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1. Can you find the MATH in your every day? Slope Unit
Covering Standards – EA- 4.1, 5.2, 5.5, 5.6, and 5.7
2. Little Notes from the authors: Time – we tried not to assign YOUR time in the unit overview due to the differences between traditional and block scheduling. As one part ends, just let another begin.
Teacher prompts – we give prompts, but we only intend these to be suggestions.
Worksheets and rubrics – we offer these, but feel free to make them your own.
3. Pre-Skills Assessment You do not have to use this, because it is not IN our 4E X 2. We are moving into this slope unit after the students have been introduced to graphing functions on graphing calculators. They can identify a function, graph a function and verify their results with a graphing calculator. We designed this for groups of two.
Teacher: see worksheet: Pre-skills assessment
4. Before getting started, have your students in groups. Our resources that we offer work around groups of three, but you may vary them as needed. Here are the hyperlinks to the various cellular companies if you need to research plans in order to add a plan to our worksheets.
Alltel – http://www.alltel.com/personal/wireless/plans/plans_individual.html
Sprint – http://nextelonline.nextel.com/NASApp/onlinestore/en/Action/DisplayPlans
T-Mobile – http://www.t-mobile.com/shop/plans/
Verizon - http://www.verizonwireless.com/b2c/store/controller?item=planFirst&action=viewPlanList&sortOption=priceSort&typeId=1&subTypeId=1&catId=323
5. 1, Engage – What do you know about cellular phone plans? Teacher: This will vary with every class. Give them a piece of paper for them to jot down what they know individually about cell phone plans. Then, in their groups, combine what they know. Now, as a class, you will highlight the similarities. You are wanting to focus in on the idea that if you go over on minutes, it will cost $.
6. 2, Explore – What do you know about cellular phone plans? With the students in their group, hand out the phone plans. Each group will get a different carrier. Each person within that carrier should pick their own plan, to explore what happens when they have overage. Every student should receive their own ‘Inquiry into phone bills’ worksheet.
Teacher: See worksheets :
Phone Plans- Inquiry into phone bills.
7. 3, Explain – What do you know about cellular phone plans? The groups will display their data.
At this time, it depends on what the students give you. We want to investigate data through a table and a graph. If one group gives any of this, we lead each group to give us this information. They will add this to their existing data, we want one graph per group with each plan a different line. The students explaining their data will lead the them to the next explore – writing a linear equation.
Teacher prompts: Once all groups have a graph and table on display, you can ask for any similarities and differences. Where does your data start? Does your data end? What is realistic? How many points did you pick and why? Is this data linear? What about predicting their bill. Could they do this with their graph?
8. 2, Explore – Writing linear equations. Teacher: see worksheet: Explore writing linear equations. We want the students to realize that they have seen these types of equations, and are capable of writing their own equations.
After individual/group exploration, have at least one equation written on their graphs to share with the class. Let these equations be incorrect if they are. We will address their thoughts in the next explain – writing linear equations.
Teacher prompts: What do you need in an equation? (=) What could you have on each side of the equality sign?
9. 3, Explain – Linear equations (This is mostly teacher oriented.) As a teacher, identify their variables, their base plan cost, and their constant rate of change in their given equations.
Teacher prompts: Ask them what makes a line? ( at least 2 points ) What do you need for a point? ( an x and y coordinate) Do you have two points? What are they? If you plug these points in, will your equation still be true? These are some questions to help identify their variables.
If they leave out the base plan cost, you could ask them ‘all you owe the phone company is overage? ‘ Where is your initial cost in your equation? These are some questions to help identify the y-intercept.
To help them identify the constant rate of change, you could point at a graph and ask, ‘What is different between these two lines? What made them different or ‘steeper’?
Now, we introduce the slope-intercept form of the equation of a line and using the procedure to find slope.
Teacher: see worksheet: Explain writing linear equations – homework.
(This may be a time that you assign problems from their textbooks or other resources.)
10. 4, Extend – To the x-intercept. Teacher: Our equation includes a y variable, a slope, an x variable, and a y-intercept. What is the y-intercept? (an ordered pair, )
We want to lead to the fact that the x coordinate is zero in the y-intercept, so that we can lead them into the next explore concerning the x-intercept.
11. 2, Explore – The x-intercept Teacher: Look again at your graph. Find the coordinates of the x-intercept.
Teacher prompt: This explore may need more prompting as you walk around the room.
You can reflect back to the fact that the x-coordinate is zero in the y-intercept. (0, y) What would you think would be true of an x-intercept? How would we write the x-intercept? How would we find the x-intercept from an equation?
12. 3, Explain – The x-intercept The groups will add at least one of their x-intercepts to their graphs by the ordered pair.
They will explain how they found it.
Teacher: Does this x-intercept make sense in our problem?
We discuss as a class, that this x-intercept does not make sense in this situation, because we will never have ‘negative’ minutes.
Teacher: see worksheet: Explain x-intercept.
13. 4, Extend – x-intercept makes sense Teacher: In groups, we ask the students to find a situation/problem, where the x-intercept does make sense. This will lead them into the next explore – x-intercept makes sense.
Teacher prompts: In order for your y-coordinate to be zero, (x,0), your x-axis will have to represent a situation that can either start at zero, or become zero. What kind of variables can be zero? (money, temperatures, time, sea level, …)
14. 2, Explore – x-intercept makes sense Now, individually, the student will write this situation into a problem, make a table, and transfer this into a graph. This individual work will be assessed. You may want to supply the paper, but we have not supplied a worksheet, because we want to see how the student will present the problem and data.
Teacher: see assessment: create your own linear scenario rubric
Teacher prompts: Weekly pay checks and wages, a submarine is built and lowered into the water, a scuba diver entering the water, paying back a loan over time (paying your parents back for your overage), temperatures, …
15. 3, Explain – x-intercept makes sense You can use this last explain to tie in the ‘textbook’ and the EOC. We have tried to offer worksheets that give them some exposure to what the EOC might have. You can point out the effects of changes in slope and the y-intercept on the graph of
16. Our goal for this slope unit was to have our students realize that a linear equation is nothing more than ‘figuring out how much trouble they are going to be in for going over 62 minutes on their cell plan.’
We hope it works!
Thank you in advance for any feedback,
Julie Davis (Berea High), Jason Fellers (Woodmont High), Elaine Romano (Greer High), and Becky Bryant (Greenville High)