Download Properties I

Assigning a PROPERTY NAME to things you already know how to do!!
Properties of Numbers
2.1 p. 66
Working with Properties
This lesson gives a “mathematical property”
name to the things you already know how to
do. Properties are guidelines that let you
know what you can and cannot do with
values.
LEARN THESE PROPERTIES!!!!!! We will refer to
them all year!!!!!!!!!!
Highlight the key definition words.
Vocabulary
Property/Operations
Meaning
Examples
Commutative
Changing ORDER does not
change the value
5(6) = 6(5)
6+5=5+6
Multiplication and Addition
Multiplication and Addition
Changing the GROUPING does (5 x 4) x 6 = 5 x (4 x 6)same order
not change the value
5 + (4 + 6) = (5 + 4) + 6 same order
Zero Property
Any term multiplied by 0 = 0
Associative
6(0) = 0
ONLY multiplication
Identity Properties
Addition:
Multiplication:
Adding 0 to any term does not 5 + 0 = 5
change its value
( 0 is the additive identity)
Any term multiplied by 1 will
keep its value
5(1) = 5
( 1 is the multiplicative identity)
Look for what is different!
Algebra
Algebra
a+b=b+a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
Ordering
Grouping
Commutative
Associative
Carlos rented golf clubs for $7 and a golf cart
for $12. He paid $23 in green fees. How much
did he spend on his golf game?
7 + 12 + 23 =
Show this grouping in your notes.
(30) + 12
Look for sums that are multiples of 10
This is using the commutative property
Use the Associative Property to
make groups of compatible
numbers.
Carlos paid $42.00
You are learning
I KNOW you
the PROPERTY
already know
NAME of what
how to do this.
you are doing!
8  3  5.
Look for products that are
multiples of 10
This is the Commutative Property.
Show this grouping in your notes.
40 (3)
120
Use the Associative Property to
group compatible numbers.
Think (3 ) 4 x 10
Reviewing Identity Properties p. 67
When a number retains its “identity,” the value
remains the same.
Identity Property of Addition a + 0 = a
12 + ? = 12 You can add 0 to any number, and
its value stays the same.
******************************************
Identity Property of Multiplication a(1) = a
10 ∙ 1 = 10 You can multiply any value by 1 and
its value stays the same.
So . . . . . .
0 can be called the “additive identity.”
1 can be called (I love this one . . . . .)
the “multiplicative identity”
REMEMBER…..
The Zero Property of Multiplication is NOT an
identity property. It says any number ( 0 ) = 0
5∙0=0
a∙0=0
Look for sums that are
multiples of 10
(81 + 6) + 9.
(6 + 81) + 9 =
This uses the commutative property.
6 + (81 + 9 ) =
6 + 90 =
96
The Associative Property shows
the new groups of compatible
numbers.
I prefer the more direct approach…….
81 + 9 + 6 = 96
Using Mental Math to Simplify
6 + 7 + 14
8 + 0 + 2 + (-7)
20 + 7 = 27
10 + (-7) = 3
5 + 12 + 18 + 5
10 + 30 = 40
19 + (-30) + 21
40 + (-30) = 10
Check Understanding
There is a grocery receipt on p. 68 of your text.
Use math properties to find the sum spent on
groceries.
$ 2.30 + 1.80 + 2.20
$ 2.30
1.80
2.20
$ 2.30 + 1 + 2 + 1 = $6.30
25 ∙ 3(4)
25 (4) ∙ 3
100∙ 3 = 300
3 ∙ 1 ∙ (-5) ∙ 8
3(-5)8
3(-40) = -120
2(-8)(-15)
2(-15)(-8)
(-30)(-8) = 240
5 ∙ 9 (6) ∙ (-2) (-1)
5 ∙ (-2) (6)(9) (-1)
(-10)(-54) = 540
Recap . . . . . Review
• Name that property:
1.
2.
3.
4.
5.
6.
7.
(Use the choices in your notes)
5x1=5 E
6xn=nx6 B
8+0=8 F
(3∙ 2) ∙ 5 = 3 ∙ (2 ∙ 5) D
12 + 4 = 4 + 12 A
2 + (5 + n) = (2 + 5) + n C
(5-5) + 3 = 3 (tricky!) F
8. (3-2) x 5 = 5 E
9.
+
=
+
A
10. (a+b) + c = (b+a) + c (be careful!) A
What Have We Accomplished?
• Hopefully, we have assigned property names
to mental processes you already know how to
do.
• Learn the property names. You will refer to
them all year.