Engage NY Lesson 5 Pink Packet pages 1922 Write an expression to represent the temperature change In the morning Harrison checked the temperature outside to find that it was 12F Later in the afternoon the temperature rose 12F What was the afternoon temperature ID: 723108
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Slide1
Using the identity & Inverse to write equivalent expressions & Proofs
Engage NY: Lesson 5
Pink Packet pages 19-22Slide2
Write an expression to represent the temperature change.
In the morning, Harrison checked the temperature outside to find that it was -12°F. Later in the afternoon, the temperature rose 12°F. What was the afternoon temperature?
Write an expression to represent the temperature changeSlide3
What is the temperature change?
In the morning, Harrison checked the temperature outside to find that it was -12°F. Later in the afternoon, the temperature rose 12°F. What was the afternoon temperature?
What is the temperature change?Slide4
Rewrite subtraction as adding the inverse & find the sum
A) – 2
2 + (-2) = 0Slide5
Rewrite subtraction as adding the inverse & find the sum
B) -4 – (-4)
(-4) + 4 = 0 Slide6
Rewrite subtraction as adding the inverse & find the sum
D) g – g
g + (-g) = 0 Slide7
The sum of additive inverses equals___?
ZEROSlide8
Add or subtract
A) 16 + 0
16 + 0 = 16Slide9
Add or subtract
B) 0 – 7 =
0 + (-7) = -7
Slide10
Add or subtract
C) -4 + 0 =
-4 + 0 = -4Slide11
Add or subtract
D) 0 + d
0 + d = d Slide12
What patterns do you notice in 4a – 4d?
The sum of any quantity and zero is equal to the value of the quantity.Slide13
What is another word for opposites?
Additive InverseSlide14
What is the additive inverse or opposite of -12.5?
-12.5 + 12.5 = 0Slide15
What is the sum of a number & its opposite?
ZEROSlide16
Guess my number…
Your younger sibling runs up to you and excitedly exclaims, “I’m thinking of a number. If I add it to the number
ten times, that is,
my number
my number
my number… and so on, then the answer is
. What is my number?”
Justify your answer.
Slide17
Additive Identity Property of Zero
Zero is the
only
number
that when summed with another number, results in that number again.
This
property makes zero special among all the numbers, so special in fact, that mathematicians have a special name for zero, called the “additive identity”; they call that property the “
Additive Identity Property of Zero
.”
8 + 0 = 8
Slide18
Proofs…
Write down the problem
Work out each problem, showing every SINGLE LITTLE step
Write what property goes with each step you take
Use your pink packet vocabulary to help you.Slide19
Additive Identity Property of Zero
- The sum of any number and zero =
ITSELF
0 + (-5) = -5
Additive Inverse-
Opposites added together that have a sum of
ZERO
2x + (-2x) = 0
Used when adding negative integers or subtracting integers
Associative Property-
Any Grouping with parenthesis
(3x + 4) + 6 = 3x + (4 + 6)
Commutative Property-
Any Order- Switch places of numbers
3x + 4 = 4 + 3x
Distributive Property-
Expanded or standard form
4 (x + 6) = 4x + 24
Addition & Subtraction PropertiesSlide20
Write the sum & then write an equivalent expression by collecting like terms. Write in proof form.
2x and -2x + 3
Always write down original problem
Then, write problem with parenthesis.
Associative property, collect like-terms
Additive
inverse
Additive
identity property of zero
(Green is not part of the proof)
Slide21
2x – 7 and the opposite of 2x
Subtraction as adding the inverse
Commutative property, associative property
Additive
inverse
Additive
identity property of zero
Slide22
The opposite of (5x – 1) and 5x
Taking the opposite is equivalent to multiplying by
Distributive property
Commutative
property, any grouping property
Additive
inverse
Additive
identity property of zero
Slide23
-4 and 4b + 4
Any order, any grouping
Additive
inverse
Additive
identity property of zero
Slide24
Complete- packet page 19
1Slide25
ReciprocalSlide26
Multiplicative InverseSlide27
No change to the signSlide28
What is the product of a multiplicative inverse?
ONESlide29
Multiplicative identity property of one
One is the only number that when multiplied with another number, results in that number again.
This property
makes
special among all the numbers, so special, in fact, that mathematicians have a special name for one, called the “multiplicative identity
”
T
hey
call that property the “
Multiplicative Identity Property of One
.”
=
Slide30
-1… is a special number
has the property that multiplying a number by it is the same as taking the opposite of the number.
-1
●
5 =
-(5) =
-1
(5)=
-(-5
) =
-1
(-5
)=
-5
-5
5Slide31
Additive Identity Property of Zero
- The sum of any number and zero =
ITSELF
0 + (-5) = -5
Multiplicative Identity Property of One-
The product of any number and its reciprocal =
ITSELF
(-
5)
● 1
=
-
5
Additive Inverse-
Opposites added together that have a sum of
ZERO
2x + (-2x) = 0
Used when adding negative integers or subtracting integers
Multiplicative Inverse-
Opposites multiplied
together that have a product of
ONE
2x + (-2x) = 0
Used when adding negative integers or subtracting
integers
Associative Property-
Any Grouping with parenthesis
(3x + 4) + 6 = 3x + (4 + 6)
Commutative Property-
Any Order- Switch places of numbers
3x + 4 = 4 + 3x
Distributive Property-
Expanded or standard form
4 (x + 6) = 4x + 24
P
R
O
P
E
R
T
I
E
SSlide32
Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step.
and
Original Problem
Multiplicative
inverse
Distributive
property
Multiplicative inverse
Slide33
The opposite of 4x and -5 + 4x
Any order, any grouping
Additive
inverse
Additive
identity property of zero
Slide34
The multiplicative inverse of
and
Distributive property
Multiplicative
inverses, multiplication
Multiplicative
identity property of one
Slide35
The multiplicative inverse of
and
Distributive property
Multiplicative
inverse
Multiplicative identity property of one
Slide36
The opposite of (– 7 – 4v) and – 4v
Taking
the opposite is equivalent to
multiplying
by
Distributive
property
Any
grouping, additive inverse
Additive
identity property of zero
Slide37
3x + (1 – 3x)
Subtraction as adding the inverse
Any order, any grouping
Additive
inverse
Additive
identity property of zero
Slide38
The opposite of -10t and t-10t
Any order, any grouping
Additive
inverse
Additive
identity property of zero
Slide39
The Reciprocal of 3 and -6y – 3x
Rewrite subtraction as an addition problem
Distributive property
Multiplicative
inverse
Multiplicative
identity property of one
Slide40
The multiplicative inverse of
and
Rewrite subtraction as an addition problem
Distributive property
Multiplicative
inverse
Multiplicative
identity property of
one
Slide41
The multiplicative inverse of
and
Rewrite subtraction as an addition problem
Distributive property
Multiplicative
inverse
Multiplicative
identity property of one