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?

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?

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?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Find all the numbers that can be made by adding the dots on two dice.

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

What could the half time scores have been in these Olympic hockey matches?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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

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?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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?

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

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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.?

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.

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

What two-digit numbers can you make with these two dice? What can't you make?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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.

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.

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.

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?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?