Tarsia: Learning from colleauges

At the start of a new year, we were joined by 3 motivated and talented new staff members in our maths department. They have showed me many new things, and I love learning from colleagues!

One of the new members introduced me to Tarsia (Free and easily accessible here) which is a marvelous technology which can allow us to pivot problem solving.

Essentially the software converts a series of equations (shown in table form below) 

and turns them into a puzzle.

Each piece is a triangle (with 3 expressions along each side). The goal is to pair the expressions, so the pieces become a shape (typically either a triangle or a hexagon)

In my class I wanted to use this activity to practise what we had learnt about surds and index laws.
I decided I wanted to ensure this activity did not 'crowd out' the quiet students, so I enforced a silent work.

I created and printed off puzzles of 3 difficulties (Green for easy, Yellow for moderate and Red for hard). I set up the classroom with tables of 4-5 with a puzzle on each and let students challenge themselves at to which colour they attempted. The students were to use their exercise book to work out the answers, and could show their peers their working, but could not say a word!

(There is little in this world more beautiful than watching students yearning to discuss their mathematically reasoning)

As puzzles were solved, there were fist pumps and muffled cheers (shhh!!) but perhaps more fun was the smiles of pride of completing a puzzle. As students completed, I allowed them to naturally swap desks, most moved up to the harder puzzles.

  

I feel that the limitations of silence and only having 4-5 students per desk, were key to encouraging collaboration and group problem solving.

As I researched this software further I found that Mr Barton's website and blog, provided a wealth of further development ideas.
 Why not put in a mistake,
  or an omission on one side,
   or faux equations around the edges of the shape,
    or multiple possible solutions.

Oh the opportunities to develop a simple activity a more thorough and robust learning experience.

I look forward to the next topic where I can explore this program further and try some more advanced applications of the triangle.