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lenny

Equation Quest

Kelsey Patterson

Tier 1
For Schools

Lesson Plan

Equation Quest Session 1

Students will review solving one- and two-step linear equations and learn to solve equations with rational coefficients, demonstrating fluency through whiteboard practice and collaborative tasks.

Mastery of one- and two-step equations and an introduction to rational coefficients builds foundational algebra skills, boosting confidence and preparing students for multi-step equation solving (CCSS 8.EE.C.7).

Audience

8th Grade

Time

30 minutes

Approach

Interactive review and guided practice with increasing complexity.

Materials

  • Equation Quest Session 1 Slide Deck, - One- and Two-Step Equation Review Worksheet, - Rational Coefficient Practice Cards, - Dry-Erase Whiteboards and Markers, and - Timer

Prep

Prepare Materials

10 minutes

  • Print and photocopy One- and Two-Step Equation Review Worksheet
  • Print and cut out Rational Coefficient Practice Cards
  • Load Equation Quest Session 1 Slide Deck on classroom computer
  • Gather dry-erase whiteboards, markers, and timer

Step 1

Launch & Objectives

5 minutes

  • Project the lesson objective from the slide deck
  • Ask students: "What steps do you remember for solving one-step equations?"
  • Record key terms and steps on board

Step 2

Review One-Step Equations

7 minutes

  • Display a one-step equation example on slides
  • Students solve on whiteboards, hold up answers
  • Call on volunteers to explain their process

Step 3

Review Two-Step Equations

7 minutes

  • Present two-step equations via slide deck
  • In pairs, students solve two problems on whiteboards
  • Share and discuss different solution paths

Step 4

Introduce Rational Coefficients

7 minutes

  • Explain how to clear fractions or decimals (multiply both sides)
  • Distribute Rational Coefficient Practice Cards
  • In pairs, students solve one card each and swap with another pair

Step 5

Exit Ticket

4 minutes

  • Distribute the exit ticket section of One- and Two-Step Equation Review Worksheet
  • Students individually solve two equations with rational coefficients
  • Collect for formative assessment
lenny

Slide Deck

Equation Quest: Session 1

CCSS 8.EE.C.7 Learning Progression
Tier 1 Classroom Lesson · 30 minutes · 8th Grade

Welcome everyone to Equation Quest Session 1! Today we’ll review one- and two-step equations and introduce equations with rational coefficients. Remind students this is CCSS 8.EE.C.7 and we have 30 minutes. Transition quickly to objectives.

Lesson Objectives

• Review solving one‐step equations
• Review solving two‐step equations
• Introduce solving equations with rational coefficients

Read each objective aloud. Emphasize that by the end of class they’ll solve equations with fractions and decimals. Ask if anyone can remind us what a learning objective is.

One‐Step Equations Review

Definition: An equation solved with a single operation to isolate the variable.

Example: x + 5 = 12
• Subtract 5 from both sides → x = 7

Ask: “What makes an equation one‐step?” Highlight that just one operation isolates the variable. Walk through the sample problem.

Practice: One‐Step Equations

  1. 3x = 15
  2. y⁄4 = 6

Have students solve each problem on dry‐erase whiteboards. After 1 minute, call for volunteers to hold up boards and explain.

Two‐Step Equations Review

Definition: Requires two inverse operations in sequence.

Example: 2x + 3 = 11

  1. Subtract 3 → 2x = 8
  2. Divide 2 → x = 4

Transition: “Now let’s build to two‐step equations.” Model subtracting then dividing on the board.

Practice: Two‐Step Equations

  1. 3x − 4 = 11
  2. 5 + 2y = 17

Put students in pairs to solve. Circulate and prompt with guiding questions if they struggle.

Introducing Rational Coefficients

Equations where the variable coefficient is a fraction or decimal.

Key Strategy: Multiply both sides by the least common denominator (LCD) or appropriate factor to clear the fraction/decimal before solving.

Explain that rational coefficients are fractions or decimals attached to variables. Stress that clearing them first simplifies solving.

