There are **141** NRICH Mathematical resources connected to **Investigations**, you may find related items under Thinking Mathematically.

Challenge Level

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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?

Challenge Level

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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?

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.

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?

Challenge Level

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

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 ...?

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.

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.

Challenge Level

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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.

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.

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?

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?

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?

Challenge Level

Ben has five coins in his pocket. How much money might he have?

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?

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?

Challenge Level

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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.

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?

Challenge Level

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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?

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?

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?

Challenge Level

How many faces can you see when you arrange these three cubes in different ways?

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?

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?

Challenge Level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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.

Challenge Level

How many different sets of numbers with at least four members can you find in the numbers in this box?

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?

Challenge Level

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Challenge Level

Formulate and investigate a simple mathematical model for the design of a table mat.

Challenge Level

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

Challenge Level

It starts quite simple but great opportunities for number discoveries and patterns!

Challenge Level

Which way of flipping over and/or turning this grid will give you the highest total? You'll need to imagine where the numbers will go in this tricky task!

Challenge Level

A challenging activity focusing on finding all possible ways of stacking rods.

Challenge Level

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Challenge Level

A follow-up activity to Tiles in the Garden.

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.

Challenge Level

In how many ways can you stack these rods, following the rules?

Challenge Level

This challenge extends the Plants investigation so now four or more children are involved.

Challenge Level

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

Challenge Level

Why does the tower look a different size in each of these pictures?

Challenge Level

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Challenge Level

Work with numbers big and small to estimate and calculate various quantities in biological contexts.