In a recent blog, I wrote about the idea of a “Free Form Friday” that I have been employing on Fridays in my classroom (you can read about it here: https://tinyurl.com/FreeForm2018). The students absolutely love it as evidenced from the responses to one of my recent reflections (I have them write reflections after each assessment):

*I think that Free Form Fridays in math are Fun because it gives us an opportunity to explore and learn what our strengths are and our weaknesses are. The games in math are also fun. I wanted to let you know it is greatly appreciated among us.*

*Something
that stood out to me in a good way is Free Form Fridays. I like that you let us
work on math that is more than a regular lesson. *

*Something
we have done in class this year that really stood out to me is Free Form
Friday. This has stood out to me in a good way because sometimes taking a break
from the lessons and learning some really cool math is good.*

I have always felt that it is as important (if not more important) for my students to think mathematically and not merely “do math” as they participate in my class each day. That can sometimes be difficult — making sure that we are doing this — as the concepts, skills or objectives of the lesson tend to take precedent.

Students (and people in general) tend to be curious about how things work … there is a natural curiosity about the world that is common across humanity.

This was the impetus for a portion of my Free Form Friday I call Mathematical Curiosities. On Fridays, after a Math Talk, I introduce the curiosity for the day. These Math Curiosities include mathematical conjectures, mathematical puzzlements, mathematical statements that seem to defy logic, mathematical games and more.

It has been incredible to watch my students take off and really run with these ideas. Borrowing from others (including Dan Meyer and Ian Byrd), I usually introduce the curiosity and then ask the following: “What do you wonder?” … “What do you notice?” … “Does it work for every case?” Below are a few of the things that we have used this year. For more specifics, I have a working document that I downloaded which you can access in my Google drive folder at: https://tinyurl.com/mathcuriosity.

- Ultimate Tic-Tac-Toe
- The Collatz Conjecture
- Numerical Palindromes
- The Four Color Problem
- The Fabulous Fibonacci Sequence
- Prime Climb

One of the first ones I used was a simple quote: “Compared to most of the everyday liquids we use, gasoline is actually fairly cheap.” Then, I followed this up with, “What do you wonder?” I had students who were not even sure about the cost of items. And then, on top of that, most every day liquids are not sold by the gallon.

So, my students took off on their journey to research it. The first thing was to look at an average cost of a gallon of gas. The discussion between teams was whether to use the local price average, or the national average (which can have some degree of variance). A team right away argued that it was a false statement. “Look at what it would cost for bottled water — less than half of the cost for gas.”

Then, others started to chime in … anything from milk to salad dressing to shampoo to nail polish. For each additional liquid, they were having to do conversions between ounces and gallons or between liters and gallons. They were curious. They were scouring the internet doing research and collecting data. They were converting between units. They were sorting data.

After a set amount of time (usually about 15 minutes or so, depending on the activity), we then move to the student choice portion of the ** Free Form Friday.** One of the choices is to continue to explore the curiosity. I had several students who kept at it. One team decided to make a Google doc and list as many liquids with their corresponding prices. They shared it with the class so that others could also add their information.

Some very interesting things we found out about a gallon of liquid:

- Kraft ranch salad dressing: $22.14
- White Out: $25.42
- Nyquil cold medicine: $178.13
- Nail polish: $890
- Chanel No. 5: $26,000
- Scorpion Venom: $39,000,000

This was incredible to watch them just keep searching. When we came to the scorpion venom, which I never knew was wanted or needed, we decided to find out why you would even want it. Turns out that there are specific medical conditions where scorpion venom would be helpful.

The protein found in scorpion venom, however, can be used to treat pain in humans who suffer from multiple sclerosis (MS), inflammatory bowel disease, and rheumatoid arthritis, as well as treating certain types of cancer and brain tumors.

So why is it so expensive? Because it has to “milked” by hand and it yields about 2 mg per event. In addition, it is a difficult process. So much learning and understanding by just being curious.

In future posts, I will expound more upon some of these in greater depth. For now, I want to encourage you to make space within your class routine (once a week, once a month, once per quarter) to press pause on the live stream of lessons and allow for students to spend time investigating mathematical topics and principles that make them stop and think “hmmmm … I wonder about that!” You, like me, will be amazed at the benefits you reap as students see math in a different light and become curious to learn more.

Here are some excellent resources that will help you get started:

- Play with your Math – www.playwithyourmath.com
- Ian Byrd – https://puzzlements.co
- Dan Meyer – blog.mrmeyer.com
- Math with Bad Drawings – https://mathwithbaddrawings.com (buy the book … it is worth it!!)
by Alfred S. Posamentier and Ingmar Lehmann.*Mathematical Curiosities: a Treasure Trove of Unexpected Entertainments*