Part One: Vocabulary Review

What is a Constant?A constant is a fixed value, a number on its own, whose value does not change. What is the constant in the expressions below?

Example: 4x + 2

In this expression 2 is a constant.click to reveal

Example: 11m - 7

In this expression -7 is a constant.click to reveal

What is a Variable?

A variable is any letter or symbol that represents a changeable or unknown value. What is the variable?

Example: 4x + 2

In this expression x is a variable.click to reveal

What is a Coefficient?A coefficient is the number multiplied by the variable. It is located in front of the variable.

What is the coefficient in the expression below?

Example: 4x + 2

In this expression 4 is a coefficient.click to reveal

Example 1: x + 4 is the same as 1x + 4

- x + 4 is the same as -1x + 4

Example 2:

If a variable contains no visible coefficient, the coefficient is 1.

Identifying Algebraic Expressions and

Equations

What does an algebraic expression contain?

An expressions consists of 3 items·numbers·variables ·operations

Click to reveal

Each term in an algebraic expression is separated by aplus (+) or minus ( - ) sign.

15w is an algebraic expression with one term.

7m - 12 is an algebraic expression with two terms.

-4x + 3y - 20 is an algebraic expression with three terms.

Let's take a look and decide if the examples are expressions or not. 5 + n

What is the constant? ______________

What is the variable? ______________

What is the coefficient? ______________

Is it an algebraic expression? ______________

If yes, how many terms does it have? ______________

Write your answers on a white board or in your notebook BEFORE checking your

answers on the next slide!

Let's take a look and decide if the examples are expressions or not. 5 + n

What is the constant? 5

What is the variable? n

What is the coefficient? 1

Is it an algebraic expression? Yes!

If yes, how many terms does it have? 2

3b - 4c -7

What is/are the constants? ______________

What is/are the variables? ______________

What is/are the coefficients? ______________

Is it an algebraic expression? ______________

If yes, how many terms does it have? ______________

Write your answers on a white board or in your notebook BEFORE checking your

answers on the next slide!

3b - 4c -7

What is/are the constants? -7

What is/are the variables? b and c

What is/are the coefficients? 3 and 4

Is it an algebraic expression? YES!

If yes, how many terms does it have? three

p

What is the constant? ______________

What is the variable? ______________

What is the coefficient? ______________

Is it an algebraic expression? ______________

If yes, how many terms does it have? ______________

Let's try a challenge.

Write your answers on a white board or in your notebook BEFORE checking your

answers on the next slide!

p

What is the constant? none

What is the variable? p

What is the coefficient? 1

Is it an algebraic expression? YES!

If yes, how many terms does it have? one

Let's try a challenge.

Translating Between Words and Expressions

Sort each as either an addition word or subtraction word.Check with a classmate or the teacher if you are unsure.

Addition Subtraction

plus

sumaddend

greater thanminusdifference

less thanhow much more

how much lesstake away

Sort each as either an addition word or subtraction word.Check with a classmate or the teacher if you are unsure.

Addition Subtraction

plussum

addend

greater than

minus

difference

less than

how much more

how much less

take away

Sort each as either a multiplication word or division word.Check with a classmate or the teacher if you are unsure!

Multiplication Division

product

factorquotient

times of

divisorshare

dividenddivide

Sort each as either a multiplication word or division word.Check with a classmate or the teacher if you are unsure!

Multiplication Division

product

factor

quotienttimes

of

divisorshare

dividend

divide

Be aware of the phrase "less than".

For example:“3 more than eight times a number” can be written as:

either 8n + 3 or 3 + 8n (both are correct)

BUT… “three less than eight times a number” Can ONLY be written as 8n - 3

It is NOT the same as 3 – 8n

Confused? Think about it this way: Mr. Baxter has $25. Ms. Foley has $6 less than

Mr. Baxter. She has $25 - $6 = $19. This is NOT the same as $6 - $25

As a rule of thumb, if you see the words "than" or "from" it means you have to reverse the order

of the two items on either side of the word.

Examples: 8 less than b means b – 83 more than x means x + 3 (although 3 + x is okay)x less than 2 means 2 – xclick to reveal

Three times j

Eight divided by j

j less than 7

5 more than j

4 less than j

TRANSLATE THE WORDS INTO AN

ALGEBRAIC EXPRESSION

Write your answers on a white board or in

your notebook BEFORE checking your answers

on the next slide!

Three times j 3j

Eight divided by j 8/j

j less than 7 7 – j

5 more than j j + 5

4 less than j j - 4

TRANSLATE THE WORDS INTO AN

ALGEBRAIC EXPRESSION

Seventy-one plus c

Write your answers on a white board or in your notebook BEFORE checking your answers on the

next slide!

Twenty-four less than d

The sum of twenty-three and m

Four times the difference of eight and j

The product of seven and w, divided by 12

The square of the sum of six and p

71+cSeventy-one plus c

Write your answers on a white board or in your notebook BEFORE checking your answers on the

next slide!

Twenty-four less than d d - 24

The sum of twenty-three and m 23 + m

Four times the difference of eight and j 4(8-j)

The product of seven and w, divided by 12 7w12

The square of the sum of six and p (6+p)2

Evaluating Expressions

Steps for Evaluating an Expression:

1. Write the expression

2. Substitute the values given for the variables (use parentheses!)

3. Simplify the Expression Remember Order of Operations!

Write - Substitute - Simplify

click to reveal

1. Solve in your journal. 2. Show all steps. (Write. Substitute. Simplify.)3. Check your work on the next slide!

What is the value of 4n + 62 when n = 3 ?

How you show your work is just as important as the answer

What is the value of 4n + 62 when n = 3 ?

4n + 62 Write!

= 4(3) + 62

Substitute.

= 4(3) + 36 Simplify.

= 12 + 36

= 48

1. Solve in your journal. 2. Show all steps. (Write. Substitute. Simplify.)3. Check your work on the next slide!

Evaluate (4n + 6)2 for n = 1

Evaluate (4n + 6)2 for n = 1

(4n + 6)2

= (4(1) + 6)2

= (4 + 6)2

= (10)2

= 100

4x + 2x3

1. Solve in your journal. 2. Show all steps. (Write. Substitute.

Simplify.)3. Check your work on the next slide!

What is the value of the expression below when x = 2 ?

4x + 2x3

= 4(2) + 2(2)3

= 4(2) + 2(8)

= 8 + 16

= 24

What is the value of the expression below when x = 2 ?