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Equation Explorers: True or False?

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Lesson Plan

Equation Explorers: True or False?

Students will be able to determine if a given number makes an equation or inequality true by using substitution.

Understanding how to check solutions is fundamental for solving more complex algebraic problems and verifying answers in real-world contexts. This skill helps students build confidence in algebraic reasoning.

Audience

6th Grade

Time

15 minutes

Approach

Direct instruction and guided practice.

Materials

Equation Explorers Slide Deck, Equation Explorers Worksheet, and Equation Explorers Answer Key

Prep

Review Materials

5 minutes

Step 1

Introduction: What Makes It True?

2 minutes

  • Greet the student and introduce the topic: "Today, we're going to be detectives, figuring out if certain numbers make math sentences true or false!"
    - Present the objective: "Our goal is to learn how to check if a number is a solution to an equation or inequality using something called substitution."
    - Use Equation Explorers Slide Deck Slide 1.

Step 2

Understanding Equations and Inequalities

3 minutes

  • Explain what an equation is: a math sentence with an equals sign (=) showing two expressions are equal. Provide a simple example like x + 3 = 7.
    - Explain what an inequality is: a math sentence with symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Provide an example like x - 2 > 5.
    - Use Equation Explorers Slide Deck Slides 2-3.

Step 3

The Power of Substitution

4 minutes

  • Introduce the concept of substitution: "Substitution is like swapping out a player in a game. We'll swap the variable for a number to see if the sentence becomes true."
    - Demonstrate with an example: x + 5 = 10. If x = 5, substitute 5 + 5 = 10, which is true. If x = 3, substitute 3 + 5 = 10, which is false.
    - Demonstrate with an inequality: y - 1 < 6. If y = 7, substitute 7 - 1 < 6, which is 6 < 6, false. If y = 5, substitute 5 - 1 < 6, which is 4 < 6, true.
    - Emphasize checking both sides of the equation/inequality.
    - Use Equation Explorers Slide Deck Slides 4-6.

Step 4

Guided Practice: Worksheet Time!

4 minutes

  • Distribute the Equation Explorers Worksheet.
    - Work through the first few problems together, guiding the student through the substitution process and checking if the statement is true or false.
    - Encourage the student to explain their reasoning aloud.
    - Use Equation Explorers Slide Deck Slide 7.

Step 5

Quick Check and Wrap-up

2 minutes

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Slide Deck

Equation Explorers: True or False?

Objective: Determine if a given number makes an equation or inequality true by using substitution.

Introduce the lesson by engaging the student and presenting the day's objective. Emphasize that checking solutions is a key skill.

What is an Equation?

• A mathematical sentence showing two expressions are equal.
• It always has an equals sign ( = ).
• Example: x + 3 = 7

Define an equation clearly, using simple language and providing a basic numerical example. Highlight the equals sign.

What is an Inequality?

• A mathematical sentence showing two expressions are NOT necessarily equal.
• Uses symbols like: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
• Example: y - 2 > 5

Explain inequalities and the different symbols. Give a concrete example to illustrate the concept.

The Power of Substitution

• Substitution: Replacing a variable with a specific number.
• We use it to check if a number makes an equation or inequality TRUE.

Introduce substitution as 'swapping' the variable for a number. Use a simple analogy if helpful (e.g., a substitute player).

Substitution Example: Equation

Is x = 5 a solution to x + 5 = 10?

  1. Replace x with 5: 5 + 5 = 10
  2. Simplify: 10 = 10
  3. Is it true? YES!

Is x = 3 a solution to x + 5 = 10?

  1. Replace x with 3: 3 + 5 = 10
  2. Simplify: 8 = 10
  3. Is it true? NO!

Walk through an equation example step-by-step. Show both a true and a false substitution to highlight the difference.

Substitution Example: Inequality

Is y = 7 a solution to y - 1 < 6?

