Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Investigate the different distances of these car journeys and find out how long they take.
Investigate what happens when you add house numbers along a street in different ways.
This article for teachers suggests ideas for activities built around 10 and 2010.
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
If the answer's 2010, what could the question be?
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
There are nasty versions of this dice game but we'll start with the nice ones...
If you have only four weights, where could you place them in order to balance this equaliser?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
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.
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?
How is it possible to predict the card?
These two group activities use mathematical reasoning - one is numerical, one geometric.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?