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

3. Announcements Last day to drop without a W is Friday, September 17th First exam: Tuesday, September 28th Sample questions will be posted on the website. Answers later. Class Notes: purchase at the bookstore; please get your copy as soon as possible.

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. Exploration 3.1 In your groups: Part 1 #1 Make up one addition story problem in Alphabitia and solve it. Read your problem to the other members of your group and discuss how you solved your problems. #2a

7. Operations with Whole Numbers Whole numbers: 0, 1, 2, 3, 4, 5, … Operations: +─×÷

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

9. 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: the commutative property. Since A + (B + C) = (A + B) + C every time, we give it a special name: the associative property.

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

11. Mental Arithmetic Add these numbers in your head—no pencil, paper, or calculator. 39 + 57

12. How did you do it?

13. 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

14. You try… 23 + 96 489 + 723

15. Exploration 3.2 Mental Addition Find the sums in the table mentally. Write a description of your method for finding each sum. Did you use the same technique for all of the sums? Discuss your methods with your group members. Did you all use the same technique for each sum? How many different techniques were used?

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

17. You have 5 seconds 382 + 147

18. Estimation 382 + 147 Actual answer: 529 Ways to estimate: 380 + 150 = 530 400 + 150 - 20 = 530 375 + 150 = 525 390 + 140 = 530

19. You try: 45 + 87 391 + 1472

20. 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

21. 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.

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

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

24. 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

25. 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.