Multiple Choice Items:
 Solve the following for x: 2x + 3 = 7
 4
 −2
 −4
 2
 Which of the following was used to solve the equation in problem 1?
 the distributive property
 the subtraction property of equality
 the multiplication property of inequality
 the lowest common denominator
 Solve the following for x: −4x − 3 > 9
 x > −3
 x < −3
 Use the equation to answer the question that follows:
Which of the following situations could most likely be represented by the equation?
 Breanne is calculating how much money she will make after 4 weeks of lawn mowing.
 Aaron wants to find out what score he needs to get on his fourth quiz for an average quiz score greater than 75.
 Breanne wants to know how many hours she needs to work in the fourth week to average exactly 80 hours per week.
 Aaron wants to find out what score he needs to get on his fourth quiz for an average quiz score of at least 80.
 Which of the following is a false number sentence?
 2x + 7 = 3x − 1
 3x + 7 < x − 2 + 2x
 −4y −4 = 0
 Which of the following is a possible solution of ?
 (6, −2)
 (1, 2)
 (−2, 2)
 (−2, 6)
 Solve the following for y:
 y = 10
 y = −10
 y = −6
 y = 6
 Which inequality is represented by the graph?
 y ≥ 3x  5
 y ≤ 3x  5
 y ≤ 3x  5
 y ≥ 3x  5
 Use the inequality to answer the question that follows:
Which of the following would have the same solution as the inequality?
 −3x > 36
 −12 x > 36
 −3 x > −36
 −12 x > −36
MultipleChoice Answer Key
 D
 B
 C
 D
 C
 D
 B
 C
 A
ShortAnswer Items:
 Solve each of the following for x. Check your answers by substituting a value from your solution into the original statement. Compare and contrast your solutions.
3 x − 5 = 10 and 3 x − 5 > 10
 Is the process below correct? If so, state a reason for each step. If not, state and correct the error.
 Solve the following inequality for x. Show each step and graph the solution on a number line.
ShortAnswer Key and Scoring Rubrics:
10. Solve each of the following for x. Check your answers by substituting a value from your solution into the original statement. Compare and contrast your solutions.
3 x − 5 = 10 and 3 x − 5 > 10
x = 5 and x > 5
3(5) − 5 = 10 and 3(6) − 5 > 10
15 − 5 = 10 18 − 5 > 10
10 = 10 13 > 10
For the equation, when we substitute 5 into the original statement it holds true. For the inequality, it will only hold true if we substitute numbers greater than 5.
Points

Description

2

 Both correct solutions given
 Understanding of the different solutions demonstrated
 Correct substitution of 5 into the equation and any number greater than 5 into the inequality
 Explanation of the contrast correct and complete

1

 Both correct solutions given
 Partial understanding of the different solutions demonstrated
 Correct substitution of solution in one statement or attempted substitution in both statements
 Explanation of the contrast correct but may be incomplete

0

 Solutions incorrect or missing
 No understanding of the different solutions demonstrated
 No attempt at substitution or substitution completely incorrect or missing
 Explanation completely incorrect or missing

11. Is the process below correct? If so, state a reason for each step. If not, state and correct the error.
correct; given
correct; subtracting 2x from either side
incorrect; should flip the sign of the inequality because both sides need to be divided by a −3;
Points

Description

2

 Written explanation and/or justification for each step correct and complete.

1

 Written explanation and/or justification for two steps correct, but incorrect for one step.

0

 Written explanation and/or justification for each step incorrect or missing (for two or more steps).

