How long did you wait between trials?

Also, the percent brightness looks vaugely exponential. Have you checked this?

What are you using for your timer?

I ran the data through Excel. You can find the graphs on my blog here. It turns out that the linear model is not the best fit.

@David Cox
I thought about doing the same thing with my thermometer and toaster. Mine has a plastic sleeve that would protect me from myself. I was going to get a standard starting temperature to do my own experiment.

BTW, I was explaining to my family what I was working on, and they think we need to get a life. ;-)

Dan, great stuff. Granted, your work is very new to me, but the application is immediate and appreciated.

So, Monday, I think I’ll show this video as an example of a linear equation to my 7th graders. We are just now exploring y=mx + b and happen to have begun a mini project around ‘school life through y=mx + b’ their work so far has been fanstastic!

The comments and overall progression are a true exemplar of the scientific method and the way I wanted my science classes to look like and feel like at all times.

Chris – I love what you did with graphing models, and this will help me (at the end of my current y=mx + b mini project) to broaden the scope of understanding with my students who are already determined to understand what to do when something isn’t linear. I thank you kindly.

I woke up at 4 am this morning with toasters and toast and outliers swirling around in my head. I couldn’t get David Cox’s nonlinear model and your almost linear model out of my thoughts to fall back asleep. What would cause one data point to not fall in line with eight others.

Then I thought about what you did differently from David Cox, namely waiting for the toaster to be cool to the touch. What about the first test? Was that on setting 1? Was the toaster ‘cool to the touch’ or was it just as cold as toasters normally are when you decide to toast bread? If it was your first time toasting, perhaps it took longer to warm the coils from ‘cold’ to ‘cool to the touch.’

I surfed the internet in an attempt to see how toasters worked and found that if your toaster uses a bi-metallic strip then a cold kitchen would make the first piece of toast darker than usual (and probably take longer).” So was the test with setting 1 your first piece of toast? Was the kitchen cold? I suggest you toast some bread, wait for the toaster to be cool to the touch again, and then re-toast on setting 1 (that is, if you aren’t sick of toast already).

So, kinda seems like we are trying REALLY hard to find a linear problem in here (time, temperature, toastiness, deliciousness?).

When I ran this with my precal students, the most valuable part (from my perspective) was when they were running the various regressions to see which type best (visually) fit, debating why one might work better or not, then seeing how close the higher setting ended up to the various regressions.

Rather than try and make the toaster fit the line, why not use this problem to talk about using the STAT menu or regression capabilities on excel, etc?

I like the linear fit. Or maybe linear with the outlier removed.

I don’t think the better fit justifies a more complex model like quadratic. After all, a degree 9 polynomial could fit perfectly.

Than I would expect, that is.

Oh, sure. Thanks.

This stuff is really neat! Thanks for looking into it.

@Aaron F.

The only “deep food-chemistry principle” I can think of is the Maillard reaction. This is the reaction that causes meat to sear, and bread to turn into toast. Apparently this is reaction combines the outer layer of carbohydrates and protein, creating the “golden brown and delicious” crusty goodness we know and love. Your question intrigued me enough to hop online and see what I could find about it. I discovered this gem on Wikipedia:

“The rate of Maillard reactions increases as the water activity increases, reaching a maximum at water activities in the range of 0.6 to 0.7. However, as the Maillard reaction produces water, further increases in water activity may inhibit Maillard reactions.”

Could this be the cause of the change in the graph? I don’t know, but it sounds good.

@Sam and Numbat

My middle school students had immediate concerns regarding the non-linear nature of the line. Their collective conversation mirrors the conversation here and on a few other blogs.

Some were not bothered with the flaws, some wanted to draw trend lines (not by name as they don’t know much about them yet) and still others, most others had complaints as to the flawed nature of the work. Ha!

Their complaints started at the beginning where the time that the toast was reported. Some felt it to be inaccurate in respect to their own observations. Finally, their complaints ended with the questions talked about on this blog regarding heat and regularity of practice in the experiment.

Never the less, they became rather good at working with y=mx+b during the process. The test results from this unit showed that it was the highest tested set of skills among the rest from the same unit. The inquiry, I hope, helped attach this learning in a solid location in their minds. my blog has a little bit of evidence of their work on it.

Dan,

I just finished doing my own toaster experiment. I went through each setting three times. You can check my results here.