Reasoning, Justifying, Convincing and Proof - Advanced

Prime Sequences

Stage: 5 Challenge Level: Challenge Level:1

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

Stats Statements

Stage: 5 Challenge Level: Challenge Level:1

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Integration Matcher

Stage: 5 Challenge Level: Challenge Level:1

Match the charts of these functions to the charts of their integrals.

Impossible Square?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make a square from these triangles?

Dodgy Proofs

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

These proofs are wrong. Can you see why?

Impossible Triangles?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these triangular jigsaws are impossible to finish?

Polynomial Interpolation

Stage: 5 Challenge Level: Challenge Level:1

Can you fit polynomials through these points?

What's a Group?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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