1. 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 8 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.

2. Suggested Practice for SOL 8.1a
Students need additional practice simplifying expressions involving a variety of grouping symbols using the order of operations. What is the value of the expression shown? 1. 2.
For SOL 8.1a, students would benefit from simplifying expressions involving a variety of grouping symbols using the order of operations. In the two examples shown, a common mistake among students is to simplify the quantity in the absolute value notation, and forget to take the absolute value. In item 1, students often simplify the square root of 225 divided by 5 and add -4 rather than the absolute value of -4. (animation 1) In item 2, students would divide -24 by 8 and add 11 instead of correctly dividing positive 24 by 8 and adding 11. (animation 2)
The correct answers are shown on the screen.

3. Suggested Practice for SOL 8.1b
Students need additional practice comparing and ordering percents, decimals, mixed numbers, and numbers written in scientific notation.
Arrange the numbers from greatest to least.
Arrange the numbers from least to greatest.
For SOL 8.1b, students need additional practice comparing and ordering percents, decimals, mixed numbers, and numbers written in scientific notation. Student performance data indicate that students find it difficult to list numbers in a designated order.
Two examples are provided. The first example has students order numbers from greatest to least, and the second example has students order numbers from least to greatest. Each of these examples provides the students an opportunity to work with numbers of larger values as well as numbers having smaller values.
The answers to the examples are shown on the screen.

4. Suggested Practice for SOL 8.3a
Students need additional practice solving multistep practical problems involving decimals and percents.
Sasha buys 2.25 pounds of ham for $4.96 per pound and pounds of cheese for $2.30 per pound. Sasha gives the clerk $ If there is no sales tax on these items, how much change should she receive?
Robert bought a pair of shoes that was on sale for 30% off the original price of $ Which is closest to the sale price of the pair of shoes?
A $ C $79.65
B $ D $103.94
For SOL 8.3a, students need additional practice solving multistep practical problems involving decimals and percents. Specifically, students struggle on problems that require more than one operation, as in the examples that are shown.
In example 1, the most common mistake for students is they evaluate the total price for ham and cheese, $15.07, and conclude this to be the answer. The correct answer, $4.93, is obtained by subtracting the total price for ham and cheese, $15.07, from $20.00.
In example 2, students will often select answer A-the amount to be deducted from the original price of $ Students would benefit from a discussion on the different ways this problem could be solved. For instance, instead of finding 30% of $79.95 and subtracting the amount of the discount, they could find 70% of $79.95.
The correct answer is shown on the screen.

5. Suggested Practice for SOL 8.3a
A librarian knows that 45% of the books currently checked out will NOT be returned on the due date. The library has a total of 5,040 books currently checked out. How many of the library’s books will be returned on the due date?
Here is another example for standard 8.3a that requires students to solve a practical problem. This answer may be determined using a variety of strategies. Students would benefit from a discussion sharing the varied ways of finding the solution.
A common error in example 3 is that students determine the number of books that will NOT be returned (2,268), rather than finding the number of books that WILL BE returned on the due date. The correct answer is shown on the screen.

6. Suggested Practice for SOL 8.3b
Students need additional practice solving practical problems involving percent increase or decrease.
Maggie has been exercising by climbing steps. Her climbing rate at the end of week 1 was 25 steps per minute. At the end of week 4, Maggie’s rate was 60 steps per minute. What is the percent increase in Maggie’s rate of climbing steps from the end of week 1 to the end of week 4?
Standard 8.3b requires students to determine the percent increase or decrease for a given situation. This example for SOL 8.3b requires students to find the percent increase in a practical problem. Students are challenged when they are required to find the percent of change when given an initial value and an ending value.
A common student error is to subtract the number of steps per minute (60-25) to get 35, rather than find the percent increase in Maggie’s rate of climbing steps.
The answer to the example is shown on the screen.

7. Suggested Practice for SOL 8.3b
At the end of December, the Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Draw a bar on the graph to represent the Cookie Shop’s profit at the end of January.
Month
(dollars)
Profit
20,000
15,000
10,000
5,000
For SOL 8.3b, students also need additional practice determining a value of increase or decrease when given the percentage. Teachers are encouraged to provide experiences that require students to find the percent increase or decrease as well as the resulting value after the increase or decrease is applied to the original value. In addition, students would benefit from opportunities that require them to represent these values on a graph.
The answer to this example is provided on the screen.
January
December

8. Suggested Practice for SOL 8.10a
Students need additional practice on problems that require them to verify the Pythagorean Theorem. These triangles are not drawn to scale. Which triangle is a right triangle? A C B D
7.1 ft
6.4 ft
9.4 ft
6.3 ft
5.2 ft
8.4 ft
SOL 8.10a requires students to verify the Pythagorean Theorem. Data indicate that students perform well when they are asked to identify the hypotenuse of a right triangle; however, students need additional practice on problems that require them to determine if a triangle is a right triangle by verifying the Pythagorean Theorem.
In the example shown, students must apply the Pythagorean Theorem to each option and then determine which is valid, thus proving the triangle is a right triangle.
The answer is shown on the screen.
6.5 ft
7.2 ft
9.7 ft
7.3 ft
5.1 ft
8.4 ft

