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Equation Escapades!

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Lesson Plan

Equation Escapades! Lesson Plan

Students will be able to solve one-step linear equations using inverse operations.

Understanding how to solve equations is a foundational skill in mathematics, essential for problem-solving in science, engineering, and everyday life. Mastering this now will make future math topics much easier!

Audience

8th Grade Students

Time

30 minutes

Approach

Through direct instruction, interactive slides, and guided practice, students will learn and apply inverse operations to solve one-step equations.

Materials

Whiteboard or Projector, Equation Escapades! Slide Deck, One-Step Equation Worksheet, and Pencils and Paper

Prep

Teacher Preparation

10 minutes

Step 1

Warm-Up: What's Missing?

5 minutes

  1. Display the 'What's Missing?' warm-up slide (Slide 1 of Equation Escapades! Slide Deck).
    2. Ask students to solve the simple missing number problems mentally or on scrap paper.
    3. Discuss answers as a class, connecting to the idea of finding an unknown value. (e.g., "What plus 5 equals 10?")

Step 2

Introduction to One-Step Equations

7 minutes

  1. Introduce the concept of equations as balanced scales using Slide 2 of Equation Escapades! Slide Deck.
    2. Explain the goal: isolating the variable.
    3. Introduce inverse operations: addition/subtraction and multiplication/division (Slide 3-4 of Equation Escapades! Slide Deck).
    4. Work through a few examples of addition/subtraction equations together (Slide 5-6).

Step 3

Guided Practice: Multiplication & Division

8 minutes

  1. Guide students through solving one-step equations involving multiplication and division using inverse operations (Slide 7-8 of Equation Escapades! Slide Deck).
    2. Emphasize performing the same operation on both sides to maintain balance.
    3. Solve several examples together, encouraging student participation and explaining each step.

Step 4

Independent Practice: Worksheet

7 minutes

  1. Distribute the One-Step Equation Worksheet.
    2. Instruct students to work independently on the worksheet problems.
    3. Circulate around the room to provide individual support and answer questions.
    4. Remind students to show their work.

Step 5

Cool Down: Exit Ticket

3 minutes

  1. Present the exit ticket question from the Cool Down: Exit Ticket material (Slide 9 of Equation Escapades! Slide Deck).
    2. Have students write their answer on a small piece of paper or designated spot.
    3. Collect exit tickets as students leave to gauge understanding.
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Slide Deck

What's Missing?

Find the missing number!

  1. 5 + ? = 12
  2. 15 - ? = 8
  3. 3 * ? = 21
  4. 24 / ? = 4

(Think about how you found your answer!)

Greet students and start with a quick mental math warm-up. Encourage them to think about what operation is needed to find the missing number.

Equations: A Balanced Act

An equation is like a balanced scale!

  • Both sides must always be equal.
  • We use a variable (a letter like 'x' or 'y') to represent an unknown number.
  • Our goal is to solve for the variable – find out what number it represents!

Introduce the concept of an equation as a balanced scale. Emphasize that whatever you do to one side, you must do to the other to keep it balanced. Define 'variable'.

Inverse Operations: Addition & Subtraction

To keep our scale balanced, we use inverse operations.

  • Addition (+) undoes subtraction (-)
  • Subtraction (-) undoes addition (+)

Example:
If you have x + 5 = 10, to get 'x' by itself, you need to subtract 5 from both sides!

Explain inverse operations for addition and subtraction. Provide simple examples of how to 'undo' an operation.

Let's Solve: x + 5 = 10

x + 5 = 10

  1. Identify the operation: We are adding 5 to x.

  2. Use the inverse operation: Subtract 5 from both sides.

    x + 5 - 5 = 10 - 5

  3. Simplify:

    x = 5

  4. Check your answer: Does 5 + 5 = 10? Yes!

Work through a clear example step-by-step. Show how to subtract 5 from both sides and verify the solution.

Inverse Operations: Multiplication & Division

Just like with addition and subtraction, we have inverse operations for multiplication and division.

  • Multiplication (*) undoes division (/)
  • Division (/) undoes multiplication (*)

Example:
If you have 3x = 18, to get 'x' by itself, you need to divide by 3 on both sides!

Introduce inverse operations for multiplication and division. Provide simple examples of how to 'undo' an operation.

Let's Solve: 3x = 18

3x = 18

  1. Identify the operation: x is being multiplied by 3.

  2. Use the inverse operation: Divide by 3 on both sides.

    3x / 3 = 18 / 3

  3. Simplify:

    x = 6

  4. Check your answer: Does 3 * 6 = 18? Yes!

Work through a clear example step-by-step. Show how to divide by 3 on both sides and verify the solution.

