Announcements• Last day to drop without a W is

12 February

• First exam: 13 February

• Class Notes in the Bookstore. Need by 19 February. Cost is $3.50.

What is wrong with saying 372 What is wrong with saying 372 base 6base 6? ?

What is a proper way of writing this What is a proper way of writing this number in base 6?number in base 6?

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.

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

0 2 4 6 8 10

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 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 exact!

You will have 5 seconds

• 382 - 147

Estimation• 382 - 147• Actual answer: 235• Ways to estimate:• 380 - 150 = 230• 400 - 150 - 20 = 230• 375 - 150 = 225• 385 - 145 = 240• 390 - 140 = 250

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

problem?

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.

Assignment• Section 3.1 p. 150-151

#5, 6, 10, 24