The Custom Ink Project: Systems of Equations

“My unicorn doesn’t fly, but it’s the most fly.”

Math, meet art.

This project for systems of equations gives students the chance to light up their creative side.  Students work in groups to design original apparel on Custom Ink, bring it to the class to see what it’s worth, build cost and revenue functions, and analyze how they’ll do if they bring it to market.  They love the balance of inspiration, collaboration, and calculation.

Find the activity worksheet here: Systems of Equations – Custom Ink Worksheet and the accompanying PowerPoint here: Systems of Equations – Custom Ink Deck.  Here’s how it works.

Implementation Tips

Stage 1:  Design

1. Organize students into groups of up to four.  Each group will need a computer.
2. Have each group click the Products link and choose a product to build.  (Tip:  The less fancy the product, the easier it’ll be to turn a big profit!)
3. Once they’ve chosen a product, they can Start Designing!  (10 minutes was plenty of time.)

Stage 2:  Pricing

For this activity to work, students need a reasonable price for their creation.  Here’s how they can get it with a 3 minute gallery walk.

1. Have each group take a whiteboard (or piece of paper), write “I would pay…” across the top, and place it on the desk next to the computer showing their design.
2. In a 3 minute gallery walk, have all students stand and check out as many designs as they can (at least 5), writing what they’d pay for each one on that group’s whiteboard.
3. Once the 3 minutes is up, students return to their groups and see what other students said they’d pay for their design.  To figure out what they might charge, they can take the average of those numbers (perhaps striking any unreasonably high or low numbers).
4. At this point, groups can write an equation representing their possible revenues.

Stage 3:  Costs

Next, students need to estimate their costs.  Because the cost per unit changes based on volume, we have students estimate their costs by figuring out what it would cost to make 25 and 250 shirts.  Given these two points, students calculate a linear equation that estimates the cost to make any number of shirts.

(Some students may learn that the cost to make each shirt is greater than the price people said they’d pay per shirt.  Raise this question with the class (What does this mean?), then consider allowing that group to raise their price so they can target a premium market.)

Stage 4:  Analysis

Now that students have revenue equation and a cost equation, they’re ready to analyze.  They begin by answering basic questions (How much does it cost to make each shirt?) and move into more advanced questions (How many shirts do you need to sell to break even?  How much money would you make if you sold 500 shirts?).  Feel free to change or add to these questions!

Final Thoughts

This one’s always a crowd favorite that consistently leads to meaningful, memorable mathematical engagement.  If you have a 60 minute period, you can do this in one day.  If not, students should still finish the first 3 stages quickly enough that they can finish the analysis for homework!

Let me know if you have any questions, suggestions, or requests!