NUMBER THEORY

ARRAY A set of objects (or numbers) ARRANGED in rows and columns

ARRAYS Each Row has SAME number of objects. Each Column has the SAME number of objects. Each Array has a rectangular shape

WHY ARE THESE NOT ARRAYS?

HOW DO WE NAME ARRAYS? x number in each row

2 x 6 = 12 (2 Rows of 6) 6 x 2 = 12 (6 Rows of 2)

3 x 4 = 12 4 x 3 = 12

Answer: 6 ways Answer: 6 ways

PATRICK MADE A MISTAKE NAMING THIS ARRAY: What should have he said?

CREATE ALL POSSIBLE ARRAYS FOR 20 (try using pennies)

GO TO NEXT SLIDE TO CHECK YOUR WORK

Commutative Property (Turn-around rule) The commutative property: The order in which you multiply numbers makes no difference in the product. Both arrays have the same product: 20. (4 x 5 = 5 x 4 )

Be Careful! Even though the commutative property says that 4 x 5 and 5 x 4 have the same product (20), they do not represent the same grouping. At recess, if 20 students want to play a game, 4 teams of 5 students is not the same as 5 teams of 4 students.

Problem Solving Challenge: (Source: The MATH FORUM)