Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
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
What is happening at each box in these machines?
Number problems at primary level that may require determination.
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Number problems at primary level that require careful consideration.
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.
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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 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 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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Resources to support understanding of multiplication and division through playing with number.
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
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 task combines spatial awareness with addition and multiplication.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you work out what a ziffle is on the planet Zargon?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
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?
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?
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 the sum of all the three digit whole numbers?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.