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Age ActivityStart with your ageStep 1: Add 5 to the ageStep 2: Multiply the result of Step 1 by 2Step 3: Subtract twice your age from the
result of Step 2Step 4: Subtract 10 from the result of Step
3
Pick different ages and try again.
Talk with the people in your group and explain why you get the answers you get.
Vocabulary for Chapter 1.1
• Variable– A letter that is used to represent one or
more numbers.
• Variable Expressions– A collection of numbers, variables and
operations.
Let’s write variable expressions from the Age Activity
Start with your ageStep 1: Add 5 to the
ageStep 2: Multiply the
result of Step 1 by 2Step 3: Subtract twice
your age from the result of Step 2
Step 4: Subtract 10 from the result of Step 3
x
(x + 5) 2
x + 5
((x + 5) 2) – 2x
(((x + 5) 2) – 2x) - 10
Steps to solving Variable Expressions
1. Write the variable expression
2. Substitute values for the variables
3. Simplify the numerical expression
y =5
8y
8(5)
40
Evaluate the expression when a = 3 and b = 4
1) a + b
3 + 4
7
2) 2a - b
2(3) - 4
6 - 4
2
3) 4
ab
4
)4)(3(
4
12
3
Find the average speed of a car that traveled 180 miles from Boise, Idaho to the Minidoka National Wildlife Refuge in 3 hours.
Average Speed = miles
hour
=distance time
3
18060 mph
==
Find the perimeter of the triangle in feet.
a = 8
b = 15
c = 17Perimeter – add all of the sides
Perimeter = a + b + c
8 + 15 + 17
40 feet
The simple interest earned by money P (the principal) at an annual interest rate r for t years is given by Prt. You deposit $650 at a rate of 8% per year. How much simple interest will you earn after one half of a year?
Simple interest = Prt
P = 650r = 8% = 0.08t = ½ = 0.5
=(650)(0.08)(0.5)= $26
Use you calculator to fill in the tables. Use the ^ key for the exponents: 2^1
for the first value2 2 2 2 2 2 2
3 3 3 3 3 3 3
4 4 4 4 4 4 4
5 5 5 5 5 5 5
1)
4)
3)
2)
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6 7
6
6
6
7
7
7
2
3 9
4 16 64 25610244096
5 25 125 625 312515625
27 81 243 729
78125
16384
2187
12864321684
Vocabulary for Chapter 1.2
• Power– An expression like
• Exponent– The number 6 in the expression
• Base– The number 4 in the expression
64
44444446
An aquarium has the shape of a cube. Each edge is 2.5 feet long. Find the volume in cubic feet.
2.5ft
2.5ft
2.5ft
Volume = length width height
Volume =lwh
Square – l=w=h=s
=s s s =s
=(2.5)
=15.625 ft
3
3 3
You are ordering a pair of jeans from a catalog. The catalog company charges sales tax on the total purchase amount, plus a shipping fee. The jeans you are ordering cost $20. The sales tax rate is 5% and the shipping fee is $3. Which is the correct way to compute your total bill? Why?A) 20 + 20 0.05 + 3 = 40 0.05 + 3 = 2 + 3 = 5
B) 20 + 20 0.05 + 3 = 20 + 1 + 3 = 21 + 3 = 24C) 20 + 20 0.05 + 3 = 40 0.05 + 3 = 40 3.05 = 122D) 20 + 20 0.05 + 3 = 20 + 20 3.05 = 20 + 61 = 81
1. 3 · (5 + 4)
3 · (9)
27
2. 3 · 4² + 1
3 · 16 + 1
48 + 1
49
3. 16 + 4 ÷ 2 – 3
16 + 2 – 3
18 – 3
15
4. 5 · 3² - (6 + )
5 · 3² - (6 + 4)
5 · 3² - 10
5 · 9 – 10
45 – 10
35
5. 10 ÷ (3 + 2) + 9
10 ÷ 5 + 9
2 + 9
11
6.3
12
1498
47
157
28
1498
28
2
1
56
28
178
472
Definitions
• Equation– When an equal sign (=) is placed between two
equal expressions
• Inequality– When an inequality symbol is placed between two
expressions
Check whether the numbers 2, 3 and 4 are solutions of the equation 4x – 2 = 10
x 4x – 2 = 10 Result Conclusion
2
3
4
4(2) – 2 = 10
4(3) – 2 = 10
4(4) – 2 = 10
6 10
10 = 10
14 10
Inequality Symbols
Symbol Meaning
>
< is less than
is less than or equal to
is greater than
is greater than or equal to
Decide whether 4 is a solution to the inequality
a) 2x – 1 < 8
b) x + 4 > 9
c) x – 3 1
2(4) – 1 < 8
7 < 8
4 + 4 > 98 > 9
4 – 3 1
1 1
8 – 1 < 8
Addition Subtraction
Multiplication
Division
times
sum
total
more than
decreased by
fewer than
plus difference
minus
quotient
product
twice
ofless
multiplied
less than
increased by
half
divided
fewer
Translate Verbal Phrases into Algebra
1) 3 more than the quantity 5 times a number n.
2) 2 less than the sum of 6 and a number m.
3) A number x decreased by the sum of 10 and the square of a number y.
4) The product of seven and a number y is 12.
5) 4 cubed divided by a number p.
3 + 5n
(6 + m) - 2
x – (10 + y²)
7y = 12
4³ ÷ p p
34
Translate Expressions into Verbal Phrases
1) 9 > 3s
2)
3) 3(x – 2) = 10
4) 5x - 12
n
20
Nine is greater than 3 times a number s.
20 divided by a number n.
Three times the difference of x and 2 is 10.
5 multiplied by x minus 12.
Using a Verbal Model
1) Ben’s hourly wage b at his after school job is $1.50 less than Eileen’s hourly wage e.
2) The distance s to school is 1/5 mile more than the distance c to the Community Center’s swimming pool.
3) The length c of the Colorado River is 3 times the length r of the Connecticut River plus 229 miles
b = e – 1.50
s = c + 1/5
c = 3r + 229