Year 8: Algebra - arithmagons
A lesson start (taken from a write up in
ACs' 2nd year of teaching!)
The students filed in as usual, in a noisyish
way, and slowly got their stuff out of their bags. I took the register
over murmurings of conversations - choosing to ignore them. I then
went to the board, with most eyes on me. I tapped with my pen and
waited for everyone's attention.
We were going to do some work on arithmagons
- I drew one in silence, put a number in two circles, paused and
filled the box inbetween, paused...put a number in the third circle...filled
in the other two boxes.
A few hands had gone up, there was silence. Another
example, still silence, a couple of students bursting to tell the
answers in the boxes, but still silence (this was surprising)...I
was making eye contact with many of the class and looking a lot
at a girl who I felt might be the last to pick up what was going
on - there was concentration, but still no understanding on her
face. A third example...I turned to look at the class and everyone's
eyes were burning into the board - I hadn't experienced this before.
Still silence...I now took two answers from the class for what should
go in the boxes, everyone's hand seemed to be up except the girl;
she was straining and seemed to have just twigged; she half whispered
an answer, not quite committing herself - but it was correct. One
more example...two boys had lost concentration, staring again brought
them back. The girl's hand was now up with the rest - the boys seemed
to be following, after all, so I nodded at her and a correct answer
I then drew an arithmagon with only the
boxes filled in and invited the class to try to find what the numbers
in the circles could have been...no one needed a further explanation,
which, for me, is rare!
· Can you find a method or strategy for solving any arithmagon?
· Are there any arithmagons that have no solution? (You might
want to write on the board any the class come up with which they
· Is there ever more than one solution?
· Can you use algebra to find a solution? (or just to describe
how they work eg if a, b and c are in the circles, what is in the
· What happens with square arithmagons? pentagonal arithmagons?