Particular to the General - Masterclass

The problems in this masterclass package are intended to offer students the opportunity to engage in a key mathematical activity: moving from particular instances to general cases. Along the way, students can notice patterns, make conjectures and choose representations to help justify and prove.

 

Summing Consecutive Numbers

Age 11 to 14
Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Marbles in a Box

Age 11 to 16
Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Route to Infinity

Age 11 to 14
Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

What's Possible?

Age 14 to 16
Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Painted Cube

Age 14 to 16
Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Amazing Card Trick

Age 11 to 14
Challenge Level

How is it possible to predict the card?

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