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.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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

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

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

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

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.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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.?

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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?

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

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

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?

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?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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

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....?

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

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?

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?

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?

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

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?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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

Number problems at primary level that require careful consideration.

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

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?