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MARS: Describing and defining quadrilaterals

The ‘Describing and defining quadrilaterals’ resource is a concept development lesson from the ‘Mathematics Assessment Resource Service’ (MARS). The resource is intended to help students name and classify quadrilaterals according to their properties. They will also identify the minimal information required to define a quadrilateral, and sketch quadrilaterals with given conditions.

The task explores how well students understand the definitions of various quadrilaterals. As an example, one question asks students if ‘all’, ‘some’ or ‘no’ rectangles are squares, and to give a reason for their choice of words.


In common with other MARS lessons, there is extensive guidance to help with suggested questions and prompts in relation to common problems that students experience with the task. For example, if a student states that ‘no’ rectangles are squares, then possible questions might be

These questions are effective in leading students to deduce that some rectangles are squares and that a square has all the properties of a rectangle with the additional property of four congruent sides.

The main activity is paired work using descriptions to draw quadrilaterals. An example of a description is given below:

The resulting shape is a parallelogram:

Students must then select the smallest set of properties cards that would enable them to draw the shape. In this case, properties 2 to 5 are sufficient to describe the shape, property 1 is not required.

At each stage, students must justify their choices to their partner, and question them on the shapes that they have drawn.

There is a formative assessment task for students to complete sometime after the lesson. This shows how well they have grasped the concepts in the lesson.

The resource includes an assessment for students to complete sometime after the lesson. This is designed to give feedback on how their understanding has improved from the initial assessment.

To download the resource click the link below:

Describing and defining quadrilaterals

The Mathematics Assessment Resource Service (MARS) is a collaboration between the University of California at Berkeley and the Shell Centre team at the University of Nottingham, with support from the Bill and Melinda Gates Foundation. The team is known around the world for its innovative work in maths education. Previous projects that members of the team have worked on include the DfE Standards Units and the Bowland Maths resources.

Mathematics Assessment Resource Service (MARS)

Article written by Simon Jowett


Age11-14, 14-16
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