9. Suggested Practice for SOL 8.10b
Students need additional practice finding the length of a missing side of a right triangle in a real world context problem. An observer is watching a bird from the ground as shown. What is the bird’s distance from the ground, in miles, as shown in the diagram? Round the distance to the nearest tenth.
1.2 miles
1.9 miles ?
Observer
SOL 8.10b states the student will apply the Pythagorean Theorem. Students would benefit from additional practice in finding the missing side of a right triangle in a real world context problem.
A common error for students, when presented a problem similar to the one on the screen, is to set up the problem correctly and correctly find the value of the missing side squared, but then omit the final step of taking the square root of that value. For the question on the screen, this error would result in an answer of 2.17, rather than the square root of 2.17, which is 1.5 when rounded to the nearest tenth.

10. Suggested Practice for SOL 8.11
Students need additional practice finding the area and perimeter of composite figures. The net of a square-based pyramid is shown. What is the area of this net?
1.5 cm
1 cm
Student performance data indicate that students need additional practice solving practical area and perimeter problems involving composite plane figures. Students find it difficult to determine area when multiple operations are involved. In the example shown on the screen, students must find the area of the square base, the area of one triangular side, recognize there are four of them and that they are congruent, and then combine these areas for the net area. It is important for students to understand the connections between SOL 8.7 and SOL In SOL 8.7, students learn that the surface area of a pyramid is the sum of the areas of the triangular faces and the area of the base.
The correct answer is shown on the screen.
An extension to this problem may be found on the next screen.

11. Suggested Practice for SOL 8.11
The net of a square-based pyramid is shown. What is the perimeter of this net?
1.5 cm
1 cm
Students also have difficulty finding the perimeter of a composite figure when they are required to find a missing side. In the example shown, students must use the Pythagorean Theorem to find the length of one side of the triangle. (Animation-green box) This measure is then used to calculate the perimeter. (Animation-green box)
Teachers are encouraged to provide opportunities that require students to apply their knowledge of the Pythagorean Theorem to practical problems.
The correct answer is shown on the screen.

12. Suggested Practice for SOL 8.12
Students need additional practice determining the probability of dependent and independent events.
Cynthia has 14 roses in a vase.
2 yellow roses
5 pink roses
3 white roses
4 red roses
Cynthia will randomly select 2 roses from the vase with no replacement. What is the probability that Cynthia will select a red rose and then a pink rose?
For standard 8.12, students would benefit from additional practice that requires them to determine the probability of dependent and independent events. In the example shown, the roses are NOT replaced, which indicates that the two events (selecting a red rose and then a pink rose) are dependent.
Data indicate that a common student error is to add 4/15 and 5/14 for a probability of 9/14.
The correct answer is shown on the screen.

13. Suggested Practice for SOL 8.12
Eric and Sue will randomly select from a treat bag containing 6 lollipops and 4 gum balls.
Eric will select a treat, replace it, and then select a second treat.
Sue will select a treat, not replace it, and then select a second treat.
Who has the greater probability of selecting 1 lollipop and then 1 gum ball?
In this example for standard 8.12, students are required to compare the probabilities of Eric’s selections and Sue’s selections. Eric replaces the treat, which indicates that his two events (selecting a lollipop and then a gum ball) are independent. Sue does not replace the treat, which indicates that her two events (selecting a lollipop and then a gum ball) are dependent.
Eric’s probability of selecting one lollipop and then one gumball is calculated by multiplying 6/10 by 4/10 to get 6/25. *animation
Sue’s probability of selecting one lollipop and then one gumball is calculated by multiplying 6/10 by 4/9 to get 4/15. *animation
The correct answer is shown on the screen.

14. Suggested Practice for SOL 8.12
Mario rolls a fair number cube with faces labeled 1 through 6 three times. Place a point on the number line to represent the probability that the number landing face up will be an even number all three times.
In the last example for 8.12, data indicate students are challenged by items requiring them to determine the probability of multiple independent events, such as flipping two coins at the same time, flipping one coin consecutively, or spinning two spinners at the same time. Teachers are also encouraged to include opportunities for students to consider the probability of events that will NOT occur. For an example of this type of item, please refer to the 2013 grade 8 mathematics PowerPoint.
In the example shown, a common misconception is for students to select ½-the probability of one of the single events of rolling the fair number cube. Mario rolls the fair number cube three times, and the probability of each of the independent events is ½. To find the probability of all these events occurring, students should multiply ½ x ½ x ½, thereby resulting in the probability of 1/8.
The answer to the example is shown on the screen.

