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.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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?

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!

If you have only four weights, where could you place them in order to balance this equaliser?

Investigate the different distances of these car journeys and find out how long they take.

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?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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. . . .

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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?

Can you hang weights in the right place to make the equaliser balance?

Can you use the information to find out which cards I have used?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

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 the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

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?

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?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Use the number weights to find different ways of balancing the equaliser.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.