Post on 22-Feb-2016
description
DISTRIBUTIVEPROPERTY
MULTIPLICATIONOVER
ADDITON
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
1. (3X 7) + (3X 2) = _____ 2. (6X 3) + (6X 5) = _____ 3. (8X2) + (8X 4) = _____
DBC
A. 3 X 7 X 2 D. 3 X 9B. 6 X (3+ 5) E. 6 + 5 + 3 C. 8 X 2+ 8 X 4 F. (8 X 2) +
4
Apply your knowledge of order of operations. Choose 3 expression from the blue box that have the same value
as expressions 1, 2, and 3 shown in the pink box.
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
TOGETHER WE WILL DISCOVER WAYS TO SHOW OR MODEL
OUR UNDERSTANDING OF
THE DISTRIBUTIVE PROPERTY
(7X4
) +
(7X
2)
= 7
X 6
7(
4+2)
= (
7X4)
+ (
7X 2
) =
7X
6
7(4+
2) =
(7X
4) +
(7X
2
TAKE A LOOKDO YOU SEE PATTERNS THAT CAN HELP EXPLAIN
THE DISTRIBUTIVE PROPERTY?
(7X4
) +
(7X
2)
= 7
X 6
7(
4+2)
= (
7X4)
+ (
7X 2
) =
7X
6
7(4+
2) =
(7X
4) +
(7X
2
HOW CAN BOTH EXPRESSIONS BE EQUAL IF ONLY ONE OF THEM HAS PARENTHESES?
WITHOUT THE PARENTHESES, THE TWO MULTIPLICATION
PROBLEMS WOULD BE SOLVED FIRST. THEN THE TWO VALUES
ADDED TOGETHER.
(7X4
) +
(7X
2)
= 7
X 6
7(
4+2)
= (
7X4)
+ (
7X 2
) =
7X
6
7(4+
2) =
(7X
4) +
(7X
2
HOW CAN BOTH EXPRESSIONS BE EQUAL IF ONLY ONE OF THEM HAS PARENTHESES?
THE SOLUTION
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
WE CAN REPRESENT
THE DISTRIBUTIVE PROPERTYUSING PICTURES AND MODELS
(7X4
) +
(7X
2)
= 7
X 6
7(
4+2)
= (
7X4)
+ (
7X 2
) =
7X
6
7(4+
2) =
(7X
4) +
(7X
2
A PICTORIAL VIEW OFTHE DISTRIBUTIVE PROPERTY
(8X2) + (8X 4) = 8X (2+4)
(8X2)(8X4)
(8X6)
16
32
(7X4
) +
(7X
2)
= 7
X 6
7(
4+2)
= (
7X4)
+ (
7X 2
) =
7X
6
7(4+
2) =
(7X
4) +
(7X
2
IT IS YOUR TURN TO MODEL THIS ONE
(3X5)
(3X3)
(3X 5) + (3X 3) = 3X (___+
___)
(3X8)
Build the two arrays for this problem.
Think about which two numbers belong in the blanks spaces
3X (_? + _?)
(7X4
) +
(7X
2)
= 7
X 6
7(
4+2)
= (
7X4)
+ (
7X 2
) =
7X
6
7(4+
2) =
(7X
4) +
(7X
2
IT IS YOUR TURN TO MODEL THIS ONE
(2X10) (2X2)
(2 X 12)
Build the two arrays for this problem.
Do you know the number that belongs in the blanks space? s
2 X (10 + _?)
(7X4
) +
(7X
2)
= 7
X 6
7(
4+2)
= (
7X4)
+ (
7X 2
) =
7X
6
7(4+
2) =
(7X
4) +
(7X
2
IT IS YOUR TURN TO MODEL THIS ONE
Build the two arrays for this problem.
What are two other ways to express(4 X 2) + (4 X 6)
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
EXAMPLE: CAN YOU USE THE MODEL TOWRITE THE EQUIVALENT EXPRESSIONS?
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
CAN YOU USE THE MODEL TO
WRITE THE EQUIVALENT EXPRESSIONS?
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
CAN YOU USE THE MODEL TO
WRITE THE EQUIVALENT EXPRESSIONS?
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
CAN YOU USE THE MODEL TO
WRITE THE EQUIVALENT EXPRESSIONS?
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
CAN YOU USE THE MODEL TO
WRITE THE EQUIVALENT EXPRESSIONS?
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
CAN YOU USE THE MODEL TO
WRITE THE EQUIVALENT EXPRESSIONS?
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
WHAT DO YOU NOTICE ABOUT EACH EXPRESSION INSIDE THE
PARENTHESES?
EACH SUM INSIDE THE PARENTHESES IS 7
7(4+
2) =
(7X
4) +
(7X
2)
= 7
X 6
REPRESENT
4 X 9 THREE DIFFERENT WAYS BY
SHADING THE GRIDS ON YOUR RECORDING SHEET