Example: Clearing Fractions

(½)x + 3 = 7
• Multiply both sides by 2 (LCD): x + 6 = 14
• Subtract 6: x = 8

Walk students step-by-step through clearing the fraction, then solving. Encourage them to copy each step.

Exit Ticket

Solve each equation. Write your answers on your paper.

  1. (¾)x − 5 = 7
  2. 2.5x + 4 = 9.5

Hand out exit‐ticket problems now. Give a 4-minute warning then collect for formative check.

lenny

Worksheet

One- and Two-Step Equation Review Worksheet

Part 1: One-Step Equations

Solve each equation. Show all steps and write your final answer.

  1. x + 7 = 12



  2. 5x = 30



  3. (\frac{y}{3}) = 9



  4. 0.25n = 5



Part 2: Two-Step Equations

Solve each equation. Show your work clearly.

  1. 2x + 3 = 11



  2. 4y − 5 = 27



  3. 0.5k + 4 = 10



  4. (\tfrac{3}{4}t) − 2 = 7



Exit Ticket: Equations with Rational Coefficients

Clear any fractions or decimals before solving.

  1. (\tfrac{3}{4}x) − 5 = 7






  2. 2.5x + 4 = 9.5






lenny
lenny

Activity

Rational Coefficient Practice Cards

Instructions: Print and cut the cards. Each card contains one equation. In pairs, solve the equation for the variable and show all steps. After solving, swap cards with another pair and solve a new equation.

  1. (1/3)x + 2 = 5



  2. (3/4)m − 6 = 3



  3. 0.5p + 1.5 = 4



  4. (2/5)t − 3 = 7



  5. 1.25y + 2.5 = 7.5



  6. (4/7)k + 8 = 10



  7. 3.2a − 1.6 = 6.4



  8. (5/6)z + 3 = 8



lenny
lenny

Warm Up

Equation Quest Warm-Up

Time: 5 minutes
Objective: Activate prior knowledge solving one-step and introductory rational-coefficient equations.

  1. Solve each equation. Show all steps and write your final answer.

    a) 4x − 3 = 9




    b) (\tfrac{1}{5})x + 2 = 3



  2. On your whiteboard, quickly jot the first step you’ll take for each equation above. Be prepared to hold it up and explain your choice.



lenny
lenny

Cool Down

Equation Quest Cool-Down

Time: 5 minutes
Objective: Reflect on today’s strategies for clearing rational coefficients and preview our next challenge: equations with variables on both sides.

  1. What is your key takeaway from solving equations with fractions and decimals today? Explain why this is important for simplifying future problems.






  2. Rate your confidence in using the LCD or multiplication to clear fractions/decimals (1 = not confident, 5 = very confident):



  3. Write one question you still have about solving equations with rational coefficients:



  4. Next session, we’ll tackle equations with variables on both sides. Based on today’s strategies, which step do you think will be most helpful, and why?






Looking Ahead: In Equation Quest Session 2, we’ll build on these skills to isolate variables on both sides of the equation!

lenny
lenny

Lesson Plan

Equation Quest Session 2

Students will learn to solve linear equations with variables on both sides by collecting like terms and isolating the variable through addition/subtraction and multiplication/division.

Mastering equations with variables on both sides is the next critical step in the CCSS 8.EE.C.7 progression, reinforcing balance and preparing students for more complex multi-step problems.

Audience

8th Grade

Time

30 minutes

Approach

Guided demo, paired practice, card activities, exit ticket.

