In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
How would you count the number of fingers in these pictures?
What is the sum of all the three digit whole numbers?
How can we help students make sense of addition and subtraction of negative numbers?
Can you substitute numbers for the letters in these sums?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Dotty Six is a simple dice game that you can adapt in many ways.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
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 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?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are nasty versions of this dice game but we'll start with the nice ones...
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Find a great variety of ways of asking questions which make 8.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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.
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?
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
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?
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?
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
What is happening at each box in these machines?
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.
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?
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
An environment which simulates working with Cuisenaire rods.
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
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?
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.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?