Chapter 1

Expressions, Equations, and Functions

1.1 Evaluate Expressions

I can evaluate algebraic expressions and

use exponents.

CC.9-12.N.Q.1

Vocabulary:

Variable – a letter used to represent one or more numbers

Algebraic expression – expression that includes at least one variable

Evaluate an Algebraic Expression

Substitute a number for each variable and simplify,if needed

Example: Evaluate the expression when c = 4a)4c

b)8/c

c)15 + c

Powers:

Note: anything to the zero power = 1

Examples:

Write the power in words and as a product.a)52

b)

31

2

Example: Evaluate the expression.

A) n5 when n = 3

B) d2 when d = 9

5

HOMEWORK:

p. 5 #1, 2, 4 – 48 even

1.2 Apply Order of Operations

I can use order of operations to evaluate

expressions.

CC.9-12.A.SSE.1

In most languages, the meaning of words depend on the order:

Ex.

Sign the check

Is not the same as

Check the sign

Mathematics is a type of language with its own syntax and grammar.

Ex. 3 + 5 X 2

What do we do first? Add or multiply?

If we add first:

3 + 5 X 2

8 X 2

16

If we multiply first:

3 + 5 X 2

103 +

13

Uh Oh! Which one is the correct answer?

What is PEMDAS?In order to make sure every person gets the same answer to a math problem, mathematicians came up with a rule called the order of operations

Parenthesis ( ) [ ]

Exponents 23

Multiplication X

Division ÷Addition +

Subtraction -

In order from left to right!

In order from left to right!

Example: Evaluate -8 + 5(1 – (-3))3

14

Example: Evaluate -4x2 + 6x – 5 when x = -3

15

HOMEWORK:

p. 10 #1, 2, 4-34 even

1.3 Write Expressions

I can translate verbal phrases into

expressions.

CC.9-12.A.SSE.1

Translate Verbal Expressions

Example: Translate the verbal phrase into an expression.

a)8 times the quantity 4 plus a number n

b)12 decreased by a number x

c)The quotient of the square of a number w and 5

Vocabulary:

Verbal model: describes real-world situations using words and math symbols

Rate: fraction that compares two quantities measured in different units

Unit rate: rate where the denominator is 1 unit

Example: A runner travel 730 yards in 5 minutes. Find the unit rate in feet per second.

* Check your unit analysis!

HOMEWORK:

p. 18 #1, 2, 4 – 28 even, 31, 32

1.4 Write Equations and Inequalities

I can translate verbal sentences into

equations or inequalities.

CC.9-12.A.CED.1

Vocabulary:

Equation:

Inequality:

Open sentence:

Symbol Meaning Words

= Equal to The same as

< Less than Fewer than

Less than or equal to

At most, no more than

> Greater than More than

Greater than or equal to

At least, no less than

Example: Write an equation or inequality.

a) The sum of twice a number r and 3 is 11.

b) The quotient of a number n and 2 is at most 16.

c) A number q is at least 5 and less than 17.

Solution of the equation or inequality:a number that makes theequation/inequality true.

Example: check whether 5 is a solution of the equation or inequality

a) 24 – 3d = 9 b) 4 + 3p > 19

HOMEWORK:

p. 24 #1, 2, 4 – 36 even, pick 3 from #39-43

1.5 Use a Problem Solving Plan

I can use a problem solving plan to solve

problems.

CC.9-12.A.CED.1

Vocabulary: Formula – equation that relates two or more quantities.

Examples:

4 Step Plan:

1)Understand

2)Plan

3)Solve

4)Check

A builder lays sod on the lawns of new homes. The installed cost for sod is $.38 per square foot. What is the cost of installing sod on a rectangular lawn that is 32 feet long and 18 feet wide?

Activity

HOMEWORK:

p. 31 #1 – 10, 14-19

1.6 Use Precision and Measurement

I can compare measurements for

precision.

CC.9-12.N.Q.3

Vocabulary: Precision – level of detail that an instrument can

measure

Significant digits – digits in a measurement that carry meaning that contributes to precision of measurement

Precision:

Choose the more precise measurement

a) 7 cm or 7.3 cm

b) 0.2 gal or 6 qt

c) 7 in or 2.02 ft

Significant Digits (figures): numbers that are important to precision of measurement

All non zero digits371.46 (5 sig figs)

Zeros to the right of the last nonzero digit and thedecimal point0.0030 (2 sig figs)

Zeros between significant digits300.2 (4 sig figs)

Example: Determine the number ofsignificant digits in each measurement.a) 250

b) 0.0620

c) 30.04

Rules for Sig Figs in Calculations:

Addition/Subtraction:Round the answer tosame place as last digitof the least precisemeasurement.

Multiplication/Division: answer must have the same number of digits as the least precise measurement.

HOMEWORK:

p. 38 #1 - 28

1.7 Represent Functions as Rules and Tables

I can represent functions as rules and as

tables.

CC.9-12.A.CED.2

Vocabulary: Function: pairing of inputs with outputs so that each

input is paired with exactly one output.

Domain: set of all inputs

Range: set of all outputs

Input Output

1 6

2 7

3 8

4 9

Example: Look at the input value and determine what rule applies to get the output value.

Example: Tell whether the pairing is a function..

a) Input output b) Input output

-3 -2 -3 -1

2 1 -1 1

3 3 1 3

2

Function Rules:

Independent variable – input variable

Dependent variable – value depends on value of input;output

Example: The domain of the function is y = x + 4 is 0, 2, 3, 6, and 7. Make a table for the function. Identify the domain and range.

HOMEWORK:

p. 44 #1 – 10, 14 - 21

1.8 Represent Functions as Graphs

I can represent functions as graphs.

CC.9-12.F.IF.4

0 1 2 3 4 5 6 7

Let n = # of triangles Let p = the perimeter of each figure

n p

1 3

2 4

3 5

4 6

5 76 8

Dependent

Model:

Table: Graph: Equation:p

n# of triangles

perimete

r

87654321

p = n + 2

Dependent

Platter Weight Price

1 lb. $2.10

2 lb. $3.60

3 lb. $5.10

4 lb. $6.60

5 lb. $8.10

This chart shows the price of sliced fruit platters.

1) How much would a 6 lb. platter cost?

2) Write an equation forthe cost of a platter thatweighs w lbs.

Let p = price of platter

p = 1.50 w + 0.603) How much would a 10 lb.platter cost?

Change StartValue

A taxi cab charges a flat rate of $2.50 and 15 cents per mile. Write a linear equation for the charge in terms of the number of miles driven. Then graph the function.

Let C = charge in dollars

Let m = # of miles driven

m

Let m = # of minutesLet V = Volume of gas in tank

V

A car’s fuel tank is filled at a rate of 1.6 gal/min.The tank held 5 gallons of gas before refueling.

Table: Graph:

Equation:

HOMEWORK:

p. 52 #1 – 13, 15 - 17