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Digital roots. Combinations. Investigations. Multiplication & division. Trial and improvement. Factors and multiples. Calculators. Working systematically. Sequences. Addition & subtraction.There are 213 results
Broad Topics > Calculations and Numerical Methods > Addition & subtraction
Exploring Wild & Wonderful Number Patterns
Age 7 to 11 Challenge Level:
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Function Machines
Age 7 to 11 Challenge Level:
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Numbers Numbers Everywhere!
Age 5 to 11
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Book Codes
Age 7 to 11 Challenge Level:
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Next Number
Age 7 to 11 Short Challenge Level:
Find the next number in this pattern: 3, 7, 19, 55 ...
Special 24
Age 7 to 11 Challenge Level:
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Mobile Numbers
Age 5 to 11 Challenge Level:
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?
Clever Keys
Age 7 to 11 Short Challenge Level:
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Zios and Zepts
Age 7 to 11 Challenge Level:
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?
Pouring the Punch Drink
Age 7 to 11 Challenge Level:
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 jugs.
Sometimes We Lose Things
Age 7 to 11 Challenge Level:
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.
Reverse Trick
Age 7 to 11 Challenge Level:
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?
Throw a 100
Age 7 to 11 Challenge Level:
Can you score 100 by throwing rings on this board? Is there more than way to do it?
On Target
Age 7 to 11 Challenge Level:
You have 5 darts and your target score is 44. How many different ways could you score 44?
A Mixed-up Clock
Age 7 to 11 Challenge Level:
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?
Rod Measures
Age 7 to 11 Challenge Level:
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?
Bean Bags for Bernard's Bag
Age 7 to 11 Challenge Level:
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?
Open Squares
Age 7 to 11 Challenge Level:
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
It's All about 64
Age 7 to 11 Challenge Level:
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.
1, 2, 3 Magic Square
Age 7 to 11 Challenge Level:
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Abundant Numbers
Age 7 to 11 Challenge Level:
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Calendar Calculations
Age 7 to 11 Challenge Level:
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Rocco's Race
Age 7 to 11 Short Challenge Level:
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.
Buckets of Thinking
Age 7 to 11 Challenge Level:
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 Juggle
Age 7 to 11 Challenge Level:
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Arranging the Tables
Age 7 to 11 Challenge Level:
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Magic Squares 4x4
Age 7 to 11 Challenge Level:
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.
Oranges and Lemons
Age 7 to 11 Challenge Level:
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?
Back to School
Age 7 to 11 Challenge Level:
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?
Hubble, Bubble
Age 7 to 11 Challenge Level:
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?
Seven Square Numbers
Age 7 to 11 Challenge Level:
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.
Dividing a Cake
Age 7 to 11 Challenge Level:
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?
The Deca Tree
Age 7 to 11 Challenge Level:
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.
A-magical Number Maze
Age 7 to 11 Challenge Level:
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!
Adding Plus
Age 7 to 11 Challenge Level:
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?
The Clockmaker's Birthday Cake
Age 7 to 11 Challenge Level:
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
The Pied Piper of Hamelin
Age 7 to 11 Challenge Level:
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!
Fingers and Hands
Age 7 to 11 Challenge Level:
How would you count the number of fingers in these pictures?
Six Is the Sum
Age 7 to 11 Challenge Level:
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Today's Date - 01/06/2009
Age 5 to 11 Challenge Level:
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Being Collaborative - Primary Number
Age 5 to 11 Challenge Level:
Number problems at primary level to work on with others.
Month Mania
Age 5 to 11 Challenge Level:
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Shapes in a Grid
Age 7 to 11 Challenge Level:
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?
Follow the Numbers
Age 7 to 11 Challenge Level:
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.
Build it up More
Age 7 to 11 Challenge Level:
This task follows on from Build it Up and takes the ideas into three dimensions!
Bundles of Cubes
Age 7 to 11 Challenge Level:
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Sums and Differences 2
Age 7 to 11 Challenge Level:
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Sums and Differences 1
Age 7 to 11 Challenge Level:
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
NRICH is part of the family of activities in the Millennium Mathematics Project.