Other tags that relate to Shape Times Shape
Factors and multiples. Visualising. Introducing algebra. Trial and improvement. Working systematically. Multiplication & division. Addition & subtraction. Combinations. Generalising. Investigations.There are 213 results
Broad Topics > Calculations and Numerical Methods > Addition & subtraction
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?
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?
Oh! Harry!
Age 7 to 11 Challenge Level:
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Polo Square
Age 7 to 11 Challenge Level:
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
All Seated
Age 7 to 11 Challenge Level:
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
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!
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!
Gift Stacks
Age 7 to 11 Challenge Level:
Use the information to work out how many gifts there are in each pile.
The Puzzling Sweet Shop
Age 7 to 11 Challenge Level:
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?
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?
Spell by Numbers
Age 7 to 11 Challenge Level:
Can you substitute numbers for the letters in these sums?
Two Egg Timers
Age 7 to 11 Challenge Level:
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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?
Prison Cells
Age 7 to 11 Challenge Level:
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Page Numbers
Age 7 to 11 Short Challenge Level:
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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.
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.
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?
Magic Circles
Age 7 to 11 Challenge Level:
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
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.
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.
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?
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.
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?
Journeys in Numberland
Age 7 to 11 Challenge Level:
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Sticky Dice
Age 7 to 11 Challenge Level:
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
X Is 5 Squares
Age 7 to 11 Challenge Level:
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
How Old?
Age 7 to 11 Challenge Level:
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Magic Constants
Age 7 to 11 Challenge Level:
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
The Dice Train
Age 7 to 11 Challenge Level:
This dice train has been made using specific rules. How many different trains can you make?
Doplication
Age 7 to 11 Challenge Level:
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
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?
Dice and Spinner Numbers
Age 7 to 11 Challenge Level:
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
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.
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!
Balance of Halves
Age 7 to 11 Challenge Level:
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
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.
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?
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.
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.
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?
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?
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.
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.
Two Primes Make One Square
Age 7 to 11 Challenge Level:
Can you make square numbers by adding two prime numbers together?
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?
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.
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.