  1. Replace y with 7: 7 - 1 < 6
  2. Simplify: 6 < 6
  3. Is it true? NO! (6 is not less than 6)

Is y = 5 a solution to y - 1 < 6?

  1. Replace y with 5: 5 - 1 < 6
  2. Simplify: 4 < 6
  3. Is it true? YES!

Walk through an inequality example. Again, show a true and a false substitution, emphasizing how the inequality symbol works.

Let's Practice!

Work through the problems on your worksheet. Remember to substitute carefully and check if the statement is true or false.

Transition to the worksheet for guided practice. Offer support and encourage the student to articulate their thinking.

Quick Check & Wrap-Up

How do you know if a number is a solution to an equation or inequality?

Why is substitution a useful skill in math?

Review the worksheet and summarize the main takeaway. Ask the student to explain the concept in their own words to check for understanding.

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Worksheet

Equation Explorers Worksheet

Directions: Substitute the given value for the variable in each equation or inequality. Then, determine if the statement is TRUE or FALSE. Show your work!

Equations

  1. Equation: x + 7 = 15
    Given Value: x = 8
    Show Your Work:







    True or False?


  2. Equation: 12 - y = 5
    Given Value: y = 6
    Show Your Work:







    True or False?


  3. Equation: 3z = 21
    Given Value: z = 7
    Show Your Work:







    True or False?


  4. Equation: w / 4 = 5
    Given Value: w = 20
    Show Your Work:







    True or False?


Inequalities

  1. Inequality: a + 3 > 10
    Given Value: a = 7
    Show Your Work:







    True or False?


  2. Inequality: 15 - b ≤ 10
    Given Value: b = 5
    Show Your Work:







    True or False?


  3. Inequality: 2c < 18
    Given Value: c = 9
    Show Your Work:







    True or False?


  4. Inequality: d / 2 ≥ 6
    Given Value: d = 10
    Show Your Work:







    True or False?


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Answer Key

Equation Explorers Answer Key

Directions: Review the solutions for each problem, paying attention to the substitution and the final true/false determination.

Equations

  1. Equation: x + 7 = 15
    Given Value: x = 8
    Show Your Work:
    Substitute 8 for x: 8 + 7 = 15
    Simplify: 15 = 15
    True or False? TRUE

  2. Equation: 12 - y = 5
    Given Value: y = 6
    Show Your Work:
    Substitute 6 for y: 12 - 6 = 5
    Simplify: 6 = 5
    True or False? FALSE

  3. Equation: 3z = 21
    Given Value: z = 7
    Show Your Work:
    Substitute 7 for z: 3 * 7 = 21
    Simplify: 21 = 21
    True or False? TRUE

  4. Equation: w / 4 = 5
    Given Value: w = 20
    Show Your Work:
    Substitute 20 for w: 20 / 4 = 5
    Simplify: 5 = 5
    True or False? TRUE

Inequalities

  1. Inequality: a + 3 > 10
    Given Value: a = 7
    Show Your Work:
    Substitute 7 for a: 7 + 3 > 10
    Simplify: 10 > 10
    True or False? FALSE (10 is not greater than 10)

  2. Inequality: 15 - b ≤ 10
    Given Value: b = 5
    Show Your Work:
    Substitute 5 for b: 15 - 5 ≤ 10
    Simplify: 10 ≤ 10
    True or False? TRUE (10 is less than or equal to 10)

  3. Inequality: 2c < 18
    Given Value: c = 9
    Show Your Work:
    Substitute 9 for c: 2 * 9 < 18
    Simplify: 18 < 18
    True or False? FALSE (18 is not less than 18)

  4. Inequality: d / 2 ≥ 6
    Given Value: d = 10
    Show Your Work:
    Substitute 10 for d: 10 / 2 ≥ 6
    Simplify: 5 ≥ 6
    True or False? FALSE (5 is not greater than or equal to 6)

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Equation Explorers: True or False? • Lenny Learning