Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Have a go at balancing this equation. Can you find different ways of doing it?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
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.
Can you work out some different ways to balance this equation?
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?
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?
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
Find a great variety of ways of asking questions which make 8.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is happening at each box in these machines?
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!
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Use the information to work out how many gifts there are in each
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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!
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Find the next number in this pattern: 3, 7, 19, 55 ...
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Number problems at primary level that require careful consideration.
Here is a chance to play a version of the classic Countdown Game.
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?
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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
If the answer's 2010, what could the question be?
Number problems at primary level that may require determination.
This number has 903 digits. What is the sum of all 903 digits?
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 the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you work out what a ziffle is on the planet Zargon?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?