Usually, we invite students to send us their solutions to a selection of problems, but this December and January we are doing things a little differently…
The problems below contain interactivities which offer students instant feedback, and we think they are particularly suitable to work on at home, perhaps with a family member, during the holiday period. We hope you enjoy the challenges we’ve selected.
Live problems
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Have you got it?
Can you explain the strategy for winning this game with any target?
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Fruity totals
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
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Connect three
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
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Crossing the bridge
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Recently solved problems
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Picturing square numbers
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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Quadratic patterns
Surprising numerical patterns can be explained using algebra and diagrams...
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Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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M, M and M
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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Slick summing
Watch the video to see how Charlie works out the sum. Can you adapt his method?
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Cyclic quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
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Tilted squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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Cuboid challenge
What's the largest volume of box you can make from a square of paper?
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Take three from five
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
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Wipeout
Can you do a little mathematical detective work to figure out which number has been wiped out? -
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Pick's theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.