part one: vocabulary review
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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. - PowerPoint PPT PresentationTRANSCRIPT
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Part One: Vocabulary Review
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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
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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
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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
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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.
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Identifying Algebraic Expressions and
Equations
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What does an algebraic expression contain?
An expressions consists of 3 items·numbers·variables ·operations
Click to reveal
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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.
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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!
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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
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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!
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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
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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!
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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.
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Translating Between Words and Expressions
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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
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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
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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
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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
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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
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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
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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!
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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
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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
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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
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Evaluating Expressions
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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
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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 ?
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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
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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
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Evaluate (4n + 6)2 for n = 1
(4n + 6)2
= (4(1) + 6)2
= (4 + 6)2
= (10)2
= 100
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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 ?
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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 ?