When I first was introduced to the rationale behind Project Based Learning, I said, “Yes! Let’s do this!” Which then quickly turned into, “How can I do this with upper level high school math?” It seemed so daunting. How on Earth am I going to come up with a meaningful real world application for high school students with topics like rational and polynomial functions? So I started with word problems.
Here is a word problem I found just by googling “composition of functions word problems worksheet”
Now this word problem got me thinking, what if students won the lottery and had a bunch of money to spend? That might get them interested in this situation. And thus, my Shopping Spree PBL was born.
I started by finding a word problem. Check.
Next, I look at the situation and ask myself, can I use this same situation or can I modify it in some way to make it more appealing to my students? How can I give students some choice? In this case, I adapted the scenario explaining to students that they have $500 to spend at any one store, and they have two magic coupons that can be applied at the same time, 1) $100 off and 2) 30% off the purchase. Their job is to figure out the order of coupons that will give them the best discount. The “student choice” element in this project is coming from how they spend their $500 and their overall shopping spree total.
Now that I have the situation handled, I think about what product my students will submit. For this, I wanted my students to submit a purchase order of the items in which they want to spend their $500 as well as their work to the 5 questions listed above, modifying them as needed for the updated scenario. It would be easy to stop here, but I always push writing in my math classroom, so I added a written component to this as well. After students figure out which order the coupons should be presented in to give them the best deal, they write a letter to their parents persuading them to let them go on this shopping spree.
RECAP
Here is how I created this project:
Google a word problem for a specific skill
Select a word problem with an interesting scenario and modify it for my students
Create or design a product for them to submit to showcase their learning
That three step process is the meat and potatoes of project planning. The fancy side dishes and desserts come from how you decide to present the project. You can present it in a PBL format - introduce the problem with an Entry Event and Knows and Need to Knows activity before teaching students about composition of functions. Or you can present it as a Performance Task after you have taught students about function composition. I have used it both ways and have had success.
Shopping Spree PBL
Timeline: 2 - 3 days
Entry Event
Ask your class, what would you do if you won the lottery? You may also want students to read this article on 23 Lottery Winners who Lost Millions and discuss any insights students have. Then you will present your problem scenario.
Knows and Need to Knows
Students will read through the Shopping Spree document and make a list of things they know and any questions they have. For example, they know that there is $100 off and a 30% discount that can be used at the same time and they might be familiar with function notation f(x), g(x), h(x), and j(x). However, they may not know the term function composition. You will use their Need to Know questions to generate your instruction.
Instruction
This is where you teach students how to compose functions using any instructional practice - direct instruction, inquiry based, experience first formalize later … You may also choose to provide skill practice and/or assess their skills in some way.
Application
Now that students know how to compose functions, they should be able to complete this problem. For this project, students will work individually since each person is going on their own shopping spree.
Grading
I use rubrics to grade all of my projects. For most of my projects, I grade 3 areas: Agency, Knowledge & Thinking, and Written Communication. Agency measures if students submit their work on time, Knowledge & Thinking measures their understanding of the math concepts and skills, and Written Communication measures how well they can express their ideas in words (I usually look for clear and concise writing, details to support main ideas, and the use of transitional phrases).
I hope this can inspire you to get started in designing your instruction for PBL. Finding a word problem and adding some pizazz is a great way to start. Let me know how your pizazzing goes!
Want this Shopping Spree problem with no additional work? Find it on my TPT store! Click on the image below!
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