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A Balancing Act

A Balancing Act. By Dawna Romney. Out of Balance. A scale with a different amount of units on each side is unbalanced. An inequality is like the unbalanced scale. 7 > 3 3 + 6 < 10. An equation is like a perfectly balanced scale.

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A Balancing Act

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  1. A Balancing Act By Dawna Romney

  2. Out of Balance • A scale with a different amount of units on each side is unbalanced. • An inequality is like the unbalanced scale. 7 > 3 3 + 6 < 10

  3. An equation is like a perfectly balanced scale. Both sides of a scale and an equation must contain the same amount of units. Equations and Scales 2 + 4 = 6 6 – 2 = 4

  4. Balance The Scales • In the Cube Factory, workers only get paid if all scales are balanced. • Someone is trying to sabotage the factory !!

  5. Mission: Keep the Scales Balanced ! • Your job is to keep the scales balanced. • You must undo all the deeds of the saboteur and save the factory ! • First figure out what the saboteur did to one side of the scale, then do the same thing to the other side to regain balance !

  6. Finished Scale. Case 1 • What Happened? • Two Cubes were taken from one side.

  7. Correction? Case 1 • Take two cubes from the other side ! You Did It !!!

  8. Three cubes were added to one side. Case 2 • Finished Scale. • What Happened?

  9. Add three cubes to the other side ! Case 2 • Correction ? Excellent !!

  10. Finished Scales: Case 3 • What Happened? • Hint: The same thing was done to both scales.

  11. Case 3 continued… • The number of cubes was tripled on one side. • Correction? • Triple the number of cubes on the other side! Wonderful !

  12. Mission Accomplished !! • You have successfully balanced the scales! • Whatever the saboteur did to one side, you did to the other! • Because an equation is like a balanced scale, we can apply the same principles to solving equations.

  13. The Golden Rule • Whatever you do to one side of an equation, You must do to the other side !!!

  14. Mathematically Speaking… If a = b, then: • a + c = b + c • a – c = b – c • a/c =b/c , where c = 0. • ac =bc

  15. Solving An Equation With One Variable • Decide what must be done to one side of the equation to get the variable alone. (This is like the sabotage at the factory !!) • Next use The Golden Rule to maintain “balance” and preserve the equation. (This is like the corrections at the factory !!)

  16. Practice, One Step At A Time ! X + 18 = 54 • Equation : -18 -18 • Sabotage and • Correction : • Solution : X = 36

  17. a = 31 Practice Makes Perfect ! a – 8 = 23 + 8 + 8

  18. More Practice!! 2x = 54 2x/2 = 54/2 x = 27

  19. Ready For Another One ? x/3 = 21 3(x/3) = 3(21) x = 63

  20. Next Time, The Two Step ! How would you handle this one? 2x + 8 = 24 to be continued…

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