We’re taking a weekend trip to 6 Flags and I’m thinking there’s something I can do with choosing your rides, mapping out your route, etc.

I also just stumbled upon http://tweetstats.com/ and thought there are LOTS of possibilities for good questions about data that can be found here.

However, I got myself into a conversation about problem solving strategies with my second year class this morning and used this as a trigger for discussion. With the picture on the board I asked simply “what is the combination?”.

The discussion that ensued was based around what further information was needed to answer the problem because the maths required to state the number of possible solutions is beyond their capabilities for now.

The class came up with a single questions that they wanted answersed before they would go any further.

How many numbers are in the code?

I only told them when they told me that they would normally find the answer to this in the question itself and what strategy they were going to try when they found out. Some sort of ordered list seemed to be the favourite and armed now with the fact there were 3 consecutive numbers in the code they continued.

Conversation and debate followed about what consectutive could mean, whether or not they could be consecutive in decreasing order and whether 0 could follow 9.

We got it down to 14 options and everyone agreed they needed more information. The code must be divisible by 2, the first number must be greater than the last and and the sum of the digits is fifteen elimiated all but one and brought us to a conclusion.

The important lesson today was not the maths – I know that my class can divide by 2, add to 15 and use number order. What was beneficial was to look for the questions that had to be answered because the answers to these normally lie in the text of the question itself if they would just remember to go looking for it!

A fantastic resource and a lesson that the pupils can direct and to some degree structure themselves with the questions their own questions. I see more potential every time I look at this and also remember that sometimes the simplest resources and ideas can provide the richest tasks.

@ Alex, I’m lovin’ the Wendy’s idea. The way I get through Combinations in my class is to first ask my class what they think of when I saw “combination” and almost 80% of the class (at least I’m walkin’ away with one good thing from the paradigm created by being a member of the fast-food generation) say “combo value meals.” After I flash a few pics of an actual value meal that I bought, but with the fries, drink and burger switched around, the students get that order doesn’t matter. That set of 3 or 4 slides alone gets the idea across that combinations aren’t the same as permutations, that nCr on their calculator means that order doesn’t matter, and the only other choice, nPr, means that order does matter.

With regard to the door lock, I’m a little impatient by nature but I usually give the answer before n=3, for fear that I might be shanked by an impatient kid with a ‘tude and a knack for carving sharp edges. It’s a little too much on the CPM side for me, and I’m always afraid that similar lines of questioning will either cause frustration or will cement in their head the wrong ideas. So, I usually start with n=3 and give them a couple of minutes after the “Awww…are you serious?” looks that I get, and then let them off the hook.

Also, we can’t necessarily get factorial from this, right? … or am I missing something? (after all, it is way past my bedtime) … Since the combination could be 7777 in a 4-digit code. Help me out here.

Another awesome lesson. Thanks, Dan! I’m diggin’ the WCYDWT series.

Also, as usual, the comments add so much more value to an already outstanding post.