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

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

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?

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

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.

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?

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

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?

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

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?

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?

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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?

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

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

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?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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?

Can you find out in which order the children are standing in this line?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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?

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

My coat has three buttons. How many ways can you find to do up all the buttons?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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.

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?

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?