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 each work out the number on your card? What do you notice?
How could you sort the cards?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Here is a version of the game 'Happy Families' for you to make and
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
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.
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
Can you make the birds from the egg tangram?
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?
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?
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?
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?
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?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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 put five cereal packets together to make different
shapes if you must put them face-to-face?
These pictures show squares split into halves. Can you find other ways?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
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.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
A brief video looking at how you can sometimes use symmetry to
distinguish knots. Can you use this idea to investigate the
differences between the granny knot and the reef knot?
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?
How do you know if your set of dominoes is complete?
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
These practical challenges are all about making a 'tray' and covering it with paper.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?