Saturday, 6 February 2016

Order the Fruit Salad

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 4 (and final) blogging challenge is “Share a Lesson”. (For my previous weeks, see “Questioning” here, “Favourite” here and “Day in the Life” here.) We were warned about this one in advance, since depending on where you work, there might not have been teaching this past week. So I had something in the back of my mind.

That said, I did teach - namely the startup of semester two, with new classes and students, while still finalizing marks for semester one. (I did mention January was the worst month...) But with the startup, I realized I should probably blog here about how I start off my Data Management class (aka Statistics) every year. Namely by making a run to the store to get an apple.


I’ve been doing my fruit lesson for at least four years. Probably longer, though I didn’t always start the semester this way. Mainly because I didn’t always start with the counting unit. I’m also cheating a bit, because this “lesson” actually spans three days.

Day One, I don’t immediately start with the fruit. My first example is the probability of getting the correct combination for a standard locker lock. Then definitions, some other simple probability examples, and THEN the fruit comes out. A grapefruit, a lemon and an orange.

With the objects, we can no longer repeat our choice (versus having a password of all ‘a’s). Once the grapefruit is down, I only have two options left. 3x2x1 = Six options total, the students are on board. That’s when I pull out the lime, as seen below. The total arrangements is easy. The number of arrangements where the lime is first requires a bit more thought.

From there, it’s into factorials, and we call it a day. The BAD news from this year, is that this intro was on a day when the busses weren’t running. And even though only 10% of our school uses busses, the bad weather means lower attendance. (Schools are never closed. Ever. We could get 20 feet of snow and they’d still be open.) So I had to do a little rerun the following day.

Day Two, we move from factorials to permutations. Here’s where the apple is added, to make things interesting. Normally I’d get all the way through my “how many ways with lemon and lime together” example - seen below. But with the “ice day”, I had to leave it with them to think about. This picture was actually taken to start off Day Three.

Oh, I physically move the fruit around too, to emphasize. (This arrangement is fine. Not this one, not this one, but this one... *I switch the position of the lemon and lime only* ...and this is fine. *groans are heard*) And normally the apple is green, to match the lime, but my wife happened to have an apple at home, so I took that one. I don’t like apples much, this is the only time I buy them.


Once the lemon/lime example is done, I don’t advance the next slide. I pull out a second orange. And they know what’s about to happen, and someone says “Sir, why would you do that to us?” THEN I advance the next slide. And sometimes someone will try to argue that the two oranges are different enough, and so I have other examples with letters and words, and they will grudgingly capitulate.

Thus the first part of Day Three is finalizing this permutations knowledge, but of course, I have one more trick up my sleeve. I pull out the grocery bag, and announce that I’m going to take three of these home for the weekend. And I grab the grapefruit, the apple and the lime, tossing them in the bag. But wait!

Does it matter that I selected the grapefruit first? It’s coming home with me, the same way as the lime is, even though I picked it last. Of course now order doesn’t matter, and so now we have combinations, to round things out. Factorials, Permutations, and Combinations, all taught with fruit.

The inspiration was in part due to the “Shad Valley” program I went to at University of Waterloo in 1993 (when I was in high school). Ed Jernigan used fruit in his math lecture, as a way of trying to categorize “fruit” for artificial intelligence. This is, by the way, the closest I get to a "3 act" lesson.

Things to watch for: Students tend to like the visual/physical presence of the fruit - two of them remarked on that aspect this time. Students also tend to ask if they can take the fruit home with them. (Someone wanted the grapefruit this time.) I’m more leery of that, in case bad things happen. Also, I like grapefruit; if they want the apple, meh. Along the same lines, one guy wanted to be in my picture (above) but while I applauded his enthusiasm, I said I probably shouldn’t do that.

Fun fact: At one point, some of them were talking about salad. I’m not sure why (this period was right before lunch), but it was easy enough to steer that conversation back to permutations and combinations. Fruit salad, anyone?


Quick bonus, the lesson I likely would have written up if I hadn’t been buying fruit this past week is the “painted cube” problem. You paint a cube, then disassemble it - how many of the component blocks have no sides with paint? One side? Two? Three? It’s a rather elegant way of having linear, quadratic and cubic patterning in a single activity. But it’s also one that educators are liable to find more familiar - maybe you’d already heard of it?

The plan is now to have lime tilapia at some point for dinner this week. But before Monday, I need to get my personified math comic coloured and uploaded! (I hit entry #250 last week.) Thanks for reading here, if you enjoyed, know that I’m all about the writing. Feel free to check out some other posts:

-Check out the Bola Fruit in the Conic Household with “Tea Leaves”
-The math song parody “Permute” is the one I use for this Data unit
-Here’s my reminder that, even in the face of other creative ideas out there, “You’re a Good Teacher” (too)


  1. This comment has been removed by the author.

  2. Whoops, tried to comment and accidentally pasted my link from the Week 4 post! Anyway, was trying to say that I like the fruit as manipulatives, especially as it addresses potential misconceptions with the math content!

    1. That's okay - the fact that your blog is called "Appetite for Instruction" makes me feel like it'd be relevant to the post. ;) Thanks for the response! You're right that the fruit are "manipulatives", and I don't know that I would have labelled them as such.

  3. This sounds fun! I love the painted cube lesson too. I did that one once in a math inservice. Good times!

    1. Glad it comes across that way. That's very possibly where I heard about the cube lesson too, I know I didn't come up with that one!

  4. Random aside - a comment by Mike Lieff on my Facebook, where I also posted this, stated that he does this with coloured cube-a-links. With restrictions on how many are unique/identical. Clever! And more re-usable year-to-year... it's recommended to buy new fruit each semester. (Though I HAVE managed to use the same lemon in Sept and Feb. Before disposing of it.)