2. Announcements Last day to drop without a W is 10 February First exam: 17 February Sample questions posted on website Class Notes in the Bookstore. Need by 10 February. Cost is $3.50.

3. What is wrong with saying 372 base 6 ? What is a proper way of writing this number in base 6?

4. Let’s add in Alphabitia BCD + DB BCD is DB isBCD + DB is

5. You try: B0B +ABC Use the manipulatives or draw pictures to help explain your answer.

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

7. You Try… D00 -B0B B0A - BD

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

9. Exploration 3.1 In your groups: Do Part 1, #1 and #2a Then do Part 2, #1 and 2

10. Begin Addition Ways to represent addition: 1.Counters 2.Number Line 3.Part-Part Whole a b c 0 2 4 6 8 10

11. Vocabulary A + B = C A and B are called Addends C is called the Sum Since A + B = B + A every time, we give it a special name: commutative property. Since A + (B + C) = (A + B) + C every time, we give it a special name: associative property.

12. Addition and Place Value If we have 154 + 69

13. Mental Arithmetic 39 + 57

14. Mental Arithmetic 39 + 57 Leading digit (30 + 50) + (9 + 7) Compensation (40 - 1) + 57 Compensation (40 + 57) - 1 Break and Bridge (39 + 50) + 7 Compatible Numbers (39 + 51) + 6

15. The name of the method is not important Put down your pencil 68 + 74 How did you do this? How might children do this?

16. You try… 23 + 96 489 + 723

17. Estimation Get a QUICK answer that is close but not exact!

18. You have 5 seconds 382 - 147

19. 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

20. You try: 45 + 87 391 + 1472

21. Estimation vs. Exact Answer Are the exact values of the addends given? Is the exact value of the sum required? In general: changing values (like population), measurement values (like distance), and predictions (like 35% chance of rain) are estimates

22. Rounding When you estimate, you are rounding to the nearest ten, hundred, million, etc. If you round up, you are making an overestimation. If you round down, you are making an underestimation.

23. A problem: I am thinking of 3 numbers whose sum is greater than 70. Look at each statement below. Mark it as true or false. Be ready to explain why. All three numbers are greater than 20. If two of the number are less than 20, the other must be greater than 20.

24. Explain the math 348 + 472 10 11 7 820

25. Explain the math 471 + 299 10 160 600 770 How is this different from the previous problem?

26. Explain why the child made the mistake 341 + 287 is the same as 340 + 290 + 7 + 3 749 + 684 is the same as 700 + 600 + 49 + 1 + 84 + 16 322 + 468 is the same as 320 + 460 Would the mistake have been made if manipulatives had been used? Explain.