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Download Dr. Ginny Horak - University of Arizona Math
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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? • 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).” Pictorial Models • Take away • Comparison Number Line Model • 7 - 9 = -2 • Why is it important to start at 0? -2 -1 0 1 2 3 4 5 6 7 8 9 10 Four related facts • If 9 - 4 = 5, then 9 - 5 = 4, 4 + 5 = 9, and 5 + 4 = 9 • You try: If 74 - 61 = 13, then … Mental Subtraction • Not as obvious as mental addition • 65 - 28 Break 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) 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 Regrouping Show a diagram for • 302 - 84 302 - 84 • Start with… Now, indicate what you are subtracting • 302 - 84: Let red be the part you take away You try: draw pictures • 58 - 37 • 47 - 29 Subtraction the way you learned it… 5 1 678 - 392 286 Why did you cross out the 6? Why did you put a little “1” next to the 7? Can you show this with pictures? Here are three other ways to think about subtraction • Explain why this works--use pictures or manipulatives - 1 87 4 9 3 6 8 6 1 6 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 Use drawings or manipulatives to explain… • Here is yet another one. • - • 3 2 6 2 94 2 -7 0 1 00 100 - 70 + 2 = 132 A real problem • Place the digits 1, 2, 3, 6, 7, 8 in the boxes to obtain: • Greatest sum Least sum Greatest difference Least difference
