Transcript Expressions

Chapter 1: Foundations for Algebra
1.1 Variables and
Expressions
Objective: to write algebraic expressions
August 17, 2015
by K.M. Showers High School
I can…
distinguish between algebraic and
numerical expressions.
identify the parts of an expression.
Translate verbal expressions into math
expressions and vice versa.(A.SSE.A.1a)
Uses the structure of an expression to identify
ways to rewrite it.(A.SSE.A.2)
Vocabulary…
Green Book: Algebra I Common Core-Pearson
Quantity…

Anything that can be measured or
counted.

Some remain constant.

Others change, or vary…they are
called variable quantities.
Algebra…

Uses symbols to represent
quantities that are unknown or that
vary.

We use symbols and operations to
represent mathematical phrases
and real-world relationships.
Question:
What is the area of a rectangle?
Length times Width
If the length is 3 meters and the width
is 2 meters, what is the area?
A=LxW
A = 3 x 2 = 6 meters2
A, L and W are the variables. It is any
symbol, usually a letter, that
represents the unknown value(s) of a
variable quantity.
An algebraic expression contains:
1) one or more numbers or variables,
and
2) one or more arithmetic operations.
Examples:
x-3
3 • 2n
4
1
m
In expressions, there are many different
ways to write multiplication.
1)
2)
3)
4)
5)
ab
a•b
a(b) or (a)b
(a)(b)
axb
We are not going to use the multiplication
symbol any more. Why?
Division, on the other hand, is
written as:
x
1)
3
2) x ÷ 3
Throughout this year, you will hear many
words that mean addition, subtraction,
multiplication, and division. Complete the
table with as many as you know.
Addition Subtraction Multiplication Division
Here are some phrases you may have
listed. The terms with * are ones that
are often used.
Addition
sum*
increase
plus
add
more than
total
Subtraction
difference*
decrease
minus
subtract
less than
Multiplication Division
product*
times
multiplied
quotient*
divided
ratio
Write an algebraic expression
for…
1) m increased by 5.
m+5
2) 7 times the product of x and t.
7xt or 7(x)(t) or 7 • x • t
3) 11 less than 4 times a number.
4n - 11
4) two more than 6 times a number.
6n + 2
5) the quotient of a number and 12.
x
12
Which of the following expressions represents
7 times a number decreased by 13?
1.
7x + 13
2.
7x - 13
3.
13 - 7x
4.
13 + 7x
Answer Now
Which one of the following expressions
represents 28 less than three times a number?
1.
28 - 3x
2.
3x - 28
3.
28 + 3x
4.
3x + 28
Answer Now
Write a verbal expression for:
1) 8 + a.
The sum of 8 and a
2) m
r
.
The ratio of m to r
Do you have a different way of writing
these?
Which of the following verbal
expressions represents 2x + 9?
1.
9 increased by twice a
number
2.
a number increased by nine
3.
twice a number decreased
by 9
4.
9 less than twice a number
Answer Now
Which of the following expressions represents
the sum of 16 and five times a number?
1.
5x - 16
2.
16x + 5
3.
16 + 5x
4.
16 - 5x
Answer Now
When looking at the expression 103, 10 is
called the
base
and 3 is called the
exponent or power.
103 means 10 • 10 • 10
103 = 1000
How is it said?
21
Two to the first power
22
Two to the second power or two
squared
23
Two to the third power or two cubed
2n7
Two times n to the seventh power
Which of the following verbal
expressions represents x2 + 2x?
1.
the sum of a number
squared and twice a
number
2.
the sum of a number and
twice the number
3.
twice a number less than
the number squared
4.
the sum of a number and
twice the number squared
Answer Now
Which of the following expressions
represents four less than the cube of a
number?
1.
4 – x3
2.
4 – 3x
3.
3x – 4
4.
x3 – 4
Answer Now
Evaluate.
21
2
22
2•2=4
23
2•2•2=8
2n7
We can’t evaluate
because we don’t know the
value of n!!
Is 35 the same as 53?
Evaluate each and find out!
35 = 3 • 3 • 3 • 3 • 3 = 243
53 = 5 • 5 • 5 = 125
243 ≠ 125
They are not the same!
Numerical Expression…
 Mathematical
Phrase that
involves numbers and
operations, but no variables.
• 3•3
• 9(5-2)
• 4 + 68
Guided Practice:
Lesson Check pp. 7, 1-8
1.
Numerical, algebraic, numerical
2.
9t, x – 1/2, m + 7.1, 207/n
3.
The product of 6 and a number c
4.
the differences of a number x and 1
5.
the quotient of a number t and 2
6.
4 less the product of a number t and 3
7.
Numerical expressions are just numbers
and operations. Algebraic expressions
have variables, numbers and operations.
8.
49 + 0.75n
Independent Practice…
 Pp.
7-9
 Problems 9-34 all
 Answers only