6th Grade Accelerated Math Unit 3 Study Guide
The questions on the study guide will show what the questions on the 4.5 week exam. Get your
parent to sign for 3 bonus points on the test. Parent Signature:______Key_________________
Write the correct answer in the blank at the right of each question.
1. Write 63 as a product of the same factor. Then find the value.
1._ 6 x 6 x 6 = 216___
2. Write 9 × 9 × 9 × 9 × 9 × 9 using an exponent.
2. _ 9 ^ 6____
Find the value of each expression use order of operations
3. 5 + 4 × 5 – 7
3. ___18_____
3
4. 8 × (3 + 2) – 11
4. ___77_____
5. 30 × 4 – 22 × 5
5. ___100_____
3
6. 55 ÷ 5 × 2 ÷ 4
6. ____22_____
7. Tanya purchased 4 hammers for $11.79 each and 7 screwdrivers for $6.65 each.
Write an expression for the total cost of the tools. Then find the total cost.
c= 4(11.49) + 7(6.65)
7. ____c = 92.51_______
𝟐
Evaluate each expression if a = 3, b = 𝟑, and c = 6. Use substitution.
8. 2a + 5
8. ____11________
9. 2c + 3a
9. ____27__________
10. 𝑐 2 + 3a × b
10. ___42___________
11. Koby took $43 to the movie theater. If he paid for 3 tickets that each cost d
dollars, he will have 43 – 3d left. How much does he have left if the tickets
cost $9.75 each?
11. _____$13.75______
Write each phrase as an algebraic expression.
12. 16 seconds faster than Najib’s time
12. ___t + 16__________
13. one piece more than twice the number of pieces
13. ____2p + 1_______
14. one third of Danielle’s height
15. six meters less than four times the width
16. Devante made and sold 8 pitchers of lemonade at his lemonade stand. He used
the same number of lemons in each pitcher. He had 3 lemons left over. Write
an expression to represent the total number of lemons Devante had in all.
17. Helen divided her colored pencils evenly among herself and three friends.
Write an expression to represent the number of pencils each person received.
1
3
14. ____ h__________
15. ___4w - 6 ________
16. ___8x + 3________
1
17. __p ÷ 4__or 4p__
Determine whether the two expressions are equivalent. If so, tell what property
is applied. Associative, Commutative, Identity, Distributive or write Not
Equivalent
18.___Associative___
18. (8 × 2) × 5 = 8 × (2 × 5)
19. __ Identity_____
19. 13 + 0 = 13
20. __Not Equivalent____
20. 12 – (5 – 3) = (12 – 5) – 3
21. Niko worked out for 45 minutes, 22 minutes, and 25 minutes last week. Use
the Commutative Property to find the total number of minutes he worked out.
Use the expression 3x + y + 15 to answer question 22-23.
22. What is the coefficient in the expression?
21. __45 + 25 +22_= 92____
22. ___3______
23. What is the constant in the expression?
23. ____15________
Use the Distributive Property to rewrite each algebraic expression.
24. 5(x + 9)
24. _____5x +45_____
25. 11(12 + r)
25. _____132+ 11r________
26. 9(v + 2)
26. _______9v +18______
27. 7(b + 3.5)
27. ______7b + 24.5______
28. Mrs. Sosa bought a T-shirt and a pair
of socks for each of her 14
grandchildren. The table lists the cost
of each item. Use the Distributive
Property to find the total amount of
money she spent on her
grandchildren.
Item
Pants
Socks
T-shirt
Cost($)
19.00
4.95
12.00
28.
14(12.00+4.95)
= $237.30
Simplify each expression by combining like terms.
29. 7x + 3x + 4x
29. ______14x_____
30. 5(2x + 4y)
30. _____10x + 20y______
31. 6x + 2y + 9x
31. _______15x + 2y_____
Factor each expression. (Hint: Find the GCF!)
32. ____9(x + 4y)____
32. 9x + 36y
33. 12x + 18y
33. _____6( 2x + 3y)____
Constructed & Extended Response Practice
Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant
drawings and justify your answers. You may show your solution in more than one way or investigate beyond the
requirements of the problem.
1. The teacher wrote this problem on the board. 3³ = ______.
Sadie answered 27. Kevin answered 9. Who answered the question correctly? Justify your answer and provide
mathematical evidence.
Sadie answered the question correctly. The problem showed a base of 3 and an exponent of 3. This is equal to 3x3x3,
which has a product of 27. Kevin made the mistake of multiplying the base times the exponent.
2. Every summer, students at Clark Middle School go on a camping trip. 150 students have signed up. For every inch of
rain, on average 5 students change their mind and decide not go on the trip.
a. Write an expression to show the total number of students going on the trip, using only a variable to represent the
inches of rain.
150 – 5i
b. If it has rained 6 inches this spring, how many students will go on the class ski trip? Write an equation and use
substitution to solve. Show and explain your work.
150 – 5i = (n) the number of students going on the class trip. 150 – 5(6) = n n= 120
The variable I represented the number of inches it rained. To solve the equation, I substituted 6 for i, since it
rained 6 inches. I multiplied 5 times 6, because 5 students decided not to go on the trip for every 1 inch of rain.
3. Evaluate 7p + 6(𝑝 ÷ 𝑞)2 – 2q if p = 10 and q = 2. Show your work and give an explanation for each step.
Step 1: use substitution to plug in the values for each variable.
7(10) + 6(10÷2)² - 2(2)
Step 2: Solve the problem by following the order of operations, beginning with the parenthesis
7(10) + 6(5)² - 2(2)
Step 3: Solve for the exponents
7(10) + 6(25) - 2(2)
Step 4: Multiply from left to right
70 + 150 – 4
Step 5: Add or subtract from left to right.
220 – 4
Answer = 216
142
Expressions