# Hockey Math!

I spent some time today tweaking a unit I did last year where my students used their knowledge of Statistics to find out whether Hockey players played harder during the Olympics or the Regular Season.  I was trying to find a way to make the topic less about the Olympics and more about Hockey and after watching Game 7 between Vancouver and the Chicago last night I realised I actually had a better guiding question for my unit:

Do Hockey Players play harder during the Regular Season or the Play Offs?

There are a couple of reasons why I really like this question:

1. It is the kind of question that seems obvious, “of course they play harder during the Play Offs”.  Turns out it is a lot more difficult to actually prove.
2. It asks the students to prove something very elusive like “playing harder”.  This question would be much easier to answer and much less interesting if it asked whether they “played better”.  If the question was about playing better then a quick comparison of Goals Scored or Points would suffice.  Asking students if a team plays harder asks them to make assumptions about what stats might best measure effort.  There is no right answer, but lots of interesting discussions.

I plan to start the unit by asking my class the guiding question and letting them have some fun with it.  We will then look at the different kinds of Hockey Stats available to us online (I like http://www.hockey-reference.com/) and discuss how they might help us answer the guiding question.  Last year we had interesting discussions about whether: more penalties meant they were trying harder; more time on ice meant they were being rewarded for trying harder; and whether shots on goal might be a better indicator than goals scored.

For Task 1 I have created a worksheet (it’s available at the end of this post) that they can use to collect Regular Season and Play Off data for 2 players (we will use the 2009-10 season data).  My objective for this task is that they become comfortable with the different Hockey Stats and realise that we need to analyse a much larger amount of data in order to have any chance of answering the guiding question.  The 3 questions on the worksheet that I hope will guide them towards this conclusion are:

1. Which of the statistics in the tables above do you think are the best measure of how hard a player is playing? Explain your reasoning.
1. Based on the data in the tables above do you think players play harder in the Play Offs or in the regular Season? Explain your reasoning.
1. What are some of the problems with using just the data you have collected so far to try and answer our guiding question? What might be some solutions to these problems?

A unexpected bonus of Question 3 emerged by accident last year when I realised that they play a different number of games in the Regular Season and the Play Offs, so in order to really compare stats my students will have to use their knowledge of ratios and proportions as well as statistics.

The next challenge is to quickly and efficiently collect enough relevant data to analyse.  To collect this data last year I set up a google form (this is the one from last year) and split up my class so that they were all responsible for gathering data on different members of a Hockey Team (I assume that this year they will want to do the Canucks).  One unintended consequence of doing it this way last year was that inevitably some students entered the wrong data in the form, which is a perfect lead in to a conversation about outliers and their effect on a data set.

Task 2 is a little more mundane but important.  They need to show me that they have met the Grade 7 Math Learning Outcomes and have the statistics skills to really analyse our data set.  This year I have made up a package of guided investigations from the JUMP Math program that they will work through with my help to make sure they have the Statistics skills and knowledge they need.  Last year having the guiding question to refer to really made them take interest during discussions about when it would be most appropriate to use mean, median or mode as they knew they would have to making that decision soon.

Task 3 is their final analysis.  I still need to tweak it for this year, but last year this is what I asked them to do:

Choose 3 different statistics to compare (these could be the same as you used to compare your 2 players, or they could be different).

For both the Regular Season and the Play Offs graph the data you have chosen (3 graphs) and calculate the Mean, Median, Mode and Range (3 sets of calculations). Decide whether or not to include outliers in your calculations.

Decide which of these Measures of Central Tendency BEST represents each data set. Explain your thinking.

Compare your results from the Regular Season data and the Olympics (you will have to do some math in order to be able to compare these data sets properly).

1. The assumptions you made when you picked the statistics to compare.
2. Your results and how accurate you think they are. Describe ALL possible sources of error.
3. You answer to the guiding question. Explain your thinking in detail.

As this is an IB MYP unit I use IB criteria to assess the final task.  If you are interested they are in the Task 3 Word Document below.

Last year this was the most interesting unit I taught and I was blown away by the deeper level of understanding my students displayed.  I can’t wait to teach it again this year.

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