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?

This article for teachers suggests ideas for activities built around 10 and 2010.

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?

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?

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

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?

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.

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

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

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

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

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. . . .

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!

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 what happens when you add house numbers along a street in different ways.

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?

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

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

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?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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?

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

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?

This challenge is about finding the difference between numbers which have the same tens digit.

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?

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?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

This task combines spatial awareness with addition and multiplication.

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?

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?

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?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

This challenge combines addition, multiplication, perseverance and even proof.

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?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?