MODULE 1 LESSON 6.notebook
DO NOW
Simplify
(a) (2 + 4)(6 + 8) (b) 2 + 4(6 + 8)
(c) 2 + (4 + 6)(8)
(d) 2(4 + 6) + 8
(e) 8(2 + 4)(6)
(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
Unit 1 - Lesson 6
Lesson Goals:
Students will use the structure of an expression to identify ways to rewrite it.
Students will use the distributive property to prove that expressions are equivalent expressions.
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MODULE 1 LESSON 6.notebook
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...
a) 21
b) 15
c) 18
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MODULE 1 LESSON 6.notebook
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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MODULE 1 LESSON 6.notebook
1. Insert parentheses to make each statement true.
( ( 5
MODULE 1 LESSON 6.notebook
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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MODULE 1 LESSON 6.notebook
Rosemary says that collecting like terms can be seen as an application of the distributive property. Is she correct?
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MODULE 1 LESSON 6.notebook
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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MODULE 1 LESSON 6.notebook
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?
Multiplication Table
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MODULE 1 LESSON 6.notebook
Given that a > b, which of the shaded regions is larger and why?
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MODULE 1 LESSON 6.notebook
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 11
MODULE 1 LESSON 6.notebook
Distribute:
2(3x + 7y ­ 10) =
3x(2x + 9) =
x(x2 + 2x ­ 3) =
2x(4x + 6y + 8) =
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MODULE 1 LESSON 6.notebook
THE BOX METHOD
A simple way to use a picture to multiply polynomials
Example: Draw a picture to represent the expression:
(a + b + 1) x (b + 1)
(a + b + 1)
(b + 1)
Use the distributive property to find the product of (a + b + 1) and (b + 1).
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MODULE 1 LESSON 6.notebook
Example:
Draw a picture to represent the expression (x + y + 7)(y + 10)
Write an equivalent expression by applying the distributive property
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MODULE 1 LESSON 6.notebook
Example:
Draw a picture to represent the expression (b + 9)2.
Write an equivalent expression by applying the distributive property
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MODULE 1 LESSON 6.notebook
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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MODULE 1 LESSON 6.notebook
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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MODULE 1 LESSON 6.notebook
Homework
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MODULE 1 LESSON 6.notebook
BONUS
Homework
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