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Pre-Algebra Power-Up

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Lesson Plan

Pre-Algebra Power-Up Lesson Plan

Students will practice solving one-variable equations and simplifying expressions through leveled worksheets, building foundational pre-algebra skills and confidence by working at their readiness level.

Differentiated practice meets each student where they are, strengthens core pre-algebra concepts, and boosts confidence—preparing learners for success in higher-level math.

Audience

8th Grade Middle School Students

Time

30 minutes

Approach

Tiered worksheets with targeted practice.

Materials

Basic Pre-Algebra Skills Worksheet, Intermediate Pre-Algebra Skills Worksheet, Advanced Pre-Algebra Skills Worksheet, and Whiteboard and Markers

Prep

Teacher Preparation

10 minutes

Step 1

Warm-Up Activity

5 minutes

  • Write a simple one-variable equation (e.g., 3x + 5 = 20) on the whiteboard.
  • Ask students to solve it independently and write their answer on a scrap of paper.
  • Invite 2–3 students to share their solutions and explain their steps.
  • Highlight key steps in solving equations on the board.

Step 2

Differentiated Worksheet Practice

20 minutes

Step 3

Cool-Down and Reflection

5 minutes

  • Have each student solve one problem from their worksheet as an exit ticket, noting one concept they find challenging.
  • Collect exit tickets to inform next-day grouping.
  • Lead a brief discussion: “What strategy helped you today?” and “What do you want to practice more?”.
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Slide Deck

Pre-Algebra Power-Up

Tier 1 Lesson | 8th Grade | 30 Minutes

Welcome students and introduce today’s lesson: practicing pre-algebra skills through leveled worksheets to build confidence and strengthen core concepts.

Lesson Objectives

• Solve one-variable equations independently
• Simplify algebraic expressions correctly
• Work at your personal readiness level
• Build confidence with foundational pre-algebra skills

Read the objectives aloud. Emphasize why we’re doing differentiated practice and how it helps everyone learn at their own pace.

Warm-Up Activity (5 min)

  1. Solve the equation on your own: 3x + 5 = 20
  2. Write your answer on a scrap of paper
  3. Volunteers share their solution process
  4. We’ll highlight key steps together

Guide students through the warm-up: write the equation, allow independent time, then invite volunteers to explain their steps.

Differentiated Practice (20 min)

• Basic skills → Basic Pre-Algebra Skills Worksheet
• Intermediate → Intermediate Pre-Algebra Skills Worksheet
• Advanced → Advanced Pre-Algebra Skills Worksheet

Teacher circulates to scaffold or enrich.
Encourage peer tutoring when ready.

Explain the tiers clearly. Distribute the correct worksheet by readiness, remind students to work quietly, and circulate to support.

Sample Problems

Basic:
• 2x + 3 = 11
• 5 + x = 12

Intermediate:
• 4(x − 2) = 12
• 3x + 2 = 2x + 9

Advanced:
• 2(3x + 1) − x = 11
• Simplify: 5x − 2(x + 4)

Offer sample problems so students know what to expect. Encourage them to refer to their worksheet for more examples.

Cool-Down & Exit Ticket (5 min)

  1. Solve one problem from today’s worksheet and write it down
  2. On the back, answer:
    – Which strategy helped you most?
    – What concept do you want to practice more?

Collect exit tickets as students leave: one solved problem and one reflection. Use data to plan next grouping.

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Worksheet

Basic Pre-Algebra Skills Worksheet

Section A: Solve the One-Step Equations

  1. x + 7 = 15


  2. x − 4 = 9


  3. 5x = 25


  4. x ÷ 3 = 6


  5. −2 + x = 3


  6. 4 − x = 2


  7. −3x = 12


Section B: Simplify the Expressions

  1. 3x + 2x


  2. 7y − 3y


  3. 5a + 0a


  4. −2m + 4m


  5. 6n − 6n + 3


Show all your work in each space provided.

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Worksheet

Intermediate Pre-Algebra Skills Worksheet

Section A: Solve the Two-Step Equations

  1. 2x + 5 = 17





  2. 3x − 4 = 11





  3. (x/2) + 3 = 9





  4. 5 − 2x = 1





  5. 4x − 7 = 9





  6. (1/3)x + 2 = 6





Section B: Distributive Property and Simplify

  1. 3(x + 2)





  2. 2(2y − 3) + y





  3. 4(a − 1) − 2a





  4. 5(2n + 1) − 3n





  5. −2(3m − 4) + 5m





Section C: Combine Like Terms

  1. 3x + 4x − 2x





  2. 5y − 2y + y





  3. 2a + 3b − a + b





  4. 4m − 2m + 3m − m





Show all your work in the space provided.

