Grade 8 Voluntary State Curriculum

1.0 Knowledge of Algebra, Patterns, and Functions – Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

A.Patterns and Functions / Item Example / Answer
1.Identify, describe, extend, and create linear patterns and functions and sequences
a)Determine the recursive relationship of arithmetic sequences represented in words, in a table or in a graph
  • Assessment limit: Provide the nth term no more than 10 terms beyond the last given term using common differences no more than 10 with integers (-100 to 5000)
/ 1.Find the 9th term in the sequence:5, 11, 17, 23, …

2.Select the answer that represents the 7th term in the sequence.
–30, –22, –14, –6, …
A.–2
B.2
C.18
D.26
3.Find the missing term in the table.

4.Select the answer that represents the 12th term in the sequence.
0.30, 0.34, 0.38, 0.42, …
A.0.66
B.0.70
C.0.74
D.0.76
BCR (3 points)
Kathy took a taxi to travel around the city. The charge for the taxi was a flat fee of $2.00 plus $0.75 for each mile. The table below shows the charges. Let m represent the number of miles and C equal the total cost of the taxi.
m / 1 / 2 / 3 / 4
C / $2.75 / $3.50 / $4.25 / $5.00
Step A
Use the pattern in the table above to determine the total cost for the taxi if Kathy were to travel 13 miles.
Step B
Use what you know about patterns to justify why your answer in Step A is correct. Use words, numbers and/or symbols in your justification.
/ 53
C
17
C
$11.75
Since patterns repeat themselves, I looked to see whether there was a constant rate of change. I found that as the number of miles, m, increased by 1, the cost of the taxi increased by $0.75. I solved this by repeating the pattern 9 more times and got my answer of $11.75. Or I could have used the equation and substituted .
b)Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph
  • Assessment limit: Provide the nth term no more than 5 terms beyond the last given term using the recursive relationship of geometric sequences with whole numbers and a common ratio of no more than 5:1 (0 -10,000)
/ 1.Determine the 8th term in the sequence below.
4, 12, 36, 108, …
A.324
B.972
C.2,916
D.8,748
2.Determine the 6th term in the sequence below.
3, 15, 75, 375, …
A.1,125
B.1,875
C.3,375
D.9,375
3.Determine the next term in the sequence below.
59049, 6561, 729, 81, …
4.Determine the 6th term in the sequence below.
48, 12, 3, , …
BCR (3 points)
Study the geometric sequence below.
96, 144, 216, 324
Step A
Find the 5th term.

Step B
Use what you know about geometric sequences to justify why your answer is correct. Use words, numbers, and/or symbols in your justification.
/ D
D
9

486
The sequence is a geometric sequence because the ratio between the terms is the same. The ratio is or . You multiply each term by the common ratio.
,
, , .
c)Determine whether relationships are linear or nonlinear when represented in words, in a table or in a graph
  • Assessment limit: Use a graph to determine if a relationship is linear or nonlinear
/ 1.Identify the graph that depicts a linear relationship.
A.B.

C.D.

2.Identify the graph that shows a non-linear relationship.
A.B.

C.D.
/ C
D
d)Determine whether relationships are linear or nonlinear when represented symbolically
B. Expressions, Equations and Inequalities
  1. Write, simplify, and evaluate expressions

a)Write an algebraic expression to represent unknown quantities
  • Assessment limit: Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)
/ 1.Jamar saved $3 less than half of what his sister Tanya saved. If x represents the amount Tanya saved, which expression represents the amount saved by Jamar?
A.
B.
C.
D.
2.Which of the following expressions represent the phrase 8 times n, plus 4?
A.
B.
C.
D.
3.Which of the following expressions represent the phrase (-7) times the sum of 5 and p?
A.
B.
C.
D.
4.A family of 2 adults and 3 children are going to a movie. The price of an adult ticket is $6.25 and the price of a child’s ticket is represented by v. Which expression represents the total cost of the family’s movie tickets?
A.
B.
C.
D.
5.Which of the following expressions is a correct translation of three times the difference between 2 and a number m?
A.
B.
C.
D.
6.Jamie bought two CD’s for x dollars each. If tax was $1.28, which expression represents the total cost of the CD’s?
A.
B.
C.
D.
7.A person earns twice as much as she did three years ago. If the person’s salary three years ago was r, which expression would represent her current salary?
A.
B.
C.
D.
8.Billy’s test scores were 82, 96, 95, and 87. He took a test on Friday and received a score of w. Which expression represents Billy’s average test score?
A.
B.
C.
D.
ECR (4 points)
Jake is saving money to purchase a digital camera. He presently has $23 and will save $6 from his allowance each week. He will also save $8 each week from his paycheck.

