3rd Grade - Multiply Numbers In Any Order

 Grade Level: 3rd Skill: Multiplication and Division Topic: Multiply Numbers in Any Order Goal: Recognize and use the commutative and associative properties of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?). Skill Description: Algebra and Functions: commutative and associative properties, multiplication The ability to understand that the order and grouping of multiplication factors does not change the product.

Sample Problems

 (1) Define commutative property of multiplication. (When numbers are multiplied, the order of the factors can be changed without changing the product.) (2) Define associative property of multiplication (When numbers are multiplied, the factors can be grouped in different ways without changing the product.) (3) Give an example of the commutative property of multiplication. (e.g. 3 x 4 = 4 x 3) (4) Give an example of the associative property of multiplication. (e.g. (5 x 3) x 4 = 5 x (3 x 4). (5) What do the parentheses mean in mathematical problems? (Do that operation first.)

Online Resources

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Extra Help Problems

 (1) Write the order that you would do these calculations to make them as quick and easy as possible: 10 x 3 x 2 [(10 x 3) x 2 = 60] (2) 2 x 10 x 4 [(10 x 4) x 2 = 80] (3) 4 x 10 x 3 [(4 x 10) x 3 = 120] (4) 3 x 2 x 5 [(5 x 3) x 2 = 30] (5) 5 x 4 x 2 [(5 x 4) x 2 = 40] (6) 50 x 14 x 2 [(50 x 2) x 14=100 x 14=1400] (7) 4 x 9 x 25 [(25 x 4) = 100 x 9 = 900] (8) 4 x 8 x 5 [(8 x 5) = 40 x 4 = 160] (9) 20 x 6 x 5 [(20 x 5) = 100 x 6 = 600] (10) 15 x 7 x 2 [(15 x 2 ) = 30 x 7 = 210] (11) 5 x 7 is the same as 7 x ? (5) (12) 8 x 9 is the same as ? x 8 (9) (13) 20 x 5 is the same as ? x ? Use the commutative property. (5 x 20) (14) 9 x 5 = 45 ? x 9 = 45 (15) Change the parentheses to show the associative property of multiplication: (4 x 3) x 2 = 4 x 3 x 2 (3 x 2) (16) 8 x (6 x 10) = 8 x 6 x 10 (8 x 6) (17) 5 x (3 x 7) = 5 x 3 x 7 (5 x 3) (18) 9 x 8 = ? x ? Show the commutative property. ( 8 x 9) (19) ? x ? = 6 x 4 Show the commutative property. (4 x 6) (20) Your neighbor, Billy, can’t seem to remember his 8 times tables. He always seems to get stuck on 8 x 2. He knows his 2 times tables. Can you give him a clue that could help him remember his 8s? (Tell Billy to think of 2 x 8 instead of 8 x 2) (21) Gina sells lemonade outside of her house. She needs to add \$5 + \$6 + \$10 to figure out how much money she’s made, but it’s taking her a long time. Is there a way you could help Gina solve the problem quickly? (Tell her to add \$5 + \$10 first and then add the \$6) (22) 4 x 5 = 5 x ? (4) (23) 20,000 x 9 = 9 x ? (20,000) (24) Is 10 – 7 the same as 7 – 10? (No, the commutative property doesn’t work for subtraction) (25) Is 120 divided by 6 the same as 6 divided by 120? (No, the commutative property doesn’t work for division)