I had come across some work by Geoff and Mr. Honner and was totally inspired by the awesome math behind the NFL Draft. I had never given a lot of thought to all of the calculations that underpin the trades that take place each year and once I got into the numbers I knew I wanted to bring it to the classroom.

For those (like me) that don’t follow football closely, the basic idea is that every year the NFL holds a player draft, where each team has the chance to on-board new players. There are a number of rounds, and each team is allotted a number of a set of picks throughout the various rounds.  The order of the picks is determined by how teams fared in the previous NFL season. (If you come in last, you get first pick).

The interesting part, from a math perspective, is that teams do quite a lot of trading with their picks. A team might wish to trade up, to get a pick earlier in a round, for instance. In order to do this, they have to trade off a few of their lower pick rounds.

In order to facilitate the trades, the NFL has produced a trade value chart, that identifies a point value for each of the picks. That way, if a team wants to trade for the 12th pick, they can sort out which trades they can provide for an equal value. The cool part? The chart is exponential!

In our class, we went a similar route to Geoff. I had students plot the Trade Value Chart and practice identifying the key features of an exponential function. From there, we looked at all of the trades made in the 2018 Draft. I went through every trade made in the 2018 Draft and compiled it in a Google Sheet. I

Note: I included trades that involved last year’s spots because I thought it made it interesting. For example, one team traded their first pick in 2017 (12th) for the other team’s first pick in 2017 (25th) & their first pick in 2018 – an unknown!  Turned out to be an excellent trade from the value perspective because the other team’s first pick in 2018 was 4th. However, you could remove the multi-year trades if you wanted. I omitted any trades that included a previously drafted player.

Students filled in the total value of each trade for the team that traded up & the team that traded down. They then had to plot the value of the trade ups vs. the trade downs to see whether teams adhered to the value chart – essentially is it a linear function?

I definitely didn’t execute on this idea perfectly, but I liked the concept for a bunch of reasons:

1. Spreadsheets are awesome tools and too few students know how to navigate them.
2. There is SO much math here. Think of the math involved just to figure out what trades you have to offer & what combination of those trades will yield the trade you want to make.
3. Conversations around using math to make real-life decisions!
4. More than one kind of function (linear & exponential) in one task is always a bonus.
5. There are great conversations to be had about the outliers – why would someone trade away a higher pick for a lower one? Why are teams sometimes willing to trade for something with far less value?

You can check out the materials I drafted (ha!) up here, and please send your feedback my way:

NFL Draft Pick – Intro doc & questions

NFL Draft Pick – Student Spreadsheet

NFL Draft Pick – Completed Spreadsheet

I figured the Nintendo Switch Dock would be a relatable problem. First, I had students share what they knew or noticed and then what they wondered. Their thoughts and wonderings led us well into the core question for the day:

What Interest Rate is Easy Home charging?

I had used the posted interest rate on EasyHome to find the “retail price” they claim and gave that information to the students.

Total Price: $19 per week for 104 weeks

EasyHome’s Retail Price: $1,236.55

Students hadn’t seen any lessons about interest or seen any interest rate formulas at this point so they were using pure problem solving and prior knowledge to solve.  Up at the blackboards, groups worked together to solve for the interest rate.

All were able to solve for the total interest charged pretty quickly. It took some guided conversations for students to get the interest rate: 29.9%/annum.

Then came the more interesting part of the problem. I asked students how much a Nintendo Switch actually costs to buy outright and it quickly dawned on them that the retail price EasyHome was claiming was way over the MSRP.

After providing them with this image, I asked students to solve for the actual interest rate being charged by EasyHome to see if it qualified as a criminal rate of interest under National Law usury under the Criminal Code of Canada (60%).

Students went right to work redoing the problem with the new Principal.

210%!

I mean, I expected it to be high. But 210%? It really is criminal.

The students were really engaged & enraged throughout this activity and it was a great entry point into learning about simple & compound interest situations.

The basic Google Slides presentation I used can be found here. A second version with PearDeck integrated is here.

Happy investigating!

I was looking for a way to introduce rational exponents. After some failed research and culling of existing examples, I just came up with a simple problem and am sharing it here for others.

Problem

You want to get a sheet of plywood cut at Home Depot and the panel saw has a digital input to set up the dimensions (kind of a stretch, but whatever it works). The input panel has some limitations:

• No decimal numbers
• Whole numbers, fractions, and exponents are permissible
• No symbols other than what’s listed above

The crux: You want a square cut with an area of 2m². What are the side lengths of the square?

We took some pauses throughout the problem solving to group together and look at patterning. This helped to concretize what students have already learned about exponents and also aided in solving the problem at hand. Students were challenged but were able to solve the problem, which to me is the right level of difficulty.

An extension question I used as a follow up:
Now you’re looking to make a storage cube for your house. The cube has a volume of 3m³. What are the side lengths of the cube?

It was an easy step for us then to talk about rational numbers & radical numbers and make the connections between those math terms and symbols. We did some practice in class and then students had the option to do some Khan Academy questions for extra practice.

Sometimes simple really is beautiful & just what we need for thinking deeply about math.

The activity was a good balance of challenging & achievable. The students were frustrated in a way that spurred them on to seek out possible solutions. The activity was great for consolidating student learning thus far about quadratic functions, and in particular using both standard and vertex form.

I liked that there was a section where the students needed to create an impossible challenge. This helped to reinforce what defines a function, as well as the possible characteristics of quadratic functions.