Step A
Write the expression that represents the amount of money that Jake has after w weeks.
Step B
  • Use what you know about writing algebraic expressions to explain how you arrived at your answer in Step A. Use words, numbers, and/or symbols in your explanation.
  • After 7 weeks, determine the amount of money Jake will have saved. Use what you know about evaluating algebraic expressions to justify why your answer is correct. Use words, numbers, and/or symbols in your justification.
/ D
C
A
D
A
C
B
C
or
I found the sum of 8 dollars and 6 dollars, because these amounts are saved. The total is multiplied by the number of weeks, or w. This is represented as 14w. The amount saved is added to the amount Jake already has, or .
To find the amount Jake saved after 7 weeks, substitute the 7 for w in. . Jake will have saved $121 after 7 weeks.
b)Evaluate an algebraic expressions
  • Assessment limit: Use one or two unknowns and up to three operations and rational numbers (-100 to 100)
/ 1.Evaluate the expression: when and .
A.5
B.13
C.43
D.51
2.Evaluate the algebraic expression when .
A.103
B.16
C.–4
D.–11
3.Evaluate the expression: when .
A.–100
B.52
C.15
D.–20
4.Evaluate the expression: if and .
5.Evaluate the expression: if and .
6.Evaluate the expression: if, and .

7.Evaluate the expression: when and.
A.13
B.1
C.–13
D.19
8.The equation represents the wingspan , of a Boeing 747 jet aircraft in relationship to its length . Find the wingspan, in feet, if the length of the jet is 231 feet.

9.Evaluate the following expression: if and .
A.–27
B.–3
C.3
D.27 / A
B
A
15
6
15.35
B
277.2
D
c)Evaluate numeric expressions using order of operations
Assessment limit: Use no more than 5 operations including exponents of no more than 3 and 2 sets of parentheses, brackets, a division bar, or absolute value with rational numbers (-100 to 100) / 1.Evaluate the expression.

2.Evaluate the expression.
A.18
B.66
C.–4
D.–24
3.Evaluate the expression.

4.Evaluate the expression.
A.18
B.14
C.4
D.–4
5.Evaluate the expression.

6.Evaluate the expression.9
A.–316
B.–186
C.25
D.774
ECR (4 points)
Given the following expression:
Step A
Evaluate the numeric expression
Step B
  • Use words, numbers, and/or symbols to explain how you found your answer.
  • Determine how replacing the absolute value symbol with parentheses would change the value of the expression. Use what you know about numeric expressions to justify why your answer is correct. Use words, numbers, and/or symbols in your justification.
BCR (3 points)
Given the expression:
StepA
Evaluate the expression.
StepB
Study the problem below and locate the error. Use what you know about order of operations to justify your response. Use words, numbers, and/or words in your justification.
/ 13
D
11.9
C
2.1
B


We would have subtracted –18 instead of 18.
3

The mistake is found in the third line, subtracting 6 minus 2 and getting 4. In the order of operations, 2 should be multiplied by 5 first, then subtracted from 6.
d)Simplify algebraic expressions by combining like terms
  • Assessment limit: Use no more than 3 variables with integers (-50 to 50), or proper fractions with denominators as factors of 20 (-20 to 20)
/ 1.Simplify the expression by combining like terms.
A.
B.
C.
D.
2.Simplify the expression by combining like terms.
A.
B.
C.
D.
3.Simplify the expression by combining like terms.
A.
B.
C.
D.
4.Simplify the expression .
A.
B.
C.
D.
5.Simplify the expression by combining like terms.
A.
B.
C.
D.
6.Simplify the expression.
A.
B.
C.
D.
7.The sum of the three angles of any triangle is 180°. Angle A of is half the size of angle B. If x represents the measure of angle B, write an expression, in simplest form, that will give the measure of angle C.
A.
B.
C.
D.
BCR (3 points)
Andy ran 3 laps around the track. His time for the second lap was 3.9 seconds more than for the first lap. His time for the third lap was 1.6 second less than the first lap.
StepA
If x represents Andy’s time for the first lap, write an expression that represents Andy’s average time in simplest terms.
StepB
Use what you know about simplifying expressions to explain your answer. Use words, numbers and/or symbols in your explanation. / A
C
A
B
C
B
D

