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 asks you to imagine a snake coiling on itself.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 focuses on finding the sum and difference of pairs of two-digit numbers.
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. . . .
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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 all unit fractions be written as the sum of two unit fractions?
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
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?
An investigation that gives you the opportunity to make and justify predictions.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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.
Are these statements always true, sometimes true or never true?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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 would be nice to have a strategy for disentangling any tangled ropes...
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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?
Can you tangle yourself up and reach any fraction?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Here are two kinds of spirals for you to explore. What do you notice?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Find the sum of all three-digit numbers each of whose digits is odd.
What happens when you round these three-digit numbers to the nearest 100?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?