1. Part One:
Vocabulary Review

2. 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
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In this expression 2 is a constant.
Example: 11m - 7
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In this expression -7 is a constant.

3. 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
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In this expression x is a variable.

4. 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
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In this expression 4 is a coefficient.

5. Example 1: x + 4 is the same as 1x + 4 - x + 4 is the same as -1x + 4
If a variable contains no visible coefficient, the coefficient is 1.
Example 1: x + 4
is the same as
1x + 4
- x + 4
is the same as
-1x + 4
Example 2:

6. Algebraic Expressions and
Identifying
Algebraic Expressions and
Equations

7. What does an algebraic expression contain?
Click to reveal
An expressions consists of 3 items
·numbers
·variables
·operations

8. Each term in an algebraic expression is separated by a
plus (+) or minus ( - ) sign.
15w is an algebraic expression with one term.
7m is an algebraic expression with two terms.
-4x + 3y is an algebraic expression with three terms.

9. Let's take a look and decide if the examples are expressions or not.
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? ______________
Answer: Yes, 2 terms
Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

10. Let's take a look and decide if the examples are expressions or not.
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
Answer: Yes, 2 terms

11. 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? ______________
Answer: Yes, 2 terms
Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

12. What is/are the constants? -7 What is/are the variables? b and c
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
Answer: Yes, 2 terms

13. Let's try a challenge. 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? ______________
Answer: Yes, 1 term
Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

14. What is the constant? none What is the variable? p
Let's try a challenge. 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
Answer: Yes, 1 term

15. Translating Between Words and Expressions

16. Sort each as either an addition word or subtraction word.
Check with a classmate or the teacher if you are unsure.
plus
minus
how much less
greater than
addend
difference
take away
sum
how much more
less than
Addition Subtraction

17. Sort each as either an addition word or subtraction word.
Check with a classmate or the teacher if you are unsure.
Addition Subtraction
minus
plus
addend
how much less
sum
difference
how much more
take away
greater than
less than

18. Sort each as either a multiplication word or division word.
Check with a classmate or the teacher if you are unsure!
product
dividend
times
quotient of
divide
factor
share
divisor
Multiplication Division

19. Sort each as either a multiplication word or division word.
Check with a classmate or the teacher if you are unsure!
Multiplication Division
quotient
product
dividend
times of
divide
share
divisor
factor

20. 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 

21. 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 – 8
3 more than x means x + 3 (although 3 + x is okay)
x less than 2 means 2 – x
click to reveal

22. TRANSLATE THE WORDS
INTO AN
ALGEBRAIC EXPRESSION
Three times j
Eight divided by j
j less than 7
5 more than j
4 less than j
Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

23. TRANSLATE THE WORDS
INTO AN
ALGEBRAIC EXPRESSION
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

24. Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!
Seventy-one plus c
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

25. Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!
Seventy-one plus c
71+c
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) 7w 12
The product of seven and w, divided by 12
The square of the sum of six and p
(6+p)2

26. Evaluating Expressions

27. Steps for Evaluating an Expression:
1. Write the expression
Substitute the values given for the variables
(use parentheses!)
3. Simplify the Expression
Remember Order of Operations!
click to reveal
Write - Substitute - Simplify

28. What is the value of 4n + 62 when n = 3 ?
Solve in your journal.
Show all steps. (Write. Substitute. Simplify.)
Check your work on the next slide!
What is the value of 4n + 62 when n = 3 ?

29. 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 Write!
= 4(3) Substitute.
= 4(3) Simplify. =
= 48

30. Solve in your journal.
Show all steps. (Write. Substitute. Simplify.)
Check your work on the next slide!
Evaluate (4n + 6)2 for n = 1

31. Evaluate (4n + 6)2 for n = 1
(4n + 6)2
= (4(1) + 6)2
= (4 + 6)2
= (10)2
= 100

32. What is the value of the expression below when x = 2 ?
Solve in your journal.
Show all steps. (Write. Substitute. Simplify.)
Check your work on the next slide!
What is the value of the expression below when x = 2 ?
4x + 2x3

33. What is the value of the expression below when x = 2 ?
4x + 2x3
= 4(2) + 2(2)3
= 4(2) + 2(8) =
= 24