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?
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?
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?
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?
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.
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.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
These practical challenges are all about making a 'tray' and covering it with paper.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you make the birds from the egg tangram?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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 three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
Here is a version of the game 'Happy Families' for you to make and play.
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?
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?
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?
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?
How many models can you find which obey these rules?
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?
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?
How many triangles can you make on the 3 by 3 pegboard?
An activity making various patterns with 2 x 1 rectangular tiles.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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 create more models that follow these rules?
Make a cube out of straws and have a go at this practical challenge.
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
These pictures show squares split into halves. Can you find other ways?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.