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

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

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Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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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?

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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?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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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?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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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?

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Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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How many different triangles can you make on a circular pegboard that has nine pegs?

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10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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In this game you are challenged to gain more columns of lily pads than your opponent.

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

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How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

Number problems for lower primary that will get you thinking.

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

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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.

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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?

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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?

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

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

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

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

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

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Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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

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

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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?

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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?

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

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

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

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How many different shapes can you make by putting four right- angled isosceles triangles together?

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First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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Find your way through the grid starting at 2 and following these operations. What number do you end on?

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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?

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This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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How many ways can you find of tiling the square patio, using square tiles of different sizes?

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Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.