Evaluating statements about length and area

This lesson develops the concepts of length and area. Particular attention is given to proving why two areas are or are not equal.

The lesson begins with three questions regarding area that students must classify as ‘sometimes, always, or never true’. An example is ‘if you join the midpoints of the opposite sides of a trapezoid, you split the trapezoid into two equal areas’.

The next task is to draw the two diagonals of a quadrilateral and test to see if the quadrilateral is divided into four equal areas.

There is a card sort activity with eight statements about areas to be evaluated as ‘sometimes, always or never true’. An example is ‘if a square and a circle have the same perimeter, the circle has the smallest area’.

For each section, students must justify their answers using both examples and mathematical proof.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.