Like so many good things that I have created in life, this post comes entirely from someone else's idea.  Dan Meyer had the first speed of light task, which I am linking for my sequel ideas, because, well, his just rock.  I wanted to include this post, because I feel like I will be able to use this version a lot easier in my grade eight class, it allows talking about cool conspiracy, moon landing stuff, Mythbusters, and is practice for me taking something that I see and turning it into something I can use in class.

I love this set up because it is what scientists actually did!  They have reflectors on the moon at which you can shoot your lasers and receive signals back to prove that people were on the rock that is orbiting our Earth! Well, now all we need to know is how long did it take for the laser to to hit the moon and come back?

This act two is simple, I would probably use this for a started (shouldn't take too long at all), but here they are...

Well there it is; a simple fun intro to the speed of light.

As promised, Dan has some awesome work with the same problem, which can be found here.  Check it out, you won't be disappointed.

A few weeks ago I was talking to a number of students in the hall at lunch.  I cherish these moments, because when outside of my classroom students remove a certain number of proverbial layers that they bring into the class.  One layer they commonly wear in class, and therefore the one that I love to see vanish most, is their fear of saying something wrong.  Often in class I see students’ puppy dog eyes, fishing for the correct answer that will allow me to move along and bother them no longer.  I am making students work for the gratification of being correct more and more, but that is for a different post.

My point however is that when out of the class I am no longer the “all mighty holder of all truths Mathematical, Sciencentific and French;” the stakes are low in their interaction with me beyond my door and that layer disappears.  I have taught some of my favourite science, math and French lessons at lunch and afterschool simply because I have students that are a) not scared of being tested, and b) genuinely interested in the learning that is occurring. They have no reason to be there other than sheer curiosity.  The other benefit of being outside of the scheduled class time is that students become much more candid.  Since they are not worried about the correct answer, they therefore reveal much more of their true thinking, worldview, and understanding.

In the particular moment that prompted this post, I was chatting with a group of students made up of a number of boys who were winded, red in the face, and generally exhausted.  The matter was that they had walked during their run in PE, and as a result had to run the route again.  This was a BIG DEAL, because it meant that any time that they spent on this second run, was time spent away from lunch hour. The boys then exclaimed, “We got our fastest time of the whole year today!”

I replied, “Great!  Now you know how fast you can really run!” This remark was met with many a disgruntled face.  One girl in the group said, very sincerely, “Mr. Piccini, that’s not how it works.  You see, what you do is you run just hard enough to make it look like your trying, but that you know you can improve your time later on, so on the record it looks like we are improving.”  This amount of utter honesty almost shocked me.

I then asked her, “Why don’t you just try your hardest and actually improve your speed?” to which she promptly said, “There’s no point!  Put me in basketball or soccer and I will run because there is a point to that game, but regular running, there is no point to that.”

This is what really hit home for me.  These students were not lazy, nor were they rebellious; they saw no point in running for the sake of running, and therefore they labeled it as something that could be done with just enough effort to get the teacher off their back. I wanted to tell them about the physical and mental health benefits, the conditioning for sports, and the pleasantness  a good run can have, but I realised like so many other lessons a lecture was not the way to show them the point.

This got me thinking about my class.  In Science, Math, and French have I shown my students the point?  Do I make it clear to them everyday why we are doing this? More importantly do I create for them moments and opportunities where they realise ‘What the crap? This is something I need to know now,’ because it is not enough simply to tell them. Necessity is the mother of all invention, and when we put students in a state of necessity, they are no longer receivers, but they are seekers and inventors.  I want to nurture a generation of such students, because once they become true seekers “the point” becomes moot; when they become seekers they do not need to hear the point, because as seekers,  they now have a new responsibility: they must create their own point.

Ever wonder why companies make the decisions that they do? My wife and I drink more pop than I am willing to admit, and one thing I noticed while at the store is that the twelve packs of Coke and Pepsi do not have the same design.  Let's look at them (warning I do not know if this works in the States). This is also a precursor to this lesson.

I asked my students which one uses the least amount of cardboard, and in relation, which company made the best choice for the environment?

This was a good starter.  I had kids talking about which looks bigger, and a trend over at least two classes (I'll see later on in the future), is that the majority of students say that Pepsi is the clearer waster, or they have equal amounts of carboard.

I ask students what do we need to know to solve this?  Students came up with volume, area, dimensions etc.  at which point I introduce them to our cm cubes.

We talk only a little bit about the difference between volume and surface area.  In fact I do not use the words in particular, we talk only about "How many cubes are necessary to build this prism?" and "How many squares can we count on the outside?" an idea I lifted from Christopher Danielson.  I gave students the following sheet and basically said, GO!

Here I talked to students a lot about short cuts.  It was great when they said they had no short cuts, and I ask, "You just counted?"

"Yes," replies the student.  I then proceed to count one-by-one each outside square.  Before I can even get to three, the student interrupts and says, "No, no, no, you times the length by width for one side, then times it by two.  You do this for three of the sides, since they each have an equal side" (paraphrased).  Bwa ha ha! I laugh to myself, they have it, and I didn't have to write a single formula on the board!

Bringing it back to the pop box now only involves asking, what do we need to know to solve the pop box, problem.  Students tell me they need the dimensions of the box so I give them these...

This is also a good time to have students talk about anything we are missing.  My wife after a few days of seeing me make this asked about the overlap, and if that makes a difference, I haven't looked into it yet, let your students do it too!

How many different configurations can you find, and which one of these uses the least amount of cardboard? Do any of them use less cardboard than Pepsi and Coke's configurations?

• Write a letter to one of the companies that explains your mathematics.  Suggest for them why you think they should switch or keep their design.

This was extremely engaging for one of my two classes.  I think for me the pay out of the reveal is not as great as most of these 3act stories, so it can lose some students.  I want to work on that out for next year.

What else I need to do is to prepare more guiding questions to start off the investigation, so students can be invested in the problem earlier.  They have not seen surface area before and so are not acquainted with it.  Students knee jerk reaction at this age is to find volume (well actually they just say lxwxh without knowing what that means), so I want to guide them away from that. If they focus on volume to early on they count the problem off to early.

What I really liked about this investigation was the next day when I wanted to teach them surface area of triangular prisms I handed them the nets, and asked what do we have to do now. Students quickly came up with the idea that we needed to find the area of each separate shape and them together.   They knew the only formula they needed was to find the area of the triangle. We talked about the relation between rectangles and triangles.  This was a fairly easy process, because students can see if you cut a rectangle down the diagonal it makes two triangles (therefore bh/2).  This was a fairly simple review of the area of a triangle and extension of their learning of Surface Area.  It was fantastic to see how quickly they adapted to the new information! Students were able to further adapt this to other nets that used basic shapes, and it was a very simple natural extension of the same logic (Thanks to Kate Nowak for the idea of nets and surface area).

My only hiccup came with cylinders.  I was ill prepared to lead students into a discovery of the area of a circle (technically they learned it last year... but they're only in grade 8), so I fell back onto lameness. I hope to alleviate the lameness, any suggestions? I have learned that great teaching comes from thinking through all aspects of the lesson and leading them through the inquiry.  My cylinders lesson bombed, because I was lazy and had little prepared!  I was humbly reminded how easily it has to slip into bad teaching, let's change that Timon!