Line Up!

I'm a regular following of Pivotal Ellie's Maths Blog (@PivotalEllie) and receive e-mails from her too which suggests loads of Active Maths tips.
To read Ellie's blog go here --> http://activemaths.edublogs.org/ I would also recommend signing up to her free e-mails.

During my Pre-IB session on the IB Mathematics I decided to get the students up and moving at various parts of the session to keep them thinking and so put into practise one of Ellie's Active Maths tips. This was the most recent e-mail I had received and was about getting students to line up and then giving alternate students a coloured piece of card and then filling the gaps by giving these students a different coloured piece of card. Then, the task is that the students have to move around each other (1 move at a time) to get all of one coloured cards on the left hand side and all of the other coloured card on the right hand side. The students then have to think about the fewest possible moves they could make to do this.

As I didn't have any coloured card I decided to, instead, use my large playing cards, which we had previously used to do a bit of 'play your cards right'. So I randomly handed out cards to start with and just got students to arrange themselves in order of smallest to largest value cards from left to right. (Ace = 1, J = 11, Q=12, K=13). I also got them to prioritise the suits so that spades were priority 1, then diamonds, hearts and then clubs. Then, I got them to arrange themselves in order of suits and value so all the spades were on the far left in numerical order, then the diamonds etc. Finally, I got students in order so they were red, black, red, black, red, black etc and then asked them to, moving 1 swap at a time, to find the lowest possible moves in order to get all the blacks on one side of the line and all reds on the other side. The students did this relatively quickly and as they moved I counted the moves (this was the trickiest bit - keeping track of them moving around!). We did this a few times to see if we could get the amount of moves down. The students tried different strategies like moving the furthest red on the right all the way down to the left 1st and then the 2nd furthest red on the right all the way down to the left etc. There were a few random trials where they just swapped based on who was most vocal at certain points of the line!
This then lead to some interesting discussion as to what was the best method, and whether or not they had the minimum amount of moves and how they could be sure.

We then later linked this to the 'frogs problem' when looking at sequences. http://www.hellam.net/maths2000/frogs.html