We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
All types of mathematical problems serve a useful purpose in
mathematics teaching, but different types of problem will achieve
different learning objectives. In generalmore open-ended problems
have. . . .
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Sort the houses in my street into different groups. Can you do it in any other ways?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
A follow-up activity to Tiles in the Garden.
Explore one of these five pictures.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
It starts quite simple but great opportunities for number discoveries and patterns!
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
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?
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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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!
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
This challenge extends the Plants investigation so now four or more children are involved.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
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.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
An activity making various patterns with 2 x 1 rectangular tiles.
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Can you find ways of joining cubes together so that 28 faces are
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 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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Have a go at this 3D extension to the Pebbles problem.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
How many models can you find which obey these rules?
Can you create more models that follow these rules?