In this feature students are invited to explore a variety of problems and are then challenged to construct convincing arguments to explain what they have discovered. They offer an opportunity for rich mathematical discussion in the classroom.

The last day for students to send in solutions to the live problems is Monday 16 May.

Plus magazine has a selection of interesting articles looking at logic, the basics of mathematical logic, its role in computer science and the philosophy of maths, and on how it's being used in applications.

*You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these activities.*

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Which of the two rectangles has the greater area?

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What is the largest number you can obtain at the top of this pyramid?

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Can you fill the circles with the numbers 1 to 6?

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Here's a neat trick you can do with an 11 by 11 square...

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There is nothing half so much worth doing as simply messing about in boats...

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Is it possible to find the angles in this rather special isosceles triangle?

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Can you rearrange the cards to make a series of correct mathematical statements?

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Can you prove these triangle theorems both ways?

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Can you work out where these 5 riders came in a not-quite-so-famous bike race?

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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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Sort these mathematical propositions into a series of 8 correct statements.