Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
56 406 is the product of two consecutive numbers. What are these
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you work out what a ziffle is on the planet Zargon?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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.
Use the information to work out how many gifts there are in each
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Number problems at primary level that require careful consideration.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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.
Number problems at primary level that may require determination.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
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?
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 this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Find a great variety of ways of asking questions which make 8.
What is happening at each box in these machines?
Find the next number in this pattern: 3, 7, 19, 55 ...
This task combines spatial awareness with addition and multiplication.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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?
Are these statements always true, sometimes true or never true?
If the answer's 2010, what could the question be?
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.
This number has 903 digits. What is the sum of all 903 digits?
What is the sum of all the three digit whole numbers?
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you replace the letters with numbers? Is there only one
solution in each case?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?