1. Using iPad Technology to Help Enhance Student Learning/Ownership
Jeff Zittergruen
Benton Community High School
Algebra 2 and Statistics

2. Lesson Background Algebra 2 Class
Learning Target: Students can optimize a given value using the linear programming process.
Standard: (A-CED.A.3) Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context.
Application and Extension of graphing systems of inequalities, putting the content into a modeling context within a business

3. Past Frustrations Very limited flexibility
Students get stuck in the middle of the process and can’t work towards deeper understanding
Limited options for pushing further forward and extending the learning for students that were ready/able to do so

4. Problem
You are screen printing t-shirts and sweatshirts for the booster club to sell at the next school event and you are working under the following situations:
You have at most 20 hours to make the shirts
You want to spend no more than $600 on supplies
You want to have at least 50 items to sell at the event
T-shirts take 10 minutes to make, cost you $4 and the profit earned is $6 per shirt
Sweatshirts take 30 minutes to make, cost you $20 and the profit earned is $20 per shirt
How many t-shirts and sweatshirts should you make to maximize your profit?

5. First Steps
Initially talk about the limitations the booster club is facing in the problem scenario
Allows for options to discuss about limitations that businesses face in different career fields
Math Connections: ability to relate to writing equations which can help to reinforce that important skill for future work

6. DESMOS Application
Inclusion of technology in this lesson really enhances the opportunities for communication and extension, not just including technology to include technology

7. Next Steps
Relate back to solution region when graphing inequalities in previous work
Instant connection to the values in the solution region within the context of a problem
Allows for students that may struggle with the graphing that can now still get the connections and purpose of the process because the technology helps them past some of their limitations

8. New Learning: Corner Point
Corner points of solution region will be the points used to maximize our profit
Math Connection: Extension for students to be able to discuss the corner points being the intersection of our constraint lines
Math Connection: allows for some students that would struggle with finding those values the ability to still build the connections without getting lost in the calculations

9. New Learning: Corner Point

10. Graphing Extension
Math Connection: the ability in DESMOS to easily manipulate the equations allows me to have great discussions with students about what happens if circumstances would change within the problem
In class we can quickly and easily see the impact of changing one of the equations and what outcomes that changes with the solution region
It also allows the students to brainstorm about additional possible limitations within a problem which leads to better work when they do their project later in the unit.

11. Final Steps: Finding an Answer
Take the corner points and use them to answer the original question
More opportunities for synthesizing information to write an equation for the profit
Testing points to find the best possible option
Allows for students that may struggle with the graphing that can now still get the connections and purpose of the process because the technology helps them past some of their limitations

12. Final Steps: Finding an Answer
Ability to easily relate the answer they see with what it means in solving the original problem
Easy tie-in to business applications with finding a value that will help to maximize the profit of the business.

13. Opportunity to Extend
In the past, without the ability to easily manipulate the graphs, we were limited in the ability to extend past the problems presented in class
Now I have students do an extension activity where the students are placed into groups and they have to create their own linear programming problem for the other students in the class to solve

14. Student Examples
A baker makes cookies and brownies to sell at a bake sale. Baking a tray of cookies takes 4 cups of sugar and 3 cups of flour. Baking a tray of brownies takes 2 cups of sugar and 3 cups of flour. The baker has 16 cups of sugar and 15 cups of flour. They make $30 profit per tray of cookies and $20 profit per tray of brownies.
How many trays of cookies and brownies should the baker make to maximize their profit?

15. Student Examples
Constraints Sugar: 4c + 2b≤ 16 Flour: 3c + 3b ≤ 15 Corners (0,5) (3,2) (4,0) Profit $30(0) + $20(5) = $100 $30(3) + $20(2) = $130 $30(4) + $20(0) = $120

16. Student Examples
An electronics store produces two types of tablets, the regular and the mini. The regular takes 4 worker-hours of manufacturing and 5 worker-hours to program. The mini takes 8 worker-hours of manufacturing and 5 worker-hours of programming. The company has at most 6000 worker-hours in a week for manufacturing and 4000 worker hours each week for programming. The company wants to make at least 50 regular and 300 mini tablets each week. If the profit is $150 for regular tablets and $200 for mini-tablets, how many of each should they make each week?

17. Student Examples
Constraints Manufacturing: 4r + 8m ≤ 6000 Programming: 5r + 5m ≤ 4000 Regular: r ≥ 50 Mini: m ≥ 300 Corners (50,725) (100,700) (500,300) Profit $150(50) + $200(725) = $152,500 $150(100) + $200(700) = $155,000 $150(500) + $200(300) = $135,000