Your Turn! Practice Problems

Solve the following equations. Remember to use inverse operations and keep the scale balanced!

  1. y - 7 = 15
  2. z / 4 = 9
  3. -2 + m = 11
  4. 0.5p = 10

Provide a few more examples for students to try on their own or with a partner. Encourage them to show their work and explain their steps. Guide them as needed.

Time to Practice!

Now it's your turn to be the equation-solving expert!

  • You will receive a One-Step Equation Worksheet.
  • Work independently to solve each problem.
  • Show your steps! This helps you understand and helps me see your thinking.
  • If you get stuck, try to remember the balanced scale and inverse operations.

Introduce the worksheet activity. Explain that this is their chance to practice what they've learned independently. Remind them to show all their steps.

Exit Ticket: What did you learn?

Solve for x:

x - 9 = 20

Write your answer and how you solved it on a piece of paper.

(Don't forget to show your steps!)

Conclude with an exit ticket. This is a quick assessment to see if students grasped the main concept. Remind them this helps you understand what they learned.

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Worksheet

One-Step Equation Practice

Directions: Solve each equation for the variable. Remember to show your work by performing the same operation on both sides of the equation. Don't forget to check your answer!

Part 1: Addition and Subtraction Equations

  1. x + 8 = 20





  2. y - 12 = 5





  3. 14 = z + 3





  4. -6 + m = 10





  5. p + (-4) = 7





Part 2: Multiplication and Division Equations

  1. 3k = 27





  2. a / 5 = 7





  3. 42 = 6b





  4. -2c = 16





  5. n / (-3) = 9





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Answer Key

One-Step Equation Answer Key

Directions: Here are the solutions and steps for each problem on the worksheet.

Part 1: Addition and Subtraction Equations

  1. x + 8 = 20

    • Thought Process: To isolate x, we need to undo the addition of 8. The inverse operation of addition is subtraction.
    • x + 8 - 8 = 20 - 8
    • x = 12
    • Check: 12 + 8 = 20 (Correct)

  2. y - 12 = 5

    • Thought Process: To isolate y, we need to undo the subtraction of 12. The inverse operation of subtraction is addition.
    • y - 12 + 12 = 5 + 12
    • y = 17
    • Check: 17 - 12 = 5 (Correct)

  3. 14 = z + 3

    • Thought Process: To isolate z, we need to undo the addition of 3. The inverse operation is subtraction.
    • 14 - 3 = z + 3 - 3
    • 11 = z
    • Check: 14 = 11 + 3 (Correct)

  4. -6 + m = 10

    • Thought Process: To isolate m, we need to undo the addition of -6 (which is the same as subtracting 6). The inverse is adding 6.
    • -6 + m + 6 = 10 + 6
    • m = 16
    • Check: -6 + 16 = 10 (Correct)

  5. p + (-4) = 7 (This can be rewritten as p - 4 = 7)

    • Thought Process: To isolate p, we need to undo the subtraction of 4. The inverse is addition.
    • p - 4 + 4 = 7 + 4
    • p = 11
    • Check: 11 + (-4) = 7 (Correct)

Part 2: Multiplication and Division Equations

  1. 3k = 27

    • Thought Process: To isolate k, we need to undo the multiplication by 3. The inverse operation is division.
    • 3k / 3 = 27 / 3
    • k = 9
    • Check: 3 * 9 = 27 (Correct)

  2. a / 5 = 7

    • Thought Process: To isolate a, we need to undo the division by 5. The inverse operation is multiplication.
    • a / 5 * 5 = 7 * 5
    • a = 35
    • Check: 35 / 5 = 7 (Correct)

  3. 42 = 6b

    • Thought Process: To isolate b, we need to undo the multiplication by 6. The inverse operation is division.
    • 42 / 6 = 6b / 6
    • 7 = b
    • Check: 42 = 6 * 7 (Correct)

  4. -2c = 16

    • Thought Process: To isolate c, we need to undo the multiplication by -2. The inverse operation is division.
    • -2c / -2 = 16 / -2
    • c = -8
    • Check: -2 * -8 = 16 (Correct)

  5. n / (-3) = 9

    • Thought Process: To isolate n, we need to undo the division by -3. The inverse operation is multiplication.
    • n / (-3) * (-3) = 9 * (-3)
    • n = -27
    • Check: -27 / (-3) = 9 (Correct)
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Cool Down

Cool Down: Solve the Equation!

Directions: On a separate piece of paper, solve the following one-step equation. Remember to show all your work!

Question:

Solve for x:

x - 9 = 20












Explain in your own words how you solved this equation.












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Equation Escapades! • Lenny Learning