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Mental Subtraction

Mental Subtraction. In your head, compute: 65 - 28 71 - 39 80 - 46 Explain what you did so that a second grader will understand. Subtraction. Vocabulary: A - B = C A is the minuend B is the subtrahend C is the difference. Try this:. Is A - B = B - A? 6 - 4 = 4 - 6?

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Mental Subtraction

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  1. Mental Subtraction In your head, compute: 65 - 28 71 - 39 80 - 46 Explain what you did so that a second grader will understand.

  2. Subtraction • Vocabulary: • A - B = CA is the minuendB is the subtrahendC is the difference

  3. Try this: • Is A - B = B - A? • 6 - 4 = 4 - 6? • What is true of 6 - 4 and 4 - 6? • One of the worst things we can say: “You can’t take a bigger number away from a smaller number.” Or “You have to put the bigger number first (in the minuend).”

  4. Pictorial Models • Take away • Comparison

  5. -2 -1 0 1 2 3 4 5 6 7 8 9 10 Number Line Model • 7 - 9 = -2 • Why is it important to start at 0?

  6. Four related facts • If 9 - 4 = 5, then9 - 5 = 4, 4 + 5 = 9, and 5 + 4 = 9 • You try: If 74 - 61 = 13, then …

  7. Mental Subtraction • Not as obvious as mental addition • 65 - 28Break apart the second number (65 - 20) - 8 • Adding up 28 + 30 = 58, 58 + 7 = 65, 30 + 7 • Compensation (65 + 2) - (28 + 2), 67-30 • Compatible Numbers (65 – 25, 40-3)

  8. The name of the strategy is not important… • You try… and be ready to explain how you did it. Are there other ways? • 73 - 82 • 97 - 39 • 301 - 293

  9. Regrouping Show a diagram for • 302 - 84

  10. 302 - 84 • Start with…

  11. Now, indicate what you are subtracting • 302 - 84: Let red be the part you take away

  12. You try: draw pictures • 58 - 37 • 47 - 29

  13. Subtraction the way you learned it… 6 7 8- 3 9 2 2 8 6 5 1 Why did you cross out the 6? Why did you put a little “1” next to the 7? Can you show this with pictures?

  14. Here are three other ways to think about subtraction • Explain why this works--use pictures or manipulatives 9 8 4- 3 6 8 6 1 6 1 7

  15. Why does this work? • This way worked because • 984 - 368 is the same as adding 10 to both numbers: • 984 + 10 = 980 + 4 + 10 = 980 + 14 • 368 + 10 = 360 + 8 + 10 = 370 + 8

  16. Use drawings or manipulatives to explain… • Here is yet another one. • 3 2 6- 2 9 4 2 -7 01 0 0 • 100 - 70 + 2 = 132

  17. A real problem • Place the digits 1, 2, 3, 6, 7, 8 in the boxes to obtain: • Greatest sumLeast sumGreatest differenceLeast difference

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