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One and Two Step Equations

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Lesson Plan

Solve It! One & Two-Step Equations

Students will be able to solve one-step and two-step algebraic equations by applying inverse operations.

Understanding how to solve equations is a fundamental skill in algebra, enabling students to find unknown variables and prepare for higher-level math. It simplifies complex problems and provides a clear path to solutions.

Audience

9th Grade Students

Time

30 minutes

Approach

Direct instruction, guided practice, and independent application.

Materials

[Solving 1 & 2-Step Equations Slide Deck](#solving-slide-deck)

,

[Solving Worksheet](#solving-worksheet)

, and

[Solving Worksheet Answer Key](#solving-answer-key)

Prep

Teacher Preparation

10 minutes

Step 1

Introduction: What is Solving Equations?

5 minutes

  • Begin by asking students what they think 'solving an equation' means in math.
    - Use the first few slides of the Solving 1 & 2-Step Equations Slide Deck to introduce the concept of solving as finding the value of the unknown variable that makes the equation true.
    - Emphasize its importance in various real-world problems.
    - Discuss: 'Why do you think solving equations might be a useful tool in math and beyond?'

Step 2

One-Step Equations: Guided Practice

10 minutes

  • Use the Solving 1 & 2-Step Equations Slide Deck to demonstrate solving one-step equations.
    - Work through examples on the board, encouraging student participation.
    - Guide students through a few practice problems together, ensuring they understand how to isolate the variable using inverse operations.
    - Example: 3x = 15. Ask students: 'How can we find the value of x?'

Step 3

Two-Step Equations: Guided Practice

10 minutes

  • Transition to two-step equations using the Solving 1 & 2-Step Equations Slide Deck.
    - Explain that two-step equations require two inverse operations.
    - Work through examples, emphasizing the order of operations (reverse PEMDAS/GEMDAS).
    - Example: 2x + 4 = 10. Ask students: 'What's the first step to isolate x? What's the second?'

Step 4

Independent Practice: Worksheet

5 minutes

  • Distribute the Solving Worksheet.
    - Have students work independently on the worksheet.
    - Circulate around the room to provide support and answer questions.
    - Collect worksheets for review or assign for homework if not completed.
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Slide Deck

Solve It! Unlocking Equations

What does it mean to 'solve' an equation?

  • In everyday life? (Think finding answers, figuring things out)
  • In math? (Finding the value of the unknown variable)

Greet students and introduce the topic. Ask them to think about what 'solving an equation' might mean in a general sense before connecting it to math.

Why Solve Equations?

It's like being a detective!

  • We want to find the hidden value of a variable (like 'x').
  • Solving helps us undo operations to isolate that variable.

Explain that solving equations in algebra helps us find the value of unknown variables. Use a simple analogy if possible, like unwrapping a present to find what's inside.

One-Step Wonders: Multiplication & Division

Let's start simple:

  • Equation: 3x = 15
  • What operation is happening between 3 and x?
  • How do we 'undo' multiplication?
  • Solution: Divide both sides by 3! x = 5

Try this:
5y = 20
4z = 24

Introduce one-step equations involving multiplication. Show the inverse operation (division). Work through an example with student input.

One-Step Wonders: Addition & Subtraction

More simple steps:

  • Equation: x + 7 = 10
  • What operation is happening with x?
  • How do we 'undo' addition?
  • Solution: Subtract 7 from both sides! x = 3

Try this:
a - 8 = 2
b + 3 = 12

Continue with one-step equations, focusing on addition and subtraction. Show the inverse operations. Work through an example with student input.

Two-Step Trek: Unpacking Equations

Now, let's add another layer!

  • Equation: 2x + 4 = 10
  • What's the first operation we need to undo?
  • What's the second?
  • Think: Reverse PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

Transition to two-step equations. Explain that these require two inverse operations, and the order matters (reverse PEMDAS/GEMDAS). Work through an example clearly.

Solving Two-Step Equations

Let's break it down:

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

Always check your answer!
2(3) + 4 = 6 + 4 = 10 (It works!)

Walk through the solution for 2x + 4 = 10 step-by-step, showing how to isolate the variable.

Your Turn: Two-Step Practice

Work through these equations:

  1. 3y - 5 = 13
  2. 4z + 2 = 18
  3. (x / 2) - 1 = 4

Provide more examples for students to try independently or in pairs. Circulate and assist as needed.

Independent Practice: Solving Worksheet

Time to show what you know!

  • You will receive a worksheet with one-step and two-step equations.
  • Work carefully and remember the steps we learned.
  • Don't be afraid to ask for help!

Introduce the worksheet and explain that it's for independent practice. Remind them to ask questions.

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Worksheet

Solving Fun: One and Two-Step Equations

Name: _____________________________

Date: _____________________________

Part 1: One-Step Equation Challenge

Solve each equation for the variable. Show your work!

  1. 5x = 35





  2. y + 12 = 20





  3. z - 9 = 4





  4. 8a = 64





  5. b / 3 = 7





  6. c + 15 = 30





  7. x - 10 = 5





  8. 7y = 42





  9. z + 6 = 18





Part 2: Two-Step Equation Thriller

Solve each equation for the variable. Remember to use reverse order of operations! Show your work!

  1. 2x + 3 = 17










  2. 4y - 6 = 18










  3. (z / 5) + 2 = 6










  4. 3a + 7 = 16










  5. (b / 2) - 8 = 1










  6. 6c - 10 = 20










  7. 5x + 1 = 26










  8. (y / 3) - 4 = 2










  9. 7z - 8 = 20










Part 3: Create Your Own!