 Solve the following inequality for x. Show each step and graph the solution on a number line.
x < 8
Multiply both sides by the LCD of 12
−9x + 84 > 8x − 36 − 2x Distributive property
−9x + 84 > 6x − 36 Combine like terms
−9x + 84 − 84 > 6x − 36 − 84 Subtract 84 from both sides or subtraction property of inequality
(Note: If the student adds −84 to both sides, this is acceptable. S/he would then need the explanation of Add −84 to both sides or addition property of inequality)
−9x > 6x − 120 Simplify or combine like terms
−9x − 6x > 6x − 120 − 6x Subtract 6x from both sides or subtraction property of inequality (adding −6x also acceptable, see previous note)
−15x > −120 Simplify or combine like terms
Divide both sides by −15 or division property of inequality (Multiplying by −1/15 also acceptable, with explanation of Multiply both sides by −1/15 or multiplication property of inequality)
(Also note: The student must reverse the inequality sign to get full credit.)
x < 8 Simplify
Points

Description

2

 Correctly and completely solves the inequality
 Demonstrates thorough understanding of finding the LCD, the distributive property, the addition/subtraction property of inequalities, and the multiplication/division property of inequalities
 Supports each step with an explanation or identification of the correct property.

1

 Correctly solves the inequality, but the answer may be incomplete and does not show all the steps or shows all the correct procedures but includes one calculation error
 Demonstrates partial understanding of finding the LCD, the distributive property, the addition/subtraction property of inequalities, or the multiplication/division property of inequalities
 Attempts to support each step with an explanation or identification of the correct property

0

 Makes no attempt at solving or incorrectly attempts to solve the inequality
 Demonstrates no understanding of finding the LCD, the distributive property, the addition/subtraction property of inequalities, or the multiplication/division property of inequalities
 Does not give any explanation or property identification

Performance Assessment:
Eighth Grade Talent Show/Fundraiser:
The Eighth Grade Student Council in your school has been given permission to use the gymnasium to hold a Talent Show to raise funds for the local food shelf. As part of the planning group, you have the chance to help.
 Set a goal of how much money you would like to raise. Think of different ways to make this money at the event, including ticket sales and refreshments. Do you want to charge the same for all ages or have separate prices? If you are using different prices, estimate the fraction of the total that will be in the different age brackets.
 After deciding upon the ticket pricing and other items to be sold, list these different amounts. Use p for the number of people attending, and if some amounts involve only some of the attendees (for example, a portion of the attendees will purchase a soda, a portion of the attendees will be under 10 years old, etc.), estimate these amounts and represent them as fractions of the total p.
 Research and determine any expenses involved with the event. These could include making programs, purchasing refreshments to sell, and producing posters and flyers to advertise the event.
 Using the amounts from problem 2, write an equation that can be used to determine the number of people attending (p) needed to make your goal amount of money. Be sure to include expenses in this equation.
 Does your answer in problem 4 sound reasonable? If it does not seem possible to get that many attendees, what other solution(s) could be used? Show how a new solution would change your equation.
 Write a plan that your group will submit to the principal. Include the estimates and equation that you wrote.
Performance Assessment Scoring Rubric:
Points

Description

4

 Responds completely with detailed explanation
 Contains no math/calculation errors
 Demonstrates complete understanding of how to model a realworld situation in mathematical terms
 Shows complete understanding of the questions, mathematical ideas, and processes
 Goes beyond what is required by the problem, shows creativity

3

 Responds completely with clear explanation
 Contains no major math errors or conceptual/procedural errors
 Demonstrates understanding of how to model a realworld situation in mathematical terms
 Shows substantial understanding of the questions, mathematical ideas, and processes
 Meets the problem requirements

2

 Responds unclearly or has some parts missing.
 Contains several minor errors or one or more serious math errors or conceptual/procedural errors
 Demonstrates some understanding of how to model realworld situations
 Shows some understanding of the problem
 Partially meets the problem requirements

1

 Misses key points and/or sections
 Contains major math errors or serious conceptual/procedural errors
 Demonstrates lack of understanding of how to model realworld situations
 Shows lack of understanding of the problem
 Does not meet the problem requirements

0

 Fails to complete or incorrectly completes most sections
 Contains major math errors or serious conceptual/procedural errors
 Demonstrates complete lack of understanding of how to model realworld situations
 Shows complete lack of understanding of the problem
 Does not meet the problem requirements
