This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Have a go at balancing this equation. Can you find different ways of doing it?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This challenge is about finding the difference between numbers which have the same tens digit.
Can you replace the letters with numbers? Is there only one
solution in each case?
Follow the clues to find the mystery number.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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 the chosen number from the grid using the clues?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What two-digit numbers can you make with these two dice? What can't you make?
Can you work out some different ways to balance this equation?
What happens when you round these three-digit numbers to the nearest 100?
This activity focuses on rounding to the nearest 10.
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 substitute numbers for the letters in these sums?
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
An investigation that gives you the opportunity to make and justify
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
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
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?
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?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
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.
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!
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
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?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Can you use the information to find out which cards I have used?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
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.