Search by Topic

Resources tagged with Investigations similar to En-counters:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 150 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Investigations

problem icon

Two Squared

Stage: 2 Challenge Level: Challenge Level:1

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

problem icon

Cubes

Stage: 1 and 2 Challenge Level: Challenge Level:1

Investigate the number of faces you can see when you arrange three cubes in different ways.

problem icon

It's a Fence!

Stage: 1 and 2 Challenge Level: Challenge Level:1

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

problem icon

Making Boxes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

problem icon

Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A follow-up activity to Tiles in the Garden.

problem icon

Fencing

Stage: 2 Challenge Level: Challenge Level:1

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

problem icon

Sticky Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Triangle Relations

Stage: 2 Challenge Level: Challenge Level:1

What do these two triangles have in common? How are they related?

problem icon

Calcunos

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

problem icon

Christmas Presents

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

problem icon

Newspapers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Opening Out

Stage: 1 and 2

Bernard Bagnall describes how to get more out of some favourite NRICH investigations.

problem icon

Making Squares

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

problem icon

Fencing Lambs

Stage: 2 Challenge Level: Challenge Level:1

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

problem icon

My New Patio

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

problem icon

Stacks of Maths!

Stage: 1, 2 and 3

In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.

problem icon

Four Layers

Stage: 1 and 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you create more models that follow these rules?

problem icon

Experiencing Problem Solving

Stage: 1 and 2

Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.

problem icon

3 Sets of Cubes, 2 Surfaces

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many models can you find which obey these rules?

problem icon

Extending Great Squares

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore one of these five pictures.

problem icon

Polygonals

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Triple Cubes

Stage: 1 and 2 Challenge Level: Challenge Level:1

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

problem icon

Olympic Rings

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is intended to get children to look really hard at something they will see many times in the next few months.

problem icon

Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

problem icon

Tea Cups

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

problem icon

Fit These Shapes

Stage: 1 and 2 Challenge Level: Challenge Level:1

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

problem icon

More Pebbles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Have a go at this 3D extension to the Pebbles problem.

problem icon

Eye View

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

More Transformations on a Pegboard

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

problem icon

Street Party

Stage: 2 Challenge Level: Challenge Level:1

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.

problem icon

Halloween Investigation

Stage: 2 Challenge Level: Challenge Level:1

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?

problem icon

Tiles on a Patio

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How many ways can you find of tiling the square patio, using square tiles of different sizes?

problem icon

Ice Cream

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

problem icon

3 Rings

Stage: 2 Challenge Level: Challenge Level:1

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?

problem icon

Great Squares

Stage: 2 and 3 Challenge Level: Challenge Level:1

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

problem icon

The Great Tiling Count

Stage: 2 Challenge Level: Challenge Level:1

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

problem icon

Lost Books

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

problem icon

Magazines

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

So It's 28

Stage: 1 Challenge Level: Challenge Level:1

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.

problem icon

Become Maths Detectives

Stage: 2 Challenge Level: Challenge Level:1

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

problem icon

28 and It's Upward and Onward

Stage: 2 Challenge Level: Challenge Level:1

Can you find ways of joining cubes together so that 28 faces are visible?

problem icon

Marvellous Matrix

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

problem icon

Sticks and Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

problem icon

It Was 2010!

Stage: 1 and 2 Challenge Level: Challenge Level:1

If the answer's 2010, what could the question be?

problem icon

Baked Bean Cans

Stage: 1 Challenge Level: Challenge Level:1

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

problem icon

Triangular Hexagons

Stage: 2 Challenge Level: Challenge Level:1

Investigate these hexagons drawn from different sized equilateral triangles.

problem icon

All Wrapped Up

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the largest cuboid you can wrap in an A3 sheet of paper?

problem icon

2 Rings

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Tessellating Transformations

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Train Carriages

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?