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Worksheet

Advanced Pre-Algebra Skills Worksheet

Section A: Solve the Multi-Step Equations

  1. 2(3x − 1) = x + 7










  2. 4(x + 2) − 3x = 5x − 6










  3. (1/2)(x − 4) + 3 = (1/4)x + 5










  4. 5x − 2(2x − 3) = 4(x + 1) − x










Section B: Simplify the Expressions (Distribute and Combine Like Terms)

  1. 3[2x − (x + 4)] + 5x










  2. −2(4y − 3) + 3(2y + 1) − y










  3. 4(3a − 2) − 2[5 − (a + 1)]










  4. 2(2m + 3n) − 3(m − 2n) + 4n










Section C: Challenge Problems

  1. Solve for x and check your solution: 3(x − 2) + 4 = 2(2x + 1) − x










  2. Simplify fully and write in simplest form: (5x − 2) − 2(3x + 1) + 4(x − 2)










Show all your work in each space provided.

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Answer Key

Pre-Algebra Skills Answer Key

This answer key provides detailed, step-by-step solutions for each problem on the three differentiated worksheets. Teachers can use these explanations to guide grading and support student understanding.

Basic Pre-Algebra Skills Worksheet Answer Key

Section A: Solve the One-Step Equations

  1. x + 7 = 15
    • Subtract 7 from both sides: x + 7 − 7 = 15 − 7
    • x = 8
  2. x − 4 = 9
    • Add 4 to both sides: x − 4 + 4 = 9 + 4
    • x = 13
  3. 5x = 25
    • Divide both sides by 5: 5x ÷ 5 = 25 ÷ 5
    • x = 5
  4. x ÷ 3 = 6
    • Multiply both sides by 3: (x ÷ 3)·3 = 6·3
    • x = 18
  5. −2 + x = 3
    • Add 2 to both sides: −2 + x + 2 = 3 + 2
    • x = 5
  6. 4 − x = 2
    • Subtract 4 from both sides: 4 − x − 4 = 2 − 4
    • −x = −2
    • Multiply by −1: x = 2
  7. −3x = 12
    • Divide both sides by −3: (−3x) ÷ (−3) = 12 ÷ (−3)
    • x = −4

Section B: Simplify the Expressions

  1. 3x + 2x
    • Combine like terms: (3 + 2)x = 5x
  2. 7y − 3y
    • Combine like terms: (7 − 3)y = 4y
  3. 5a + 0a
    • 0a = 0, so 5a + 0 = 5a
  4. −2m + 4m
    • Combine like terms: (−2 + 4)m = 2m
  5. 6n − 6n + 3
    • 6n − 6n = 0, so 0 + 3 = 3

Intermediate Pre-Algebra Skills Worksheet Answer Key

Section A: Solve the Two-Step Equations

  1. 2x + 5 = 17
    • Subtract 5: 2x = 12
    • Divide by 2: x = 6
  2. 3x − 4 = 11
    • Add 4: 3x = 15
    • Divide by 3: x = 5
  3. (x/2) + 3 = 9
    • Subtract 3: x/2 = 6
    • Multiply by 2: x = 12
  4. 5 − 2x = 1
    • Subtract 5: −2x = 1 − 5 = −4
    • Divide by −2: x = 2
  5. 4x − 7 = 9
    • Add 7: 4x = 16
    • Divide by 4: x = 4
  6. (1/3)x + 2 = 6
    • Subtract 2: (1/3)x = 4
    • Multiply by 3: x = 12

Section B: Distributive Property and Simplify

  1. 3(x + 2)
    • Distribute 3: 3x + 6
  2. 2(2y − 3) + y
    • Distribute 2: 4y − 6
    • Add y: (4y + y) − 6 = 5y − 6
  3. 4(a − 1) − 2a
    • Distribute 4: 4a − 4
    • Combine like terms: (4a − 2a) − 4 = 2a − 4
  4. 5(2n + 1) − 3n
    • Distribute 5: 10n + 5
    • Combine like terms: (10n − 3n) + 5 = 7n + 5
  5. −2(3m − 4) + 5m
    • Distribute −2: −6m + 8
    • Combine like terms: (−6m + 5m) + 8 = −m + 8

