An investigation that gives you the opportunity to make and justify
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Can you draw a square in which the perimeter is numerically equal
to the area?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
The pages of my calendar have got mixed up. Can you sort them out?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you make square numbers by adding two prime numbers together?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake