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?
This article for teachers suggests ideas for activities built around 10 and 2010.
Investigate the different distances of these car journeys and find out how long they take.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Here is a chance to play a fractions version of the classic Countdown Game.
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Here is a chance to play a version of the classic Countdown Game.
Replace each letter with a digit to make this addition correct.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Surprise your friends with this magic square trick.
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
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?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different ways could you score 44?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
How many different differences can you make?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
This Sudoku, based on differences. Using the one clue number can you find the solution?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
How is it possible to predict the card?