1. Using Student Performance Analysis
Using Grade 6 Mathematics
Standards of Learning

2. Practice for SOL 6.1
a) Write the ratio of 6 shirts to 5 pants using two different
notations.
Represent the ratio of shirts to pants using numbers other than 6 and 5.

3. Practice for SOL 6.1
A box contains red marbles and blue marbles. The ratio of red marbles to blue marbles in the box is 8 to 3. Select each statement that could represent the number of red marbles and blue marbles in this box. There are exactly 3 red marbles and 8 blue marbles in the box. There are exactly 64 red marbles and 24 blue marbles in the box. There are exactly 18 red marbles and 13 blue marbles in the box. There are exactly 48 red marbles and 18 blue marbles in the box.
For SOL 6.1, students need additional practice identifying a practical situation that corresponds to a given ratio, such as the example provided on the screen.
The answers to the example are shown.

4. Practice for SOL 6.1
A board contains stars and triangles. The ratio of triangles to stars is 3 to 1. Select each picture that could represent the number of stars and triangles on this board.
Student performance for this standard also indicated that students need additional practice identifying pictorial representations of a given ratio in a non-multiple choice format. In this example, it is important for students to recognize that the given ratio compares triangles to stars and not stars to triangles.
The answers are shown on the screen.

5. Practice for SOL 6.1
Identify each picture that has a ratio of 2:3 for the number of triangles to the number of circles.

6. Practice for SOL 6.2 a) Which ratio is equivalent to 4.2? a) b) c) d)
b) What ratio is equivalent to 0.3% ?

7. Practice for SOL 6.2 Which number could represent point K? a) b) c) d)1 K

8. Practice for SOL 6.2
Select all of the given numbers that lie between 0.01 and 0.10 on the number line
0.10
0.01

9. Practice for SOL 6.2a
Which number is equivalent to the ratio ? A C B D
For SOL 6.2a, students need additional practice describing a ratio as a percent, particularly when the ratio is greater than 1. Students should understand that a ratio or fraction greater than one is equivalent to a decimal number greater than one and a percent greater than 100%.
The most common error when converting an improper fraction to other forms is to divide the denominator by the numerator rather than the numerator by the denominator. Presumably, this is because students typically think of a fraction as a number less than one. This division error would result in students picking either option a, which is equivalent to five eighths, or option b which uses the same numerals but has a different value. The correct answer is option d as shown on the screen.

10. Practice for SOL 6.2c Which statement is true? A C B D
Similarly, for SOL 6.2c, students had difficulty identifying equivalent relationships between percents and fractions, particularly when the percent was greater than one hundred percent. The correct answer to this problem is option b. The most common error in the example shown on the screen is the selection of option c. In option c, students recognize that three and one fifth is equivalent to three and two tenths, but overlook the percent sign next to the three and two tenths, which changes its value.
There are multiple ways to solve this problem. One method is to rewrite the left and right sides of the equations into the same form and then determine which equation yields an equivalent relationship. If students rewrite option B using decimal form, they will see that both values are equivalent to one and seventy five hundredths.

11. Practice for SOL 6.2b
This model is shaded to Write a fraction, decimal, and represent one whole. percent to represent the shaded part of each model.
For bullet b of this standard, students should be able to describe a given representation using a fraction, decimal, and percent.
The answers to this question are shown on the screen.
An extension of this question could be to ask students to represent these models on a number line or a grid.

12. Practice for SOL 6.2c Identify each statement that is true.
For bullet c of this standard, which appears in the non-calculator section of the test, students showed inconsistent performance identifying and demonstrating equivalent relationships among fractions, decimals, and percents. Students would benefit from additional practice with items similar to the one shown. Students will need to evaluate each statement to decide how many correct answers there are. Note that this item uses numbers with similar digits.
The answers to this question are shown on the screen.
It is important to note that if this question were on an SOL test, students would have to select all three correct answers, and only those answers, to get this item correct.

13. Practice for SOL 6.3
Identify each number that is an integer.

14. Practice for SOL 6.4
Which product is represented by the shading of the model? a) c) b) d)
𝟐 𝟔 ⋅ 𝟓 𝟔

15. Practice for SOL 6.4
This figure represents one whole divided into five equal parts. Exactly how many are in 7 ?
𝟐 𝟓

16. Practice for SOL 6.6a What is the product of and in simplest form?
For SOL 6.6a, students need additional practice multiplying a mixed number by a fraction.
The answer to the question is shown on the screen.

