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 make the birds from the egg tangram?
A game to make and play based on the number line.
Here is a version of the game 'Happy Families' for you to make and play.
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.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
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?
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?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
An activity making various patterns with 2 x 1 rectangular tiles.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
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?
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?
Use the tangram pieces to make our pictures, or to design some of your own!
How many models can you find which obey these rules?
These practical challenges are all about making a 'tray' and covering it with paper.
How many triangles can you make on the 3 by 3 pegboard?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
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?
Delight your friends with this cunning trick! Can you explain how it works?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
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.
What is the greatest number of squares you can make by overlapping three squares?
Can you create more models that follow these rules?
Reasoning about the number of matches needed to build squares that share their sides.
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.