Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
How many centimetres of rope will I need to make another mat just like the one I have here?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
An investigation that gives you the opportunity to make and justify predictions.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
It starts quite simple but great opportunities for number discoveries and patterns!
Find the sum of all three-digit numbers each of whose digits is odd.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Can you find sets of sloping lines that enclose a square?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Can you tangle yourself up and reach any fraction?
This challenge asks you to imagine a snake coiling on itself.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
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. . . .
Charlie has moved between countries and the average income of both has increased. How can this be so?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
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?