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

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**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 9 February • First exam: 11 February • Sample questions will be posted on the website. Answers later. • Class Notes: purchase at the bookstore; you need to have them by February 11th.**Let’s add in Alphabitia**BCD+ DB BCD is DB is BCD + DB is**You try:**B0B+ABC Use the manipulatives or draw pictures to help explain your answer.**Exploration 3.1**• In your groups: Do Part 1, #1 and #2a**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**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.**Addition and Place Value**• If we have 154 + 69**Mental Arithmetic**• 39 + 57**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**The name of the method is not important**• Put down your pencil • 68 + 74 • How did you do this? • How might children do this?**You try…**• 23 + 96 • 489 + 723**Estimation**• Get a QUICK answer that is close but not necessarily exact!**You have 5 seconds**382 + 147**Estimation**382 + 147 Actual answer: 529 Ways to estimate: 380 + 150 = 530 400 + 150 - 20 = 530 375 + 150 = 525 390 + 140 = 530**You try:**• 45 + 87 • 391 + 1472**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**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.**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.**Explain the math**348+ 472 10 11 7 820**Explain the math**471+ 299 10 160 600 770 How is this different from the previous example?**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.