Download How do you rewrite rational numbers and decimals, take square

1.1 Expressing Rational Numbers
as Decimals
EQ: How do you rewrite rational numbers
and decimals, take square roots and cube
roots and approximate irrational numbers?
A decimal number that has digits
What is a
terminating that do not go on forever.
decimal?
.025
3.0375
What is a
A decimal number that has
terminating digits that repeat forever.
decimal?
.0333…
0.142857142857…
1.1 Expressing Decimals as
Rational Numbers
EQ: How do you rewrite rational numbers
and decimals, take square roots and cube
roots and approximate irrational numbers?
Decimal to Look at the last digit and
Fraction
determine the place value.
.375 = 375 = 75 = 3
1000 200 8
1.1 Expressing Decimals as
Rational Numbers
EQ: How do you rewrite rational numbers
and decimals, take square roots and cube
roots and approximate irrational numbers?
Repeating 1. Let x = the number
Decimal to 2. Identify the place value of
the last repeating digit.
Fraction
3. Multiply (by 10, 100,
1000)
4. Subtract x
5. Divide
1.1 Finding Square Roots and Cube
Roots
EQ: How do you take square roots and cube
roots?
Square Root There are two square roots
for every positive number.
62 = 36 and (−62 ) = 36
36 = ±6
1.1 Finding Square Roots and Cube
Roots
EQ: How do you rewrite rational numbers
and decimals, take square roots and cube
roots and approximate irrational numbers?
Cube Root There is one cube root for
every positive number.
The cube root of 8 is 2
because 23 = 8 .
3
8=2
2⋅2⋅2=8
1.2 Classifying Real Numbers
EQ: How can you describe relationships
between sets of real numbers?
Real
Set of rational numbers and
Numbers irrational numbers.
1.3 Comparing Irrational Numbers
EQ: How do you order a set of real
numbers?
Compare Use perfect squares to
estimate the square root.
Real
Numbers
2
1 =1
2
2
2 =4
A number between 1 and 2.
2.1 Simplifying Expressions with Powers
EQ: How can you develop and use the
properties of integer exponents?
2.2 Scientific Notation with Positive
Powers of 10
EQ: How can you scientific notation to
express very large quantities?
Scientific
Notation
Move the decimal behind
the first number and drop
the zeros.
Count the number of
places the decimal was
moved.
11
1.2300000000 = 1.23 x 10
2.3 Scientific Notation with
Negative Powers of 10
EQ: How can you use scientific notation to
express very small quantities?
Scientific Move the decimal after the
Notation first nonzero number.
Count the number of places
the decimal was moved.
When the number is between
0 and 1 the exponent is
negative.
3.1 Representing Proportional
Relationships with Equations
EQ: How can you use tables, graphs and
equations to represent proportional
situations?
Proportional Ratio of one quantity to
the other is constant.
Relationship
Described by one of
Constant of
Proportionality these equations:
𝑦
𝑘=
𝑦 = 𝑘𝑥
𝑥
Representing Proportions with Equations
Step 2
For the number of hours, write the
relationship of the amount earned and the number
of hours as a ratio (another word for ratio: _____)
in simplest form.
𝑦
𝑘=
𝑥
amount earned 12

number of hours 1
24

48

Is the relationship proportional?
Yes / No Explain.
96

Representing Proportions with Equations
Step 3
Write an equation
amount earned
Let x = ____________________
number of hours
Let y = ____________________
Use the equation y  kx
The equation is: y  12 x
3.1 Representing Proportional
Relationships with Graphs
EQ: How can you use tables, graphs and
equations to represent proportional
situations?
Proportional Graph will be a line that
Graph
goes through the origin
(0,0).
Representing Proportions with Graphs
The graph shows the
relationship between the
weight of an object on the
Moon and its weight on Earth.
Write an equation for this
relationship.
Step 1
Use the points on
the graph to make a table.
Earth weight
(lbs)
Moon weight
(lbs)
6
12
18
30
Representing Proportions with Equations
Step 2
𝑦
𝑘=
𝑥
Find the constant of proportionality.
Moon weight
Earth weight
1

6
2

3

5
The constant of proportionality is:

Representing Proportions with Graphs
Step 3
Write an equation
weight on Earth
Let x = ____________________
weight on Moon
Let y = ____________________
Use the equation y  kx
1
The equation is: y  x
6
3.2 Rate of Change
EQ: How do you find a rate of change?
Rate of chg. in dependent variable ( y )
Change chg. in independent variable ( x)
Example
The cost is $0.75 per Snickers.
constant rate
Dependent y  .75 x  b
variable
Independent
variable
The cost
depends
on the
number
you buy.
Rate of Change
Eve keeps record of the number of lawns she has
mowed and the money she has earned. Tell
whether the rates of change are constant or
variable.
Step 1
Identify the independent and
dependent variables.
# of lawns
Independent Variable _____________________
$ earned
Dependent Variable _______________________
The amount earned depends on the
Explain ________________________________
number of lawns mowed.
Rate of Change
Step 2
Find the rates of change
Day 1 to Day 2:
change in $
change in lawns
45  15
30


3 1
2
 15
90  45

63
45

 15
3
120  90 30  15
change in $
Day 3 to Day 4:

change in lawns 
2
86
change in $
Day 2 to Day 3:
change in lawns
The
rates of
of change
are constant.
The rates
change are
/ are not constant.
Price
$15.
Price per
per lawn
lawn is
is _________.
3.2 Slope
EQ: How do you find the slope of a line?
Slope (m)
The steepness of a line.
rise y2  y1
m

run x2  x1
x
x
x
x
Method 1
Label ordered pairs
1, 4   3, 5 
 x1 , y1   x2 , y2 
Write down formula
y2  y1
m
x2  x1
Substitute values
5  4 9 9
m


3  1  4 4
Method 2
Write ordered pairs
Subtract y values
and x values
 1 , 4
 3, 5 
4   5  9

1   3 4
Method 3
Plot the points
 1 , 4
 3, 5 
Find the rise / run
3.3 Interpreting Unit Rate as Slope
EQ: How do you interpret the unit rate as
slope?
Rate
Ratio comparing quantities
measured in different units.
Unit Rate Ratio where the second
quantity is 1.
Example $ per orange oranges per $1
dollars
oranges
$2 10 $0.20
 
10 10
1
oranges
dollars
10 2 5
 
$2 2 $1
A storm is raging on Misty Mountain. The
graph shows the constant rate of change of
the snow level on the mountain.
4.2 Determining Slope & Y-intercept
EQ: How can you determine the slope and
y-intercept of a line?
𝑦
=
𝑚𝑥
+
𝑏
Slope Intercept
Form of an
slope
y-int
Equation
Rate of Start value
Change
Find the slope (m) and Y-intercept (b).
change in 𝑦
=
change in 𝑥
change in 𝑦
=
change in 𝑥
change in 𝑦
=
change in 𝑥
The rate of change (m) is ____
The start value (b) is ____
4.2 Determining Slope & Y-intercept
EQ: How can you graph a line using the
slope and y-intercept?
𝑦 = 𝑚𝑥 + 𝑏
slope
Step 1
Step 2
Step 3
y-int
Identify m and b
Plot the point of the yintercept.
Use the slope to find a
second point.
4.4 Proportional and Nonproportional
EQ: How can you distinguish between
proportional and nonproportional
situations?
Proportional
𝑦 = 𝑚𝑥
Line goes through
the point (0,0)
Nonproportional
𝑦 = 𝑚𝑥 + 𝑏
Starting point of line
is the y-intercept