Transcript Just the facts

Math Properties
Warm - up
Just-In
Power point
Just the Facts
Guided Practice
Developing Story
Independent Practice
Questions and Answers
Just In
(warm up)
Which problem situation matches the equation below?
(80 + 95+86+100+x) = 90
5
A) The weights of four packages are 80 ounces, 95 ounces, 86 ounces,
and 100 ounces. Find x, the sum of the weights of the four packages.
B) Juan talked 80 minutes, 95 minutes, 86 minutes, and 100 minutes on
his cell phone. Find x, the average time Juan talked on his phone.
C) Courtney’s first four quiz grades were 80, 95, 86, and 100. Find x, the
grade Courtney needs on her fifth quiz to have an average of 90.
D) The heights of four trees in a park are 80 feet, 95 feet, 86 feet, and
100 feet. Find x, the average height of the trees.
Just In
(warm up key)
Which problem situation matches the equation below?
(80 + 95 + 86 + 100 + x) = 90
5
A The weights of four packages are 80 ounces, 95 ounces, 86 ounces,
and 100 ounces. Find x, the sum of the weights of the four packages.
False, x is the missing weight of the package
B Juan talked 80 minutes, 95 minutes, 86 minutes, and 100 minutes on
his cell phone. Find x, the average time Juan talked on his phone.
False, the average time have already been identified as 90
C
Courtney’s first four quiz grades were 80, 95, 86, and 100. Find x, the
grade Courtney needs on her fifth quiz to have an average of 90.
True, in order to calculate the average, base on five items one number is missing
D The heights of four trees in a park are 80 feet, 95 feet, 86
feet, and 100 feet. Find x, the average height of the trees.
False, x is the missing value that related o the others numbers not a combine amount of what is
already given.
Developing Story
Just the Facts
• Hello Everyone, classrooms across the district are learning about
the properties of math.
• Properties are statements that are true for all numbers.
• During today’s math lesson, we will explore the characteristics for
each property and create a model of its function in order to
demonstrate the purpose and action of each.
Who can name and elaborate on the math properties?
Commutative
Distributive Property
Math
Properties
When I is
multiplied to a
factor, it does not
affect the
product.
•to spread
The order
in which two numbers are added or
out
Identity Property
multiplied does not change the sum or product
.
Commutative Property
Travel back and forth
Associative Property
To connect or
combine
When zero
is added to
a number, it
does not
change its
sum.
Identity Property
• The identity
property of zero.
states the number
0 can be added to
any real number
without changing
its value.
a+0=a
•
Workmat
Examples:
(positive integers)
(algebraic notation)
8+0=8
a+0=a
(negative integers)
-4 + 0 = -4
(fractions)
3/4 + 0 = 3/4
(decimals)
2.2 + 0 = 2.2
Identity Property
• The multiplicative
identity for the set of
all real numbers is 1
(one). Any real
number can be
multiplied by the
number 1 without
changing its value.
Workmat
(positive integers)
8*1=8
(algebraic notation)
a*1=a
•
(negative integers)
(decimals)
-8 * 1 = -8
(fractions)
2/5 * 1 = 2/5
2.2 * 1 = 2.2
Commutative
Property of Addition
• No matter he order
in which you add two
numbers, the sum is
always the same.
• Workmat
model
order a
different way
a + b
b
6+3
3+6
a+b=b+a
+
Let’s create a
model this
property.
=9
+ a
+
= 9
Commutative Property of Addition
model 8 + 5
•
a+b
8+5
workmat
• Different _o _r d_ _e _r
• b+a
5+8
workmat
+
+
= 13
= 13
Commutative
Property of Multiplication
• The order in which
two numbers are
multiplied does not
change its product.
a*b = b*a
Let’s use our
algebra tiles
to model this
property.
•
workmat
Order different way
Factors
will vary
( Associative)
Property of
Addition
(a + b) + c = a + (b + c)
(a * b) * c = c = (b * c)
• The way in which three numbers are grouped when added
or multiplied does not change the sum or product.
(a + b) + c = a + (b + c)
(6 + 3) + 4 = 6 + (3 + 4)
Associative of Addition Property
When you add three numbers
together, the sum will be the
same no matter how the
numbers are grouped.
(a*b) * c = c = (b * a)
(5*3) * 6 = 6 = (3 *5)
Associative of Multiplication Property
No matter how you group the
numbers when you multiply,
the answer will always be the
same product.
( Associative)
Property of Addition
Which expression can be written as
(1 + r) + s
Justify your response
A 1*+(r +s)
B 1 *(r *s)
C 1 +(r *s)
D 1 +(r +s)
(Associate )
Property of Multiplication
• A change in the way
multiplied numbers are
grouped does not affect
the product.
a x (b x c)
•
b x (a x c)
Associate- connect or combine.
workmat
a* (b* c)
Show a
different group
2* (6* 9)
(b*c) * a
(9*2) * 6
Distributive Property
• The Distributive Property allows the choice of
multiplication followed by addition or addition
followed by multiplication.
a (b + c) = ab + ac
3 (x+1) and 3x + 3 are equivalent
x
x
x
x
Distributive Property
A(B+C) = AB + AC
• Write an equivalent
expression for
3(x+2)
Picture Model using tiles
X
X
X
3*x + 3*2
Equivalent Representation
3x + 6
Distributive Property
Try this using your
algebra tiles
x
3(X - 2)
x
-
-
x
-
-
Describe in your
own words, the
distributive
property. Support
your description
with examples,
and draw a model
to illustrate the
property.
-
-
Distributive Property
• Model using algebra tiles
• (2+5)3
7*3
7
7
7
Can you apply your new info and
solve this problem ? Let’s try
• Jared deposited $5 into his
saving account. Six months
later, his account balance
had doubled. If his balance
was b dollars, which of the
following would be
equivalent to his new
balance of 2(b+5) dollars?
• F 2b + 5
H b + 10
• G 2b + 7
J 2b + 10
Developing Story
(Guided practice)
1. Which is an example of the Associative Property?
A 8+0=8
C 6+8=8+6
B 9 + 8 + 2 = 9 + (8+2)
D 5 * (12 +3) = 5 *12 + 5 * 3
2. Which property of 3(4+8) = (3*4) + (3*8) an example of?
A Associative
B Commutative
C
D
Distributive
Identity
3. Define in your own words and write an example of each property
A Commutative
B Identity
C Distributive
D Associative
Developing Story
(Guided practice key)
1. Which is an example of the Associative Property?
A 8+0=8
C 6+8=8+6
B 9 + 8 + 2= 9 + (8+2)
D 5 * (12 +3) = 5 *12 + 5 * 3
2. Which property of 3 * (4+8) = (3*4) + (3*8) an example of?
A Associative
C Distributive
B Commutative
D Identity
3. Define in your own words and write an example of each property:
Answers will vary
A Commutative- When you add numbers, regardless of the order, the sum
is the same. 4 + 8 = 12
8 + 4 = 12
B Identity - The sum of 0 and any number is the number. The product of 1 and any
number is the number. 6+0=6 a+0=a 6*1=6 a*1=a
C Distributive- To multiply the sum of two numbers, you can first add, then
multiply. Or you can first do each multiplication, then add.
4 x (5+2)
or 4 x 5 + 4 x 2
4x7
D Associative – multiply numbers, regardless of how they are
grouped. Example (4 x36)x19 = 4 x(36 x 19)