Grade: Grade 6 Subject: SAT/ACT Skills Unit: Algebra Readiness SAT: Algebra ACT: Math

Mixed Set

Learn

Real standardized tests don't organize questions by type. You'll see evaluate, solve, simplify, and translate questions all mixed together. This lesson gives you practice switching between problem types, just like on test day.

Test-Taking Strategies for Mixed Sets

The STOP Method

  1. S - Scan: Read the problem quickly. What type is it?
  2. T - Think: What strategy will you use?
  3. O - Operate: Do the math carefully
  4. P - Prove: Check your answer makes sense

Quick Type Identification

If you see... It's probably...
"If x = ..." or "when n = ..." Evaluate
"Solve" or "Find the value of" Solve
"Simplify" or "Combine" Simplify
"Write an equation" or "Which equation represents" Translate

Time Management

  • Don't spend more than 1 minute on any single problem
  • If stuck, mark it and move on
  • Return to skipped problems if time remains
  • Trust your first instinct (don't second-guess unless you find an error)

Examples: Using the STOP Method

Example 1

Problem: If m = 5, what is the value of 2m + 3m - 4?

S - Scan: "If m = 5" tells me this is an Evaluate problem

T - Think: I could substitute first, or simplify first. Simplifying first is faster.

O - Operate: 2m + 3m - 4 = 5m - 4. When m = 5: 5(5) - 4 = 25 - 4 = 21

P - Prove: Check: 2(5) + 3(5) - 4 = 10 + 15 - 4 = 21. Confirmed!

Answer: 21

Example 2

Problem: A rectangle has a perimeter of 30 cm. If the width is w and the length is w + 5, which equation represents this situation?

S - Scan: "Which equation represents" tells me this is Translate

T - Think: Perimeter = 2(length) + 2(width)

O - Operate: 2(w + 5) + 2(w) = 30, which simplifies to 2w + 10 + 2w = 30, or 4w + 10 = 30

P - Prove: Does this make sense? If w = 5, length = 10, perimeter = 2(5) + 2(10) = 30. Yes!

Answer: 2(w + 5) + 2w = 30 or 4w + 10 = 30

Practice: Mixed Problem Set

Instructions: Complete all 12 problems. Target time: 12 minutes. Use the STOP method for each.

1. If x = 3, what is 4x - 5?

A) 2    B) 7    C) 12    D) 17

2. Solve for n: n + 14 = 32

A) 18    B) 46    C) 14    D) 22

3. Simplify: 7y + 3 - 2y + 8

A) 5y + 11    B) 9y + 11    C) 5y + 5    D) 16y

4. "Three times a number, decreased by 4, equals 17." Which equation represents this?

A) 3n - 4 = 17    B) 3(n - 4) = 17    C) 3n + 4 = 17    D) n - 4 = 17

5. Solve for p: 5p = 45

A) 40    B) 50    C) 9    D) 225

6. If a = 2 and b = 4, what is 3a + 2b?

A) 10    B) 14    C) 18    D) 24

7. Simplify: 6c + 2c - c

A) 7c    B) 8c    C) 5c    D) 9c

8. Solve for k: k - 9 = 21

A) 12    B) 30    C) 189    D) 27

9. If t = 6, what is t + 2t + 3?

A) 11    B) 15    C) 21    D) 27

10. "The quotient of a number and 8 is 6." Write the equation.

A) 8n = 6    B) n/8 = 6    C) n - 8 = 6    D) 8/n = 6

11. Simplify: 4(x + 2)

A) 4x + 2    B) 4x + 8    C) x + 8    D) 4x + 6

12. Solve for w: w/3 = 12

A) 4    B) 15    C) 36    D) 9

Answer Key

  1. B) 7 (4(3) - 5 = 12 - 5 = 7)
  2. A) 18 (32 - 14 = 18)
  3. A) 5y + 11 (7y - 2y = 5y; 3 + 8 = 11)
  4. A) 3n - 4 = 17
  5. C) 9 (45 / 5 = 9)
  6. B) 14 (3(2) + 2(4) = 6 + 8 = 14)
  7. A) 7c (6 + 2 - 1 = 7)
  8. B) 30 (21 + 9 = 30)
  9. C) 21 (6 + 12 + 3 = 21, since t + 2t = 3t = 18)
  10. B) n/8 = 6
  11. B) 4x + 8 (distribute: 4 times x = 4x, 4 times 2 = 8)
  12. C) 36 (12 times 3 = 36)

Check Your Understanding

1. How many did you get correct out of 12? ____

2. How long did it take you? ____ minutes

3. Which problem types were easiest for you?

4. Which problem types need more practice?

5. For any problems you missed, classify the error (Careless, Concept, or Strategy).

Performance Goals

Score Time Level
10-12 correct Under 10 min Advanced - Ready for Grade 7
10-12 correct 10-12 min Proficient - On track
8-9 correct Any time Developing - Review weak areas
Below 8 Any time Needs Practice - Redo unit lessons

Next Steps

  • Add any missed problems to your error log
  • If you scored below 10/12, revisit the specific lesson for your weak areas
  • Practice this mixed set again in a few days to track improvement
  • Celebrate your progress - you've completed the Algebra Readiness unit!
  • Continue to the next SAT/ACT Skills unit when ready

Unit Complete!

You have finished all 6 lessons in Algebra Readiness. This foundation will help you succeed in Grade 7 algebra and beyond.