Section C: Combine Like Terms

  1. 3x + 4x − 2x
    • (3 + 4 − 2)x = 5x
  2. 5y − 2y + y
    • (5 − 2 + 1)y = 4y
  3. 2a + 3b − a + b
    • Combine a’s: (2 − 1)a = 1a
    • Combine b’s: (3 + 1)b = 4b
    • Result: a + 4b
  4. 4m − 2m + 3m − m
    • Combine: (4 − 2 + 3 − 1)m = 4m

Advanced Pre-Algebra Skills Worksheet Answer Key

Section A: Solve the Multi-Step Equations

  1. 2(3x − 1) = x + 7
    • Distribute left: 6x − 2 = x + 7
    • Subtract x: 6x − x − 2 = 7 → 5x − 2 = 7
    • Add 2: 5x = 9
    • Divide by 5: x = 9/5 or 1.8
  2. 4(x + 2) − 3x = 5x − 6
    • Distribute: 4x + 8 − 3x = 5x − 6 → (4x − 3x) + 8 = 5x − 6 → x + 8 = 5x − 6
    • Subtract x: 8 = 4x − 6
    • Add 6: 14 = 4x
    • Divide by 4: x = 14/4 = 7/2
  3. (1/2)(x − 4) + 3 = (1/4)x + 5
    • Distribute left: (1/2)x − 2 + 3 = (1/4)x + 5 → (1/2)x + 1 = (1/4)x + 5
    • Subtract (1/4)x: (1/2 − 1/4)x + 1 = 5 → (1/4)x + 1 = 5
    • Subtract 1: (1/4)x = 4
    • Multiply by 4: x = 16
  4. 5x − 2(2x − 3) = 4(x + 1) − x
    • Distribute: 5x − [4x − 6] = 4x + 4 − x → 5x − 4x + 6 = 3x + 4
    • Simplify left: (5x − 4x) + 6 = x + 6 → x + 6 = 3x + 4
    • Subtract x: 6 = 2x + 4
    • Subtract 4: 2 = 2x
    • Divide by 2: x = 1

Section B: Simplify the Expressions (Distribute and Combine Like Terms)

  1. 3[2x − (x + 4)] + 5x
    • Inside bracket: 2x − x − 4 = x − 4
    • Distribute 3: 3x − 12
    • Add 5x: (3x + 5x) − 12 = 8x − 12
  2. −2(4y − 3) + 3(2y + 1) − y
    • Distribute: −8y + 6 + 6y + 3 − y
    • Combine y-terms: (−8y + 6y − y) = −3y
    • Combine constants: 6 + 3 = 9
    • Result: −3y + 9
  3. 4(3a − 2) − 2[5 − (a + 1)]
    • First part: 12a − 8
    • Inside second bracket: 5 − a − 1 = 4 − a
    • Distribute −2: −8 + 2a
    • Combine with first: (12a + 2a) + (−8 − 8) = 14a − 16
  4. 2(2m + 3n) − 3(m − 2n) + 4n
    • Distribute: 4m + 6n − 3m + 6n + 4n
    • Combine m-terms: 4m − 3m = m
    • Combine n-terms: 6n + 6n + 4n = 16n
    • Result: m + 16n

Section C: Challenge Problems

  1. 3(x − 2) + 4 = 2(2x + 1) − x
    • Distribute: 3x − 6 + 4 = 4x + 2 − x → 3x − 2 = 3x + 2
    • Subtract 3x: −2 = 2
    • This is a contradiction, so no solution.
  2. (5x − 2) − 2(3x + 1) + 4(x − 2)
    • Distribute: 5x − 2 − 6x − 2 + 4x − 8
    • Combine x-terms: (5x − 6x + 4x) = 3x
    • Combine constants: (−2 − 2 − 8) = −12
    • Result: 3x − 12

Use this key to provide clear, consistent feedback. Teachers may share select steps with students to reinforce methodical problem solving and error analysis.

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Cool Down

Understood! The exit ticket reflection is already embedded in both the lesson plan and slide deck under Cool-Down & Exit Ticket (5 min). No separate cool-down document is needed.

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