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Triangles Within Squares

Age 14 to 16
Challenge Level Yellow starYellow star
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Why not encourage pupils to discover rules of their own?

This problem links to "Triangles withinTriangles " and the problem "Triangles within Pentagons"

There are many different ways to visualise this question and pupils should be encouraged to explain how they "know" their rule works.

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Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Triangular Triples

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

Iff

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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