10 shaded, students could write 7/10> 6/9 or 6/9<7/10. Additionally, since both 7/10 and 6/9 have 3 unshaded portions, students might also use the reasoning that 3/10<3/9 or 3/9>3/10 to defend the decision that this answer option does not have a value equal to the fraction shaded in Model 1. As another extension to this example, the teacher might ask students to represent another fraction that has the same value as Model 1, but to use a different type of model such as a measurement or number line model, a set of objects, or a rectangular region.

Practice for SOL 3.3 Which of these correctly compares the fractions represented by the shaded regions in each model? Select all that are correct. For every model, this represents one whole:

Practice for SOL 3.3 Carla made two cakes that were the same size and served them to guests at her party. The figures have been shaded to represent the fraction of each cake that was left after the party. Which correctly compares the shaded parts of the two figures? A B C D Students continue to have difficulty when symbolic notation is used in comparisons. Teachers are encouraged to explore whether students are having difficulty determining which modeled fraction is greater, whether the symbolic notation (the less than or greater than symbol) is the confusing issue, or whether students are struggling with both of these issues. The answer to the example is shown on the screen.

Practice for SOL 3.3a What fraction is represented by point B on this number line? 1 B Student performance indicates that naming fractions represented on a number line is more difficult than naming fractions represented by a set or area model. The answer to the example is shown on the screen. Students’ errors on items of this nature suggest that students have difficulty determining what to count (Do I count the hatch marks or the spaces between them?) and/or where to start and end the counting (Do I count the marks at zero and at B ?). Using the example provided, a common error is to name this fraction as 4/8 rather than 3/8.

Practice for SOL 3.3c Select each number sentence that correctly compares the fractions represented by the shaded regions of each figure. All figures are the same size. For SOL 3.3c, student performance continues to be inconsistent when comparing fractions with unlike denominators using symbolic notation. The answers to this example are shown on the screen. Additional examples for this skill may be found in the 2013 Student Performance Analysis presentation for Grade 3 Mathematics located on the Virginia Department of Education website.

Practice for SOL 3.4 This table shows the number of lunches sold in the school cafeteria on three days this week. Last week a total of 770 lunches were sold on Monday and Wednesday. Find the difference in the number of lunches sold on Monday and Wednesday this week and the same two days last week. The cafeteria manager wants to sell a total of 1,500 lunches each week. How many more lunches must be sold on Thursday and Friday combined to reach that goal? School Lunches Day Number of Lunches Sold Monday 362 Tuesday 349 Wednesday 371 Students need additional practice solving multistep problems involving the addition and/or subtraction of whole numbers, in particular when information is presented in a table. The questions here provide practice with both addition and subtraction; students continue to find problems of this nature challenging. The answers to the questions are shown on the screen.

Number of Books Checked Out Number of Books Returned
Practice for SOL 3.4 This table shows the number of books that students checked out and returned at the school library on three days. Exactly how many more books were checked out on Tuesday and Wednesday combined than returned on those same two days? Exactly how many more books were returned on Tuesday and Wednesday combined than on Thursday? About how many more books were checked out on Wednesday and Thursday combined than on Tuesday? Day Number of Books Checked Out Number of Books Returned Tuesday 247 223 Wednesday 118 136 Thursday 204 198

Practice for SOL 3.4 Solve: 1. 2. 3.
Student performance was weaker on single-step subtraction problems when regrouping in more than one place value position was required, as in the examples provided. The answers to these examples are shown on the screen.

Practice for SOL 3.4 The numbers of chairs in three different rooms at Maple Elementary School are shown in the table. What is the difference between the number of chairs in the school library and the total number of chairs in Ms. Smith’s and Mr. Taylor’s classrooms? Room Ms. Smith’s Classroom Mr. Taylor’s Classroom School Library Number of Chairs 24 23 72 Students would benefit from additional practice solving multistep practical problems involving subtraction, particularly when information that must be used to solve the problem is presented within a table. One way to solve the example provided is shown on the screen. Please note that additional examples for this SOL are included in the 2013 Student Performance Analysis presentation for Grade 3 Mathematics, located on the Virginia Department of Education Web site.

