Example - WALDEN GREEN MONTESSORI

Expressions & Equations

(Intro to Variables)

Simplify the following:

©2017 Math in Demand

I can ___________________

_______________________

identify coefficients and

variables given a term.

A variable is an unknown. This

means that we don’t know what the

quantity (number) is or it may change.

It can be any number.

a.) 6 x 7 = ____ b.) 3 ⋅ 9 = ____ c.) (8)(4) = ____

All of the problems above involve ____________.

Take a good look at part (a) from above. We are

used to seeing an “x” that represents

____________. However, today you are going to

learn that “x” can represent a ____________.

42 27 32

multiplication

multiplication

variable

Vocab:

What is a ____________? variable

variable

A ___________

has a _________ in front

of it. This is implied

___________.

A _________ is a number

that never changes its value

and is not multiplied by a

__________.

Example:

Usually

represented as

a _________.

Examples:

letter

x, y, m, a

variable

coefficient

multiplication Identify the variable,

constant and coefficient: 6y

y is the variable;

6 is the coefficient;

and there is no constant.

constant

variable


(Evaluating Expressions)

What is an algebraic expression?


I can ___________________

_______________________

evaluate an algebraic

expression.

45

4

Evaluating an Expression:

Example:

9x 5

We can evaluate expressions by _________ in a

given value for the variable.

plugging

Example:

Examples:

Imagine a machine! Think

about __________ a

value into an algebraic

expression. This will give

us an ________.

inputting

output input

output

Let’s say we want to input 5 into the

expression 9x.

A mathematical phrase that contains

variables and has operators (addition,

subtraction, multiplication, and division).

Evaluate the

following expression

given that x = 4:

4x

4x = 4(4) = 16

Evaluate the

following expression

given that y = 3:

7y

7y = 7(3) = 21

x - 4


(Writing Algebraic Expressions)

You just learned how to evaluate an algebraic expression. Now,

you are going to write an algebraic expression. Remember, an

algebraic expression contains a _________ and __________.

I can ___________________

_______________________


Some key words to look out for are:

Addition: Subtraction: - Sum - Plus

- Add - More than

- Combine - Altogether

- Increase - Perimeter

- Larger

Multiplication:

variable operator

write an algebraic

expression given a word phrase.

- Subtract - Fewer than

- Difference - Less than

- Minus - Take away

- Decrease - Deduct

- Multiply - Triple (x3)

- Times - Half (x½)

- Product - Area

- Double (x2)

- Divide - Half (÷2)

- Quotient - Third (÷3)

- Ratio of - Fourth (÷4)

- Split - Average

Division:

Example: 7 added to a number

n + 7

Example: Subtract 4

from a number

n - 4

Example: 2 multiplied by a number

2n

Example: Quotient of

a number and 6

n ÷ 6


(Solving One-Step Equations)

Use Inverse

Operations

to Solve for the

Variables

x + 10 = 17

-10 -10

x = 7

x - 2 = 14

+2 +2

x = 16

6x = 12

6 6

x = 2

𝑥4 = 2

4 ⋅ ቀ𝑥4

ቁ = 2⋅4

x = 8

What are one-step equations?

INVERSE OPERATIONS

Important Note: Do Not Forget to balance the equations! You must do

the same operation on both sides of the equation!


I can ___________________

_______________________

+

-

x

÷

solve one-step equations

with one variable.

1𝑎

a

One-step equations mean that there is only one step in order to

solve for the variable (unknown).


(Intro to Inequalities)

I can ___________________

_______________________

Examples:


Glue > Here Glue < Here Glue ≥ Here Glue ≤ Here

What is an inequality?

An inequality is used to

compare the relative size of two values.

There are 4 inequalities:

compare numbers by

using inequalities.

Greater

than

Less

than

Less

than or

equal

Greater

than or

equal

We use these inequalities to __________ numbers.

For example:

x > 17 means…

compare

x is greater than 17;

In other words, x is a number greater

than 17.

