Unlocking the Distributive Property: A Visual Approach

Mathematics Grades 7th Grade 4:56 Video
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Lesson Description

Explore the distributive property of multiplication over addition with visual aids and practical examples. Learn how to simplify expressions by distributing and understand why this property works.

Video Resource

The distributive law of multiplication over addition | Pre-Algebra | Khan Academy

Khan Academy

Duration: 4:56
Watch on YouTube

Key Concepts

  • Distributive Property
  • Multiplication over Addition
  • Simplifying Expressions
  • Equivalent Expressions

Learning Objectives

  • Students will be able to apply the distributive property to simplify numerical expressions.
  • Students will be able to explain why the distributive property works using visual models.
  • Students will be able to verify that applying the distributive property results in an equivalent expression.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the order of operations (PEMDAS/BODMAS). Briefly discuss situations where simplifying within parentheses first might not be the most efficient approach. Introduce the concept of the distributive property as an alternative method.
  • Video Viewing (10 mins)
    Play the Khan Academy video: "The distributive law of multiplication over addition | Pre-Algebra | Khan Academy." Instruct students to take notes on the two methods presented for simplifying the expression and the visual explanation of the distributive property.
  • Guided Practice (15 mins)
    Work through example problems similar to the one in the video, demonstrating the distributive property. Emphasize the importance of distributing the multiplier to *every* term inside the parentheses. Relate each step to the visual model presented in the video. Example: 5 * (4 + 2) = (5 * 4) + (5 * 2)
  • Independent Practice (15 mins)
    Provide students with a set of practice problems to solve independently. Encourage them to use the distributive property and then check their answers by simplifying the original expression using the order of operations. Offer assistance as needed.
  • Wrap-up and Discussion (5 mins)
    Review the key concepts of the distributive property. Address any remaining questions or misconceptions. Preview how the distributive property will be used in future lessons (e.g., solving algebraic equations).

Interactive Exercises

  • Visual Representation
    Present students with expressions like 3 * (2 + 4) and have them draw a visual representation similar to the circles in the Khan Academy video to demonstrate the distributive property.
  • Distributive Property Matching
    Create cards with expressions on them (e.g., 2 * (x + 3)). Have students match each card with its equivalent expression after applying the distributive property (e.g., 2x + 6).

Discussion Questions

  • Why is it called the 'distributive' property?
  • Can you think of real-world situations where you might use the distributive property?
  • How does the distributive property relate to the order of operations?
  • Does the distributive property work with subtraction? (e.g., a * (b - c) = (a * b) - (a * c))

Skills Developed

  • Applying the Distributive Property
  • Simplifying Expressions
  • Visual Representation of Mathematical Concepts
  • Problem-Solving

Multiple Choice Questions

Question 1:

Which of the following shows the correct application of the distributive property to the expression 6 * (5 + 2)?

Correct Answer: 6 * 5 + 6 * 2

Question 2:

Using the distributive property, what is 4 * (x + 3) equal to?

Correct Answer: 4x + 12

Question 3:

What is the first step in applying the distributive property to 2 * (7 + 1)?

Correct Answer: Both B and C

Question 4:

Which expression is equivalent to 3 * (a + b) using the distributive property?

Correct Answer: 3a + 3b

Question 5:

What value will you get if you use the distributive property on 5 * (3 + 4) and simplify?

Correct Answer: 45

Question 6:

The distributive property is mainly used for?

Correct Answer: Simplifying expressions

Question 7:

Which equation shows the distributive property?

Correct Answer: a(b + c) = ab + ac

Question 8:

What is the result of applying the distributive property to 7 * (2 + 5)?

Correct Answer: 14 + 35

Question 9:

Simplify: 2 * (x + 6)

Correct Answer: 2x + 12

Question 10:

Which expression is equivalent to 9 * (4 + y)?

Correct Answer: 36 + 9y

Fill in the Blank Questions

Question 1:

The distributive property states that a * (b + c) = (a * b) + (a * _____).

Correct Answer: c

Question 2:

To apply the distributive property, you must ___________ the number outside the parentheses to each term inside.

Correct Answer: multiply

Question 3:

Using the distributive property, 3 * (5 + 2) is equal to (3 * 5) + (3 * ______).

Correct Answer: 2

Question 4:

The distributive property is a way to ___________ expressions.

Correct Answer: simplify

Question 5:

Applying the distributive property to 4 * (x + 1) gives you 4x + ______.

Correct Answer: 4

Question 6:

When using the distributive property, you are ____________ the multiplication across the addition or subtraction.

Correct Answer: distributing

Question 7:

6 * (2 + 3) = (6 * 2) + (6 * 3) is an example of the _______________ property.

Correct Answer: distributive

Question 8:

The opposite of distributing is _____________, where you find a common factor.

Correct Answer: factoring

Question 9:

Using the distributive property on 8 * (y + 5) results in 8y + ______.

Correct Answer: 40

Question 10:

To check if you correctly used the distributive property, you can simplify both the original and distributed expressions and see if they are ____________.

Correct Answer: equal

Educational Standards

7.A.4.1:Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. 7.A.4.2:Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols.

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