Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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!
Have a go at balancing this equation. Can you find different ways of doing it?
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
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.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Can you work out some different ways to balance this equation?
Can you replace the letters with numbers? Is there only one solution in each case?
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.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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!
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Here is a chance to play a version of the classic Countdown Game.
Find a great variety of ways of asking questions which make 8.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Can you complete this jigsaw of the multiplication square?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
What is happening at each box in these machines?
Use the information to work out how many gifts there are in each
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Choose a symbol to put into the number sentence.
If the answer's 2010, what could the question be?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?