Materials

  • Equation Quest Session 2 Slide Deck, - Variables on Both Sides Practice Worksheet, - Both-Sides Equation Practice Cards, - Dry-Erase Whiteboards and Markers, and - Timer

Prep

Prepare Materials

10 minutes

  • Print and photocopy Variables on Both Sides Practice Worksheet
  • Print and cut out Both-Sides Equation Practice Cards
  • Load Equation Quest Session 2 Slide Deck on classroom computer
  • Gather dry-erase whiteboards, markers, and timer

Step 1

Launch & Recap

5 minutes

  • Project objectives from the slide deck
  • Ask: “What strategies do we use to clear fractions and decimals?”
  • Quickly solve one rational-coefficient equation on whiteboards to warm up

Step 2

Demonstrate Both-Sides Technique

7 minutes

  • Use slides to show step-by-step process:
    • Simplify each side (combine like terms)
    • Move variable terms to one side (add/sub)
    • Move constants to opposite side (add/sub)
    • Divide by coefficient to solve
  • Work through example: 3x + 4 = x + 10

Step 3

Guided Pair Practice

7 minutes

  • Distribute Variables on Both Sides Practice Worksheet
  • In pairs, students solve the first two problems on page 1 using whiteboards
  • Circulate and prompt with guiding questions if students get stuck

Step 4

Card Swap Activity

7 minutes

  • Hand out Both-Sides Equation Practice Cards
  • In pairs, solve one card and then swap with another pair
  • Encourage explicit recording of each step

Step 5

Exit Ticket

4 minutes

  • Have students complete the exit section of Variables on Both Sides Practice Worksheet
  • Collect for formative assessment
lenny

Slide Deck

Equation Quest: Session 2

CCSS 8.EE.C.7 Learning Progression
Tier 1 Classroom Lesson · 30 minutes · 8th Grade

Welcome to Equation Quest Session 2! Today we’ll focus on solving equations with variables on both sides. Remind students this continues our CCSS 8.EE.C.7 progression. Transition quickly to objectives.

Lesson Objectives

• Recap clearing fractions and decimals
• Learn steps to solve equations with variables on both sides
• Practice solving multi-step equations and showing each step clearly

Read each objective aloud. Emphasize building on yesterday’s work clearing fractions and decimals. Ask: “Who can remind us of the strategy for clearing rational coefficients?”

Recap: Rational Coefficients

Solve this on your whiteboard:
(½)x + 3 = 8
• Clear the fraction
• Find x

Hold up your solution in 1 minute!

Quick warm-up: have students solve the equation on their whiteboards. Circulate and prompt any who get stuck.

Steps: Variables on Both Sides

  1. Simplify each side (combine like terms)
  2. Move variable terms to one side (add/subtract)
  3. Move constants to the other side (add/subtract)
  4. Divide by the coefficient to solve

Explain and display the four main steps. Encourage students to copy these into their notes.

Example: 3x + 4 = x + 10

  1. Subtract x from both sides: 2x + 4 = 10
  2. Subtract 4: 2x = 6
  3. Divide by 2: x = 3

Work through this example line by line. After each step, pause for questions and confirm understanding.

Practice: Variables on Both Sides

  1. 5x − 3 = 2x + 9
  2. 1.5x + 2 = 0.5x + 7

Place students in pairs. They should solve both problems on whiteboards, explicitly writing each step. After 4 minutes, review answers as a class.

Exit Ticket

Solve each equation. Show all work.

  1. 4x + 2 = x + 11
  2. (¾)x − 5 = (½)x + 3

Distribute exit-ticket problems now. Students work independently. Collect papers at end for formative assessment.

lenny

Worksheet

Variables on Both Sides Practice Worksheet

Part 1: Guided Practice

Solve each equation. Show all work and write your final answer.

  1. 3x + 4 = x + 10






  2. 5x − 3 = 2x + 9






  3. 1.5x + 2 = 0.5x + 7






  4. (¾)x − 5 = (½)x + 3






Exit Ticket: Independent Practice

Solve each equation on your own. Show every step clearly.

  1. 4x + 2 = x + 11











  2. (¾)x − 5 = (½)x + 3











lenny
lenny

Activity

Both-Sides Equation Practice Cards

Instructions: Print and cut the cards. Each card contains one equation with variables on both sides. In pairs, solve the equation for the variable and show all steps. After solving, swap cards with another pair and solve a new equation.

