1. Warm up problem: What is wrong with saying 372 base 6 ? What is a better way of writing this number in base 6?

2. Exploring Addition Addition in Alphabitia Exploration 3.1, Part 1 Use manipulatives to help you

3. Homework for Wednesday Read Section 3.1 in the textbook Exercises pp. 150-151: 5, 6, 24

4. Important announcements First exam: Wednesday, September 19th 1.2, 1.3, 1.4, 1.7; 2.3; 3.1, 3.2 and Explorations Last day to drop without a W is 9/14 Pick up 302A packet at the bookstore-- need by Monday, September 17th

5. Mental addition 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

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

7. Vocabulary of addition 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.

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

9. 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

10. No pencils! 23 + 96 489 + 723

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

12. 5 seconds to get a quick estimate 382 - 147

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

14. You try some 45 + 87 391 + 1472

15. 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

16. 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.

17. 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.

18. Explain the math 348 + 472 10 11 7__ 820

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

20. 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.

21. Subtraction Take-away Comparison

22. Subtraction vocabulary 89Minuend - 24 Subtrahend 65 Difference

23. Strategies Break the number apart Using negative numbers Adding up

24. The Standard Algorithm