17. Practice for SOL 6.6b
The length of a rope is feet. James cut feet from this length of rope to use on a project. Exactly what length of rope remained unused?
For SOL 6.6b, students need additional practice solving single-step practical problems involving subtraction of mixed numbers with unlike denominators. For the example shown on the screen, note that the fraction portion of the subtrahend is greater than the fraction portion of the minuend, and that these two mixed numbers have unlike denominators. Problems of this nature have shown to be more challenging for students.
The answer to the question is shown on the screen.

18. Practice for SOL 6.6b
Each cup of milk has 4 grams of protein. Exactly how many grams of protein are in cups of milk? A 7 grams B 8 grams C 14 grams D 28 grams
Here is another example for SOL 6.6b, which is a multistep practical problem involving mixed numbers. There are multiple ways to solve this problem. One method is to determine how many half-cup servings of milk are in three and one-half cups of milk and then multiply that number by four.
The correct answer is shown on the screen. The most common student error is to multiply three and one-half by four to get fourteen grams.

19. Practice for SOL 6.6b Jill had 3 full pans of brownies.
Each pan was the same size.
She gave of the original amount of brownies to her friends.
She gave of the original amount of brownies to her teacher.
Exactly how many pans of brownies does Jill have left over?
Students need opportunities to solve practical problems involving fractions using different strategies. The example shown on the screen is a multistep practical problem involving fractions. Teachers are encouraged to ask students to solve this problem in more than one way.
The answer to the question is shown on the screen.

20. Practice for SOL 6.6b
Kendra recorded the amount of water she used in one week for four activities.
1. What is the total amount of water, in gallons, recorded for these activities?
2. How much more water was
used doing laundry than cooking?
Activity
Amount of Water
(in gallons)
Bathing
Doing Laundry
Washing Car
Cooking
For this standard, students also need additional practice adding and subtracting fractions with regrouping.
The answers to these questions are shown on the screen.
As an extension, the information in the table can be used to ask questions such as, “What is the total amount of water Kendra would use for these activities if she cut the amount of water used for cooking in half?”

21. Practice for SOL 6.7
Jake made punch by combining 2.75 liters of orange juice, 1.25 liters of pineapple juice, and 3.5 liters of soda. He then poured equal amounts of all the punch into 3 different containers. How much punch did Jake pour into each container?

22. Practice for SOL 6.10
Clinton purchased a circular rug to cover part of a floor. The diameter of the rug is 8 feet. Rounded to the nearest whole number, what area of the floor will the rug cover?
A circular pool has a radius of 12 feet. What is the approximate distance around the pool, rounded to the nearest foot?
Dana has a rectangular garden that she wishes to fence in. If the dimensions of the garden are 15 feet by 13 feet, what is the minimum amount of fencing that she needs to enclose her garden?

23. Practice for SOL 6.10b
Leo is designing a circular table top with a diameter of 10 feet.
1. Which is closest to the Which is closest to
circumference of this table the area of this table
top? top?
314.2 feet a) feet
78.5 square feet b) 78.5 square feet
31.4 feet c) 31.4 feet
15.7 square feet d) 15.7 square feet
For SOL 6.10b, students need additional practice solving practical problems involving circumference and area, particularly when a figure is not provided. Student performance also indicates that students do not know whether the diameter or radius should be used in a calculation, and whether the resulting units are linear or square units. Questions like the ones on the screen give students practice finding circumference and area when given a diameter, as well as deciding the appropriate unit of measure for their answers.
The answers are shown on the screen.

24. Practice for SOL 6.10b
A circular plate has a diameter of 11 inches. Which is closest to the area of this plate? A 17.3 square inches B 34.6 square inches C 95.0 square inches D square inches
For SOL 6.10b, students did very well finding the circumference of a circle but did not do as well when finding the area. For the question shown on the screen, students are asked to find the area of a circular plate, given its diameter. The most common error (multiplying pi by the diameter) and the answer are shown on the screen. The common error indicates that many students are applying the formula for circumference to an area problem, or it is possible that they are using the correct area formula, but incorrectly calculating the square of the radius as the radius times two.

