# DISTRIBUTIVE PROPERTY MULTIPLICATION OVER ADDITON (4+2) = (7X4) DISTRIBUTIVE PROPERTY MULTIPLICATION OVER ADDITON (4+2) = (7X4) + (7X 2) = 7X 6 D 1. (3X 7) + (3X 2) = _____

2. (6X 3) + (6X 5) = B _____ C 3. (8X2) + (8X 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. A. 3 X 7 X 2 B. 6 X (3+ 5)

C. 8 X 2+ 8 X 4 4 D. 3 X 9 E. 6 + 5 + 3 F. (8 X 2) + (4+2) = (7X4) + (7X 2) = 7X 6 TOGETHER WE WILL DISCOVER

WAYS TO SHOW OR MODEL OUR UNDERSTANDING OF THE DISTRIBUTIVE PROPERTY (7X4) + (7X 2) = 7X 6 7(4+2) = (7X4) + (7X 2 7(4+2) = (7X4) + (7X 2) = 7X 6 TAKE A LOOK DO YOU SEE PATTERNS THAT CAN HELP EXPLAIN

THE DISTRIBUTIVE PROPERTY ? (7X4) + (7X 2) = 7X 6 7(4+2) = (7X4) + (7X 2 7(4+2) = (7X4) + (7X 2) = 7X 6 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) = 7X 6 7(4+2) = (7X4) + (7X 2 7(4+2) = (7X4) + (7X 2) = 7X 6

HOW CAN BOTH EXPRESSIONS BE EQUAL IF ONLY ONE OF THEM HAS PARENTHESES? THE SOLUTION (4+2) = (7X4) + (7X 2) = 7X 6 WE CAN REPRESENT

THE DISTRIBUTIVE PROPERTY USING PICTURES AND MODELS (7X4) + (7X 2) = 7X 6 7(4+2) = (7X4) + (7X 2 7(4+2) = (7X4) + (7X 2) = 7X 6 A PICTORIAL VIEW OF THE DISTRIBUTIVE PROPERTY (8X2) + (8X 4) = 8X (2+4)

(8X2 ) (8X4 ) 16 (8X6 ) 32

(7X4) + (7X 2) = 7X 6 7(4+2) = (7X4) + (7X 2 7(4+2) = (7X4) + (7X 2) = 7X 6 IT IS YOUR TURN TO MODEL THIS ONE (3X 5) + (3X 3) = 3X (___+ ___) (3X5

(3X3 ) ) Build the two arrays for this problem. Think about which two numbers belong in the blanks spaces 3X (_? + _?) (3X8 )

(7X4) + (7X 2) = 7X 6 7(4+2) = (7X4) + (7X 2 7(4+2) = (7X4) + (7X 2) = 7X 6 IT IS YOUR TURN TO MODEL THIS ONE (2X10) (2X2)

Build the two arrays for this problem. Do you know the number that belongs in the blanks space? s (2 X 12) 2 X (10 + _?) (7X4) + (7X 2) = 7X 6 7(4+2) = (7X4) + (7X 2 7(4+2) = (7X4) + (7X 2) = 7X 6 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) = (7X4) + (7X 2) = 7X 6 EXAMPLE: CAN YOU USE THE MODEL TO WRITE THE EQUIVALENT EXPRESSIONS?

7(4+2) = (7X4) + (7X 2) = 7X 6 CAN YOU USE THE MODEL TO WRITE THE EQUIVALENT EXPRESSIONS? 7(4+2) = (7X4) + (7X 2) = 7X 6

CAN YOU USE THE MODEL TO WRITE THE EQUIVALENT EXPRESSIONS? 7(4+2) = (7X4) + (7X 2) = 7X 6 CAN YOU USE THE MODEL TO WRITE THE EQUIVALENT EXPRESSIONS? 7(4+2) = (7X4) + (7X 2) = 7X

6 CAN YOU USE THE MODEL TO WRITE THE EQUIVALENT EXPRESSIONS? 7(4+2) = (7X4) + (7X 2) = 7X 6 CAN YOU USE THE MODEL TO WRITE THE EQUIVALENT

EXPRESSIONS? (4+2) = (7X4) + (7X 2) = 7X 6 WHAT DO YOU NOTICE ABOUT EACH EXPRESSION INSIDE THE PARENTHESES? EACH SUM INSIDE THE PARENTHESES IS 7

(4+2) = (7X4) + (7X 2) = 7X 6 REPRESENT 4X9 THREE DIFFERENT WAYS BY SHADING THE GRIDS ON YOUR RECORDING SHEET