So the guy crushes walnuts with his head and what we get is a linear relationship. There are a few things here. First off, there is a 3 Act task. I modelled the 3 Act task off of @Gfletchy's similar task for rope jumping. Secondly, I timed how long it took for each walnut to get crushed and collected in file (if you are interested, I slowed the video down by 50% then used an online timer to get the splits). So now you can do some analysis. It's not a particularly interesting data set but it might give a fun context to look at linear relationships.
3 Act Task
Act 1 - Watch the movie
How many walnuts will he be able to crush with his head in 60 seconds? Estimate
Write an estimate you know is too high. Write an estimate you know is too low.
Act 2b - Show this video for information with more accessible math
Act 2c - Show this video for information with even more accessible math
Act 3 - Show this video to reveal the answer.
Analysis
I guess the question that most comes to my mind (after "does he have a headache") is he crushing the walnuts at a constant rate. Careful observation might find a couple of spots where he hesitates a bit and you might want to discuss whether that shows up in the data. But is the data linear? Looking at the graph you can see that for the most part it is, but there is a slightly faster rate at the beginning and a slightly slower at the end but each section seems pretty linear.Another thing you might want to discuss is whether it should be Time vs Walnuts or Walnuts vs Time. Since rates are usually per unit time then it probably makes sense to do Walnuts vs Time but you could argue that the total time depends on the number of walnuts or that the total number of walnuts you could crush depends on how much time you have. Note that the easiest way to swap the axes in a Google spreadsheet is by changing the position of the columns so to do that I just copied the Time column to both sides of the Walnuts column.
Sample Questions
Besides the above questions you could certainly ask:
- What's the line of best fit?
- What's the correlation?
- How many walnuts do you think he could crush if it were two minutes? 10 minutes?
- Is there a better fit than linear?
- How many nuts would he have cracked if he kept at the same pace as the first 10 seconds?
- If you only saw the first 5 seconds, what would be your prediction of the number crushed in 1 minute?
- Can you tell, on the graph, when he hesitated?
- What if he would have had the pace he finished with throughout the whole minute, how many nuts would he have cracked then? I think this was the previous record of 281.
Download the Data
- Original video: https://youtu.be/i1PQX64cTgY
- Google Sheets Version
- CODAP Version
- Comma Separated Version
- Desmos Version
