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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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?

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?

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

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?

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

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

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?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Given the products of diagonally opposite cells - can you complete this Sudoku?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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?

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?

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

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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

This article for primary teachers suggests ways in which to help children become better at working systematically.

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?