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.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Try out the lottery that is played in a far-away land. What is the chance of winning?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
Follow the clues to find the mystery number.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 the clues to colour each square.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
A challenging activity focusing on finding all possible ways of stacking rods.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you use the information to find out which cards I have used?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you find all the different ways of lining up these Cuisenaire rods?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
An investigation that gives you the opportunity to make and justify predictions.
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?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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.
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Number problems at primary level that require careful consideration.