An investigation that gives you the opportunity to make and justify
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?
If the answer's 2010, what could the question be?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
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.
This article for teachers suggests ideas for activities built around 10 and 2010.
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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
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?
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.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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.
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?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
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?
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?
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 tiles do we need to tile these patios?
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!
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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 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
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 how many ways can you stack these rods, following the rules?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
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.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Have a go at this 3D extension to the Pebbles problem.
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
"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
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
I cut this square into two different shapes. What can you say about
the relationship between them?
Why does the tower look a different size in each of these pictures?
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?