Practice for SOL 3.6 1) A store has 5 hair clips in each of 64 packages. What is the total number of hair clips in these packages? 2) Mr. Baker has 4 shelves of textbooks. There are 28 textbooks on each of these shelves. How many textbooks in all are on these shelves? 3) Each third grade class at a school has exactly 24 students in each of 3 classes. What is the total number of third grade students at this school? For SOL 3.6, students need additional practice solving multiplication problems presented in the context of a word problem. The story problems provided on this screen involve situations that are multiplicative, although students might use a less efficient method to arrive at a correct solution. The answers to these problems are shown on the screen.

Number of Students in each Class
Practice for SOL 3.6 This table has information about the classes and students at a school. How many students are in grade 3? What is the total number of students in grade 5? Grade Level Number of Classes Number of Students in each Class 3 5 22 4 25 27

Practice for SOL 3.6 3) A bookcase has 5 shelves. Each shelf holds exactly 38 reading books. How many of these reading books will the bookcase hold in all? 4) A hotel has vans to transport its guests to the airport. Exactly 1 driver and 14 guests can ride in each van at the same time. How many guests can ride in 4 vans?

Practice for SOL 3.6 Solve: 1. 57 3 = _________ 4 83 = _________ 2.
= _________ = _________ 2. 3. Luisa is making bracelets. She uses 5 beads for each bracelet. What is the total number of beads she will need to make 28 of these bracelets? For SOL 3.6, students would benefit from additional practice solving multiplication problems presented in a horizontal format like the first two examples provided. Teachers are encouraged to continue providing students with practice solving multiplication story problems, as in example 3. The answers to these examples are shown on the screen.

Practice for SOL 3.7 This model is shaded to represent one whole.
These models are each shaded to represent a fraction. Model Model 2 What is the difference between the fraction shaded in Model 1 and the fraction shaded in Model 2? For SOL 3.7, students need additional practice subtracting fractions with like denominators. Models should be provided. In addition to having a strategy to subtract fractions that are modeled, students must understand the vocabulary associated with both addition and subtraction. Experiences with both multiple-choice and free response or fill-in-the-blank situations are strongly encouraged. The answer to this multiple-choice example is shown on the screen. As an extension to this example, the teacher might ask students to represent 2/8 using another fraction model such as a measurement or number line model, a set of objects, or a rectangular region. Or, students could find the sum of the two models and then represent the resulting mixed number and improper fraction numerically and/or as a model.

These two models are each shaded to represent a fraction. Model A Model B Which model is shaded to show the difference between Model A and Model B? a) c) b) d)

These two models are each shaded to represent a fraction. Model 1 Model 2 What is the difference between these two fractions? For SOL 3.7, students need additional practice subtracting fractions with like denominators. Models should be provided. In addition to having a strategy to subtract fractions that are modeled, students must understand the vocabulary associated with both addition and subtraction. The denominator indicates how many equal parts are in the whole and the numerator tells how many of those parts are being described or in this case, how many parts remain. The answer to the example is shown on the screen. In problems like the example provided, students frequently find the sum, 1 4/8, instead of the difference 2/8.

Practice for SOL 3.8 Juana’s lunch cost exactly $2.73. She paid with a five-dollar bill. Which set of money shows the amount of change she should receive? A C B D Students need additional practice determining which collection of coins and bills represents the correct amount of change for a given situation. The correct answer is shown on the screen. The most common error on an item like this is selecting option A (second animation). Students selecting option A may be combining the three dollars in this set of money with the two dollars in the context of the story to arrive at five dollars; or, students selecting option A may recognize that the 27 cents added to the 73 cents will make a dollar but then fail to add that dollar to the total, which would make $6 instead of $5.

