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```Expressions, Equations and Inequalities
Unit Test Date:
Monday: September 15th
Unit Objectives:
• Model real-world situations with variables
• Evaluate and simplify algebraic expressions
• Solve algebraic equations and inequalities, including
absolute values.
Today’s Objective:
Patterns, Real Numbers, Algebraic Expressions
Identify
&
Describe
Patterns
You are playing a video game. You reach a
locked gate. The lock is a square with 9
sections. Near the gate is a carving of a pattern
of squares. The key to the gate is the eighth
image in the pattern. Draw the key.
How many toothpicks for 20th figure?
Variable:
symbol that represents a number
Numerical Expression: Phrase with numbers
& operations
Algebraic Expression: Phrase with numbers,
variables & operations
Fig.
number of
#
Process toothpicks
input
Output
1
1(4)
2
2(4)
4
8
3
3(4)
12
⋮
⋮
n
4(n)
⋮
4n
Properties of Real Numbers
You use emoticons in text messages. How can
you describe a set of that includes five of the
emoticons but not the sixth?
Multiplication
Closure
a + b is real
ab is real
Commutative
a+b=b+a
ab = ba
Associative
(a+b)+c=a+(b+c)
(ab)c=a(bc)
Identity
∙1=
a+0=a
Inverse
a+(− a)=0
1
∙ =1

Distributive: a(b + c) = ab + ac
Algebraic Expressions
During summer vacation, you work two jobs. You walk three dogs several times a
week, and you work part time as a receptionist at a hair studio. You earn \$8 per
hour as a receptionist and \$20 per week per dog. Your weekly schedule (shown
below) is the same each week. How much will you earn in 10 weeks? Explain.
\$2,200
Write an algebraic expression for each.
Seven fewer than a number t
−7
two times the sum of a and b 2( + )
Algebraic Expressions
Evaluate: Substitute a number for
7 + 4 when a = 3
each variable and simplify
7(3) + 4 = 24
Term: Product of a number and one
or more variables
Coefficient: Numerical factor of a
3 2 + 5 2 + 9 3  + 2 − 4 3
term
Constant Term: Term with no
variables
8 2 + 5 3  + 2
Like Terms: Terms with same
variables raised to the
same powers
```
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