Other tags that relate to The Number Crunching Machine
Investigations. Combinations. Factors and multiples. Place value. Working systematically. Addition & subtraction. Generalising. Multiplication & division. Trial and improvement. Functions and their inverses.There are 210 results
Broad Topics > Calculations and Numerical Methods > Addition & subtraction
The Number Crunching Machine
Age 7 to 11 Challenge Level:
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
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.
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?
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?
Spell by Numbers
Age 7 to 11 Challenge Level:
Can you substitute numbers for the letters in these sums?
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?
Sisters and Brothers
Age 7 to 11 Challenge Level:
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?
Magic Triangle
Age 7 to 11 Challenge Level:
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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.
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?
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.
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.
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?
Clock Face
Age 7 to 11 Challenge Level:
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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!
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?
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.
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?
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?
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).
Digit Addition
Age 5 to 11 Challenge Level:
Try out this number trick. What happens with different starting numbers? What do you notice?
One Wasn't Square
Age 7 to 11 Challenge Level:
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
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!
Cows and Sheep
Age 7 to 11 Challenge Level:
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Developing Number Fluency - What, Why and How
Age 5 to 11
In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.
Place Value as a Building Block for Developing Fluency in the Calculation Process
Age 5 to 11
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Journeys
Age 7 to 11 Challenge Level:
Investigate the different distances of these car journeys and find out how long they take.
How Do You Do It?
Age 7 to 11 Challenge Level:
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
Next Number
Age 7 to 11 Short Challenge Level:
Find the next number in this pattern: 3, 7, 19, 55 ...
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 Resourceful - Primary Number
Age 5 to 11 Challenge Level:
Number problems at primary level that require careful consideration.
Rabbits in the Pen
Age 7 to 11 Challenge Level:
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Cherries Come in Twos
Age 7 to 11 Challenge Level:
Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?
Dart Target
Age 7 to 11 Challenge Level:
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
Zargon Glasses
Age 7 to 11 Challenge Level:
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
A Numbered Route
Age 7 to 11 Challenge Level:
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
Numbered Cars
Age 7 to 11 Challenge Level:
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
How Much Did it Cost?
Age 7 to 11 Challenge Level:
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Scoring with Dice
Age 7 to 11 Challenge Level:
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?
Penta Post
Age 7 to 11 Challenge Level:
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?
Napier's Bones
Age 7 to 11 Challenge Level:
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?
How Many Eggs?
Age 7 to 11 Challenge Level:
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
Let's Face It
Age 7 to 11 Challenge Level:
In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.
Gift Stacks
Age 7 to 11 Challenge Level:
Use the information to work out how many gifts there are in each pile.
NRICH is part of the family of activities in the Millennium Mathematics Project.