Post on 24-Dec-2015
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 thanminus
difference
less thanhow much more
how much less
take away
Sort each as either an addition word or subtraction word.Check with a classmate or the teacher if you are unsure.
Addition Subtraction
plus
sum
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
dividend
divide
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 ?