A conjecture is a mathematical statement which seems likely to be true but has not been proved to be true under rules of logic. It is usually based on evidence that is not complete. For example, children may conjecture that there are equal numbers of odd and even numbers lying between 0 and 20 (which is untrue), or that it is impossible to draw a shape with four straight sides with exactly three right angles (which is true).

Other examples would be:

The number of sides in a polygon is always the same as the number of angles.

The number of lines of symmetry in a 2-D shape is the same as the number of edges.

Children may form a hypothesis about the outcome of an enquiry or an investigation, which they then test, for example that children with longer legs run and jump further, or that the favourite colour of children in Year 1 is red.

Other examples of hypotheses which could be tested are:

More than half of the people in the class have at least one brother or sister.

All Smarties boxes have the same number of Smarties.

Children in our class prefer fruit sweets to chocolate.

What this might look like in the classroom

Question:
Are these statements true or false? How do you know?

All lines are straight

All squares are rectangles

All boxes are cuboids

Children can be asked to sort cards into a true and false grid, giving justification for their decision.

True

False

Answer:

True

False

All lines are straight

All squares are rectangles

All boxes are cuboids

The importance of this activity is in the reasoning the children use in their discussions.

Hypothesise

Children could be asked to pose a question that they want to investigate. For example,

‘All children with brown hair have brown eyes’.

Pupils think how they could ‘test’ this idea and discuss it together in groups.

The importance of the learning in this activity is in posing the question and the discussion about the design of the test. The outcome of the test focuses on further questions rather than specific answers.

Taking this mathematics further

Investigating conjectures is an excellent context for developing purposeful mathematical discussion between children. Developing pedagogical understanding has ideas about what ‘purposeful talk’ actually is, and suggestions for further reading.

Concept cartoons are a structured way to develop discussion about conjectures. Put ‘concept cartoon’ into a search engine and look at the images it returns to help you develop your own ideas.

Related information and resources from other sites

This NRich article on rich tasks discusses how rich tasks are ones which enable children to make and test hypotheses.

Mathematical Mysteries: Goldbach’s Conjecture is a short article about a simple sounding conjecture about prime numbers that remains unsolved many years after it was first formulated.