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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Use the information to work out how many gifts there are in each
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Number problems at primary level that require careful consideration.
Investigate what happens when you add house numbers along a street
in different ways.
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 score 100 by throwing rings on this board? Is there more
than way to do it?
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
What is happening at each box in these machines?
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
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
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.
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.
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
Can you make square numbers by adding two prime numbers together?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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.