How can we help students make sense of addition and subtraction of negative numbers?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
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?
How would you count the number of fingers in these pictures?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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?
What is the sum of all the three digit whole numbers?
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.
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).
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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?
Can you substitute numbers for the letters in these sums?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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
Find a great variety of ways of asking questions which make 8.
There are nasty versions of this dice game but we'll start with the nice ones...
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.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
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.
There were 22 legs creeping across the web. How many flies? How many spiders?
Here is a chance to play a version of the classic Countdown Game.
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Are these domino games fair? Can you explain why or why not?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
An environment which simulates working with Cuisenaire rods.
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