Create one one-step equation and one two-step equation. Then, solve them!

  1. Your One-Step Equation:




    Solution:












  2. Your Two-Step Equation:




    Solution:












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Answer Key

Solving Fun: One and Two-Step Equations - Answer Key

Part 1: One-Step Equation Challenge

  1. 5x = 35
    Thought Process: To isolate x, I need to undo the multiplication by 5. The inverse operation of multiplication is division. I will divide both sides of the equation by 5.
    5x / 5 = 35 / 5
    x = 7

  2. y + 12 = 20
    Thought Process: To isolate y, I need to undo the addition of 12. The inverse operation of addition is subtraction. I will subtract 12 from both sides of the equation.
    y + 12 - 12 = 20 - 12
    y = 8

  3. z - 9 = 4
    Thought Process: To isolate z, I need to undo the subtraction of 9. The inverse operation of subtraction is addition. I will add 9 to both sides of the equation.
    z - 9 + 9 = 4 + 9
    z = 13

  4. 8a = 64
    Thought Process: To isolate a, I need to undo the multiplication by 8. The inverse operation of multiplication is division. I will divide both sides of the equation by 8.
    8a / 8 = 64 / 8
    a = 8

  5. b / 3 = 7
    Thought Process: To isolate b, I need to undo the division by 3. The inverse operation of division is multiplication. I will multiply both sides of the equation by 3.
    (b / 3) * 3 = 7 * 3
    b = 21

  6. c + 15 = 30
    Thought Process: To isolate c, I need to undo the addition of 15. The inverse operation of addition is subtraction. I will subtract 15 from both sides of the equation.
    c + 15 - 15 = 30 - 15
    c = 15

  7. x - 10 = 5
    Thought Process: To isolate x, I need to undo the subtraction of 10. The inverse operation of subtraction is addition. I will add 10 to both sides of the equation.
    x - 10 + 10 = 5 + 10
    x = 15

  8. 7y = 42
    Thought Process: To isolate y, I need to undo the multiplication by 7. The inverse operation of multiplication is division. I will divide both sides of the equation by 7.
    7y / 7 = 42 / 7
    y = 6

  9. z + 6 = 18
    Thought Process: To isolate z, I need to undo the addition of 6. The inverse operation of addition is subtraction. I will subtract 6 from both sides of the equation.
    z + 6 - 6 = 18 - 6
    z = 12

Part 2: Two-Step Equation Thriller

  1. 2x + 3 = 17
    Thought Process: First, I need to undo the addition of 3 by subtracting 3 from both sides. Then, I need to undo the multiplication by 2 by dividing both sides by 2.
    2x + 3 - 3 = 17 - 3
    2x = 14
    2x / 2 = 14 / 2
    x = 7

  2. 4y - 6 = 18
    Thought Process: First, I need to undo the subtraction of 6 by adding 6 to both sides. Then, I need to undo the multiplication by 4 by dividing both sides by 4.
    4y - 6 + 6 = 18 + 6
    4y = 24
    4y / 4 = 24 / 4
    y = 6

  3. (z / 5) + 2 = 6
    Thought Process: First, I need to undo the addition of 2 by subtracting 2 from both sides. Then, I need to undo the division by 5 by multiplying both sides by 5.
    (z / 5) + 2 - 2 = 6 - 2
    z / 5 = 4
    (z / 5) * 5 = 4 * 5
    z = 20

  4. 3a + 7 = 16
    Thought Process: First, I need to undo the addition of 7 by subtracting 7 from both sides. Then, I need to undo the multiplication by 3 by dividing both sides by 3.
    3a + 7 - 7 = 16 - 7
    3a = 9
    3a / 3 = 9 / 3
    a = 3

  5. (b / 2) - 8 = 1
    Thought Process: First, I need to undo the subtraction of 8 by adding 8 to both sides. Then, I need to undo the division by 2 by multiplying both sides by 2.
    (b / 2) - 8 + 8 = 1 + 8
    b / 2 = 9
    (b / 2) * 2 = 9 * 2
    b = 18

  6. 6c - 10 = 20
    Thought Process: First, I need to undo the subtraction of 10 by adding 10 to both sides. Then, I need to undo the multiplication by 6 by dividing both sides by 6.
    6c - 10 + 10 = 20 + 10
    6c = 30
    6c / 6 = 30 / 6
    c = 5

  7. 5x + 1 = 26
    Thought Process: First, I need to undo the addition of 1 by subtracting 1 from both sides. Then, I need to undo the multiplication by 5 by dividing both sides by 5.
    5x + 1 - 1 = 26 - 1
    5x = 25
    5x / 5 = 25 / 5
    x = 5

  8. (y / 3) - 4 = 2
    Thought Process: First, I need to undo the subtraction of 4 by adding 4 to both sides. Then, I need to undo the division by 3 by multiplying both sides by 3.
    (y / 3) - 4 + 4 = 2 + 4
    y / 3 = 6
    (y / 3) * 3 = 6 * 3
    y = 18

  9. 7z - 8 = 20
    Thought Process: First, I need to undo the subtraction of 8 by adding 8 to both sides. Then, I need to undo the multiplication by 7 by dividing both sides by 7.
    7z - 8 + 8 = 20 + 8
    7z = 28
    7z / 7 = 28 / 7
    z = 4

Part 3: Create Your Own!

(Answers will vary, check for correct equation setup and solution)

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