These practical challenges are all about making a 'tray' and covering it with paper.
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.
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?
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
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?
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 models can you find which obey these rules?
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 can you put five cereal packets together to make different
shapes if you must put them face-to-face?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
How many triangles can you make on the 3 by 3 pegboard?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you make the birds from the egg tangram?
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?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
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 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?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
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 fit the tangram pieces into the outline of this shape. How would you describe it?
This activity investigates how you might make squares and pentominoes from Polydron.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of this telephone?