Can you tangle yourself up and reach any fraction?
It would be nice to have a strategy for disentangling any tangled
Can all unit fractions be written as the sum of two unit fractions?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
This challenge asks you to imagine a snake coiling on itself.
The Egyptians expressed all fractions as the sum of different unit
fractions. Here is a chance to explore how they could have written
What would you get if you continued this sequence of fraction sums?
1/2 + 2/1 =
2/3 + 3/2 =
3/4 + 4/3 =
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
A package contains a set of resources designed to develop
pupils’ mathematical thinking. This package places a
particular emphasis on “generalising” and is designed
to meet the. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Charlie has moved between countries and the average income of both
has increased. How can this be so?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
How many centimetres of rope will I need to make another mat just
like the one I have here?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
Find out what a "fault-free" rectangle is and try to make some of
This task follows on from Build it Up and takes the ideas into three dimensions!
Here are two kinds of spirals for you to explore. What do you notice?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Jo has three numbers which she adds together in pairs. When she
does this she has three different totals: 11, 17 and 22 What are
the three numbers Jo had to start with?”
A collection of games on the NIM theme
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
Are these statements always true, sometimes true or never true?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Can you find the values at the vertices when you know the values on
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these numbers to the nearest whole number?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Can you describe this route to infinity? Where will the arrows take you next?
It starts quite simple but great opportunities for number discoveries and patterns!
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
What happens when you round these three-digit numbers to the nearest 100?