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.
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge asks you to imagine a snake coiling on itself.
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?
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.
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
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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?
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.
What would you get if you continued this sequence of fraction sums?
1/2 + 2/1 =
2/3 + 3/2 =
3/4 + 4/3 =
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. . . .
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.
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.
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.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
The Egyptians expressed all fractions as the sum of different unit
fractions. Here is a chance to explore how they could have written
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?
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.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
An investigation that gives you the opportunity to make and justify
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?
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Can you tangle yourself up and reach any fraction?
This activity involves rounding four-digit numbers to the nearest thousand.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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. . . .
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?
Find the sum of all three-digit numbers each of whose digits is
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?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Delight your friends with this cunning trick! Can you explain how
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?