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?
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?
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?
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?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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 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.
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?
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
These practical challenges are all about making a 'tray' and covering it with paper.
How many models can you find which obey these rules?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Make a cube out of straws and have a go at this practical
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
Explore the triangles that can be made with seven sticks of the
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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 fit the tangram pieces into the outline of this junk?
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?
You'll need a collection of cups for this activity.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you see which tile is the odd one out in this design? Using the
basic tile, can you make a repeating pattern to decorate our wall?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
If you'd like to know more about Primary Maths Masterclasses, this
is the package to read! Find out about current groups in your
region or how to set up your own.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
For this activity which explores capacity, you will need to collect some bottles and jars.
Can you fit the tangram pieces into the outline of this telephone?
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 the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?