Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
This article for teachers suggests ideas for activities built around 10 and 2010.
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Here is a chance to play a version of the classic Countdown Game.
An old game but lots of arithmetic!
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?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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!
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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 numbers.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
What is the sum of all the three digit whole numbers?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
A game that tests your understanding of remainders.
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Number problems at primary level that require careful consideration.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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!
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?