There are 204 NRICH Mathematical resources connected to Investigations, you may find related items under Thinking Mathematically.
Broad Topics > Thinking Mathematically > Investigations
Division Rules
Age 7 to 11
Challenge Level
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
The Domesday Project
Age 7 to 11
Challenge Level
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
Olympic Rings
Age 5 to 7
Challenge Level
This problem is intended to get children to look really hard at something they will see many times in the next few months.
How Tall?
Age 5 to 11
Challenge Level
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
So It's Times!
Age 7 to 14
Challenge Level
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
Track Design
Age 14 to 16
Challenge Level
Where should runners start the 200m race so that they have all run the same distance by the finish?
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?
Shaping It
Age 5 to 11
Challenge Level
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
The Car That Passes
Age 7 to 11
Challenge Level
What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?
In the Playground
Age 5 to 11
Challenge Level
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Ip Dip
Age 5 to 11
Challenge Level
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Triple Cubes
Age 5 to 11
Challenge Level
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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.
The Numbers Give the Design
Age 7 to 11
Challenge Level
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Escape from Planet Earth
Age 16 to 18
Challenge Level
How fast would you have to throw a ball upwards so that it would never land?
Repeating Patterns
Age 5 to 7
Challenge Level
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Taking Trigonometry Series-ly
Age 16 to 18
Challenge Level
Look at the advanced way of viewing sin and cos through their power series.
Scale Invariance
Age 16 to 18
Challenge Level
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Making More Tracks
Age 16 to 18
Challenge Level
Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?
More Bridge Building
Age 16 to 18
Challenge Level
Which parts of these framework bridges are in tension and which parts are in compression?
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?
Turning
Age 5 to 7
Challenge Level
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
2 Rings
Age 5 to 7
Challenge Level
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
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?
Brush Loads
Age 7 to 11
Challenge Level
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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.
Spokes
Age 16 to 18
Challenge Level
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
Halving
Age 5 to 7
Challenge Level
These pictures show squares split into halves. Can you find other ways?
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?
Egyptian Rope
Age 7 to 11
Challenge Level
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
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?
Colouring Triangles
Age 5 to 7
Challenge Level
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
Five Coins
Age 5 to 11
Challenge Level
Ben has five coins in his pocket. How much money might he have?
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?
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?
Making Boxes
Age 7 to 11
Challenge Level
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
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"?
Round and Round the Circle
Age 7 to 11
Challenge Level
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
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?
Bracelets
Age 7 to 11
Challenge Level
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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?
Roll These Dice
Age 7 to 11
Challenge Level
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
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?
Cubes
Age 7 to 11
Challenge Level
How many faces can you see when you arrange these three cubes in different ways?
Plants
Age 5 to 14
Challenge Level
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Chocolate
Age 7 to 14
Challenge Level
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.