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
0
• 3. Part-Part Whole
2
4
6
a
c
8
10
b
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.