Transcript Properties of Addition - Mrs. McDavid's 3rd Grade Website

Properties of
Addition
Lesson 1-4
Three Properties of Addition
1. Commutative
2. Associative
3. Identity
The Commutative Property
• Background
– The word commutative comes from the
verb “to commute.”
– Definition on dictionary.com
• Commuting means changing, replacing, or
exchanging
– People who travel back and forth to
work are called commuters.
• Traffic Reports given during rush hours are
also called commuter reports.
Here are two families of commuters.
Commuter
B
Commuter
A
Commuter A & Commuter B
changed lanes.
Remember… commute
means to change.
Commuter
B
Commuter
A
Here is another example…
Think of this hypothetical situation:
Every day you ride your bike to school.
The distance from home to school is 2 miles.
The distance from school to home is also 2 miles.
How do we know this?
Did you notice that hypothetical and hypothesis look almost the same?
Hmmmm... Think about what hypothesis means…
Home
School
The distance from Home to School is the
same as the distance from school to home.
Home + School = School + Home
H+S=S+H
A+B=B+A
The Commutative Property
A+B=B+A
Three Properties of Addition
1. Commutative
2. Associative
3. Identity
The Associative Property
• Background
– The word associative comes from the
verb “to associate.”
– Definition on dictionary.com
• Associate means connected, joined, or
related
– People who work together are called
associates.
• They are joined together by business, and
they do talk to one another.
Let’s look at another hypothetical situation
Three people work together.
Associate B needs to call Associates A and
C to share some news.
Does it matter who he calls first?
Here are three associates.
B calls A first
He calls C
last
B
A
If he called C first,
then called A, would
it have made a
difference?
NO!
C
(The Role of Parentheses)
• In math, we use parentheses to show groups.
• In the order of operations, the numbers and
operations in parentheses are done first.
(PEMDAS)
So….
The Associative Property
The parentheses identify which two associates talked first.
(A + B) + C = A + (B + C)
B
A
B
THEN
THEN
C
A
C
Three Properties of Addition
1. Commutative
2. Associative
3. Identity
The Identity Property of Addition
I am me!
You cannot change
My identity!
Zero is the only number
you can add to something
and see no change.
Identity Property of Addition
+0=
A+0=A
Let’s practice !
Look at the problem.
Identify which property it represents.
(9 + 8) + 7 = 9 + (8 + 7)
The Associative Property of Addition
It is the only addition property that
has parentheses.
12 + 0 = 12
The Identity Property of Addition
It is the only addition property that
has two addends and one of them
is a zero.
9+7=7+9
The Commutative Property of Addition
It is the only addition property that
has numbers that change places.
4+6=6+4
The Commutative Property of Addition
Numbers change places.
3+0=3
The Identity Property of Addition
See the zero?
(4 + 3) + 2 = 4 + (3 + 2)
The Associative Property of Addition
It has parentheses!
a+0=a
The Identity Property of Addition
Zero!
a+b=b+a
The Commutative Property of Addition
Moving numbers!
(a + b) + c = a + (b + c)
The Associative Property of Addition
Parentheses!
B
A
C