25. Practice for SOL 6.10c
This triangle represents a section of a garden. (Figure is not drawn to scale.) What are the area and perimeter of the garden?
5 m
4 m
3 m
13 m
13.3 m
For SOL 6.10c, students need additional practice solving practical problems involving area and perimeter. Student performance was inconsistent when students had to determine which information to use to answer the question. For instance, in this example, students need to determine which measurements to use to find the area, and which measurements to use to find the perimeter. As in the previous example, students also need practice determining the correct unit of measure to use when labeling the answers.
The answers are shown on the screen.

26. Practice for SOL 6.11 1) Identify the location of the point (10,0).
In Quadrant I
In Quadrant III
On the x-axis
On the y-axis
2) Select the two points that are located on the y-axis.
(0,0) (0,1) (1,1) (-1,-1) (1,0)

27. Practice for SOL 6.13
Name each figure using the given attributes with its most precise name.
What term most accurately classifies all of these figures?
What term most accurately classifies figures 1, 3, 4, and 6?
What term most accurately classifies figures 1 and 3? 4 5 6 1 2 3
Each angle is 90°
Each angle is 90°

28. Practice for SOL 6.13
Create a list of angle measures that could represent the four angle measures of a quadrilateral. , , ,
For SOL 6.13, students need additional practice identifying the angles that could describe a quadrilateral. On test questions that required students to find a missing angle when given a diagram and three of the angles of the quadrilateral, students performed well. They were more challenged with this concept when asked to identify a list of angles that could represent the angles of a quadrilateral. The answer to the question is shown on the screen.
The question on the screen is an open response question that will help facilitate discussion in the classroom regarding the characteristics of the angle measures of a quadrilateral. The discussion will be enhanced by comparing and contrasting the angle measures of different types of quadrilaterals. Activities of this nature may help students generalize characteristics that are true for all quadrilaterals.

29. Practice for SOL 6.14b
A car salesman sold 40 cars last month. The circle graph shows the results of his sales by car color. 1. Identify the car color that most likely represents exactly 10 cars. 2. Identify two car colors that most likely represent a combined total of 25 cars.
Blue
Green
Red
Purple
For SOL 6.14b, students need additional practice solving problems involving circle graphs.
Take a moment to read the example shown on the screen.
Students are having difficulty making the connection between the percent or fraction represented by a section of the graph and the number of data elements represented by the same section.
In the first example provided, 10 out of 40 cars represents 25%, or ¼ of the data. Students must, in turn, recognize that the green section of the graph most closely represents 25% or ¼ of the data. Student performance data indicate that a common student misconception is to attribute 25 data elements to the green section because it represents 25% of the data. Therefore, students would NOT correctly name the green section as representative of 10 cars.
Similarly, in example 2, a common student error might be to choose the purple and red sections of the graph as representing 25 cars since those combined pieces represent about 25% of the data.
The answers are shown on the screen.

30. Practice for SOL 6.14b
Mr. Walker surveyed 24 students. He asked each student to rate a television show. The results are shown in this circle graph.
Which fraction of the students best represents those who rated the show as “Above Average?”
A B C D
Rating of Television Show
For SOL 6.14b, students need additional practice interpreting information presented in a circle graph. In the example provided, students should recognize that the different-sized sections of the circle represent different fractions of the whole. The most common error in a question similar to the one shown on the screen was to interpret each piece of the circle graph to be one fifth of the whole. Students should be able to accurately estimate the fractional size of the section of a circle graph. The answer to the question is shown on the screen.

31. Practice for SOL 6.14c
Bob asked a group of people to identify their favorite vegetable. The circle graph shows the results. Which graph on the next slide could represent the same data?
Corn
Carrots
Beans
Broccoli
Asparagus
For this standard, students need additional practice comparing data in circle graphs with data in other graphs. In particular, students need additional practice using the data in a circle graph when specific numbers are not provided.
Teachers are encouraged to have students discuss the data in the circle graph and what conclusions can be drawn, even though the number of people surveyed is not given. For example, in this graph, asparagus was selected by the fewest people. It also appears that half of the people surveyed selected beans as their favorite vegetable and ¼ of the people surveyed selected corn . This means there were twice as many people who selected beans as their favorite vegetable as there were people who selected corn as their favorite vegetable. Another conclusion is that the sum of the number of people who selected carrots, broccoli, and asparagus should equal the number of people who selected corn. Once students have drawn conclusions based on the circle graph, they can proceed to analyze other graphs to determine which one represents the same data. See the next slide for the remainder of this question.

