Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
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?
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?
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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
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?
56 406 is the product of two consecutive numbers. What are these
Number problems at primary level that require careful consideration.
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 may require determination.
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
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 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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
What is happening at each box in these machines?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Use the information to work out how many gifts there are in each
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Resources to support understanding of multiplication and division through playing with number.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
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?
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?
This task combines spatial awareness with addition and multiplication.
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
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?
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?
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.