17.001, 17.5, 18, 19, … Examples:

x < 5 means… x ≥ 6 means…

x is less than 5

4 Examples:

4.99, 4, 3.5, 3¼

4 Examples:

6, 7, 8.5, 100

x is greater or equal

to 6


(Solving One-Step Inequalities)

I can ___________________

_______________________

Examples:


The 4 inequalities are:

solve one-step

inequalities.

Greater

than

Less

than

Less

than or

equal

Greater

than or

equal

> ≥ < ≤

We solve one-step inequalities just like one-step

equations.

x + 4 > 7

- 4 - 4

x > 3

This means x is

greater than 3.

x - 6 < 9

+ 6 + 6

x < 15

This means x is

less than 15.

2x ≤ 12

2 2

x ≤ 6

This means x is less

than or equal to 6.

𝑥5 > 1

5 ⋅ ቀ𝑥5ቁ > 1 ⋅ 5

x > 5

This means that x

is greater than 5.


(Dependent vs Independent

Variables)

We can identify dependent and independent

variables

by the

following:

Dependent: Independent:


Examples:

I can ___________________

_______________________

determine the dependent

and independent variables.

A variable the

changes in value due

to another variable

(output)

A variable that

does not depend on

another variable

(input)

Henry is building a

bookcase for his books.

The numbers of shelves will

be based on how many

books he owns.

Dependent variable:

Independent variable:

Info:

Info:

- Graphed on the

y-axis

- The column or row

containing y-values in a

table

- Graphed on the

x-axis

- The column or row

containing x-values in a

table

The number of books

The number of shelves

Kelly is throwing a

party at her house. The

more people that attend

her party, the more

hotdogs she will cook.

Dependent variable:

Independent variable:

The number of people

The number of hotdogs


(Combining Like Terms)

What does it mean to combine like terms?

Give some terms

that would combine

with

5x


I can ___________________

_______________________

8x

x

3x

simplify expressions by

combining like terms.

Combining like terms is a mathematical process used

to simplify an expression. You add or subtract terms

whose variables are the same.

Steps to Combine Like Terms

1 The terms must have identical variables. If they

do not, you cannot combine them (leave them

alone).

2 If the terms have identical variables, then you

add or subtract the coefficients. Keep the

variables.

Examples: Simplify the

following: 9x + 12x

21x

Simplify the

following: 12y – 7y

5y


(Distributive Property)

What is the distributive property?

a(b+c) =

Use the distributive property to

solve the following:

4(5+3) = 4(5) + 4(3) = 20 + 12 = 32

Now, let’s try the distributive property with a variable:

8(x+2) = 8(x) + 8(2) = 8x + 16

Now, we can also use the distributive property to

determine area of a rectangle or square:


I can ___________________

_______________________

a(b+c) = ab + ac

use the distributive

property to simplify expressions.

The distributive property is used to simplify

expressions by multiplying a single term by two or

more terms inside parentheses.

The distributive property states that:

This means

a times b

or a∙b

8

x

3

x + 3

Area of a rectangle = ______

Area = ___________

Area = ___________

Area = ___________

b ⋅ h

8(x+3)

8(x) + 8(3)

8x + 24


(Writing Equivalent Expressions)

What is the meaning of equivalent?

You have already learned how to apply the

________ _______ and _______ ____ _____.

These give us an _________ __________.


I can ___________________

_______________________

identify and write

equivalent expressions.

Now, we can _________ the __________

_________ when we are given two _____ that

have a ________ _____. For example,

3x + 6

Equivalent means that it has the same value.

In other words, equivalent means equal.

If we apply the

distributive property to

6(x+2) then we get the

equivalent expressions:

6(x) + 6(2) AND 6x + 12

reverse

distributive

property

terms

common

factor

In this example, 3 is a common factor. This

means that both 3 and 6 are divisible by 3. So, I

can take out a common factor of 3. Hence,

3(x+2)

is an equivalent expression to 3x + 6.

equivalent

expression

distributive

property

combine

like

terms

If we combine like

terms to 3x + 4x then we

get the equivalent

expressions:

7x OR x⋅7

6(x+2)

3x + 4x

Example - WALDEN GREEN MONTESSORI

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