Numbers arranged in a square but some exceptional spatial awareness probably needed.
A challenging activity focusing on finding all possible ways of stacking rods.
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
I cut this square into two different shapes. What can you say about
the relationship between them?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
How many tiles do we need to tile these patios?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
This article for teachers suggests ideas for activities built around 10 and 2010.
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
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.
An investigation that gives you the opportunity to make and justify
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.
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.
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
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Bernard Bagnall describes how to get more out of some favourite
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?
"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 we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Follow the directions for circling numbers in the matrix. Add all
the circled numbers together. Note your answer. Try again with a
different starting number. What do you notice?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
If the answer's 2010, what could the question be?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
Here are many ideas for you to investigate - all linked with the
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?
An activity making various patterns with 2 x 1 rectangular tiles.
In how many ways can you stack these rods, following the rules?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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.
This activity asks you to collect information about the birds you
see in the garden. Are there patterns in the data or do the birds
seem to visit randomly?
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.
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?
Investigate the number of faces you can see when you arrange three cubes in different ways.
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?
What do these two triangles have in common? How are they related?
What is the largest cuboid you can wrap in an A3 sheet of paper?
A follow-up activity to Tiles in the Garden.
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?