Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

This task follows on from Build it Up and takes the ideas into three dimensions!

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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

The Zargoes use almost the same alphabet as English. What does this birthday message say?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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.

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

This dice train has been made using specific rules. How many different trains can you make?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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

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

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.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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