When an idea starts to take shape - Part 2
In order to test out some challenge activities I went to a local High School to run the first activity with a lower ability Year 8 class.
Premise:
- buy tiles
- build convex deltahedra (shapes made from triangles where all the edges point out from the shape)
- sell model
Each pair of students were given 10 squares as currency. 1 triangle = 1 square. They could then buy triangles. An offer of a helpsheet with suggested models to make for two squares units was made and most groups bought it in either in this, or the next round.
It may have been obvious that the currency squares were superfluous (given the exchange rate!), hindsight being a wonderful commodity. and this idea was dropped in the later session.
They were shown a tetrahedron as an example and then purchased their triangles. The pairs were then given 1 minute construction time. All students could each make a tetrahedron in this time.
The tetrahedra were then sold. The value of the shape was equal to the number of edges it had, so 6 units for the tetrahedron. The class teacher and myself put a degree of quality assurance on the process and did not accept poorly constructed shapes. Then, rather than giving out squares and then rebuying triangles, just the profit was given out in triangles to speed the process. It was important that each round started with separate triangles. Models not broken down were considered obsolete and removed (could be under the guise of Health and Safety)
The process was then repeated. In subsequent rounds construction time increased by 30 seconds. It was noted that as pairs has more material to work with, in trying more complicated models they sometimes had nothing completed to sell.
After round three tetrahedrons became obsolete and could no longer be sold.
Rounds four and five introduced ratios. (double points for using more than two colours and triple points for ratio 2:1).
The session was well received by the students, who showed good engagement throughout.
I was now ready to expand the idea to 3 new mixed ability sets in the hall (with their class teachers). So with around 75 students, triads of 3 were formed.
The premise was the same as before and despite having a greater ability range similar outcomes were observed.
Rounds four and five introduced ratios as before and squares. These cost 2 triangles and doubled edge score, if the shape included at least 1 square. This started to mean some teams scoring large numbers of points so in future it would be better only to award double points if the shape had a majority of squares. Also double points for using tiles with colours in the ratio 2:1. Shapes still needed to be convex and the helpsheet steered them towards the Archimedean solids.
It was clear that students were concentrating on the construction rather than the value of the completed shape which was sometimes ‘sold back' at less than the market value.
"I can't get the colours in ratio 2:1 on a 10 sided shape!"
"can I use triangles to make squares?"
Teachers commented that they nearly ran out of triangles but I did not see as a problem as these could now become obsolete as shapes forcing the groups to work more with squares.
One teacher noted the lower ability student leading his group because he had better spatial awareness/reasoning than the other 2 supposedly more able students, who were quicker 'calculators' of algorithms. This outcome was particularly appreciated, as I find it invaluable when teachers start to see students with new eyes. This was a major impact.
The sessions each lasted about 1 and a half hours which was about right as an initial activity but an extra half an hour would allow for greater depth into some of the key reasoning of particular decisions if repeated.
Andy Parkinson
Teaching and Learning Adviser Mathematics and Numeracy Education Department, Highlands Campus, Jersey