october 13, 2014 warm-up 10.13 - mrs. drake's math...
TRANSCRIPT
Expressions Review and One Step Equations drake.notebook
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October 13, 2014
warm-up 10.13.14
Copy each problem then evaluate following PEMDAS. Your paper
should have six "slices of pizza" on it when you're done! See
example below.
Ex. -3 + (6-14)
-3+-8
-11
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October 13, 2014
With your partner, talk about the following
words. What do they mean - outside the Math
classroom? Write 1 or 2 sentences to define
each one.
1. Term
2. Phrase
3. Sentence
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How do these words relate to math?
Well, math uses similar vocabulary.
Mathematical terms make up mathematical
phrases. Those phrases can be made into
mathematical sentences.
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Term
Here are some terms: 60 42x y 4x2
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Expressions
Expressions are mathematical phrases made
up of mathematical terms
These phrases have no equal sign
3x + 1
y + 25 + (-3)
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Equivalent Expressions are algebraic
expressions that have the same value for all
values of the variable(s).
x + x + 3 + 2andex:
Come up with one example on your own. Write
it in your notes. QUICKLY share examples with
someone at your table and see if they agree.
huh?
what if x = 4
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Here are some numerical expressions: 60 + 25 42 ÷ 7 4
Numerical Expression
a mathematical phrase that contains onlynumbers and operation symbols
Algebraic ExpressionHere are some algebraic expressions:
(means 7 x
an expression that is a combination of variables, numbers, and at least one operation.
Numerical Expression
Algebraic Expression
What Is The Difference?
Talk
With
Your
Table
Write ONLY 1 sentence that describes the
difference while also defining numerical
expression and algebraic expression.
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Examples:
two plus four
a number increased by two
Verbal expressions can be translated to numerical or
algebraic expressions by identifying numerical values,
variables, and key terms that signal an operation.
Verbal Expression
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Equations
Equations are mathematical sentences made
up of mathematical phrases set equal to a
mathematical term or another mathematical
phrase
These sentences have an equal sign
Let's dissect one
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Let's practice changing verbal expressions into
algebraic and/or numerical expressions...
The sum of a number and 4
4 decreased by a number, n
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verbal expression algebraic
expression
addition
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verbal expression algebraic
expression
subtraction
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verbal expression algebraic
expression
multiplication
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verbal expression algebraic
expression
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You Try... Translate these verbal expressions
into algebraic expressions
a number
a number and 10
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2n + 3b. 2(3n)d.4n - 6a. (n - 6)4c.Match.
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Properties of Expressions
Additive Identity
Multiplicative Identity
Commutative Property
Associative Property
Multiplicative Property of 0
Distributive Property
Multiplicative Property of -1
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https://www.youtube.com/watch?v=-v6zc3JlsoY
Video:
While we watch the video, pay attention to how
we apply these properties to expressions.
Write down any information about the
properties that you may not have known prior
to the video, one thing you still want to know
about the property, or an example he gives that
you think is particularly good.
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Simplify using the properties of expressions.
Justify each step.
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Multiplicative Property of -1
In the video... he called this the inverse
property
This property is important because it is how
we get "the opposite of"
Without this property, we couldn't say that -x2
is really (-1)(x2)
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October 13, 2014
Simple Distributive Property examples:
Addition: 3(6+4)
5(x+7)
Subtraction: 2(7-3)
6(y-10)
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(5 5x) + (5 -2y)
25x + -10y
25 x - 10y
(10 -6x) + (10 5y)
-60x + 50y
Trickier
Distributive Example:
Addition
Trickier Distributive Example:
Subtraction
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Simplifying Expressions Sometimes an expression will have multiple terms and operations that
can be simplified. An expression is in simplest form when there are
no parentheses, no like terms, and when all division,
multiplication and exponents have been simplified
It is important to simplify expressions before you evaluate expressions
How can the properties we just looked at
help us simplify expressions like this?
+ + + + +
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October 13, 2014
Simplifying Expressions:
Combining Like Terms
What does it mean to "combine"?
What does it mean for terms to be "like terms"?
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Like Terms:
Must have the same variable or combination of
variables but may have different coefficients
5ab, 8ab 6c2, 10c2
13a, 8ab
2x, 5x
4x, 5x2Sort:
Like Terms Not Like Terms
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1
Name the coefficient in the following terms:
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Circle like terms from the list below:
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So let's revisit..... How can the properties
we just looked at help us simplify
expressions like this?
+ + + + +
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Let's try to combine the like terms by adding the coefficients of the terms with like variables to the same power. Write the simplified expression.
10t + 9w2 + 17v
3t + 7t + 5w2 + 4w2 + 9v + 8v
3t + 7t + 5w2 + 4w2 + 9v + 8v What Property
lets us
rearrange the
terms in this
way?
+ + + ++
What Property
lets us group
the terms in
this way?
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3x + 5y + 10 + 12x + 31y + 14
Let's Simplify One Together...
Another easy way to simplify expressions (other than using the properties) is to create a table of
the variables you have and add together the coefficients
1st Variable 2nd Variable 3rd Variable Constants
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https://www.youtube.com/watch?v=US95J1g6iY4
How could combining like terms help in this
situation?
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How can we re-write the expression?
What are the coefficients in this expression?
On your own, determine what you think about the following. After a minute, discuss with your
table and come up with an answer.
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Both of these terms
have a coefficient of
-17
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The sign of the
operation is the sign
of the term!!!Take a minute to talk with your group about what this means...
3x + 5y + 10 + 12x + 31y + 14
Refer to this example, if you wish.
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October 13, 2014
-8x + 5y - 8x + -6z - 2y + 10z + 4x - 3
-8x + 5y - 8x + -6z - 2y + 10z + 4x - 3
(-8x + -8x + 4x) + (5y + -2y) + (-6z + 10z) + (-3)
-12x + 3y + 4z - 3
x y z constant
Fill in the table below for the following expression and
simplify...
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October 13, 2014
3x - 8y + -7 - 12x + 15y + 14
Try This One Using the Table Method....
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4y + y
6 - 3n + 3n
9y - 4 - 11y + 7
6n - 7n - 4 + 6s - 10r + 5s - n + -15r
7x + -2 - 7x + 8t + 6 - t
2g - 3 + 11 - 8g
6x -2x
14p -8 -5p
4n + 5n + 7
10d - 15f + 5e - 2(d - f) + 3(e + d) + -5f + -(2 + d)
Try these on your
own. You have 4
minutes to get
through as many
as you can. Do
not worry if you
don't finish
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October 13, 2014
Evaluating Expressions
in the expression.
Example: Evaluate + 7, for
replace the with the given value, + 7 perform the operation (add)
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What is the difference between
EVALUATING and SOLVING?
Evaluate - simplifying to find a known value
We Evaluate Expressions
Solving - working to find an unknown value
We Solve Equations
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Evaluate the following...
Work on your own, get through as
many as you can in the given time
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1.
2.
3.
4.
5.
6.
7.
8.
9.
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1. What is the variable?
2. What is attached to the variable?
3. How is it attached to the variable?
4. How do we un-do that?
5. Do it to both sides.
Questions to ask and answer...
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October 13, 2014
x + 5 = 20
a - 14 = 32
15y = 275
b
9= 6
Solve these using the ask-answer questions
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October 13, 2014
a. Define your variable
b. Write your equation
c. Solve your equation
Expressions Review and One Step Equations drake.notebook
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October 13, 2014
a. Define your variable
b. Write your equation
c. Solve your equation