MODULE 1 LESSON 6.notebook 1 DO NOW Simplify (a) (2 + 4)(6 + 8) (c) 2 + (4 + 6)(8) (b) 2 + 4(6 + 8) (e) 8(2 + 4)(6) (d) 2(4 + 6) + 8 (f) 4(2 + 6) + 8 In your own words, describe what the distributive property is, or what it means.
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MODULE 1 LESSON 6.notebook
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DO NOWSimplify(a) (2 + 4)(6 + 8)
(c) 2 + (4 + 6)(8)
(b) 2 + 4(6 + 8)
(e) 8(2 + 4)(6)
(d) 2(4 + 6) + 8
(f) 4(2 + 6) + 8
In your own words, describe what the distributive property is, or what it means.
MODULE 1 LESSON 6.notebook
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Unit 1 - Lesson 6
Students will use the structure of an expression to identify ways to rewrite it.
Lesson Goals:
Students will use the distributive property to prove that expressions are equivalent expressions.
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Use only the addition and multiplication operations and the numbers 1, 2, 3, and 4 each exactly once, to build a numeric expression (with parenthesis to show order used to build the expression) that evaluates to...
b) 15
a) 21
c) 18
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Using the numbers 1, 2, 3, and 4 (each exactly once), what is the largest number you can create using only addition, multiplication, and parenthesis (if you want)?
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1. Insert parentheses to make each statement true.
( )( )
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Luis wants to play the 4‑number game with the numbers 1, 2, 3, and 4 and the operations of addition, multiplication, AND subtraction.
Brendon responds, “Or we could just play the 4‑number game with just the operations of addition and multiplication, but now with the numbers –1, –2, –3, –4, 1, 2, 3, and 4 instead.”
What observation is Brendon trying to point out to Luis?
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Rosemary says that collecting like terms can be seen as an application of the distributive property. Is she correct?
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3 + 3 + 3 + 3 + 3 + 3 =
What is another way we could write this problem?
3x + 3x + 3x + 3x =
What is another way we could write this problem?
(3 + x) + (3 + x) + (3 + x) + (3 + x) + (3 + x) =
What is another way we could write this problem?
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Multiplication Table
Ms. Benjamin wants to explain how to read the table to her daughter, MiMi. In your own words, how would you explain the table to MiMi?
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Given that a > b, which of the shaded regions is larger and why?
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Distributive Property
The Distributive Property of Multiplication is the property that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. The Distributive Property says that if a, b, and c are real numbers, then:
a(b + c) = ab + ac
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Distribute:
2(3x + 7y 10) =
3x(2x + 9) =
x(x2 + 2x 3) =
2x(4x + 6y + 8) =
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THE BOX METHOD
A simple way to use a picture to multiply polynomials
Example: Draw a picture to represent the expression:
(a + b + 1) (b + 1)x
(a + b + 1) (b + 1)
Use the distributive property to find the product of (a + b + 1) and (b + 1).
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Example:
Draw a picture to represent the expression (y + 10)(x + y + 7)
Write an equivalent expression by applying the distributive property
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Example:
Draw a picture to represent the expression (b + 9)2.
Write an equivalent expression by applying the distributive property
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Draw a picture to represent the expression (a + b)(c + d)(e + f + g). * Just draw the picture...you do not have to distribute to find the product.
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Shannon thinks that (a + b)2 = a2 + b2. Is she correct? Use a picture to illustrate your reasoning.
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MODULE 1 LESSON 6.notebook
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Homework
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BONUS
Homework
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