Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Here is a version of the game 'Happy Families' for you to make and play.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Use the tangram pieces to make our pictures, or to design some of your own!
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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.
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
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?
How many triangles can you make on the 3 by 3 pegboard?
How many models can you find which obey these rules?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
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?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
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?
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.
In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .
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?
Surprise your friends with this magic square trick.
What is the greatest number of squares you can make by overlapping three squares?
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?
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?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
How do you know if your set of dominoes is complete?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Can you deduce the pattern that has been used to lay out these bottle tops?
Can you each work out what shape you have part of on your card? What will the rest of it look like?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?