Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
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?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
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.
What is happening at each box in these machines?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
56 406 is the product of two consecutive numbers. What are these
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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!
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.
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.
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
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Imagine you were given the chance to win some money... and imagine
you had nothing to lose...
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?
Use the information to work out how many gifts there are in each
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
This task combines spatial awareness with addition and multiplication.
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?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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 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 the next number in this pattern: 3, 7, 19, 55 ...
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Number problems at primary level that require careful consideration.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?