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Working systematically. Multiplication & division. Games. Combinations. Visualising. Counting. Addition & subtraction. Comparing and ordering numbers. Investigations. Practical Activity.There are 147 results
Broad Topics > Thinking Mathematically > Investigations
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.
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?
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?
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.
Move a Match
Age 7 to 11
Challenge Level
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
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.
Taking a Die for a Walk
Age 5 to 11
Challenge Level
Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.
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?
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?
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?
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.
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?
Buying a Balloon
Age 7 to 11
Challenge Level
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?
New House
Age 7 to 11
Challenge Level
In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
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?
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?
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?
Count the Digits
Age 5 to 11
Challenge Level
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
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.
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?
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?
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?
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?
3 Rings
Age 7 to 11
Challenge Level
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Street Party
Age 7 to 11
Challenge Level
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
Train Carriages
Age 5 to 11
Challenge Level
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Magazines
Age 7 to 11
Challenge Level
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
Halloween Investigation
Age 7 to 11
Challenge Level
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they 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.
More Children and Plants
Age 7 to 14
Challenge Level
This challenge extends the Plants investigation so now four or more children are involved.
Repeating Patterns
Age 5 to 7
Challenge Level
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Building with Longer Rods
Age 7 to 14
Challenge Level
A challenging activity focusing on finding all possible ways of stacking rods.
Triangle Relations
Age 7 to 11
Challenge Level
What do these two triangles have in common? How are they related?
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?
All Wrapped Up
Age 7 to 11
Challenge Level
What is the largest cuboid you can wrap in an A3 sheet of paper?
Cuboid-in-a-box
Age 7 to 11
Challenge Level
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Tessellating Transformations
Age 7 to 11
Challenge Level
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
Sticky Triangles
Age 7 to 11
Challenge Level
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Tiling Into Slanted Rectangles
Age 7 to 11
Challenge Level
A follow-up activity to Tiles in the Garden.
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?
Colouring Triangles
Age 5 to 7
Challenge Level
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
Two by One
Age 7 to 11
Challenge Level
An activity making various patterns with 2 x 1 rectangular tiles.
Street Sequences
Age 5 to 11
Challenge Level
Investigate what happens when you add house numbers along a street in different ways.
Cubes
Age 7 to 11
Challenge Level
How many faces can you see when you arrange these three cubes in different ways?
Are You a Smart Shopper?
Age 7 to 11
Challenge Level
In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?
Sort the Street
Age 5 to 7
Challenge Level
Sort the houses in my street into different groups. Can you do it in any other ways?
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?
More Transformations on a Pegboard
Age 7 to 11
Challenge Level
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
My New Patio
Age 7 to 11
Challenge Level
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
NRICH is part of the family of activities in the Millennium Mathematics Project.