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.

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

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


Announcements
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
Let’s add in Alphabitia

BCD+ DB

BCD is DB is BCD + DB is


You try
You try:

B0B+ABC

Use the manipulatives or draw pictures to help explain your answer.


Exploration 3 1
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
Operations with Whole Numbers

Whole numbers:

0, 1, 2, 3, 4, 5, …

Operations:

+ ─ × ÷


Addition of whole numbers

0 2 4 6 8 10

a

b

c

Addition of Whole Numbers

  • Ways to represent addition:

  • 1. Counters

  • 2. Number Line

  • 3. Part-Part Whole


Vocabulary
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
Addition and Place Value

  • If we have 154 + 69


Mental arithmetic
Mental Arithmetic

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

39 + 57



Mental arithmetic1
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 try1
You try…

  • 23 + 96

  • 489 + 723


Exploration 3 2
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
Estimation

  • Get a QUICK answer that is close but not necessarily exact!



Estimation1
Estimation

382 + 147

Actual answer: 529

Ways to estimate:

380 + 150 = 530

400 + 150 - 20 = 530

375 + 150 = 525

390 + 140 = 530


You try2
You try:

  • 45 + 87

  • 391 + 1472


Estimation vs exact answer
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
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

348+ 472 10 11 7

820


Explain the math1
Explain the math

471+ 299 10 160 600

770

How is this different from the previous example?


Explain why the child made the mistake
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
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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