List

Logically Speaking

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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.

problem

Sliding Rectangles

Age

11 to 16

Challenge level

Which of the two rectangles has the greater area?

problem

Maxi Pyramid

Age

11 to 16

Challenge level

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

problem

Positive Differences

Age

11 to 16

Challenge level

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

problem

11x11 square

Age

11 to 16

Challenge level

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

problem

River Crossing

Age

11 to 18

Challenge level

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

problem

Favourite

Isosceles Seven

Age

14 to 16

Challenge level

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

problem

Favourite

Iffy logic

Age

14 to 18

Challenge level

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

problem

IFFY triangles

Age

14 to 18

Challenge level

Can you prove these triangle theorems both ways?

problem

The Tour de Clochemerle

Age

14 to 18

Challenge level

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

problem

Favourite

Iff

Age

14 to 18

Challenge level

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

$Mind your \Ps and \Qs$

problem

Mind your Ps and Qs

Age

16 to 18

Challenge level

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