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Number Properties

Essential Question: How can you select the representation that models one of the arithmetic properties (commutative, associative, or distributive) ? . Number Properties. SPI: 0606.1.4) /CC.6EE.3 /CC.6EE.4 / CC.6.EE.2. Investigation. What is the value of this expression? 5 + 2 + 4= ?

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Number Properties

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  1. Essential Question: How can you select the representation that models one of the arithmetic properties (commutative, associative, or distributive)?  Number Properties SPI: 0606.1.4) /CC.6EE.3 /CC.6EE.4 / CC.6.EE.2

  2. Investigation What is the value of this expression? 5 + 2 + 4= ? What is the value of this expression? 4 + 5 + 2= ? Explain why the value you determined is the same for both expressions.

  3. Commutative Property The order in which numbers are added or multiplied does not change the sum or product. Examples: Numbers: 13 + 6 = 19 10 x 7 = 70 6 + 13 = 19 7 x 10 = 70 Letters: A + B = B + A Pictures: + = +

  4. Stop and Jot…. • How can you prove that order doesn't matter when adding or multiplying? • Check your Understanding: https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-exp-pattern-topic/cc-3rd-grade-properties-patterns/v/order-doesn-t-matter-when-purely-multiplying#!

  5. Commutative Property • Will the communicative property work for division and subtraction? Prove or disprove it…

  6. Associative Property The way in which numbers are grouped does not change the sum or product. Examples: Numbers: (7 + 2) + 9 = 18 (12 x 2) x 4 = 96 7 + (2 + 9) = 18 12 x (2 x 4) = 96 Letters: (A + B) + C = A + (B +C) Pictures: ( +) += + ( + )

  7. Example: Commutative Property (changing order): 6 - 4 = 2 where as 4 – 6 = -2 Example: Commutative Property (changing order): 6 - 4 = 2 where as 4 – 6 = -2 Stop and Jot…. • Does the commutative and associative property work for operations involving subtracting and dividing? Explain your reasoning using words and examples. • Check your Understanding: No; Commutative Property (changing order): 6 - 4 = 2 where as 4 – 6 = -2

  8. Distributive Property To multiply a sum by a number, multiply each addend by the number outside the parentheses Distribute 6 x (10 + 4) = (6 x 10) + (6 x 4) 60 + 24 = 84 Order of Operations 6 x (10 + 4) = 6 x (14) =84

  9. Distributive Property Factoring It Out by Place Value To use Mental Math Examples: Numbers: 54 x 2 = 50 x 2 + 4 x 2 100 + 8 108

  10. Distributive Property Letter: Picture: x ( + ) = ( x ) + ( x ) A x (B + C) = (A x B) + (A x C)

  11. Stop and Jot…. • How can you use the Distributive Property to multiply mentally? • Check your Understanding: 6 ● 99 = ? 6 ● 90 + 6 ● 9 Use the distributive property to break down the problem by place value. 540 + 54 594OR 6 (100 -1) = 6 (100) – 6 (1) Mental math by breaking down the numbers. 6 (99) = 600 – 6 100 – 1 = 99 594 = 594

  12. Guided Practice Name the property and explain why. • 2 x 15 = 15 x 2 • 4 x (2 + 1) = (4 x 2) + (4 x 1) • (3 x 6) x 2 = 3 x (6 x 2) Fill in the blank. Name the property. • 8 + (5 + 3) = (8 + __) + 3 • 6 x 7 = __ x 6 • 4 X (7 x __) = (4 x __) x 9 • 8 x (2 + __) = (8 x __) + ( __ x 4) • __ x 15 = __ x 12 Commutative; changing order Distributive; distributing 4 Associative; changing groups Associative; 5 Commutative; 7 Associative; 9; 7 Distributive; 4; 2; 8 Commutative; 12; 15

  13. Exit Ticket Record answers on Exit Ticket Let x, y, and z represent three different numbers. Use them to write equations showing each property. • commutative, • associative, and • distributive property

  14. Properties Project • Represent EACH property with a definition, numbers, letters, and pictures (symbols). (commutative, associative, distributive) • EACH property needs its own sheet of paper • Be creative, use graphics, but make sure content is accurate!!! View grading rubric.

  15. Don’t use my example!! Be creative and design your own!! Project Example Commutative Property - Changing order…… • Letters A + B = B + A • Numbers 96 + 14 = 14 + 96 • Picture or Symbols += +

  16. Additional Resources • Interactive Game: http://ltcconline.net/greenl/java/BasicMath/numberProperties.htm • Number Property Video: http://www.youtube.com/watch?v=7HFRH_M1nAc

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