Unlocking the Distributive Property: Multiplication Over Subtraction

Mathematics Grades 7th Grade 2:11 Video
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Lesson Description

Explore how the distributive property simplifies expressions by multiplying a number by a group of numbers being subtracted. Learn to apply and understand this essential math concept.

Video Resource

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

Khan Academy

Duration: 2:11
Watch on YouTube

Key Concepts

  • Distributive Property of Multiplication over Subtraction
  • Order of Operations (PEMDAS/BODMAS)
  • Simplifying Expressions

Learning Objectives

  • Students will be able to apply the distributive property to rewrite expressions involving multiplication over subtraction.
  • Students will be able to simplify numerical expressions using the distributive property and order of operations.
  • Students will be able to verify that applying the distributive property yields the same result as direct evaluation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of the distributive property in general (multiplication over addition). Briefly discuss why it's a useful tool for simplifying expressions. Introduce the concept of the distributive property of multiplication over subtraction, explaining that it's a similar principle.
  • Video Explanation (10 mins)
    Play the Khan Academy video "The distributive law of multiplication over subtraction | Pre-Algebra | Khan Academy." Encourage students to take notes on the example problem and the steps involved in applying the distributive property.
  • Guided Practice (15 mins)
    Work through a few example problems on the board, demonstrating how to apply the distributive property of multiplication over subtraction. Include examples with different numbers and complexities. For each example, show how to solve the problem both using the distributive property and by directly evaluating the expression inside the parentheses first. Have students follow along and participate by answering questions.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing several problems that require them to apply the distributive property. Encourage them to work independently and check their answers with a partner. Circulate the classroom to provide assistance and answer questions.
  • Review and Conclusion (5 mins)
    Review the key concepts of the lesson, emphasizing the importance of the distributive property. Answer any remaining questions. Preview upcoming topics.

Interactive Exercises

  • Distributive Property Matching Game
    Create a matching game where students match expressions (e.g., 3(7-2)) with their equivalent expressions after applying the distributive property (e.g., 3*7 - 3*2).
  • Online Practice Problems
    Use websites like Khan Academy or IXL to provide students with interactive practice problems on the distributive property.

Discussion Questions

  • Why is the distributive property useful?
  • Can you think of a real-world example where the distributive property might be helpful?
  • What happens if you don't distribute the number correctly?
  • How does the distributive property relate to the order of operations?

Skills Developed

  • Applying the distributive property
  • Simplifying expressions
  • Problem-solving
  • Attention to Detail

Multiple Choice Questions

Question 1:

Which expression is equivalent to 4(8 - 3) using the distributive property?

Correct Answer: 4 * 8 - 4 * 3

Question 2:

What is the simplified value of 2(10 - 5) using the distributive property?

Correct Answer: 10

Question 3:

Using the distributive property, which of the following is equal to 6(7 - 2)?

Correct Answer: 6 * 7 - 6 * 2

Question 4:

What is the first step in simplifying 5(9 - 4) using the distributive property?

Correct Answer: Multiply 5 * 9

Question 5:

If you evaluate 3(6 - 1) using the distributive property, what do you get?

Correct Answer: 15

Question 6:

Which of the following demonstrates the distributive property correctly?

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

Question 7:

What is the value of 7(5 - 2) when simplified using the distributive property?

Correct Answer: 21

Question 8:

What is the correct expansion of 8(x - 3) using the distributive property?

Correct Answer: 8x - 24

Question 9:

Which expression shows the correct application of the distributive property to 9(4 - 1)?

Correct Answer: 9 * 4 - 9 * 1

Question 10:

Simplify: 10(6-3)

Correct Answer: 30

Fill in the Blank Questions

Question 1:

The distributive property of multiplication over subtraction states that a(b - c) = ab - ____.

Correct Answer: ac

Question 2:

Using the distributive property, 3(8 - 2) is equal to 3 * 8 minus 3 * ____.

Correct Answer: 2

Question 3:

To apply the distributive property to 5(7 - 3), you first multiply 5 by ____, then 5 by 3.

Correct Answer: 7

Question 4:

The simplified value of 4(6 - 1) using the distributive property is ____.

Correct Answer: 20

Question 5:

When using the distributive property, you are ____ the number outside the parentheses to each number inside the parentheses.

Correct Answer: multiplying

Question 6:

According to the order of operations, you should evaluate the expression in the parentheses ____ applying the distributive property as an alternative.

Correct Answer: before

Question 7:

Applying the distributive property to 2(9 - 4) yields 2*9 ____ 2*4.

Correct Answer: minus

Question 8:

The expression 6(5 - x) can be rewritten as 30 ____ 6x using the distributive property.

Correct Answer: minus

Question 9:

The distributive property is a rule that lets you rewrite expressions by multiplying a number by each term ____ the parentheses.

Correct Answer: inside

Question 10:

The distributive property helps to ____ expressions before evaluating them

Correct Answer: simplify

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. 7.N.2.3:Multiply and divide integers in a variety of situations; use efficient and generalizable procedures, including standard algorithms.

Teaching Materials

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