To find the average, add the three expressions representing the number of laps and divide by 3 since there are three laps. Then, to combine like terms, add the variable terms together and the constants together.
e)Describe a real-world situation represented by an algebraic expression
2. Identify, write, solve, and apply equations and inequalities / ECR (4 points)
(addresses 1.B.2.a and 1.B.2.b)
Frontier Town charges $2.00 a day to get into the park and $1.50 for each round of miniature golf. Sam has $16 to spend that day.
Step A
Write the inequality that describes the maximum number of rounds of miniature golf, x, that Sam can play.
Step B
Determine the maximum number of rounds of golf, x, that Sam can play that day at Frontier Town. Use what you know about solving inequalities to justify why your answer is correct. Use words, numbers and/or symbols in your justification.
BCR (3 points)
The sum of the interior angles of a quadrilateral equals 360˚.
Step A
The measures of the angles in a given quadrilateral are 120˚, 3x, 2x and x. Write an equation to represent the sum of the angles in this quadrilateral.
Step B
Determine the measure of each angle. Use what you know about solving equations to justify why your answer is correct. Use words, numbers and/or symbols in your justification. /

so Sam can play at most 9 rounds of golf. He doesn’t have enough money for 10 rounds since it would cost and he only has $16.

The angle measures are 120, 120, 80, and 40 in this quadrilateral.
.
a) Write equations and inequalities to represent relationships
  • Assessment limit: Use a variable, the appropriate relational symbols (>, , <, , =), and no more than 3 operational symbols (+, -, , ) on either side and rational numbers (-1000 to 1000)
/ 1.Write an equation to represent the sentence, the sum of three hundred twenty-six and forty-nine equals the difference between a number and five hundred ninety.
A.
B.
C.
D.
2.Write an inequality for the sentence, the difference between one hundred sixty-seven and the product of 5 and a number is greater than ninety-six increased by eighty-eight minus seventy-two.
A.
B.
C.
D.
3.Write an inequality for the sentence, twice a number decreased by the quotient of that number and 4 is greater than or equal to 14.
A.
B.
C.
D.
4.Amy earns $200 per week, plus a 9% commission on the cost, c, of the cars she sells. Amy has a weekly goal of earning at least $680. Which inequality could be used to find the cost of the cars she must sell to reach her goal?
A.
B.
C.
D.
5.According to a survey in the middle school, 657 students can speak Spanish. This is 240 fewer than 3 times the number of students that cannot speak Spanish. Which equation represents this situation if n represents the number of students who cannot speak Spanish?
A.
B.
C.
D.
6.John earns $8.50 per hour for the first 7 hours and 1.5 times his hourly rate for any additional hours. John works 10 hours. What expression would represent the amount of money, a, John earned that day?
A.
B.
C.
D.
7.Bill has $150.00 to take his friends and himself to a restaurant. Each meal, m, will cost $12.99 and he wants to leave a $20.00 tip. Which inequality represents the number of meals Bill can buy?
A.
B.
C.
D.
/ D
A
D
D
A
B
A
b)Solve for the unknown in a linear equation
  • Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and rational numbers (-2000 to 2000)
/ 1.Solve for :
A.93.3
B.7
C.70
D.840
2.Solve for :
A.–16
B.–9
C.9
D.16
3.Solve for :
A.14
B.13
C.–14
D.10
4.Solve for :
A.–3
B.3
C.–1
D.1
5.Solve for :
A.–6
B.12
C.3
D.–12 / C
D
D
A
C
c)Solve for the unknown in an inequality
  • Assessment limit: Use a one- or two-operation inequality with one variable on one side no more than 3 times whose result after combining coefficients is a positive whole number coefficient with integers (-100 to 100)
/ 1.Solve for :
A.
B.
C.
D.
2.Solve for :
A.
B.
C.
D.
3.Solve for :

4.Solve for :
A.
B.
C.
D.
5.Solve for :
A.
B.
C.
D. / C
D
8
A
D
d)Identify or graph solutions of inequalities on a number line
  • Assessment limit: Use one variable once with a positive whole number coefficient and integers (-100 to 100)
/ 1.Which of the inequalities is represented on the number line?


