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Mathematical inquiry

 

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Inquiry prompt

 

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Find more examples.

Change the prompt.

Decide on the aim of the inquiry.

Test different

types of cases.

Analyse the structure.

Decide if the prompt is always true.

Make a generalisation.

Prove a generalisation.

More examples in which the difference between the integers is one.

What if not?

  • Integers
  • Difference of one
  • Squares

 

Describe the pattern for all cases mathematically – precisely and without redundancy.

Identify a pattern and decide if it holds for your cases.

Explain the generalisation with a visual representation (diagram).

Prove the generalisation for every case using algebra.

Inquiry Maths

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Inquiry Maths

Find more examples

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Inquiry Maths

Analyse the structure

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Visual representation

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Make and prove a generalisation

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Inquiry Maths

The difference between the squares of two consecutive positive integers equals the sum of those integers.

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Inquiry Maths

Test different types of cases

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Visual representation

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Inquiry Maths

Make and prove a generalisation

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Visual representation

 

 

 

 

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Visual representation

 

 

 

 

 

 

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Inquiry Maths

The difference between the squares of two positive integers equals the product of the difference and sum of those integers.

 

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Inquiry Maths

The difference between the squares of two positive integers equals the product of the difference and sum of those integers.

 

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Guided

poster

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Difference of two cubes

 

 

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Inquiry prompt

 

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Expand triple brackets

Pascal’s triangle, 1665

Yang Hui’s triangle, 1303

 

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Find more examples

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Make and prove a generalisation

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Compare and contrast the two algebraic proofs.

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Test different types of cases

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Inquiry Maths

 

 

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Analyse the structure

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Visual representation

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Prove a generalisation

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Guided

poster

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Further inquiry

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