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

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 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.

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

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

- 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

You try…

- 23 + 96
- 489 + 723

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?

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.

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

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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