A.
B.
C.
D.
2.Which graph represents the inequality:?
A.
B.
C.
D.
3.Which inequality is represented on the graph?

A.
B.
C.
D.
4.Which graph represents the inequality:?
A.
B.
C.
D.

BCR (3 points)
Given the inequality:
Step A
Graph the solutions for the inequality.

Step B
Use what you know about graphing inequalities to explain how you got your answer. Use words, numbers and/or symbols in your explanation. / D
C
A
A

Solve the inequality using inverse operations. The solution is so use an open circle at point 5 and the arrow of the line should point to the right.
e)Identify equivalent equations
  • Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and integers (-2000 to 2000)
/ 1.Which one of the following equations is NOT equivalent to:
?
A.16a = 48
B.16a-8 = 40
C.-8a+24a-8 = 40
D.-8a+24a+8 = 40
2.Given , choose the equation that is equivalent.
A.
B.
C.
D.
3.Which of the following equations is not equivalent to:

A.
B.
C.
D.
4.Given , choose the equation that is equivalent.
A.
B.
C.
D.
5.Given , choose the equation that is equivalent.
A.
B.
C.
D. / D
C
C
B
D
f)Apply given formulas to a problem-solving situation
  • Assessment limit: Use no more than four variables and up to three operations with rational numbers (-500 to 500)
/ 1.Water pressure can be found using the formula , where P is the pressure in atmospheres and d is the depth in feet. Find the amount of pressure experienced by a diver at a depth of 66 feet.

2.1-800-Cell-Connect charges $0.25 for the first minute and $0.15 for each additional minute. The cost of a phone call can then be expressed by the formula , where C is the total cost in dollars and m is the number of minutes. Determine the cost if you talk for 11 minutes.

3.Use the area formula , to find the area of the trapezoid, given cm, cm, and cm.
A.28.6
B.86.1
C.196.8
D.393.6
4.Jake deposits $400 into a savings account paying 5% interest. Use the formula , to determinehis balance, A, after 4 years, where t is the number of years, r is the annual interest rate, and P is the principal.
A.$80
B.$480
C.$800
D.$1200 / 3
1.75
C
B
g)Write equations and inequalities that describe real-world problems
C.Numeric and Graphic Representations of Relationships
1.Locate points on a number line and in a coordinate plane.
a)Graph linear equations in a coordinate plane
  • Assessment limit: Use two unknowns having integer coefficients (–9 to 9) and integer constants (–20 to 20)
/ 1.Which of these graphs represents?
A.B.

C.D.

2.Which of these graphs represents?
A.B.

C.D.
/ B
D
2.Analyze linear relationships
a)Determine the slope of a graph in a linear relationship
  • Assessment limit: Use an equation with integer coefficients (–9 to 9) and integer constants (–20 to 20) and a given graph of the relationship
/ 1.Determine the slope of the line given below.

A.
B.
C.
D.
  1. At 12:05 p.m., a parachutist is 7,000 feet above the ground. At 12:10 p.m., the parachutist is 5,500 feet above the ground. Find the average rate of change in feet per minute.

A.
B.
C.
D.
BCR (3 points)
Jason was training for an upcoming long-distance bicycle race. His coach collected time and distance data at two checkpoints during his last training session. The data is shown in the graph below.
Step A
During which interval, A or B, was Jason traveling the fastest?
Step B
Use what you know about slope to explain how you determined your answer. Use words, numbers, and/or symbols in your explanation. / C
A
Jason was traveling the fastest during interval A.
The slope of interval A is and the slope of interval B is . The higher the slope, the steeper the line, the greater the rate of change. Since interval A has a greater slope, and steeper line, it has a greater rate of change. Thus, he is traveling faster during the interval A.
b)Determine the slope of a linear relationship represented numerically or algebraically

Grade 8 VSC 1.0