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!

So I love Geogebra, and I am trying to use it in class.  I haven't made specific applets before, and so this is my first time creating one for classroom use.

This year I wanted to give students a way of playing around with estimating square roots, and last year I just didn't have a method that kids could play around with, but this applet gives them more of that chance.  Tell me what you think.  Where should I go from here?

Find the applet right here.

Well here it is!  One of my best moments of stumbling onto curriculum.  I would first and foremost like to thank Delano Pauw.  He is the creator of all the media and the toppling artist; I just happened to find him on youtube.  Check out his channel.  He really is amazing, and with a quick e-mail he gave me Raw footage, dimension shots, and estimates.  All from way off in the Netherlands (this interweb thing is so cool!).

Without Further Ado, here is the domino spiral (now featuring sound).

Based on twitter results the most natural question to ask is how long will it take for all the dominoes to fall?  That is what this WCYDWT is based on.

So here it is, I wanted to make students work for the dimensions a bit.  Is  this too mean?  Anyway these work well!

I will give students a printed copy of the picture from which they can gather the dimensions.  Then play the first lap of the spiral to have students get the rate of fall.  If you want to make this whole process longer give them dominoes instead of the video and have them come up with the rate of fall from experimentation.  If you are physics minded throw this in their face. I am pretty sure I don't understand a single thing in that pdf, but I haven't taken the time to go through it, but it could give some neat extensions.

Here it is, the moment we have all waited for!

This is the part that I find the hardest.  Where can this lesson grow legs.  Please give me a hand with making this more worthwhile, but here are some ideas that I have so far.

• How many dominoes of each colour?
• Graph the time of each revolution vs. its radius, find the slope (I don't actually know if this is worthwhile I haven't tried it).
  
• Switch the variables around and find some bigger domino topples, ask them how many dominoes were used.

They are kind of lame, but like I said I cannot think of any.  Delano did speak about the calculations that he had to go through in creating this, maybe he can comment about that, and an extension could be that kids make their own (I am all about building these as a project).

One spot where I am a total n00b when it comes to inquiry and teaching is my question techniques.  I want to learn good leading questions that prompt students just enough to get them over hurdles.  If you guys could give me some in the comboxes that would be excellent!  Here is my start.

• What are we trying to solve?
• What unit will it be in?
• What would make our final time longer or slower?
• How can we determine how fast the dominoes are falling?

Once again, no skills here so I need your help.

Enjoy.

For anyone that does not know how to properly pronounce this mini-activity's title please watch this...

...and substitute "Coke" for spoon.

With that being said, I introduce you to this!

What questions do you have about this image?  Post them on my twitter.  Then continue reading...

So this is my new lesson/starter activity.  I plan on using this to get kids thinking about volume again, and my future goals for this lesson will be elaborated further down.  Anyway this all started when I was thinking about the recent trend in twelve pack boxes for pop.  They use to be 3x4 and now they are 6x2.  My students had a lot of problems this year with Surface Area (mostly due to me), and I thought this would be a great way to introduce it by buying some, and asking the question, "Which box is better for the environment?"  I liked the idea and, so I was stuck thinking about pop.

I went shopping with my dad last weekend (we were home for a family event) and there were these new "100 calories" Coca Cola Slim packs and I grabbed out my phone and snapped some picture (Dad looked at me funny he is not used to this side of me yet).  Anyway I walked down the aisle, and found the new Pepsi slim cans!  But they were a different shape, but same price!  Boo ya! Math lesson here I come.  Anyway I bought those as fast as I can, and this weekend I went to town.  I'll present this once more in Mr. Meyer's three acts since I appreciate the narrative...

A nice simple video, and Twitter has quickly shown (not from hundreds of people), that I was on track with my question.  Students will ask questions about the video, and share them on the board.  I am anticipating that students will either inquire about volume or surface area, both tracks I am willing to head down.