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Games. Multiplication & division. Addition & subtraction. Combinations. Trial and improvement. Dominoes. Generalising. Factors and multiples. Working systematically. Investigations.There are 147 results
Broad Topics > Thinking Mathematically > Investigations
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.
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!
Calendar Patterns
Age 7 to 11
Challenge Level
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
Consecutive Numbers
Age 7 to 14
Challenge Level
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Five Coins
Age 5 to 11
Challenge Level
Ben has five coins in his pocket. How much money might he have?
Caterpillars
Age 5 to 7
Challenge Level
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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.
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?
It Figures
Age 7 to 11
Challenge Level
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
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?
Marvellous Matrix
Age 7 to 11
Challenge Level
Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?
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?
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.
Number Squares
Age 5 to 11
Challenge Level
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
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.
Worms
Age 7 to 11
Challenge Level
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Sending Cards
Age 7 to 11
Challenge Level
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Homes
Age 5 to 7
Challenge Level
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
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?
Calcunos
Age 7 to 11
Challenge Level
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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.
Pebbles
Age 7 to 11
Challenge Level
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Stairs
Age 5 to 11
Challenge Level
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
Alien Counting
Age 7 to 11
Challenge Level
Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.
Room Doubling
Age 7 to 11
Challenge Level
Investigate the different ways you could split up these rooms so that you have double the number.
Sets of Numbers
Age 7 to 11
Challenge Level
How many different sets of numbers with at least four members can you find in the numbers in this box?
Watch Your Feet
Age 7 to 11
Challenge Level
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
Two on Five
Age 5 to 11
Challenge Level
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Sweets in a Box
Age 7 to 11
Challenge Level
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Street Sequences
Age 5 to 11
Challenge Level
Investigate what happens when you add house numbers along a street in different ways.
Let's Investigate Triangles
Age 5 to 7
Challenge Level
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Birthday Cake Candles
Age 7 to 11
Challenge Level
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
Cubes Here and There
Age 7 to 11
Challenge Level
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
So It's 28
Age 5 to 7
Challenge Level
Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.
Sticks and Triangles
Age 7 to 11
Challenge Level
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Sorting the Numbers
Age 5 to 11
Challenge Level
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?
Gran, How Old Are You?
Age 7 to 11
Challenge Level
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Polygonals
Age 7 to 11
Challenge Level
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
More Children and Plants
Age 7 to 14
Challenge Level
This challenge extends the Plants investigation so now four or more children are involved.
More Plant Spaces
Age 7 to 14
Challenge Level
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Crossing the Town Square
Age 7 to 11
Challenge Level
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Building with Rods
Age 7 to 11
Challenge Level
In how many ways can you stack these rods, following the rules?
Tiling
Age 7 to 11
Challenge Level
An investigation that gives you the opportunity to make and justify predictions.
Making Cuboids
Age 7 to 11
Challenge Level
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Ice Cream
Age 7 to 11
Challenge Level
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Lost Books
Age 7 to 11
Challenge Level
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Newspapers
Age 7 to 11
Challenge Level
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Tea Cups
Age 7 to 14
Challenge Level
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
NRICH is part of the family of activities in the Millennium Mathematics Project.