Readiness for Algebra
Students who do exceptionally well in the Math 7 class this year will be given the opportunity to take a placement test at the end of the school year to determine readiness for placement into Algebra in eighth grade. Please note that this option will require additional study and preparation by the student as many of the standards required for Algebra are not taught in the Math 7 class.
Prerequisite Skills Needed
The standards listed below are prerequisites for Algebra, but are NOT taught in Math 7. Math 7 students will need to demonstrate understanding of these skills and concepts on the Algebra placement test.
Irrational Numbers
Approximate irrational numbers (square and cube roots and pi) to compare size and order them on a number line.
Integer Exponents
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- Product/Quotient of Like Bases
- Power to a Power
- Product/Quotient to a Power
Equations
Write and solve multistep equations in one variable with the variable on both sides of the equation.
Understand if an equation has one solution, infinitely many solutions, or no solution and be able to provide examples of each.
Solve systems of two linear equations in two variables:
- Graphically
- Algebraically (substitution method)
Linear Equations & Slope
Calculate the slope of a line from a graph or given two points.
Graph a line given its equation in slope-intercept form (y = mx + b).
Derive the equation of a line in slope-intercept form given its graph, two points, or a data table.
For extra help on learning these topics please go to the following websites:
- KhanAcademy(
- IXL (
- Buzz Math (Buzzmath.com)
The following pages provide sample questions for students to use to better understand the prerequisite skills that will be on the Algebra placement test.
Irrational Numbers: Sample Assessment Questions
DOK 1
Evaluate each expression. Round your answer to the nearest tenth if necessary.
1) 2) 3) 4)
DOK 2
5) Evaluate:
6) Joe says that the number is rational because it is the quotient of two integers. Is Joe correct? Explain your reasoning.
DOK 3
7) Robert was completing a test question that asked him to place the following numbers in order from least to greatest:
Robert’s answer to the test question is given below:
a. Is Robert correct? Explain. If you do not think he is correct, also show the correct answer.
b. Robert’s teacher added two new numbers to the list above: and
Plot all seven numbers on the number line below.
Integer Exponents: Sample Assessment Questions
DOK 1– Evaluate each expression.
1) 2) 3)
4) 5) 6)
DOK 2
7) Which of the following expressions is equivalent to ? Show your work for each expression and explain your answer.
a)b) c) d)
Equations: Sample Assessment Questions
DOK 1
For #1-3, solve each equation:
1) 2) 3)
For #4-6, state whether each equation has no solution, one solution, or infinitely many solutions. Show your work to justify your answer.
4) 5) 6)
DOK 2
7) The length of a rectangle is eight more than its width. The perimeter of the rectangle is triple the length. What is the length and width of the rectangle? Write an equation to solve the problem.
8) A bike costs $100.00 more than a scooter. A scooter costs $60.00 more than a skateboard. The total cost of the 3 items is $310.00. How much does each item cost?
DOK 3
8) Consider the equation: . Find one value of a and one value of bso that there are infinitely many values of x that make the equation true. Justify your answer.
Linear Equations and Slope: Sample Assessment Questions
DOK 1 – Recall & Reproduction
1) Find the slope of the line passing through the points:
a) (3, 5) and (−2, −10)b) (−14, 3) and (12, 3)
2) Graph 3) Write the equation in slope-intercept form.
Equation: ______
DOK 2 – Routine
Show all of your work for each question.
4) Write the equation of a line with a slope of that passes through the point (−6, 1).
5) Write the equation of a line that passes through (4, 3) and (−8, 0).
6) Give the coordinates of two points that lie on a line with an undefined slope. Justify your answer by showing work or writing an explanation.
DOK 3 – Non-Routine
7) Zekial, Zander, and Zachary were in a crawling race. They each gave their time and distance data in a different format shown below.
Zekial made a graph: Zander made a table: Zach wrote an equation:
xTime(sec.) / y
Distance (meters)
4 / 4
6 / 4.50
8 / 5
12 / 6
a) Who is the fastest crawler? Explain your reasoning.
b) Write an equation for Zekial and Zander in slope-intercept form.
Zekial: ______Zander: ______
Systems of Equations: Sample Assessment Questions
DOK 1 –Recall & Reproduction
Solve the system of equations by graphing.
1.
Solution: ______
DOK 2 – Routine
Solve the system of equations using substitution. Show all work!
2. 3.
DOK 3 – Non-Routine
Write a system of equations and solve algebraically. Show all your work.
4.A fashion photographer needs to hire a stylist to prepare her models. Ronald charges$180 for showing up, plus$74per hour. Sasha charges$189plus$71per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her the same amount. What would the duration be? What would the cost be?