Algebra 1 Lesson Notes 1.1A Date ______
Objective: Evaluate algebraic expressions
variable: a letter that is used to represent one or more numbers.
The numbers are the values of the variable.
The values may or may not be known.
expression: any representation consisting of numbers, variables, and operations.
e.g. 6 × 3 x + 4
algebraic or variable expression: an expression that includes at least one variable.
e.g.
evaluate an algebraic expression: substitute a number for each variable, perform the
operations, and simplify the result, if necessary.
Example 1 (p 2): Evaluate algebraic expressions
Evaluate the expression when c = 4.
a. 4c
b. 8/c
c. 15 – c
d. c + 7
¥ CW: p 2 Guided Practice #1-4
Variable expressions can have meaning, represent situations:
example: If b represents boys in the class and g represents girls in the class, what does
b + g represent?
If I go to the next classroom, does b + g make sense? Would the values be
the same?
Example 2 (p 3): Evaluate an expression
a. Assume that a is the cost of admission at a movie theater and r is the cost of refreshments. Write a variable expression that would represent the total cost of going to the movies?
If admission is $7.50 and you spent $5.25 for soda and candy, evaluate a + r.
If admission is $7.50 and you spent $7.25 for popcorn and soda, evaluate a + r.
The value of r changes depending on what you buy for refreshments. Why might the
value of a change?
What could 4a represent? What could 2a + r represent?
b. You are ordering a skateboard and a helmet from an online store.
If s represents the weight of the skateboard and h represents the weight of the helmet,
write a variable expression to represent the total weight of the items.
Find the total weight if the helmet weighs 1.3 kg and the skateboard weighs 5.4 kg.
How would you represent the total weigh of an order for 5 skateboards and 6 helmets?
What could 10(s + r) represent?
HW: A1 p 5-7 #4-15, 40-45
Algebra 1 Lesson Plan 1.1B Date ______
Objective: Use exponents and evaluate powers
power: an expression that represents repeated multiplication of the same factor.
(Remember, a factor is a number or variable that is being multiplied.)
81 is a power of 3 because 34 = 81
base of a power: the number or variable that is used as a factor.
exponent: The number of times the base will be multiplied.
e.g. 34 { identify the base and the exponent
34 = 3×3×3×3 = 81
Example 3 (p 3): Read and write powers
62 Þ 6 squared or 6 to the second power Þ 6 × 6 Þ 36
(1/5)3 Þ 1/5 cubed or 1/5 to the third power Þ 1/5 × 1/5 × 1/5 Þ 1/125
q6 Þ q to the sixth power Þ q × q × q × q× q × q
³ Special note:
The first power is usually not written as a power; just write the number or the
variable.
71 Þ 7 to the first power Þ 7
x1 Þ x to the first power Þ x
³ FYI: any number or variable to the zero power is equal to 1.
350 Þ 1
(7/1200)0 Þ 1
q0 Þ 1
Example 4 (p 4): Evaluate powers
a. Evaluate n5 when n = 3
35 = 3×3×3×3×3 = 243
b. Evaluate d2 when d = 9/5
(9/5)2 = 9/5 × 9/5 = 81/25 Ü Notice proper notation to raise a fraction
to a power!
Ü Remember how to multiply fractions!
c. Evaluate b7 when b = 2
d. Evaluate h3 when h = 4/3
¥ CW p 3 Guided Practice #6-8
Application of powers: Exponents are used in formulas for area and volume.
Example 5 (p 4): Evaluate a power
Area = s2 Volume = s3
If s = 3 ft, find area and volume.
If perimeter = 40 cm, find area and volume.
¥ CW p 4 Guided Practice #9-11
ADDITIONAL RESOURCES! Look at EXTRA PRACTICE on p 938
Try ONLINE QUIZ at classzone.com
HW: A2 pp 5-7 #16-36 even, 49-54
HW: A1-2 pp 5-7 #3-45 odd, 49-54
fms-Algebra 1 Lesson Notes 1.1 Last printed 7/11/2007 5:12:00 PM Page 4 of 4