Announcements Last day to drop without a W is 10 February First exam: 17 February Sample questions posted on website Class Notes in the Bookstore. Need by 10 February. Cost is $3.50.

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

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.

Let’s subtract CBD - ADC= CBD is ADC is CBD - ADC is

You Try… D00 -B0B B0A - BD

You try: Use manipulatives or drawings to explain BBC - A0C A0A0D - BCA

Exploration 3.1 In your groups: Do Part 1, #1 and #2a Then do Part 2, #1 and 2

Begin Addition 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: commutative property. Since A + (B + C) = (A + B) + C every time, we give it a special name: associative property.

Addition and Place Value If we have

Mental Arithmetic

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

The name of the method is not important Put down your pencil How did you do this? How might children do this?

You try…

Estimation Get a QUICK answer that is close but not exact!

You have 5 seconds

Estimation Actual answer: 235 Ways to estimate: = = = = = 250

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.

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

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

Explain why the child made the mistake is the same as is the same as is the same as Would the mistake have been made if manipulatives had been used? Explain.