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Tuesday, Oct. 25, 2011

Tuesday, Oct. 25, 2011. Bellwork : Integer Quiz. Think!. JaQuan’s time to complete the race this year was 27 minutes. If JaQuan’s time to finish the race was 6 minutes less than it was last year, how fast did he run the race last year?. What is an inverse operation?. Operations….

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Tuesday, Oct. 25, 2011

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  1. Tuesday, Oct. 25, 2011 Bellwork: Integer Quiz

  2. Think! JaQuan’s time to complete the race this year was 27 minutes. If JaQuan’s time to finish the race was 6 minutes less than it was last year, how fast did he run the race last year?

  3. What is an inverse operation?

  4. Operations… • Addition • Subtraction • Multiplication • Division

  5. INVERSE

  6. INVERSE

  7. INVERSE

  8. INVERSE

  9. INVERSE

  10. INVERSE

  11. 11 An INVERSE OPERATION undoes an operation

  12. What operation UNDOES addition? We can UNDO addition with subtraction

  13. 9 miles 4 miles What operation UNDOES addition?

  14. 9 miles 4 miles What operation UNDOES addition?

  15. 9 miles 4 miles Subtraction UNDOES Addition 4 miles + 5 miles – 5 miles puts us back where we started

  16. What operation UNDOES subtraction?

  17. What operation UNDOES subtraction?

  18. We can UNDO subtraction with addition 15,000 ft– 8,000 ft + 8,000 ft puts us back where we started

  19. Stand Up! Now Undo it!

  20. 11 With a Partner… (3 minutes) 1) Create a table and list the inverse operation for each operation below. 2) Then, in your own words, write a definition for Inverse Operation. Give two examples.

  21. We use INVERSE OPERATIONS to ISOLATE variables when solving equations =

  22. To solve an equation, first think about what is being done to the variable in the ORIGINAL equation. This is the DO in your Do/Undo table addition • x + 6 = 10 • y – 8 = 4 • 3p = 21 • s/4 = 5 subtraction multiplication division

  23. Then determine the inverse operation you will need to isolate the variable. This is the UNDO in your Do/Undo table. DO UNDO subtraction addition • x + 6 = 10 • y – 8 = 4 • 3p = 21 • s/4 = 5 addition subtraction multiplication division division multiplication

  24. What operation will you use to isolate the variables in the following equations? Hint: What is the “DO” operation in the original equation, and what operation will you use to “UNDO” it?. DO UNDO x – 7 = 14 y – 2 = 10 p – 20 = -5 Subtraction Addition

  25. 11 The Addition Property of Equality says that if you add the same thing to both sides of an equation, both sides remain equal. x – 12 = 14 x – 12 = 14 x = 26 * Have to add same thing to both sides! + 12 + 12

  26. 11 The Subtraction Property of Equality says that if you subtract the same thing from both sides of an equation, both sides remain equal. x + 6 = 11 x + 6 = 11 x = 5 * Have to subtract same thing from both sides! - 6 - 6

  27. 11 The Division Property of Equality says that if you divide both sides of an equation by the same number, both sides remain equal. -7x = 14 x = -2 * Have to divide both sides by same number! __ -7 __ -7

  28. These properties of equality help us solve equations by using inverse operations to find the value of the variable.

  29. 11 Once we solve, we check our answer to make sure it works in our original equation. We can remember these steps with DUCK . x – 12 = 14 x – 12 = 14 x = 26 26 – 12 = 14 14 = 14 Do Undo Check K + 12 + 12 

  30. 11 Practice with a Partner: What operation will you use to isolate the variables in the following equations? Create a Do/Undo table for each and solve using DUCK. Be sure to show all of your steps. x – 7 = 14 y + 2 = 10 -5p = -20

  31. 12 HOMEWORK: Solve Using DUCK For each equation, create a Do/Undo Table and show all steps in solving the equation, including the CK (Check your work!). • x – 4 = 10 • y + 11 = 3 • 8p = -32 • s – 6 = -8 • 9 + t = 15

  32. TICKET OUT THE DOOR What is an INVERSE Operation? Name the inverse operations for Addition Subtraction Multiplication Division

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