Transcript Variable - Southgate Schools

CH 1 NOTES
Variables, Function Patterns, Graphs
Winter, 2010-2011
CH 1-1 Using Variables
Background:
In STEM careers, it is typical to make observations of an event and
try to explain a relationship to describe that event.
Ex. a nurse monitoring a patient’s heart rate after giving that patient
some medication.
Vocabulary:
STEM career: Any career involving Science, Technology,
Engineering and Math.
Variable: a symbol representing any number. Ex. x, y, n
Expression: a phrase, with variables and any mathematical
operators (EXCEPT the = sign!)
Equation: expression written WITH the = sign
CH 1-1 Using Variables
How To Use Them:
Ex.1: State whether each one below is a variable, expression, or
equation.
a) z°
variable (measured in degrees)
b) z°+5s
expression
c) 2x
expression
d) 2x=6
equation
e) b (cm)
variable (measured in cm)
CH 1-1 Using Variables
How To Use Them Cont.:
Ex.2 Write an expression for the following data
collected by an accountant:
Hours Worked (h)
Answer:
Pay ($/hr)
1
$7.50∙1
2
$7.50∙2
3
$7.50∙3
ANSWER: ______
___________
h = hours worked (define your variable)
$7.50∙h
CH 1-1 Using Variables
How to Use It Cont.:
Before we can “translate” words into algebraic expressions, let’s
review some definitions from elementary school:
Sum/More than tells us to: _________________
Difference tells us to: _______________________
Product tells us to: _________________________
Times tells us to: ___________________________
Quotient tells us to: ________________________
Is tells us to: ______________________________
Can you think of any others?
CH 1-1 Using Variables
How to Use Them Cont.:
Ex.3 Write an algebraic expression for each phrase.
a) p multiplied by 3
3p
b) n less 7
n-7
c) 3 plus m
3+m
NOTE: MAKE SURE YOU WRITE THINGS EXACTLY
IN THE ORDER GIVEN!!!!!
CH 1-1 Using Variables
NOW, YOU DO ODDS,
#’s 1-9 IN 10 MINUTES!
READY…….
SET……..
GO!
CH 1-1 Using Variables
How to Use It Cont.:
Ex. 4 Define a variable and write an algebraic expression
for each phrase.
a) the sum of 4 and a number
define variable: n= number
write expression: 4+ n
b) 3 increased by a number
define variable: x= number
write expression: 3 + x
CH 1-1 Using Variables
NOW, YOU DO ODDS,
#’s 11-15 IN 10 MINUTES!
READY…….
SET……..
GO!
CH 1-1 Using Variables
How to Use It Cont.:
Ex. 5 Define a variable and write an algebraic expression to
model each situation.
a) The number of gal of water used to water trees is 30 times
the number of trees.
define variable: y = number of gallons of water used
x = number of trees
write expression: y = 30∙x
b) What is the cost of buying several pairs of jeans at $32.95
per pair?
define variable: z = total cost, t = number of pairs of jeans
write expression: z = 32.95∙t
CH 1-1 Using Variables
Think About It:
WOULD YOU RATHER WRITE:
The number of gal of water used to water trees is 30 times the
number of trees.
OR:
y = 30∙x
????????????????
Algebra lets you take shortcuts!!!!!!
CH 1-1 Using Variables
NOW, YOU DO ODDS,
#’s 17-27 IN 10 MINUTES!
READY…….
SET……..
GO!
CH 1-2 Order of Operations
Background:
If we don’t all agree on the order of simplifying
expressions, we will all have different answers!
Scientists and Mathematicians gathered and
decided on PEMDAS.
Vocabulary:
PEMDAS: Please Excuse My Dear Aunt Sally
CH 1-2 Order of Operations
Please
(Parentheses first)
Excuse
(Exponents/Powers next)
My
(Multiply next)
Dear
(Division next)
Aunt
(Add next)
Sally
(Subtract last)
CH 1-2 Order of Operations
How to Use It:
a) (72-32)/8
P (72 - 32) /8
P&E (49-9)/8
E (40)/8
M (none in this problem)
D (40)/8 = 5
A (none in this problem)
S (none in this problem)
Ex. 1 Simplify each expression.
b) (102-4*8)/(8+9)
P (102-4*8) /(8+9)
P&E (100 – 32)/ (8+9)
E (68)/(17)
M (none in this problem)
D 68/17 = 4
A (none in this problem)
S (none in this problem)
CH 1-2 Order of Operations
NOW, YOU DO ODDS IN YOUR BOOK,
PAGE 12 ODDS #’s 1-39
ANSWERS ON PAGE 836!!!!!!
READY…….
SET……..
GO!
Ch 1-3 Exploring Real Numbers
Background:
All numbers are not created equally. John Venn, this
statistician dude from 1880 England, came up with a way to
classify all numbers.
Vocabulary:
Natural #s: “Counting numbers” 1,2,3,…..
Whole #s: “Counting #’s plus 0” 0,1,2,3,……
Integers: All - and + whole numbers …-3,-2,-1,0,1,2,3,…
Rational #s: All fractions or decimals, but denominator ≠0.
All fractions are terminating or repeating. 3.72 or ⅛
Irrational #s: All the weird stuff: √, i, non-repeating, nonterminated fractions, Π, etc.
Ch 1-3 Exploring Real Numbers
Vocabulary Continued:
Real #s: all rational numbers and irrational numbers.
Venn Diagram: A circle diagram that shows how sets of
things are related.
Real Numbers
Rational Numbers
5/8
0.75
Irrational Numbers
-2/3
√10
0.31
Integers
200
-3
Whole Numbers
0
40000
√2/3
Nat
5 #
1,2
0.101001000…..
√1.6
π
-2000000
i
Ch 1-3 Exploring Real Numbers
How To Use Them:
Ex.1 Name the set(s) of numbers to which each number
belongs.
a. -0.002
rational number, real number
b. 8
whole number, natural number, integer, rational, & real
c. √7
irrational number, real number
d. -3.4
rational number, real number
CH 1-3 Exploring Real Numbers
NOW, YOU DO EVENS
#2 - #8, and 26 & 28
READY…….
SET……..
GO!
Ch 1-3 Exploring Real Numbers
Vocabulary Contd:
Counterexample: An example that proves a statement
false.
Ex. 2 Everyone in this room has dark hair.
Counterexample: Ron and Christen have light colored
hair.
Ex.3 True or False: All negative numbers are integers.
False: -1/2 is a negative RATIONAL number
Now YOU try #’s 10 & 12!
Ch 1-3 Exploring Real Numbers
Vocabulary Contd:
Inequality: Statement that compares the value of two
expressions using < or > symbols.
Less than is <
Greater than is >
Ex. 4 Use < = or > to compare these expressions.
a) -10.98 _____ -10.99
-10.98 > -10.99
b) 3/8 ________ 9/16
3/8 (0.375) < 9/16 (0.5625)
CH 1-3 Exploring Real Numbers
NOW, YOU DO EVENS:
#14- #24
READY…….
SET……..
GO!
Ch 1-3 Exploring Real Numbers
Vocabulary Contd:
Absolute Value: The absolute value of a number is the
distance it is from 0. We write |-3| with absolute value
bars.
Ex. 5 Find the absolute value of the following numbers.
a) |-5.44|
5.44
b) |3|
3
Now, you do #s 30 & 32