This activity investigates how you might make squares and pentominoes from Polydron.
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
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?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
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?
If you had 36 cubes, what different cuboids could you make?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
Use the clues about the symmetrical properties of these letters to place them on the grid.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
How many triangles can you make on the 3 by 3 pegboard?
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.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
How many models can you find which obey these rules?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
What happens when you try and fit the triomino pieces into these two grids?
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?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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?
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?
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?
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.
This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Can you fill in the empty boxes in the grid with the right shape and colour?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
Find all the numbers that can be made by adding the dots on two dice.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
This challenge is about finding the difference between numbers which have the same tens digit.
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?