Can you work out some different ways to balance this equation?
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?
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
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do 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.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Find a great variety of ways of asking questions which make 8.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
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!
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
This number has 903 digits. What is the sum of all 903 digits?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
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?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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 arrange 5 different digits (from 0 - 9) in the cross in the
What is happening at each box in these machines?
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 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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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!
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Given the products of adjacent cells, can you complete this Sudoku?
Use the information to work out how many gifts there are in each
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the 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?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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 task combines spatial awareness with addition and multiplication.
Number problems at primary level that may require determination.
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
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.
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?
Are these statements always true, sometimes true or never true?
Here is a chance to play a version of the classic Countdown Game.