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?

What is a terminating decimal?

A decimal number that has digits that do not go on forever.

.025 3.0375

What is a terminating decimal?

A decimal number that has digits that repeat forever.

.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 Fraction

Look at the last digit and determine the place value.

.375 = 375 = 75 = 31000 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 Decimal to Fraction

1. Let x = the number2. Identify the place value of

the last repeating digit.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

38 = 2

2 ⋅ 2 ⋅ 2 = 8

1.2 Classifying Real Numbers

EQ: How can you describe relationships between sets of real numbers?

Real Numbers

Set of rational numbers and irrational numbers.

1.3 Comparing Irrational Numbers

EQ: How do you order a set of real numbers?

Compare Real Numbers

Use perfect squares to estimate the square root.

2 12 = 122 = 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?

Move the decimal behind the first number and drop the zeros.

Count the number of places the decimal was moved.

Scientific Notation

1.2300000000 = 1.23 x 1011

2.3 Scientific Notation with Negative Powers of 10

Move the decimal after the first nonzero number.

Count the number of places the decimal was moved.

Scientific Notation

EQ: How can you use scientific notation to express very small quantities?

When the number is between 0 and 1 the exponent is negative.

3.1 Representing Proportional Relationships with Equations

Ratio of one quantity to the other is constant.

ProportionalRelationship

EQ: How can you use tables, graphs and equations to represent proportional situations?

Described by one of these equations:

Constant of Proportionality

𝑘 =𝑦

𝑥𝑦 = 𝑘𝑥

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.

amount earned

number of hours

12

1

24

48

96

Is the relationship proportional? Yes / No Explain.

𝑘 =𝑦

𝑥

Representing Proportions with Equations

Step 3 Write an equation

Let x = ____________________

Let y = ____________________

Use the equation y kx

The equation is:

amount earned

number of hours

12y x

3.1 Representing Proportional Relationships with Graphs

Graph will be a line that goes through the origin (0,0).

ProportionalGraph

EQ: How can you use tables, graphs and equations to represent proportional situations?

Representing Proportions with Graphs

Earth weight

(lbs)6 12 18 30

Moon weight

(lbs)

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.

Representing Proportions with Equations

Step 2 Find the constant of proportionality.

Moon weight

Earth weight

1

6

2

3

5

The constant of proportionality is:

𝑘 =𝑦

𝑥

Representing Proportions with Graphs

Step 3 Write an equation

Let x = ____________________

Let y = ____________________

Use the equation y kx

The equation is:

weight on Earth

weight on Moon

1

6y x

3.2 Rate of Change

Rate of Change

EQ: How do you find a rate of change?

constant rateThe cost is $0.75 per Snickers.

.75y x b

Example

Dependent variable Independent

variable

The cost depends on the number you buy.

chg. in dependent variable ( )

chg. in independent variable ( )

y

x

Rate of ChangeEve 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.

Independent Variable _____________________

Dependent Variable _______________________

Explain ________________________________

# of lawns

$ earnedThe amount earned depends on the number of lawns mowed.

Rate of ChangeStep 2 Find the rates of change

Day 1 to Day 2: change in $

change in lawns

45 15

3 1

30

2 15

Day 2 to Day 3:

Day 3 to Day 4:

change in $

change in lawns

change in $

change in lawns

90 45

6 3

120 90

8 6

45

3

30

2

15

15

The rates of change are / are not constant. Price per lawn is _________.

The rates of change are constant. Price per lawn is $15.

3.2 Slope

Slope (m)EQ: How do you find the slope of a line?

2 1

2 1

rise

run

y ym

x x

The steepness of a line.

x x

x x

Method 1

Label ordered pairs

1 1 2 2

1,4 3, 5

, ,x y x y

Write down formula 2 1

2 1

y ym

x x

Substitute values 5 4 9 9

3 1 4 4m

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

Find the rise / run

1 , 4

3, 5

3.3 Interpreting Unit Rate as Slope

Rate

EQ: How do you interpret the unit rate as slope?

dollars

oranges

Ratio comparing quantities measured in different units.

Unit Rate Ratio where the second quantity is 1.

Example $ per orange oranges per $1oranges

dollars

$2 10 $0.20

10 10 1

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

Slope Intercept Form of an Equation

EQ: How can you determine the slope and y-intercept of a line?

Rate of Change

𝑦 = 𝑚𝑥 + 𝑏

slope y-int

Start value

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

Step 1

EQ: How can you graph a line using the slope and y-intercept?

𝑦 = 𝑚𝑥 + 𝑏

slope y-int

Identify m and b

Step 2 Plot the point of the y-intercept.Use the slope to find a second point.

Step 3

4.4 Proportional and Nonproportional

Proportional

EQ: How can you distinguish between proportional and nonproportionalsituations?

𝑦 = 𝑚𝑥

Nonproportional 𝑦 = 𝑚𝑥 + 𝑏

Line goes through the point (0,0)

Starting point of line is the y-intercept