# An Afternoon With Keena

I enjoy working with nearly all my pupils, but this year Keena was right at the top of the list.  It’s fair to say that many of her successes are hard won, but she’ll tackle everything, and when things go wrong she’d far rather have another go to sort things out than ask for my help, and she does it all with a big smile on her face.

One day last term she left with an even bigger smile.

A nice accessible starter challenge is to ask children to fold a piece of paper so that when you make a single straight cut you’re left with a square hole in your piece of paper.  It probably takes a couple of tries, but nobody minds having another go:

So if everyone can do a square, then creating an oblong (just one single straight cut, remember) can’t be hard, can it?

It was so obviously an easy challenge that I hadn’t bothered checking it out completely myself, and I contributed fully to the increasing number of rejects on the table.  I think it took a little over five minutes and it was a deadheat between Keena and myself, though I do claim my expression of satisfaction was a little more restrained than Keena’s warwhoop.

Could she do it again?  Yes indeed, and now they knew it was possible, everyone else tackled the challenge with renewed intensity.  Soon everyone, with perhaps a little advice from Keena, could do it.  Keena, meanwhile, was busy exploring more shapes.  An equilateral triangle?  Certainly.  A regular hexagon?  Why not?

Comfortingly, there’s a wonderful lesson plan from Joel Hamkins on his website at http://jdh.hamkins.org/math-for-nine-year-olds-fold-punch-cut/   He mentions that – incredibly – any shape whatsoever that’s made up of straight lines can be made in this way, and we ended the lesson trying to make a five-pointed star.

Keena wasn’t the only one to leave with a smile on her face.  I think we all did.  I was delighted that we’d found something that had given her so much success, but more widely it had proved yet again how powerful a good Low Threshold High Ceiling activity can be.  No matter what may be included in your list of requirements for a good starter I reckon this one ticks all the boxes.

(It probably helps if you’re on good terms with the caretaker, but that’s another story.  Oh Heck, let’s include it here.  I’ve known John since he joined the school around 1980.  At that time I used to run the six miles into school once a week, and he does a lot of running as well – i.e. unlike me, he still does.  We sponsored him to run in the Ottawa Marathon recently and when I coughed up the money he looked a bit frazzled.  He explained that before committing himself he’d checked that the run is normally in a nice comfortable 17°.  A week before he checked the weather forecast and was a little worried at the predicted temperature of 27°.  On the day itself it was a quite ludicrous 37° !  Yes, he completed the full 26 miles, but not surprisingly he’s decided he won’t do another.)

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### 2 responses

1. In the first sentence of the last paragraph are you saying that all this cutting is a really messy activity that will leave paper scraps all over the floor?

1. With several of you making lots of attempts I’m afraid it can be, though if there are just a handful of well-disciplined people with a large waste paper basket close to hand there’s no problem.