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 in Alphabitia CBD − ADC

3. Let’s subtract CBD - ADC= CBD is CBD - ADC is

4. You Try… D00 -B0B B0A - BD

5. You try: Use manipulatives or drawings to explain BBC - A0C A0A0D - BCA

6. Exploration 3.1 Part 2 #1 Write two subtraction story problems. One must require regrouping. Share these in your group. #2 What interpretations of subtraction can you describe?

7. Estimation 382 - 147 Actual answer: 235 Ways to estimate: 380 - 150 = 230 400 - 150 - 20 = 230 375 - 150 = 225 385 - 145 = 240 390 - 140 = 250

8. Subtraction Vocabulary: A - B = C A is the minuend B is the subtrahend C is the difference

9. 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).”

10. Pictorial Models Take away Comparison

11. 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

12. 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 …

13. Mental Subtraction Subtract mentally: 65 − 28

14. 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)

15. You try… and be ready to explain how you did it. Are there other ways? 73 - 82 97 - 39 301 - 293

16. Regrouping Show a diagram for 302 - 84

17. Start with…

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

19. You try: draw pictures 58 - 37 47 - 29

20. 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?

21. 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 7 1

22. 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

23. Use drawings or manipulatives to explain… Here is yet another one. 3 2 6 - 2 9 4 2 -7 0 1 0 0 100 - 70 + 2 = 132

24. 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