ANSWER KEYS - Teacher Use Only

Expressions & Equations | Grade 6

Student Concept Worksheet Answers
1
x + 8
"8 more than a number" = x + 8
2
x / 5 or x/5
"A number divided by 5" = x / 5
3
21
2x + 9 when x = 6: 2(6) + 9 = 12 + 9 = 21
4
x = 8
x + 7 = 15. Subtract 7 from both sides: x = 8. Check: 8 + 7 = 15. Yes!
5
x = 7
5x = 35. Divide both sides by 5: x = 7. Check: 5(7) = 35. Yes!
6
x = 13
x - 4 = 9. Add 4 to both sides: x = 13. Check: 13 - 4 = 9. Yes!
Practice Worksheet Answers

Part A: Write Algebraic Expressions

# Phrase Expression
16 more than a numberx + 6
2A number times 99x
34 less than a numberx - 4
4A number divided by 6x / 6 or x/6
5Twice a number plus 32x + 3
610 minus a number10 - x

Part B: Evaluate Expressions

# Expression Work Answer
74x + 3 when x = 54(5) + 3 = 20 + 323
87y - 2 when y = 47(4) - 2 = 28 - 226
9n/3 + 8 when n = 1212/3 + 8 = 4 + 812
102(x + 5) when x = 72(7 + 5) = 2(12)24

Part C: Solve One-Step Equations

# Equation Operation Answer
11x + 8 = 15Subtract 8 from both sidesx = 7
12y - 6 = 11Add 6 to both sidesy = 17
137m = 42Divide both sides by 7m = 6
14n/4 = 9Multiply both sides by 4n = 36
15x + 15 = 27Subtract 15 from both sidesx = 12
169p = 63Divide both sides by 9p = 7

Part D: Word Problems

17
x + 12 = 35; x = 23 stickers
Sarah started with x stickers, got 12 more, now has 35. x + 12 = 35, so x = 23
18
x / 6 = 8; x = 48 cards
Total cards divided by 6 friends = 8 each. x / 6 = 8, so x = 48
19
5x = 45; x = 9
5x = 45, divide by 5, x = 9
20
x - 7 = 18; x = $25
Book is $7 less than game: game - 7 = 18, so game = $25

Challenge Questions:

#21: Many answers possible. Example: "Three friends split the cost of a $24 pizza equally. How much did each person pay?" Answer: 3x = 24, x = $8 per person.

#22: First solve 2x + 5 = 17. Subtract 5: 2x = 12. Divide by 2: x = 6. Now find 3x: 3(6) = 18

FAST Practice Quiz Answers
1
B) x - 7
"7 less than a number" means subtract 7 from the number: x - 7. Note: A (7 - x) means "a number less than 7" which is different!
2
B) 23
3x + 8 when x = 5: 3(5) + 8 = 15 + 8 = 23
3
B) x = 15
x + 9 = 24. Subtract 9 from both sides: x = 24 - 9 = 15. Check: 15 + 9 = 24. Yes!
4
Select: x + 4 = 10, 3x = 18, and x / 2 = 3
x + 4 = 10: 6 + 4 = 10. Yes!
3x = 18: 3(6) = 18. Yes!
x - 2 = 8: 6 - 2 = 4, not 8. No!
x / 2 = 3: 6 / 2 = 3. Yes!
2x = 10: 2(6) = 12, not 10. No!
5
B) x - 15 = 28
Maya started with x coins, gave away 15, has 28 left: x - 15 = 28. Solve: x = 43 coins.
6
A) m = 9
8m = 72. Divide both sides by 8: m = 72 / 8 = 9. Check: 8(9) = 72. Yes!
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for two-step equations. Introduce equations with variables on both sides.
4-5/6 Approaching Mastery Review the specific concept missed. Focus on translating words to expressions if that was the issue.
2-3/6 Developing Reteach inverse operations using balance scale model. Practice with simpler equations first.
0-1/6 Needs Intervention Small group instruction. Start with understanding what variables represent before solving equations.
FAST Success Kit | Grade 6 | FL B.E.S.T. Standards: MA.6.AR.2.1, MA.6.AR.2.2, MA.6.AR.2.3 | Answer Key - Teacher Use Only