This article for teachers suggests ideas for activities built around 10 and 2010.
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
I cut this square into two different shapes. What can you say about
the relationship between them?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
An investigation that gives you the opportunity to make and justify
Investigate these hexagons drawn from different sized equilateral
Bernard Bagnall describes how to get more out of some favourite
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
In my local town there are three supermarkets which each has a
special deal on some products. If you bought all your shopping in
one shop, where would be the cheapest?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Investigate what happens when you add house numbers along a street
in different ways.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
Investigate the numbers that come up on a die as you roll it in the
direction of north, south, east and west, without going over the
path it's already made.
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
If the answer's 2010, what could the question be?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
How many tiles do we need to tile these patios?
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
Why does the tower look a different size in each of these pictures?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
If I use 12 green tiles to represent my lawn, how many different
ways could I arrange them? How many border tiles would I need each
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!