32. Practice for SOL 6.14c Which bar graph could represent the same data?
Corn
Carrots
Beans
Broccoli
Asparagus
Which bar graph could represent the same data?
When comparing these bar graphs to the circle graph, students need to identify the bar graph that represents the data in the same relationships as shown in the circle graph. Students should reference the conclusions they drew from the circle graph, when selecting the correct answer.
For example, one of the conclusions drawn from the circle graph was that asparagus was selected by the fewest people. In each of the bar graphs, asparagus was selected by the fewest people, so that statement will not help eliminate a choice. Another conclusion drawn from the circle graph was that there were twice as many people who selected beans as there favorite vegetable as there were people who selected corn as their favorite vegetable. This statement will eliminate the first and second graph, because these graphs do not show this relationship. The other conclusion previously drawn, that the sum of the number of people who selected carrots, broccoli, and asparagus should equal the number of people who selected corn, can be checked against the third graph to confirm its selection.
It is important for students to be asked to explain their reasoning for eliminating a graph, and eventually selecting the correct graph.

33. Practice for SOL 6.14c
Twelve students answered a question that had answer choices labeled as A, B, C, and D. This circle graph represents the answer choices selected by the 12 students.
Answer Choices Selected
For SOL 6.14c, students need additional practice comparing and contrasting graphs that represent the same data set. The information shown on this screen should be used to answer the question shown on the next screen.
*The accompanying question is shown on the next screen.

34. Practice for SOL 6.14c
Which of these represents the data shown in the circle graph? A C B D
Answer Choices Selected
Answer Choices Selected
Answer Choices Selected
Answer Choices Selected
For this example, students need to pay particular attention to the key, which indicates that each circle represents two students. The answer is shown on the screen.

35. Practice for SOL 6.15
This line plot shows the number of books that a group of students have read. Use this data to determine where on the line plot the mean will appear. x

36. Practice for SOL 6.15a
Jill recorded the number of pull-ups each of ten students did on this line plot. What is the balance point for this data?
Pull-Ups X X X X X X
For SOL 6.15a, students need additional practice interpreting data represented on line plots to determine the balance point.
The answer to this question is shown on the screen.
Students should be able to connect the terms “balance point” and “arithmetic mean.” As an extension, teachers could ask students to compare the balance point with the median and mode and ask which is a better representation of the average number of pull-ups for these ten students. This will help students with the skills associated with SOL 6.15b, which was also an area where students struggled. X X X X
Number of Pull-Ups
Each X represents 1 student.

37. Practice for SOL 6.15
This data shows the ages of members of a youth book club and the age of the facilitator What is the most appropriate measure of center for this data?

38. Practice for SOL 6.15b
Andy surveyed his friends to determine the number of books each of them read in February. These are the results of the survey.
3, 2, 3, 19, 2, 1, 2, 2, 2, 2
What is the mean for this data set?
What is the median for this data set?
Is the mean or median a more appropriate measure of
center to use for this data? Why?
For SOL 6.15b, students showed inconsistent performance when determining which measure of center was most appropriate for a data set.
The answers to these questions are shown on the screen.
Teachers are encouraged to have students plot this data on a line plot as it will provide a visual representation that may help them understand why the median is a better measure of center for this data set.

39. Practice for SOL 6.15b
The number of cookies that were made at a bakery for each of seven days is shown: 108, 96, 96, 84, 108, 240, and 84 The best measure of center for this data set is the- A. mean because all of the values are close to one another in value B. median because all of the values are close to one another in value C. mean because 240 is much higher than the other numbers in the data set D. median because 240 is much higher than the other numbers in the data set
For SOL 6.15, students need additional practice determining which measure of center is most appropriate for a given situation. Using the mean is best when the set of data has no especially high or especially low numbers. These especially high or especially low numbers are typically referred to as outliers, though test questions in grade six do not specifically use the word “outlier.” Using the median to describe a data set is a good choice when there are one or more outliers in the data set, as the median is not as susceptible to the influence of an outlier or outliers as the mean. Mode is best when the set of data is categorical or when a numerical data set has many elements of the same value.
The answer to the question is shown on the screen.

