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

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

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

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

  2. 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.

  3. Let’s add in Alphabitia BCD+ DB BCD is DB is BCD + DB is

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

  5. 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

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

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

  8. 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.

  9. Addition and Place Value • If we have 154 + 69

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

  11. How did you do it?

  12. 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

  13. You try… • 23 + 96 • 489 + 723

  14. 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?

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

  16. You have 5 seconds 382 + 147

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

  18. You try: • 45 + 87 • 391 + 1472

  19. 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

  20. 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.

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

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

  23. 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

  24. 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.

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