Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you tangle yourself up and reach any fraction?
It would be nice to have a strategy for disentangling any tangled ropes...
This challenge asks you to imagine a snake coiling on itself.
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.
Can all unit fractions be written as the sum of two unit fractions?
An investigation that gives you the opportunity to make and justify predictions.
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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. . . .
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
It starts quite simple but great opportunities for number discoveries and patterns!
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
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?
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. . . .
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Charlie has moved between countries and the average income of both has increased. How can this be so?