Practice for SOL 3.8 Sarah bought apples for $3.40. She gave the clerk a $5.00 bill. Which set of money shows the change Sarah should receive from the clerk? a) c) b) d)

Practice for SOL 3.9a David has a scooter like the one shown in the picture. Which is the most reasonable estimate for the height of this scooter, measured from the ground to the handlebar? A foot B centimeters C yard D meters ? Students would benefit from additional experiences that require them to estimate a linear measurement, especially when U.S. Customary units are involved. The answer to this question is shown on the screen. In items like this example provided, students most frequently selected the measurement with the incorrect U.S. Customary unit- in this case, 1 foot. This error seems to indicate a lack of understanding of the relationship that exists between feet and yards.

Practice for SOL 3.9d Which are closest to the area and perimeter of this figure? A Area = 10 square inches and perimeter = 7 inches B Area = 7 square inches and perimeter = 10 inches C Area = 12 square inches and perimeter = 14 inches D Area =14 square inches and perimeter = 12 inches For SOL 3.9d, students need additional practice estimating to determine the area and perimeter of a given figure. The answer to the example is shown on the screen. The most common error students make indicates that they are confusing area and perimeter. In this example, students with this misconception would most likely choose option D. Key: = 1 square inch

Practice for SOL 3.10 Look at the shaded figure on the grid. Key
= 1 square unit 1 unit Using the key, find the perimeter and area of the shaded figure. Perimeter = _______________ and Area = ________________ For SOL 3.10, students need additional practice determining the perimeter of a figure on a grid. When students are given a figure on a grid and asked to find the perimeter, a common error is to respond with the area of the figure. When a question asks for the perimeter and area of the figure, similar to the example shown on the screen, a common error is to interchange these answers. Student performance on items that ask only for the area of a figure on a grid remains high. Student performance on items that require the use of a ruler to determine the perimeter of a given figure has shown improvement from the spring 2012 student performance data. The answers to this example are shown on the screen.

Practice for SOL 3.10 1) Use the inch ruler to find the perimeter of this figure.

Practice for SOL 3.10 2) What is the perimeter of the shaded figure?
1 unit Key

Practice for SOL 3.10a Use your inch ruler to help you answer this question. Which is closest to the perimeter of this figure? A 8 inches C inches B 10 inches D 14 inches For SOL 3.10a, students need additional practice measuring the distance around a polygon to determine its perimeter. The lengths of the sides and answer to this example are shown on the screen. The most common error students make is to select the response that indicates they have not included the length of one or more sides in the perimeter. In this example, students who leave out any two of the shorter sides would select option A. Viewers should be cautioned that printing the slides may skew the measurements given. The measurements are based on the ruler gridlines within the PowerPoint program.

Practice for SOL 3.11 . Circle the clock that best shows 11:50.
For SOL 3.11, students need additional practice determining which clock shows a given time. Students would benefit from additional practice reading the time shown on an analog clock. In addition to determining what time is shown on a single given clock, students should be able to determine which of several clocks shows a given time. Student performance is weaker on items like the one shown. The answer to this example is shown on the screen.

10:23 4:35 11:57 6:44 12:57 9:38 4:51 7:23 Practice for SOL 3.11
Circle the time that is shown on each clock. 10:23 4:35 11:57 6:44 12:57 9:38 4:51 7:23

Practice for SOL 3.11 Aaron watched television for 2 hours. He stopped watching television at 8:00 p.m. What time did Aaron start watching television?

Practice for SOL 3.11 Joy left home to visit her grandmother at the time shown on this clock. Joy arrived back at home 4 hours later. At what time did Joy arrive back at home? Student performance data also indicate a need for additional practice determining elapsed time. In the example provided, students must correctly read the analog clock to determine the starting time and then apply the elapsed time provided within the description to determine the ending time. The answer to this problem is shown on the screen.

Practice for SOL 3.11a Which clock best shows 2:48? A C B D
For SOL 3.11a, students would benefit from additional practice telling time to the nearest minute using analog clocks. The most common error is for students to select the clock having the minute hand in the correct position on the clock face but the hour hand in an incorrect position. Using the example provided, students should realize that for 2:48, the hour hand will be between the 2 and the 3 (first animation) and NOT between the 1 and the 2 (second animation), as in option A. The answer to the example is shown on the screen.

