In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
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.
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.
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Investigate and explain the patterns that you see from recording
just the units digits of numbers in the times tables.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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.
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Here are many ideas for you to investigate - all linked with the
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
"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
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
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!
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
If the answer's 2010, what could the question be?
This article for teachers suggests ideas for activities built around 10 and 2010.
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?
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
An investigation that gives you the opportunity to make and justify
The red ring is inside the blue ring in this picture. Can you
rearrange the rings in different ways? Perhaps you can overlap them
or put one outside another?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
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?
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?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
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?
Investigate what happens when you add house numbers along a street
in different ways.
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?
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
Explore ways of colouring this set of triangles. Can you make
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?