An activity making various patterns with 2 x 1 rectangular tiles.

This activity investigates how you might make squares and pentominoes from Polydron.

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Use the clues about the symmetrical properties of these letters to place them on the grid.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

How many trapeziums, of various sizes, are hidden in this picture?

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

If you had 36 cubes, what different cuboids could you make?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

What happens when you try and fit the triomino pieces into these two grids?

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. . . .

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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.

Can you find all the different triangles on these peg boards, and find their angles?

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?

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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?

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?

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

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?

Can you draw a square in which the perimeter is numerically equal to the area?

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?

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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 possible answers?

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