Practice for SOL 3.13 °C °F Part of two thermometers are shown. The labels on top of the thermometers indicate if the temperature shown is in degrees Celsius or degrees Fahrenheit. What are the temperatures shown on these thermometers? ___ °C and ___°F

Practice for SOL 3.17 X X X X X X Each X represents 1 neighbor. Exactly how many of Simon’s neighbors owned less than 3 pets? 2) What was the total number of pets owned by Simon’s neighbors? Simon collected data on the number of pets owned by each of his neighbors. He made this line plot to represent the data. Number of Pets Owned Students would benefit from additional practice with questions that require interpretation and analysis of line plots. Student performance is much stronger when questions do not require analysis. Take a moment to read the example. For the example shown on the screen a lower level question could be, “How many neighbors own exactly 1 pet?” Questions such as the ones shown require students to consider what each X represents. For example, students should understand that the two X’s located above the zero on the number line represent the fact that two of Simon’s neighbors own zero pets; the two X’s located above the one on the number line represent the fact that two of Simon’s neighbors each own one pet; the one X located above the two on the number line represents the fact that one of Simon’s neighbors owns two pets; and finally, the one X located above the three on the number line represents the fact that one of Simon’s neighbors owns three pets. The answers to the questions are provided on the screen. A common mistake that students might make in answering the second question would be to simply count all of the X’s, which is the number of neighbors polled. In the equation shown for the solution to the second question, each of the addends is represented by an X on the line plot.

Practice for SOL 3.17 This graph represents the number of points scored by a basketball team on three days. According to the graph, what was the difference in the number of points scored on Tuesday and Thursday combined when compared to the points scored on Saturday? If the team had scored 24 points on Tuesday, how would you change the graph to show this number of points?

Practice for SOL 3.17 The graph shows the number of pictures collected by each of four students. Based on the graph, select all statements that are true. Nancy collected more pictures that Bryan and Kristen combined. Ricardo collected the most pictures. Ricardo collected more pictures than Bryan and Kristen combined. Nancy collected 2 more pictures than Bryan. The four students collected a total of 20 pictures.

Practice for SOL 3.17 This graph represents the number of points scored by a team on three days. Based on the graph, which statement(s) are true? The team scored a total of 43 points on these 3 days combined. The team scored more points on Tuesday than it scored on Thursday and Saturday combined. Exactly 5 more points were scored on Saturday than on Thursday. Exactly five more points were scored on Tuesday than on Saturday. Students continue to need practice analyzing information presented in pictographs. This item is also an example of how teachers can provide experience with questions that may have more than one correct answer. The correct answers are shown on the screen.

Practice for SOL 3.17b Mrs. Smith is making this line plot to show the number of books read by each of her 22 students. Mrs. Smith has not recorded all the data for her students. For exactly how many students does she still need to record the number of books read? A B C D 7 Number of Books Read X X X X Each X represents one student. Number of Books 1 5 4 3 2 For SOL 3.17b, students need additional practice constructing line plots. In the example provided, students are given information about the data that will be represented on the line plot and must use this information and the partially completed line plot to determine what still needs to be added to the plot. The answer to this example and the most common error are shown on the screen.

Practice for SOL 3.17c Tricia made this graph to show the number of miles she biked for five days. Based on this graph, Tricia biked-- A a total of 13 miles on these five days B a total of 4 miles on Monday and Friday C 2 fewer miles on Thursday than on Wednesday D 2 more miles on Tuesday than on Thursday Number of Miles Days Students need additional practice interpreting bar graphs, particularly with determining which of several statements about the graph is true. The answer to this example and most common error are shown on the screen.

