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Expression Magic!

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Lesson Plan

Expression Magic!

Students will be able to identify and apply the commutative, associative, and distributive properties to generate equivalent algebraic expressions.

Understanding equivalent expressions is fundamental to algebra, problem-solving, and simplifying complex mathematical situations. This lesson builds a strong foundation for future math concepts.

Audience

7th Grade Students

Time

30 minutes

Approach

Through interactive slides, guided practice, and doodle notes, students will explore properties.

Materials

Whiteboard or Projector, Markers/Pens, Expression Magic Slide Deck, Properties of Operations Doodle Notes, and Doodle Notes Answer Key

Prep

Teacher Preparation

15 minutes

Step 1

Warm-up & Introduction (5 minutes)

5 minutes

  • Display the first slide of the Expression Magic Slide Deck (Title Slide).
    - Ask students: "What does 'equivalent' mean in math? What about 'expression'?" Allow for quick responses.
    - Introduce the lesson objective: Today, we're going to learn how to make expressions look different but still mean the same thing, using some special math rules! This is like having different outfits for the same person! We'll call these rules 'properties of operations.'

Step 2

Exploring Properties (15 minutes)

15 minutes

  • Navigate through the Expression Magic Slide Deck, introducing each property: Commutative, Associative, and Distributive.
    - For each property:
    - Explain the definition clearly.
    - Show simple numerical examples first.
    - Then, show algebraic examples.
    - Engage students with questions: "Can anyone give me another example? How does this property help us?"
    - Distribute the Properties of Operations Doodle Notes. Guide students to fill in the key information and doodle/annotate as you go through the slides.
    - Emphasize that these properties are tools to rewrite expressions without changing their value.

Step 3

Guided Practice & Doodle Time (7 minutes)

7 minutes

  • Use the practice problems on the Expression Magic Slide Deck and have students work on the corresponding sections in their Properties of Operations Doodle Notes.
    - Circulate the room, offering support and checking for understanding.
    - Encourage students to color, draw, and personalize their doodle notes to help them remember the concepts.

Step 4

Wrap-up & Cool-down (3 minutes)

3 minutes

  • Briefly review the three properties covered. Ask students to share one thing they learned or found interesting.
    - Collect the Properties of Operations Doodle Notes for a quick check or assign finishing them as homework.
    - End with a quick thought question: "How might understanding these properties help you solve problems in the future?"
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Slide Deck

Expression Magic! ✨

Unlocking the Power of Equivalent Expressions

Objective: Identify and apply properties of operations to create equivalent expressions.

Welcome students and introduce the exciting journey of making expressions look different but still mean the same. Ask students what 'equivalent' and 'expression' mean to them.

What are Equivalent Expressions?

They are expressions that have the same value, even if they look different.

  • Think of it like different words meaning the same thing (synonyms!).
  • Example: 2 + 3 and 5 are equivalent. x + x and 2x are equivalent.

Explain that equivalent expressions are like having different ways to say the same thing in math. Use a simple example like 2+3 and 5.

Commutative Property: Order Matters (Not!)

You can swap numbers around in addition and multiplication and still get the same answer!

  • Addition: a + b = b + a

    • Example: 5 + 8 = 8 + 5 (Both equal 13)
    • Algebraic: x + 7 = 7 + x

  • Multiplication: a × b = b × a

    • Example: 4 × 9 = 9 × 4 (Both equal 36)
    • Algebraic: 3y = y × 3

Introduce the Commutative Property. Emphasize that the order changes, but the result stays the same. Use both addition and multiplication examples.

Associative Property: Grouping Together

You can group numbers in different ways in addition and multiplication and still get the same answer!

  • Addition: (a + b) + c = a + (b + c)

    • Example: (2 + 3) + 4 = 2 + (3 + 4) (Both equal 9)
    • Algebraic: (x + 5) + 2 = x + (5 + 2)

  • Multiplication: (a × b) × c = a × (b × c)

    • Example: (6 × 2) × 5 = 6 × (2 × 5) (Both equal 60)
    • Algebraic: (4z) × 3 = 4 × (z × 3)

Introduce the Associative Property. Explain that this property deals with grouping when you have three or more numbers. Use parentheses to illustrate grouping.

Distributive Property: Share the Love!

Multiply a number by a sum or difference, and you'll get the same result as multiplying that number by each part and then adding/subtracting.

  • a × (b + c) = (a × b) + (a × c)
    • Example: 3 × (4 + 5) = (3 × 4) + (3 × 5)
      • 3 × 9 = 12 + 15
      • 27 = 27
    • Algebraic: 5(x + 2) = 5x + 10

Introduce the Distributive Property. This one is often the trickiest, so explain it as 'sharing' or 'distributing' multiplication over addition/subtraction.

Time to Practice! 🤔

Use the properties to write an equivalent expression for each of the following:

  1. 6 + m
  2. 8 × (p × 2)
  3. 4(x + 3)
  4. (10 + y) + 7
  5. 2(5 - z)

(Work on these in your Properties of Operations Doodle Notes!)

Provide practice problems for students to apply the properties. Encourage them to use their doodle notes. Walk around and offer help.

