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.

Let’s add in Alphabitia BCD + DB BCD is DB isBCD + DB is

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

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

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

Addition of Whole Numbers Ways to represent addition: 1.Counters 2.Number Line 3.Part-Part Whole a b c

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

Mental Arithmetic Add these numbers in your head—no pencil, paper, or calculator

How did you do it?

Mental Arithmetic Leading digit ( ) + (9 + 7) Compensation (40 - 1) + 57 Compensation ( ) - 1 Break and Bridge ( ) + 7 Compatible Numbers ( ) + 6

You try…

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

Estimation Actual answer: 529 Ways to estimate: = = = = 530

You try:

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 the math

Explain the math How is this different from the previous example?

Explain why the child made the mistake is the same as is the same as is the same as

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.