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 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:

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 Wholea 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: 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

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

39 + 57

How did you do it?

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 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

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.