## UNIT 4 - WEEK 11

Discovering Algebra

## SummaryBuilding on the skills learned in Week 10, students begin to explore the idea that algebraic functions can be created to model many of the situations we encounter on a daily basis and the value of quantifying these situations.
We look at standard way to represent tables of values, independent and dependent variables, and further solidify working with graphs and their meanings. |

## Week 11 - Lesson 1 |
Topic of the Day/Driving Question:
How do we create useful equations that can easily be used to represent many different situations? Good Questions: - In the previous unit what were we using to represent the price of pizza, and what about the number of toppings?
- Can we create similar equations to represent different What does independent mean?
- Why do we want to be creating general equations as opposed to trying to create one every time we need to use it.
In class activity: Suppose that the Microsoft is considering a rental service on their XBOX One console. What information would we need in order to come up with an equation and determine at what point it would be better for us to for us to just purchase the game? Once you have your equations, use DESMOS.com or any other online graphing tool to show what this looks like graphically. What happens at the point where it is cheaper for us to purchase. Homework:Students are expected to contribute their findings in an online discussion created in the LMS. They are to discuss if they think the renting option is something Microsoft should pursue or not. They should also comment on whether they would be inclined to use the service or not. |

## Week 11 - Lesson 2 |
Topic of the Day/Driving Question:
Is there a standard way for us to represent our (x,y) data before we graph it? Good Questions: - What is a table of values and why is it important?
- Recall independent and dependent variables, how do they impact our table of values?
- How do we figure out what numbers go in the table of values?
- How should we graph these values?
In class activity: Explore the concept of a table of values by revisiting our shoe size activity. Determine if the number of students or the shoe size is the independent variable. Then create a two column table and explain that it is generally accepted that the independent variable goes in the first column because it is what determines the value of the second column. Take a poll of the class and determine what each student’s shoe size is. As all students have their own device, you may choose to implement an online polling system. If you use a polling system, it may present your findings in a table similar to what we are working with. This is a great opportunity to show that it is a very effective way to show data. We can now plot this data on a cartesian plane (use GeoGebra or DESMOS) and ask the students if this is a linear set of data? Why is it not? What are we encountering as we look at real data? We are finding that many things are not going to fall into the generic linear equation (y=mx+b). Now consider an existing linear equation (y=3x+2 or anything you choose). In this form, we see that x is the independent variable and y is the dependent variable. How do we complete a table of values for this equation? How many numbers do I need to use? For the purpose of this course, we find that five values for x and thus 5 values for y are sufficient to create an accurate graph. Homework: Students are to complete the table of values for our equation y=3x+2 for homework. Create a space in the LMS where students can dialogue with each other and post questions. Next class will continue with a discussion on the table of values. |