Using Variables
Write, Read, and Evaluate Expressions
Solving Problems with Equations
Number Lines & Coordinate Planes
Using the Coordinate Plane
100
A video game costs $45, and you have $20 saved. Write an expression for how much more money you need.
What is x + 20 = 45?
100
Evaluate the expression x+5 when x=3.
8
100
Solve: x+7=12
x=5
100
Plot the point (3, 2) on a coordinate plane.
A point located a +3 on the x-axis and +2 on the y-axis.
100
A rectangle has vertices at (1,1), (4,1), (4,3), and (1,3). What is the length of the bottom side?
3 units
200
If one notebook costs n dollars, write an expression for the cost of 6 notebooks.
What is 6n?
200
Write an algebraic expression for "a number multiplied by 4." Then evaluate it when the number is 6.
Expression: 4n; when n=6, 24
200
Solve: 3y=18. Then check your answer.
y=6; 3(6)=18
200
Plot the points (2, -1) and (-3, 2). What quadrant is each point in?
Quadrants IV and II.
200
Plot a triangle with vertices at (0,0), (3,0), and (3,4). Find the length of each side.
3, 4, and 5 units
300
A recipe calls for 2 cups of flour. Write an expression for the total flour needed for b batches. If you make 5 batches, how much flour do you need?
Expression: 2b; For 5 batches: 10 cups
300
Evaluate the expression 2a+7 when a=5. Identify the coefficient, variable, and constant in the expression.
2(5)+7=17; Coefficient: 2, Variable: a, Constant: 7
300
A book costs $12 and a notebook costs n dollars. If you spend $20 total on both items, write and solve an equation to find the cost of the notebook.
12 + n = 20; n = $8
300
On a number line, plot −2.5 and 1.5. Which number is closer to zero? Explain your reasoning.
1.5 is closer to zero; it is 1.51.5 units away while −2.5−2.5 is 2.52.5 units away.
300
A rectangle has vertices at (0,0), (6,0), (6,4), and (0,4). Find the perimeter and area of the rectangle.
Perimeter: 20 units; Area: 24 square units
400
A rectangle has a length that is 3 units more than its width w. Write expressions for the length and the perimeter of the rectangle. What is the perimeter if w=5 units?
Length: w+3; Perimeter: 2(w+(w+3))=4w+62(w+(w+3))=4w+6; When w=5: 26 units
400
Write an expression for "the sum of twice a number and 8, divided by 2." Evaluate it when the number is 10. Show your work.
400
You have $50 and want to buy video games that cost $8 each. Write and solve an equation to find how many games you can buy if you also need to keep $6 for bus fare.
8g = 50 - 6; g = 5.5, so you can buy 5 games
400
Plot the ordered pairs (2,3), (2,−3), (−2,3), and (−2,−3) on a coordinate plane. Describe the pattern and explain why these points are symmetric.
All four points form a rectangle centered at the origin; they are reflections across both axes
400
A quadrilateral has vertices at (1,1), (5,1), (5,4), and (1,4). Find the perimeter and area. Then, if you moved all vertices 2 units to the right and 1 unit up, what would be the new coordinates?
Perimeter: 18 units; Area: 12 square units; New vertices: (3,2), (7,2), (7,5), (3,5)
500
A phone plan charges a base fee of $30 per month plus $0.10 per text message. Write an expression for the total monthly cost if you send t text messages. If you send 250 texts, what is your total bill?
Expression: 30+0.10t; For 250 texts: $55
500
Evaluate the expression
3x^2-2x+4
when x=2. Explain the order of operations you used to solve this problem.
12
500
A store is having a sale where items are 25% off. You pay $15 for a shirt after the discount. Write and solve an equation to find the original price of the shirt. Show your work.
0.75p = 15; p = $20
500
A point is located 4 units to the left of the origin and 3 units above the origin. Write the ordered pair and plot it.
Ordered pair: (−4,3)(−4,3); Quadrant II
500
A garden is shaped like a trapezoid with vertices at (0,0), (8,0), (6,5), and (2,5). Find the lengths of the parallel sides and the height. Then calculate the area.
Parallel Sides = 8 and 4, Height = 5
Area = 30 square units