A few months ago I ran my version of a 3 act math task. I presented my 7th grade students with a video, a short snippet of discovery channel’s top rated week, Shark Week. Hooked, my students watched with intrigue. The video starts with various clips of sharks and the amount of inquiry that we as humans have around sharks, which is evident as my students cannot peel their eyes away. The movie cuts out after the statement of “we will count down the top 10 world’s most deadly sharks.” Hook set. Children are gasping and yelling at me, “what are the 10 ten deadliest sharks!?!?” They’re just dying to know. Now, my version of a 3act math task differs a little here. The questioning is present, the noticing is present, but we frame the thinking a bit more for the kids into “facts” and “questions.” We then sort the questions into various categories: I = Information question we can easily look upIC = Information we need/seek but may require some calculationNR = Interesting question, but not relevant to the topicMQ = Main question The questions the students came up with were the following: - How many type of sharks are there?
- Which sharks have the most attacks?
- Which shark is the deadliest?
- What is considered deadly?
- What sharks have the strongest bite?
- Are the sharks considered only relevant to the US?
- What makes a shark deadly?
- Is the great white the shark that kills the most people?
We also classify the facts gained from the video as necessary to the problem or not. - Talking about sharks
- Top 10 deadliest sharks
- Many different types of sharks
- Sharks are close to humans
Now, we are talking. Context is always important for our children. How often do our kids read a word problem and have no idea what they’re talking about? I mean, you could have watched the video and thought you were a diver in the ocean and sharks were an irrelevant portion to the storyboard. Always make sure that the context of your problem is there. If not, make it apparent to the kids.So we sat and had a lengthy discussion about the questions they had, which were important, which required calculation, which were not necessarily relevant but interesting (and perhaps seeking some insight later on), and finally what is our main question. Everyone settled on “how can we figure out what makes a shark deadly?” Brilliant. So we debated, and debated… and debated. We made lists, we submitted google forms on what attributes of a shark make a shark deadly. Here was our list: - Bite force
- Size of bite
- Size of shark
- Speed of shark
- Number of attacks
- Deaths by attack
- Location (where the shark most frequents)
- Number of teeth
- Size of teeth
- Number of the species
Our list seemed almost too long. So we set out to narrow it, not by my suggestion (I was keen on making some sort of judgement (read: equation) based on as many factors of deadliness we could think of! …but I lost that battle. Oh well! The kids voted and the final “important factors” were as followed: - Bite force
- Size of shark
- # of deadly attacks
- # of total attacks
- Location
- Speed
- Type of shark
After researching we had much discussion and debate about how to compare these values in order to come to “deadliness value” the students discussed how to relate certain factors to one another. For example, many students said you could find the percentage of deadly attacks per attack. How amazing! Percents! The related bite force to the size of a shark with the argument that greenland sharks are very large but probably do not have a huge bite force as their main prey isn’t one they have to “kill quickly.” They know their sharks! We had to give a value to location +1 for coming in contact with humans often, 0 for sharks that were moderately in contact, and -1 for sharks that rarely contacted humans. The speed they decided to list in mph as a pure value (ex: if a shark swam 35mph, their speed value was 35). We finally arrived at the equation: Deadly Factor (df) = (# of deadly attacks ÷ # of attacks * 100) + (Bite Force ÷ Size) + Location Factor + Speed of SharkWe then made a list of sharks they thought could be considered, or at least sharks that they knew existed. They came up with a list of 20 sharks and did the research to plug into their equation. After a few sharks we quickly discovered something. Not all factors weighed in as much as they should. For example, they fully believed that the percentage of deadly attacks should be the #1 indicator of a sharks’ deadliness, so they multiplied that value by 1.25 (25% increase). They also increased the bite force by 25%. They modified the location factor to be: +10 for coming in contact with humans often, 0 for sharks that were moderately in contact, and -10 for sharks that rarely contacted humans. The new equation looked something like this: Deadly Factor (df) = (# of deadly attacks ÷ # of attacks * 100)*1.25 + (Bite Force ÷ Size)*1.25 + Location Factor + Speed of Shark The equation was theirs. I had minimal to no input. They came up with the list of sharks to investigate, the factors to look into and finally the equation to input the factors into. They made sense of a problem presented to them in a way that made sense to them and was meaningful to them. The result? Something amazing. Upon the reveal, which involved watching the edited version of the top 10 countdown (I didn’t have 45 minutes for explanations…) the students took notes on our list versus Discovery’s.On the left is our list that came out after we researched and inputted our values into our equation. The right was the discovery channel’s list. What do you notice? What do you wonder? I should add that the reef shark, blue shark and sand tiger sharks did not make our list to investigate (oops!) The kids noticed this and as an extra we researched the sharks and they would have made our list somewhere. The kids also noted the infamous cookie cutter shark on their list which did not make the discovery channel list, but if you have watched the show, made an honorable mention.The students, like the show admitted their obsession with bite force per size of shark. The cookie cutter, though not deadly packs one hell of a bite for it’s size! Now you know! The reason this was a powerful lesson for my kids was that it made math real, tangible and gave them the power. I didn’t give them an equation, they created an equation in order to make sense of the information presented to them. Were there other ways to calculate a deadly shark? Sure, but what was their percentage of error? Math proved useful in a meaningful context and for once the teacher didn’t feed them the equation and the information to plug in. Many parents came to me the following weeks saying how their children LOVE my class and raved about the shark problem. THe parents were beside themselves that their kids were able to take a seemingly complex and impossible task and make it tangible using maths! +1 for me and the kiddos… I may have also inspired many of them to get jobs at Discovery Channel, calculating deadly animals… look out!
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## Jen McAleerMS Math Department Head located in Massachusetts. I mainly work with LBDB students teaching them meaningful mathematical procedures through context. I also look to open students' eyes to the mathematical world around them ## Archives
January 2017
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