1. February 3, 2009 If only you and dead people can read “hex” (base 16), then how many people can read “hex”?

2. February 3, 2009 Another homework note Buy Class Notes in bookstore Exam 1: Thursday, 2/12 Covers 1.2 – 1.4, 1.7, 2.3, 3.1, 3.2 in text, explorations 1.1, 1.4, 1.7, 2.7, 2.9, 3.1, 3.6 and notes/problems from class. Sample questions online Drop deadline: Tuesday, 2/10 Section 3.1 covered today

3. Homework note Most of you mentioned in the darts problem that odd + odd + odd + odd = even Why is this true?

4. Review Start with the number 141 (base 10) 1.Write it in Roman, Mayan, Egyptian, Babylonian and Alphabetian. 2.Next, write it in base 6, base 16 & base 2.

5. Review (answers) 141: 1.CXLI       A0CA

6. Review (answers) 141: 2.Base 6: 353 Base 16:8d Base 2:10001101

7. 3.1 - Addition Ways to represent addition: 1.Counters 2.Number Line 3.Part-Part Whole a b c 0 2 4 6 8 10

8. 3.1 (cont’d) Vocabulary: for 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.

9. 3.1 (cont’d) Addition and place value: Ex: If we have 154 + 69

10. 3.1 (cont’d) Mental Arithmetic (see also Expl. 3.3) Ex: 39 + 57 Leading digit (30 + 50) + (9 + 7) Compensation (40 – 1) + 57 then, (40 + 57) – 1 Break and Bridge (39 + 50) + 7 Compatible Numbers (39 + 51) + 6

11. 3.1 (cont’d) The name of the method is NOT important – only the strategy is. Ex: Sit on your hands – no writing allowed Find 68 + 74 How did you do this? How might children do this?

12. 3.1 (cont’d) More to try: Ex: 23 + 96 Ex: 489 + 723 Note: In mental arithmetic, you still want the exact answer!

13. 3.1 (cont’d) Estimation: Like mental arithmetic, this gives a quick answer BUT unlike mental arithmetic, estimation is close, but not exact!

14. 3.1 (cont’d) Estimation: Quick, estimate: 382 – 147

15. 3.1 (cont’d) 382 – 147 Actual (exact) answer: 235 Ways to estimate: 380 – 150 = 230 400 – 150 – 20 = 230 375 – 150 = 225 385 – 145 = 240 390 – 140 = 250

16. 3.1 (cont’d) More estimation (you try these): Ex: 45 + 87 Ex: 391 + 1472

17. 3.1 (cont’d) Estimates vs. Exact Answers Are the given addends exact, or estimates? Is the exact value of the sum required? In general, values that change frequently (like population), measurements (like weight) and predictions (like the chance of rain) are estimates

18. 3.1 (cont’d) Rounding: When you estimate, you are rounding to the nearest hundred, million, etc. If you round up, you will get an overestimate. If you round down, you will get an underestimate.

19. Homework Due Thursday, 2/5: Read section 3.1 (pages 128 – 150) Do textbook problems listed on website