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?

How many different symmetrical shapes can you make by shading triangles or squares?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Use the clues about the symmetrical properties of these letters to place them on the grid.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

A challenging activity focusing on finding all possible ways of stacking rods.

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

This activity investigates how you might make squares and pentominoes from Polydron.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

In how many ways can you stack these rods, following the rules?

The pages of my calendar have got mixed up. Can you sort them out?

In this matching game, you have to decide how long different events take.

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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?

An investigation that gives you the opportunity to make and justify predictions.

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Find out about Magic Squares in this article written for students. Why are they magic?!

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

Number problems at primary level that require careful consideration.

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Can you find all the different ways of lining up these Cuisenaire rods?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Two sudokus in one. Challenge yourself to make the necessary connections.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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'.

Find out what a "fault-free" rectangle is and try to make some of your own.

How many different triangles can you make on a circular pegboard that has nine pegs?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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?

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