1. Liberal Arts Math Bell Work: Explain the following:
What are the parts of an algebraic expression?
What is an algebraic expression?
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

2. Proportional Reasoning
Definition: is a form of mathematical reasoning that involves a sense of co-variation and of multiple comparisons, and the ability to mentally store and process several pieces of information.
It also refers to the ability to compare two things using multiplicative thinking, and then apply this to a new situation.  It is also frequently defined as just the ability to compare quantities multiplicatively.
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

3. Proportional Reasoning
Example:
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

4. Proportional Reasoning
Practice Problems:
Wayne paid $5 for 4 notebooks.  How much would he pay for a dozen?
Jill's new car can travel 32 miles per gallon.  How far can she travel on 18 gallons?
The ratio of tulips to daffodils in Mrs. Smith's garden is 5 : 7.  If there are 21 daffodils, how many tulips are there?
Marie can run 10 kilometers in 45 minutes.  In how many minutes can she run 3 kilometers?
The ratio of soccer players to basketball players in the auditorium is 4 to 7.  If there are 132 students in the auditorium how many soccer players are there?
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

5. Proportional Reasoning
Exit Ticket:
What in the real world would suggest to you, to use proportional reasoning?
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

6. Liberal Arts Bell Work:
Review your notes for questions for test? Write down 5 Questions you may have?
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

7. Review Example 1: Write each sentence as an algebraic equation.
Sentence
Algebraic Equation
A number increased by nine is fifteen.
y + 9 = 15
Twice a number is eighteen.
2n = 18
Four less than a number is twenty.
x - 4 = 20
A number divided by six is eight.
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

8. Proportional Reasoning
Review
Proportional Reasoning
Problem: The ratio of dogs to cats in the animal shelter is 2:5.  If there are 91 dogs and cats how many cats are there in the shelter?
Solution:
Set up the ratio as :
Since the ratio tells us there are 5 cats out of 7 total (2+5=7) then:
To solve, cross multiply…
7x = 5(91)
7x = 455
X = 65
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

9. Review
Questions:
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world

10. Test
EQ: What is proportional reasoning and how do we use it in the real world?
I will: be able to show how proportional reasoning is related to the real world