Are these statements always true, sometimes true or never true?
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?
Ben’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?
Got It game for an adult and child. How can you play so that you know you will always win?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
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.
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?
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!
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
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Here are two kinds of spirals for you to explore. What do you notice?
An investigation that gives you the opportunity to make and justify
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
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?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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.
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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. . . .
Find the sum of all three-digit numbers each of whose digits is
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Find out what a "fault-free" rectangle is and try to make some of
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?
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 some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
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?