October 13, 2014 warm-up 10.13 - Mrs. Drake's Math...

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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expression

subtraction


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expression

multiplication


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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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October 13, 2014

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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Distributive Property


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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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October 13, 2014

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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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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October 13, 2014

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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-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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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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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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Homework


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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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x + 5 = 20

a - 14 = 32

15y = 275

b

9= 6

Solve these using the ask-answer questions


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Solve. Show all work.


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a. Define your variable

b. Write your equation

c. Solve your equation


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a. Define your variable

b. Write your equation

c. Solve your equation


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October 13, 2014

Solve the following word problems. Show

all steps. Be sure to define your variable.

October 13, 2014 warm-up 10.13 - Mrs. Drake's Math...

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