  1. 4x + 2 = x + 10



  2. 3x − 5 = 2x + 1



  3. 1.5x + 3 = 0.5x + 9



  4. (¾)x − 2 = (¼)x + 3



  5. 2x + 7 = 3x − 5



  6. (2/5)x + 4 = (3/5)x − 1



  7. 5.2z − 1.2 = 2.2z + 3.8



  8. (4/7)n + 1 = (2/7)n + 5



lenny
lenny

Warm Up

Equation Quest Warm-Up (Session 2)

Time: 5 minutes
Objective: Recap strategies for clearing rational coefficients from equations.

  1. Solve each equation. Show all steps and write your final answer.
    a) ((1/2)x + 3 = 8)







    b) (0.75y ;−; 2.25 = 4.5)






  2. On your whiteboard, record the first operation you used to clear the coefficient in each equation above. Be ready to hold it up and explain your choice.






lenny
lenny

Cool Down

Equation Quest Cool-Down (Session 2)

Time: 5 minutes
Objective: Reflect on today’s strategies for solving equations with variables on both sides and preview our next challenge: tackling more complex multi-step equations with rational coefficients.

  1. What is your key insight from solving equations with variables on both sides today? Why is collecting like terms and moving variable terms helpful?






  2. Rate your confidence in solving equations with variables on both sides (1 = not confident, 5 = very confident):



  3. Describe one challenge or question you still have about today’s process:






  4. In our next session, we’ll combine clearing fractions/decimals with variables on both sides for more complex problems. Which strategy from today do you think will be most important, and why?






Looking Ahead: In Equation Quest Session 3, we’ll apply these skills to solve multi-step equations that include rational coefficients on both sides!

lenny
lenny

Lesson Plan

Equation Quest Session 3

Students will consolidate skills by solving multi-step linear equations that include rational coefficients and variables on both sides, clearly documenting each step.

Combining fraction-clearing and both-sides techniques solidifies CCSS 8.EE.C.7 mastery, ensuring students can tackle complex equations with confidence.

Audience

8th Grade

Time

30 minutes

Approach

Demo, paired practice, card swaps, exit ticket

Materials

  • Equation Quest Session 3 Slide Deck, - Multi-Step Rational and Both-Sides Practice Worksheet, - Multi-Step Equation Challenge Cards, - Dry-Erase Whiteboards and Markers, and - Timer

Prep

Prepare Materials

10 minutes

  • Print and photocopy Multi-Step Rational and Both-Sides Practice Worksheet
  • Print and cut out Multi-Step Equation Challenge Cards
  • Load Equation Quest Session 3 Slide Deck on classroom computer
  • Gather dry-erase whiteboards, markers, and timer

Step 1

Launch & Warm-Up

5 minutes

  • Project the lesson objectives from the slide deck
  • Distribute Equation Quest Warm-Up Session 3
  • Students solve both warm-up problems on whiteboards and hold up solutions

Step 2

Demonstrate Multi-Step Technique

7 minutes

  • Use slides to model solving a complex equation step-by-step (e.g., (¾)x − 2 = (½)x + 5)
  • Steps: clear fractions (multiply LCD), combine like terms, move variables to one side, move constants, divide to isolate variable
  • Pause after each step for questions

Step 3

Guided Pair Practice

7 minutes

  • Hand out Multi-Step Rational and Both-Sides Practice Worksheet
  • In pairs, students solve the first two problems on whiteboards, showing all steps
  • Circulate and support with guiding questions

Step 4

Card Swap Activity

7 minutes

  • Give each pair one Multi-Step Equation Challenge Card
  • Pairs solve their card and then swap with another pair to solve a new equation
  • Encourage clear step-by-step recording

Step 5

Exit Ticket

4 minutes

  • Students complete the exit section of Multi-Step Rational and Both-Sides Practice Worksheet independently
  • Collect for formative assessment
lenny

Slide Deck

Equation Quest: Session 3

CCSS 8.EE.C.7 Learning Progression
Tier 1 Classroom Lesson · 30 minutes · 8th Grade

Welcome to Equation Quest Session 3! Today we’ll combine our skills to solve multi-step equations with rational coefficients and variables on both sides. Remind students of CCSS 8.EE.C.7 and the 30-minute time frame—let’s get started!