15. Suggested Practice for SOL 8.13a
Students would benefit from experiences with data represented in a variety of graphical forms. The circle graph displays the items sold at the football concession stand. The concession stand sold a total of 450 items. How many more nachos were purchased than popcorn?
Items Sold at Football Concession Stand
Popcorn
Students have difficulty making inferences when data is represented in a graph and is not represented as a set of numbers. Teachers are encouraged to provide experiences where data is represented in a variety of graphical forms such as bar graphs, circle graphs, and line graphs.
In the example shown, students need to note that a total of 450 items were sold as well as the percentage of each item sold.
Data analysis indicated a common student error would be to subtract the percent of popcorn sold from the percent of nachos sold and get an answer of 6.
The correct answer is shown on the screen.
Hot Chocolate
Gatorade
Cotton Candy
Nachos

16. Suggested Practice for SOL 8.13a
Mr. Robert took a survey of his sixth period class to determine what breeds of dogs the students have as pets. The results are shown in this graph. What percentage of the dogs owned by Mr. Robert’s class are a beagle or a terrier?
In this example for SOL 8.13, students are referring to a bar graph to determine what percentage of the dogs owned by Mr. Robert’s sixth period class are Beagles or Terriers. A common student error in a problem similar to this would be for students to add the number of Beagles and Terriers (7), convert it to a percentage by dividing (1/7) and mistakenly think 14% is the answer.
The correct answer is shown on the screen.

17. Suggested Practice for SOL 8.15b
Students need additional practice solving two-step linear inequalities. What is the solution to this inequality? A C B D
For SOL 8.15b, students need additional practice solving two-step inequalities that include decimals and variables that have negative coefficients.
Data indicate that some students do not reverse the inequality sign when dividing by a negative, which would result in selecting answer choice B. Another common error is to add and -4.5 incorrectly and not reverse the inequality, which would result in selecting answer choice C.
The answer to the example is provided on the screen.
As an extension to this problem, have students graph the solution on a number line.
The answer to the extension is shown on the screen. 1 -1
Graph the solution to the inequality on the number line.

18. Suggested Practice for SOL 8.15b
Solve this inequality for x and graph the solution on the number line.
Also for SOL 8.15b, students need additional practice solving two-step inequalities that include fractions with the variable in the numerator and then graphing the solution on a number line.
In the example shown, data indicate that some students who first add negative five to both sides of the inequality mistakenly end up with 3< X/4, thereby getting an incorrect answer of positive 12 < X. Another common student error is to reverse the inequality when adding the negative five to both sides, or to reverse the inequality when the multiplication results in a negative product.
The solution and its graph are shown on the screen.

19. Suggested Practice for SOL 8.15c
Students need additional practice identifying the properties of operations used to solve an equation. Eric solved the equation as shown. What property justifies Eric’s work from Step 2 to Step 3?
For SOL 8.15c, students need additional practice identifying the properties of operations used to solve an equation. Although students have had prior experiences recognizing all of the properties of operations used to solve equations, students are having difficulty distinguishing between the application of properties.
The answer to the example is shown on the screen.

20. Suggested Practice for SOL 8.16
Students need additional practice determining missing table values.
Alana is creating a table of values to graph the
equation
What is the missing y-value?
A C
B D
For this standard, data indicate students are able to determine which table of values satisfies an equation but may benefit from additional practice determining missing table values.
One way to solve for the missing y value is to substitute -3 into the equation to get 2(-3) + 3y =9. A common error in this question would be for students to subtract 6 from both sides of the equation, rather than add six. Students would then divide both sides of the equation by 3, yielding an incorrect response of 1.
The correct answer is shown on the screen.

21. Suggested Practice for SOL 8.16
Students need additional practice identifying the graph represented by a linear equation.
Which graph best represents the function ?
A C
B D
For SOL 8.16 students also need additional practice identifying the graph represented by a linear equation.
Data indicate that students would frequently select the graph with the correct y-intercept (option B) without further investigating other points on the line.
The correct answer is shown on the screen.

22. Suggested Practice for SOL 8.17
Students need additional practice determining the domain and
range of a relation from a set of points presented graphically.
What are the domain and range of this relation?
For standard 8.17, data indicate that students perform better on items in which they identify the domain or range when given a set of ordered pairs. Students would benefit from additional practice when the relation is provided graphically.
The answer to the example is shown on the screen.

23. Suggested Practice for SOL 8.17
Students need additional practice determining the domain or range when given an equation and a set of values.
What is the range of for the domain of ?
Students need additional practice determining the domain or range when given an equation and an identified set of values.
The answer is shown on the screen.

24. Suggested Practice for SOL 8.17
Students need additional practice identifying the dependent
variable and independent variable in a practical problem.
Determine the independent and dependent variable in each situation.
Sarah has hired a contractor to replace the windows in her house. The more people that work, the less time it takes to install the windows.
Leon sells ice cream cones in the park. He has observed that when the outside temperature exceeds ninety degrees, he sells more ice cream cones.
Students also need additional practice identifying the dependent variable and independent variable when given a practical problem.
The answers to the two examples are shown on the screen.