Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This number has 903 digits. What is the sum of all 903 digits?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
There were 22 legs creeping across the web. How many flies? How many spiders?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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!
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What is happening at each box in these machines?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Find all the numbers that can be made by adding the dots on two dice.
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you make square numbers by adding two prime numbers together?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Ben has five coins in his pocket. How much money might he have?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
An environment which simulates working with Cuisenaire rods.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you substitute numbers for the letters in these sums?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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 find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?