Practice Answers! ✅

  1. m + 6 (Commutative Property of Addition)
  2. (8 × p) × 2 or 16p (Associative Property of Multiplication/Commutative)
  3. 4x + 12 (Distributive Property)
  4. 10 + (y + 7) or y + 17 (Associative Property of Addition/Commutative)
  5. 10 - 2z (Distributive Property)

Review the answers to the practice problems, discussing each one. Emphasize how each property was used. Refer students to the Doodle Notes Answer Key for verification.

You're an Expression Magician!

You now have three powerful tools to transform expressions:

  • Commutative Property: Change order (addition/multiplication)
  • Associative Property: Change grouping (addition/multiplication)
  • Distributive Property: Share multiplication over addition/subtraction

These properties help us simplify and understand expressions better! Keep practicing the magic!

Conclude the lesson by reiterating the importance of these properties and how they simplify expressions. Ask a final reflective question.

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Worksheet

Properties of Operations: Doodle Notes!

Name: __________________________ Date: __________________________

✨ Unlocking Expression Magic! ✨

Equivalent Expressions are expressions that have the same value, even if they look different. Think of them like synonyms in math!





🔄 1. Commutative Property: Order Doesn't Matter!

This property lets you change the order of numbers when you are adding or multiplying without changing the sum or product.

Commutative Property of Addition

Rule: a + b = b + a

My Example/Doodle:


Algebraic Example: x + 7 =


Commutative Property of Multiplication

Rule: a × b = b × a

My Example/Doodle:


Algebraic Example: 3y =


🤝 2. Associative Property: Grouping Together!

This property lets you change the grouping of numbers when you are adding or multiplying without changing the sum or product.

Associative Property of Addition

Rule: (a + b) + c = a + (b + c)

My Example/Doodle:


Algebraic Example: (x + 5) + 2 =


Associative Property of Multiplication

Rule: (a × b) × c = a × (b × c)

My Example/Doodle:


Algebraic Example: (4z) × 3 =


🎁 3. Distributive Property: Share the Love!

This property lets you multiply a number by a sum or difference by multiplying that number by each part inside the parentheses and then adding or subtracting.

Rule: a × (b + c) = (a × b) + (a × c)

My Example/Doodle:


Algebraic Example: 5(x + 2) =


🤔 Practice Time!

Use the properties of operations to write an equivalent expression for each of the following. Try to doodle or make a small note about which property you used!

  1. 6 + m



  2. 8 × (p × 2)



  3. 4(x + 3)



  4. (10 + y) + 7



  5. 2(5 - z)



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Answer Key

Properties of Operations: Doodle Notes Answer Key!

✨ Unlocking Expression Magic! ✨

Equivalent Expressions are expressions that have the same value, even if they look different. Think of them like synonyms in math!

Self-check understanding of this concept.

🔄 1. Commutative Property: Order Doesn't Matter!

This property lets you change the order of numbers when you are adding or multiplying without changing the sum or product.

Commutative Property of Addition

Rule: a + b = b + a

My Example/Doodle: 3 + 2 = 2 + 3 (Both equal 5)
Students can use their own numerical examples and simple doodles like two items swapping places.

Algebraic Example: x + 7 = 7 + x

Commutative Property of Multiplication

Rule: a × b = b × a

My Example/Doodle: 4 × 5 = 5 × 4 (Both equal 20)
Students can use their own numerical examples and simple doodles like two groups swapping places.

Algebraic Example: 3y = y × 3 or 3 * y = y * 3

🤝 2. Associative Property: Grouping Together!

This property lets you change the grouping of numbers when you are adding or multiplying without changing the sum or product.

Associative Property of Addition

Rule: (a + b) + c = a + (b + c)

My Example/Doodle: (1 + 2) + 3 = 1 + (2 + 3) (Both equal 6)
Students can use their own numerical examples and doodles showing different groupings of objects.

Algebraic Example: (x + 5) + 2 = x + (5 + 2) or x + 7

Associative Property of Multiplication

Rule: (a × b) × c = a × (b × c)

My Example/Doodle: (2 × 3) × 4 = 2 × (3 × 4) (Both equal 24)
Students can use their own numerical examples and doodles showing different groupings of items.

Algebraic Example: (4z) × 3 = 4 × (z × 3) or 12z

🎁 3. Distributive Property: Share the Love!

This property lets you multiply a number by a sum or difference by multiplying that number by each part inside the parentheses and then adding or subtracting.

Rule: a × (b + c) = (a × b) + (a × c)

My Example/Doodle: 2 × (3 + 4) = (2 × 3) + (2 × 4) (Both equal 14)
Students can use their own numerical examples and doodles showing something being distributed, like mail to houses.

Algebraic Example: 5(x + 2) = 5x + 10

🤔 Practice Time!

Use the properties of operations to write an equivalent expression for each of the following. Try to doodle or make a small note about which property you used!

  1. 6 + m
    m + 6 (Commutative Property of Addition)

  2. 8 × (p × 2)
    (8 × p) × 2 or 16p (Associative Property of Multiplication; can also apply Commutative to get 8 * (2 * p) then (8 * 2) * p)

  3. 4(x + 3)
    4x + 12 (Distributive Property)

  4. (10 + y) + 7
    10 + (y + 7) or y + 17 (Associative Property of Addition; can also apply Commutative to rearrange terms before or after associating)

  5. 2(5 - z)
    10 - 2z (Distributive Property)

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