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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.

 

Sliding Rectangles
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Sliding rectangles

Age
11 to 16
Challenge level
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Which of the two rectangles has the greater area?
Maxi Pyramid
problem

Maxi pyramid

Age
11 to 16
Challenge level
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What is the largest number you can obtain at the top of this pyramid?
Positive Differences
problem

Positive differences

Age
11 to 16
Challenge level
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Can you fill the circles with the numbers 1 to 6?
11x11 square
problem

11x11 square

Age
11 to 16
Challenge level
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Here's a neat trick you can do with an 11 by 11 square...
River Crossing
problem

River crossing

Age
11 to 18
Challenge level
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There is nothing half so much worth doing as simply messing about in boats...
Isosceles Seven
problem
Favourite

Isosceles seven

Age
14 to 16
Challenge level
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Is it possible to find the angles in this rather special isosceles triangle?
Iffy logic
problem
Favourite

Iffy logic

Age
14 to 18
Challenge level
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Can you rearrange the cards to make a series of correct mathematical statements?
IFFY triangles
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IFFY triangles

Age
14 to 18
Challenge level
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Can you prove these triangle theorems both ways?

The Tour de Clochemerle
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The Tour de Clochemerle

Age
14 to 18
Challenge level
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Can you work out where these 5 riders came in a not-quite-so-famous bike race?

Iff
problem
Favourite

Iff

Age
14 to 18
Challenge level
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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?
Mind your \Ps and \Qs
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Mind your Ps and Qs

Age
16 to 18
Challenge level
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Sort these mathematical propositions into a series of 8 correct statements.