article
Modulus arithmetic and a solution to differences
Peter Zimmerman, a Year 13 student at Mill Hill County High School
in Barnet, London wrote this account of modulus arithmetic.
Odd and even numbers
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articleImpossible sandwiches
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot. -
articleMultiplication series: number arrays
This article for teachers describes how number arrays can be a useful representation for many number concepts. -
articleAll is number
Read all about Pythagoras' mathematical discoveries in this article written for students.
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articleTake one example
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure. -
problemSummats clear
Age16 to 18Challenge level
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab. -
problemArrangements
Age7 to 11Challenge level
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....? -
problemScore
Age11 to 14Challenge level
There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers? -
problemComparing continued fractions
Age16 to 18Challenge level
Which of these continued fractions is bigger and why? -
problemGreat Granddad
Age11 to 14Challenge level
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?