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Welcome to
Math 112
Class #2 – 16-17
• Pick a puzzle piece and find the table where
your piece matches the description. This is
your new group for the next few classes.
• Introduce yourself to your new teammates!
• Please turn in HW #1 – make sure your
NAME is printed neatly on the first page
and put it in a neat pile!
• Then do the warm up (bar graph questions)
What does your quote
have to do with this
class?
Warmup
For those of you who received add
cards last week:
You must officially enroll
and pay for the course by
Monday, 2/20, or you will
be dropped from the class.
Time for Multiplication
practice!
Tonight’s Agenda
1.
Turn in HW #1 and do warmup
2.
Multiplication practice
3.
Class norms
4.
Review order of operations
5.
Fractions
1.
2.
3.
4.
5.
Fraction vocabulary
Finding equivalent fractions
Simplifying fractions
Adding and subtracting fractions
Area of a rectangle
6.
The Apartment Problem
7.
Quiz #1
Tonight’s
positive
quote!
Tonight’s focus:
Math practice #1
Make sense of problems
and persevere in solving
them.
Persevere - Continue in a
course of action even in the
face of difficulty or with little
or no prospect of success
Class norms
When students shout out answers in math class, the teacher should
___________________________________
When a student walks in late, the teacher should
________________________________
When several students have conversations during class, the teacher
should _________________________________________
When working in groups, team members should
__________________________________________
What I think about texting or using a cell phone to surf the
internet during class is
_____________________________________________
Class norms
 Be respectful
 Listen when others are speaking
 Use cell phones outside
 Clean up after yourself
Reminders!
 Complete Student Survey & turn in tonight (if you
didn’t do this last week)
 Test #1 is next week! It will be similar to
tonight’s team quiz.
 If you do not take the first test you will be
dropped from the course!
Persevere
Continue in a course of
action even in the face of
difficulty or with little
or no prospect of success
More
Order of
Operations
Order of Operations
review
Ex. 1
6 + 16 ÷ 2 ∙4 - 8
Ex. 2 Place parentheses in the
expression so that the
multiplication is done first.
Simplify your new expression.
6 + 16 ÷ 2 ∙4 - 8
Ex. 3 Place parentheses in the
expression so that the addition
is done first. Simplify your
new expression.
6 + 16 ÷ 2 ∙4 - 8
Ex. 4 Find the error and circle
it. Then copy over and simplify
it correctly.
[6 + 2(8 ÷ 4 ∙2)] - 8
[6 + 2(2∙2)] - 8
[6 + 2(4)] - 8
[8(4)] - 8
32- 8 = 24
Intro to Fractions
Fractions
Essential question: What is the vocabulary used for fractions?
Foldable
Example:
2/3
Numerator is 2
Bar means divide
Denominator is 3
This means 2

3
1/3
 The numerator is 1
 The denominator is 3
Proper Fraction
A fraction that is less
than one, with the
numerator less than the
denominator.
Example: 2/3
Improper Fraction
A fraction that is greater
than one or equal to one,
with the numerator larger
than (or equal to) the
denominator.
Example: 7/4 or 7/7
Mixed Number
A whole number plus
a fraction
Example: 1 ½ or 1 ¾
Equivalent Fractions
Fractions that have the same
value
Example: ½ = 2/4 = 4/8
Equivalent Fractions
How can we find equivalent fractions using an area model?
 Is there another way to represent 1/3?
1 ?
=
3 ?
Equivalent Fractions
How can we find equivalent fractions using an area model?
 Make 2 rows
1 ?
=
3 ?
Equivalent Fractions
How can we find equivalent fractions using an area model?
 Make 3 rows
1 ?
=
3 ?
Equivalent Fractions
How can we find equivalent fractions using an area model?
 Make 4 rows
1 ?
=
3 ?
Equivalent Fractions
How can we find equivalent fractions using the Giant 1?
 Multiplying by 1 does not change the value of a number
 A fraction with the same numerator and denominator
has a value of 1.
 The Giant One:
Equivalent Fractions
How can we find equivalent fractions using the giant 1?
Find 3 equivalent fractions for 1/3 multiplying by the
giant 1:
⅓×
⅓×
⅓×
Reducing Fractions to
Lowest Terms
How do I simplify fractions to lowest terms?
Ex. 1 Simplify 48/64
 What is the largest factor that is common to 48 and 64?
This is called the Greatest Common Factor (GCF).
 Use a factor tree to find the GCF.
 Next rewrite the fraction 48/64 using the GCF
 Find the giant 1. The remaining fraction is the simplified
fraction.
Ex. 2 Simplify 16/24
 What is the largest factor that is common to 16 and 24?
This is called the Greatest Common Factor (GCF).
 Use a factor tree to find the GCF.
 Next rewrite the fraction 16/24 using the GCF
 Find the giant 1. The remaining fraction is the simplified
fraction.
Ex. 2 Simplify 18/54
 What is the largest factor that is common to 18 and 54?
This is called the Greatest Common Factor (GCF).
 Use a factor tree to find the GCF.
 Next rewrite the fraction 18/54 using the GCF
 Find the giant 1. The remaining fraction is the simplified
fraction.
Ex. 3 Simplify 30/12
 What is the largest factor that is common to 30 and 12?
This is called the Greatest Common Factor (GCF).
 Use a factor tree to find the GCF.
 Next rewrite the fraction 30/12 using the GCF
 Find the giant 1. The remaining fraction is the simplified
fraction.
Always reduce fractions to
lowest terms
You do not need to change
improper fractions to mixed
expressions. (In other
words, 4/3 is an acceptable
answer – you do not need to
change it to 1 ⅓)!
Adding and Subtracting
Fractions
How can we use an area model to + and – fractions?
Adding and Subtracting
Fractions
 Before fractions can be added
or subtracted, the fractions
must have the same
denominator. This is also
called a common denominator.
Make equivalent fractions
Adding and Subtracting
Fractions
How can we use the giant 1 to + and – fractions?
Example 1: ¼ + ⅓
 First list the multiples of 4 and 3.
 Circle the first multiple they have in common. This is the
COMMON DENOMINATOR.
 Multiply ¼ by a giant 1 to get a new fraction with the
common denominator.
 Multiply ⅓ by a giant 1 to get a new fraction with the
common denominator.
 Add the fractions (add numerators, keep the common
denominator) and simplify, if necessary.
Area of a Rectangle
Apartment
Problem
P. 22
(1-40)
Problem 1-40
The Apartment
Your task: Find the
possible dimensions
for every room in
the apartment.
Section 1.2.1 (P. 22)
How can I solve it?
Solving Problems with Guess and
Check
Objectives:
To solve a complex problem
and develop a new problemsolving strategy called
“Guess and Check”
How can we organize our
work for the apartment
problem using a table?
Here’s an example:
Team Quiz #1
 Everyone gets a copy of the quiz.
 Show all work on your own paper
and consult with your team!
 All papers will be collected.
Homework #2
 Handout
 Test #1 will be at the beginning
of class next week. If you
arrive late you will not be given
extra time, so plan accordingly!