A Cartesian Puzzle

You could play a game of 'twenty questions' to begin with so that pupils get a chance to familiarise themselves with properties of shapes. Choose a quadrilateral and write the name of it on a piece of paper. Invite the class to ask questions to guess what your quadrilateral is, but you can only answer yes or no. Keep a tally of the number of questions asked - if they get it in less than twenty, they win, otherwise you win. You could repeat this a few times with pupils choosing shapes.

You could start on the problem itself by showing it to the group on an interactive whiteboard or data projector. Alternatively, if they are already very familiar with coordinates in the first quadrant, you could get them to work in pairs from a printed sheet of the problem from the beginning. It is important that they are able to talk through their ideas with a partner while doing the problem. This sheet of the first quadrant could be used for both rough working and the final results. Otherwise supply plenty of squared paper! It might help learners to know that the coordinates of each quadrilateral are given going round in an anti-clockwise direction.

One of the nice things about this problem is that learners will know that they have solved it correctly. In the plenary, therefore, you can concentrate on asking some pairs to explain the way they tackled the problem, rather than focusing on the answer. Were some ways more efficient than others?

What kind of quadrilateral do you think this one is?

Where is its fourth vertex?

You might want to tell some childrenthat the shapes include one parallelogram, one trapezium and one rhombus, and are otherwise squares and rectangles.