Got It game for an adult and child. How can you play so that you know you will always win?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
This challenge asks you to imagine a snake coiling on itself.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you explain the strategy for winning this game with any target?
Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
This task follows on from Build it Up and takes the ideas into three dimensions!
Are these statements always true, sometimes true or never true?
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?
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 find all the ways to get 15 at the top of this triangle of numbers?
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Here are two kinds of spirals for you to explore. What do you notice?
Find the sum of all three-digit numbers each of whose digits is odd.
This activity involves rounding four-digit numbers to the nearest thousand.
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.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
An investigation that gives you the opportunity to make and justify predictions.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
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?
Can you tangle yourself up and reach any fraction?
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.
It would be nice to have a strategy for disentangling any tangled ropes...
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.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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. . . .