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?
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?
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?
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?
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 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?
An activity making various patterns with 2 x 1 rectangular tiles.
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 different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
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.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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?
How many triangles can you make on the 3 by 3 pegboard?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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.
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?
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?
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?
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?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
What shape is made when you fold using this crease pattern? Can you make a ring design?
What do these two triangles have in common? How are they related?
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?
Exploring and predicting folding, cutting and punching holes and making spirals.
Make a flower design using the same shape made out of different sizes of paper.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Make a cube out of straws and have a go at this practical challenge.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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 make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
These pictures show squares split into halves. Can you find other ways?
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?
Can you cut up a square in the way shown and make the pieces into a triangle?