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# National Curriculum - Reasoning and Problem-solving : Key Stage 1 : Mathematics Content Knowledge

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Key Stage 1
National Curriculum - Reasoning and Problem-solving
Question 1 of 14

# 1. How confident are you that you can select and give relevant examples from KS1 mathematics to illustrate what it means to:

## Example

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

 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.

Developing Logical Thinking: the Place of Strategy Games is an NRich article which discusses the way that simple strategy games can be used to develop hypotheses about winning strategies.

## Making connections

Young children are naturally curious and their own questions can be used as starting points for discussion.

Questions such as:

• Why does 3 come before 4?
• Why do triangles have 3 sides?
• Why do numbers go on forever?

can be used to develop mathematical thinking. These could be turned into conjectures to discuss:

• The number before an even number is always an odd number. You never get two even numbers next to each other when you’re counting. Is that true?
• I think there are some shapes with three sides that aren’t triangles. Am I right?
• I think one million is the biggest number. Am I right?

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