Cones Used at the Snack Bar
Practice for SOL 3.17c The manager at a snack bar made a graph to show the number of cones used on four different days. Circle the statement about the graph that is true. Exactly three more cones were used on Friday than on Thursday. Exactly six fewer cones were used on Sunday than on Saturday. The number of cones used on Saturday was twice the number of cones used on Friday. The number of cones used on Thursday was half the number of cones used on Friday. Cones Used at the Snack Bar Day Number of Cones Thursday Friday Saturday Sunday Key: = 2 Cones Students continue to need additional practice interpreting pictographs. Pictographs are a form of picture graph that use symbols to represent one or more objects to show and compare information. Student performance indicates that students do not apply the information in the key when comparing and contrasting the information presented. The answer to this example is shown on the screen. Statewide, students are likely to disregard the information in the key and select the statement that would be true if the symbol used in the graph represented 1 item. For example, on this question (animation 2), it is likely that students would select the first statement, which would be true if each triangle represented 1 cone. While the example provided has only one correct answer, teachers are encouraged to provide experiences with questions that may have more than one correct answer. Additional examples for this skill may be found in the 2013 Student Performance Analysis presentation for Grade 3 Mathematics located on the Virginia Department of Education website.

Practice for SOL 3.18 A box contains 6 candies that are the same size and shape. Julia will pick one candy from this box without looking. Place candies in the box so that the probability of Julia selecting a red candy is certain. Candies d red brown yellow blue Students need additional practice describing the probability of a situation as the chance that an event will happen. Students should be able to apply their understanding of chance to create a situation that fits given criteria. In the example provided, students must understand that if it is certain that Julia will select a red candy, then all the candy in the box must be red. The answer to this example is shown on the screen. The next two screens provide extension questions for this same situation.

Practice for SOL 3.18 This table shows the flavors and shapes of animal crackers in a bowl. Make a list to show all the possible flavor and shape choices for one animal cracker. Flavors of the Animal Crackers Shapes of the Animal Crackers Chocolate Monkey Vanilla Lion Bear

Practice for SOL 3.18 A box contains 6 candies that are the same size and shape. Julia will pick one candy from this box without looking. Place 6 candies in the box so that the probability of Julia selecting a brown candy is impossible. Candies red brown yellow blue In the first extension question, students must understand that for this situation to be impossible, none of the six candies can be brown. Any combination of six candies that does not include any brown candies would be a correct response to this question. One correct response is shown on the screen.

Practice for SOL 3.18 A box contains 6 candies that are the same size and shape. Julia will pick one candy from this box without looking. Place candies in the box so that the probability of Julia selecting a blue candy is equally likely as selecting a red candy. Candies blue red In this extension to the situation, students must create a set that has equal amounts of blue candies and red candies. In the correct response shown on the screen, there are 3 red and 3 blue candies.

Practice for SOL 3.18 The chart shows the Which shows all the possible color color and shape choices and shape choices for one balloon? for balloons at a store. Balloon Choices A B C D Blue Red Blue Color Shape Blue Red Blue Blue Red Red Blue Blue Blue Red Red Red Students need additional practice listing all the possible results of a given situation. The correct response to the question is shown on the screen. The most common error for questions like this example is to select an option in which each of the shapes is represented once. Blue Red Blue Blue Red Blue

Practice for SOL 3.19 What is the missing number in this pattern? 10, 25, 40, 55, ____ , 85, 100 A 60 B 65 C 70 D 75 Students would benefit from additional practice with number patterns involving two-digit numbers. The answer to this example is shown on the screen.

Practice for SOL 3.19 Each table has a number pattern. For each table, fill in the missing number and describe the rule. 1) The rule for this pattern is _________________________________. 2) 12 37 62 87 112 162 1 2 4 7 11 16 22 29

Identity Property of Addition
Practice for SOL 3.20 Select an equation to match each property. You will not use two of the equations. Property Name Equation = = 27 = 9 = 9 X 1 6 X 7 = 7 X 6 4 X 2 = 4 X 2 Identity Property of Addition Commutative Property of Addition Identity Property of Multiplication Students would benefit from additional practice identifying examples of the commutative and associative properties of addition and multiplication. The answers to this example are shown on the screen.

Practice for SOL 3.20 = 15 + 1= 16 11= 8 + 9= Which number sentence shows the identity property of multiplication? 2 x 12=12 x 2 8 x 0=0 2 x 6= 3 x 4 45 x 1 =45 Which number sentence shows the commutative property of addition?

Using the Student Performance Analysis

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