I used the Area Two starter by Transum with my year 10 group today before we moved on to areas of sectors. The problem asks how many shapes can be made with an area of 2 on the grid shown below, by joining dots with straight lines.
A very simple premise, this got all the group thinking. They started with the standard shape, with squares, rectangles and triangles popping up. Then a few saw the parallelograms and the trapeziums. After a few minutes of working on it, ideas started to become more imaginative with flag-like shapes appearing, along with others. Between the class they must have found about 30-40 different shapes (though some did not strictly fit the rules, such as arrowheads with a point between dots, and even some semicircles).
To finish the activity, I had them come to the front to use the nice interactive part of the activity on the board to show one of their shapes, and explain why it was an area of 2, and how they thought of it.
It was a really good 15 minute starter to our double lesson, but could easily be extneded to a whole lesson activity for younger groups, which I fully intend to do at some point with my year 7 group. Definitely worth a look!
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.