EDU 290H PowerPoint

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A PowerPoint presentation/lesson on the properties of numbers and the distributive property.

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EDU 290H PowerPoint

  1. 1. Mental Math Warm - Up1. 18 + (2+7) = 272. (18+2) + 7 = 273. (95)  4 = 1804. 9 (54) = 180
  2. 2. Commutative Properties ofAddition and MultiplicationThe order of the values does NOT change the sum or product.
  3. 3. Commutative Property of Additionand Multiplication (Cont.) Arithmetic Algebra 7+3=3+7 a+b=b+a 24=42 ab=ba
  4. 4. Example 1
  5. 5. Associative Property ofAddition and Multiplication The grouping of the valuesdoes NOT change the sum or product.
  6. 6. Associative Property of Additionand Multiplication (Cont.) Arithmetic Algebra(2 + 7) + 3 = 2 + (7 + 3) (a + b) + c = a + (b + c) (9  4)5 = 9(4  5) (ab)c = a(bc)
  7. 7. At the Movies…Tickets Popcorn Candy DrinksChild - $3 Small - $3 Small - $2 Small - $1Adult - $5 Medium - $4 Medium - $3 Medium - $2Senior - $3 Large - $5 Large - $5 Large - $3 At the movies you buy an adult ticket, small popcorn, and a small drink. What was your total cost? $9 What property/properties could you use? Associative Property (5 + 3) +1 5 + (3 +1)
  8. 8. Example 2Use mental math and properties to solve thefollowing problem: 100  3  2(100  2)  3 Commutative Property100  (2  3) Associative Property= 100  6 Multiply within parentheses= 600 Solve
  9. 9. Identity Property ofAdditionThe sum of any number and zero is the original number. 7+0=7 0+x=x
  10. 10. Identity Property ofMultiplicationThe product of any number and 1 is the original number. 15  1 = 15 1b=b
  11. 11. Example 3Name each property shown.34=43 Commutative Property of Multiplicationz1=z Identity Property of Multiplication +★=★+ Commutative Property of Addition5(xy) = (5x)y Associative Property of Multiplication
  12. 12. Distributive Property To multiply a sum or difference, multiply each number within the parentheses by the number outside the parentheses. 3(2+6) = 3(2) + 3(6) (2-6)3 = 2(3) – 6(3) a(b+c) = a(b) + a(c) (b-c)a = ba – ca
  13. 13. Distributive Property(cont.)
  14. 14. Example 4Use the Distributive Property to find 20(102) mentally.20(102) = 20(100 + 2) Think of 102 as 100 + 220(100 + 2) = 20(100) + 20(2) Use Distributive Property= 2000 + 40 Multiply= 2,040 Add
  15. 15. Example 5You have 3 friends and want to give each friend 6cupcakes, 5 cookies, and 4 brownies. How many bakedgoods will you have all together? 3(6+5+4) 3(6) + 3(5) + 3(4) 18 + 15 + 12 = 45 baked goods
  16. 16.  = Cookies  = Brownies  = Cupcakes Friend 1:    Friend 2:    Friend 3:    Total:   = 45 baked goods Example 5 (cont.) We can also use mathematical models to demonstrate the distributive property.
  17. 17. Practice Problems1. 3(6+7) = ? 3(6) + 3(7) = 18 + 21 = 392. 4(22+3) = ? 4(22) + 4(3) = 88 + 12 = 1003. 6(b+5) = ? 6(b) + 6(5) = 6b + 304. 9(2h-1) = ? 9(2h) – 9(1) = 18h - 95. 3(5-3w) = ? 3(5) – 3(3w) = 15 – 9w
  18. 18. Practice Problems (Cont.)6. Suppose your friend wrote 7(2m+t) = 14m + t.What error did your friend make? What is thecorrect answer?He or she forgot to distribute the 7 to the variable t. The correct answer should be: 7(2m) + 7(t) = 14m + 7t
  19. 19. Picture Citations:Light Bulb Guy Picture (Slide 2) -http://www.cascadewellnessclinic.com/articles/2003art/0311art.shtmlShopping Bag Picture (Slide 5) –http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/structure/st275ma.htmDistributive Arrow picture (Slide 14) - http://www.coolmath.com/reference/math-dictionary-D.htmlDistributive Property Balance (Slide 13) -http://www.leslienettling.com/6thNewsletters/6thSep8-06.htm
  20. 20. Content CitationsBadur, Michalina Central Michigan University studentDavison, David M., Marsha S. Landau, Leah McCracken, and Linda Thompson. Prentice Hall Pre-algebra: Tools for a Changing World. Upper Saddle River, NJ: Prentice Hall, 2001. Print.

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