Lesson Objectives

• Solve multi-step equations with rational coefficients and variables on both sides
• Document each step clearly
• Build confidence in tackling complex problems

Read each objective aloud and ensure students understand how today’s work builds on Sessions 1 and 2. Emphasize clear step documentation.

Warm-Up

Solve each equation. Show all steps on your whiteboard and be ready to share your process:

  1. ((2/3)x + 4 = (1/3)x + 8)
  2. (1.2m - 0.6 = \tfrac{1}{2}m + 1.4)

Distribute whiteboards and ask students to solve these quickly. Circulate and prompt students to explain each step.

Example: Multi-Step Equation

Solve: ((¾)x - 2 = (½)x + 5)

  1. Multiply both sides by 4 (LCD): 3x - 8 = 2x + 20
  2. Subtract 2x: x - 8 = 20
  3. Add 8: x = 28

Model each step clearly, pausing after every operation. Highlight when and why we clear fractions, combine like terms, and isolate variables.

Exit Ticket

Solve each equation. Show every step:

  1. ((2/5)x + 3 = (3/5)x - 1)
  2. (0.75y - 1.5 = (1/4)y + 2.5)

Hand out exit ticket now. Give students 4 minutes to complete independently, then collect for formative feedback.

lenny

Worksheet

Multi-Step Rational and Both-Sides Practice Worksheet

Part 1: Guided Practice

Solve each equation. Show all steps and write your final answer.

  1. (2/3)x + 4 = (1/3)x + 8






  2. 1.2m − 0.6 = 0.5m + 1.4






Exit Ticket: Independent Practice

Solve each equation on your own. Show every step clearly.

  1. (2/5)x + 3 = (3/5)x − 1











  2. 0.75y − 1.5 = (1/4)y + 2.5











lenny
lenny

Activity

Multi-Step Equation Challenge Cards

Instructions: Print and cut the cards. Each card contains one multi-step equation involving rational coefficients and variables on both sides. In pairs, choose a card, solve the equation step-by-step—show how you clear fractions/decimals, combine like terms, move variables and constants, then isolate the variable. Once solved, swap cards with another pair and tackle a new challenge.

  1. (¾)x − 2 = (½)x + 5



  2. (2/5)x + 3 = (3/5)x − 1



  3. 1.25x − 1 = 0.75x + 3



  4. (4/7)y + 2 = (2/7)y + 8



  5. 2.5m − 0.5 = 1.5m + 2



  6. (5/6)k − 3 = (1/6)k + 1



  7. 3.2z + 0.8 = 1.2z + 4.4



  8. (7/8)n − 1.75 = (3/8)n + 2.25



lenny
lenny

Warm Up

Equation Quest Warm-Up (Session 3)

Time: 5 minutes
Objective: Activate strategies for solving multi-step equations combining rational coefficients and variables on both sides.

  1. Solve each equation. Show all steps and write your final answer.

    a) (\frac{2}{3})x + 4 = (\frac{1}{3})x + 8







    b) 1.2m − 0.6 = 0.5m + 1.4






  2. On your whiteboard, jot the first operation you’ll perform for each equation above (e.g., multiply to clear fractions, combine like terms). Be ready to hold it up and explain your choice.



lenny
lenny

Cool Down

Equation Quest Cool-Down (Session 3)

Time: 5 minutes
Objective: Reflect on your mastery of multi-step equations with rational coefficients and variables on both sides, and solidify strategies for future problem solving.

  1. What is your biggest takeaway from solving multi-step equations today? Why is documenting each step beneficial for your understanding and accuracy?











  2. Rate your confidence in tackling complex equations that combine fractions/decimals and variables on both sides (1 = not confident, 5 = very confident):



  3. Which strategy did you find most helpful (e.g., clearing fractions first, combining like terms, isolating variables)? Describe how you’ll apply it in future problems.






  4. Identify one question or challenge you still have about multi-step equation solving.






  5. Reflect on your growth since Session 1. What skills have you improved, and what advice would you give yourself at the start of this unit?














lenny
lenny