40. Practice for SOL 6.16
This chart shows the three pairs of pants and four shirts that Bobby
packed for a trip. Bobby will randomly select an outfit to wear. He
can choose one pair of pants and one shirt. Using the chart,
determine the probability that he will select a pair of blue jeans and
the yellow shirt.
Pants
Shirt Color
Blue Jeans
Orange
Yellow
Khakis
Green
Red

41. Practice for SOL 6.16 Alexis has a deck of cards labeled as follows:
3 cards with a heart
2 cards with a circle
1 card with a flower
1 card with a ball
What is the probability that she will randomly select a card with a heart, replace it, and then select a card with a ball?
What is the probability that she will randomly select a card with a circle, NOT replace it, and then select a card with a circle?

42. Practice for SOL 6.16b
There are 6 classic rock CD’s, 2 jazz CD’s, and 5 country CD’s in a bin. Teagan will randomly select a CD, give it to her brother, and then randomly select another CD. Which of these can be used to find the probability that Teagan will select a jazz CD as her first selection and a country CD as her second selection? A. C. B. D.
For SOL 6.16b, students need additional practice determining probabilities for dependent and independent events. The example on the screen asks for the probability of two dependent events. Since Teagan is randomly selecting a CD, and not replacing it before she selects another, the events are considered dependent events without replacement. The most common error students make is not realizing the denominator of the probability for the second event is one less than the denominator of the probability for the first event. In other test questions, student performance indicated that students can generally identify events as dependent or independent, but performance of items like the one shown on the screen indicate that perhaps students are not making the connection between this identification and its impact on the denominator of the second fraction.
The correct answer is shown on the screen.

43. Practice for SOL 6.16b
This table shows the drink and dessert selections at a party. Kayla will randomly select one drink and one dessert from these lists. What is the probability that Kayla will select water and apple pie? A. C. B. D.
Drink
Dessert
Apple Juice
Chocolate Cake
Orange Juice
Apple Pie
Cola
Water
Here is another example for SOL 6.16b. The most common student error in a question like the one on the screen is to surmise that the sample space is six rather than eight, and erroneously determine that the probability of the event is two-sixths, which is equivalent to one-third. Students should understand that there are eight possible outcomes in the sample space from which Kayla can select a drink and dessert, and the “water and apple pie” selection is one out of the eight possible drink/dessert selections. Alternately, students can also multiply the probabilities of these two independent events, one-fourth and one-half, to get one-eighth.

44. Practice for SOL 6.17
This circle pattern represents terms in a sequence.
What is the numerical value for each term in the sequence?
What rule is applied from one set of circles to the next?
Is this sequence arithmetic or geometric?
How many circles would be in the 6th term of this sequence?
1st term
2nd term
3rd term
4th term

45. Practice for SOL 6.17
1. What is the common ratio of this sequence? 5, 25, 125, 625, 3125, What is the common ratio of this sequence? 3125, 625, 125, 25, 5, What is the common difference of this sequence? 55, 58, 61, 64, 67, What is the common difference of this sequence? 67, 64, 61, 58, 55, . . .
For SOL 6.17, students showed inconsistent performance in determining the common ratio or common difference.
Students had difficulty determining whether a common ratio is a whole number or a fraction. Questions like number one and number two give students opportunities to determine which has a common ratio of 5 and which has a common ratio of 1/5.
The answers to questions one and two are shown on the screen.
Students also had difficulty determining whether a common difference is positive or negative. In questions three and four, students must determine which has a common difference of 3 and which has a common difference of -3.
The answers to questions three and four are shown on the screen.

46. Practice for SOL 6.17 Look at this sequence. 108, 112, 116, 120, . . .
108, 112, 116, 120, . . .
Does this sequence have a common difference or a common ratio?
What is it?
What is the 8th term of this sequence?

47. Practice for SOL 6.18 Solve each equation. 1. 4. 2. 5. 3. 6.
For SOL 6.18, students need additional practice solving one-step equations when answer options are NOT presented in multiple choice format. In addition, students need opportunities to solve equations that result in solutions that have decimals or fractions.
The answers are shown on the screen.

48. Practice for SOL 6.20 Graph each inequality. a) b) c) d) 2 -2 2 -2 22 -2 2 -2 2 -2 2 -2 48

49. Practice for SOL 6.20
Which graph best represents the inequality ? a. b. c. d.
For SOL 6.20, students need additional practice graphing inequalities on a number line when the variable is on the right side of the inequality. The most common error and the correct answer are shown on the screen.