Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

Cutting it Out

Age 5 to 11 Challenge Level:

I cut this square into two different shapes. What can you say about the relationship between them?

Great Squares

Age 7 to 11 Challenge Level:

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

Fencing Lambs

Age 7 to 11 Challenge Level:

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

Triangle Relations

Age 7 to 11 Challenge Level:

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

Lawn Border

Age 5 to 11 Challenge Level:

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

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?

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.

Tiles in the Garden

Age 7 to 11 Challenge Level:

How many tiles do we need to tile these patios?

Tiling Into Slanted Rectangles

Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

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?

Tri.'s

Age 7 to 11 Challenge Level:

How many triangles can you make on the 3 by 3 pegboard?

Cutting Corners

Age 7 to 11 Challenge Level:

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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?

Opening Out

Age 5 to 11

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

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?

Escher Tessellations

Age 7 to 11 Challenge Level:

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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.

All Wrapped Up

Age 7 to 11 Challenge Level:

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

Making Squares

Age 7 to 11

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?

It's a Fence!

Age 5 to 11 Challenge Level:

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

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?

Presents

Age 7 to 11 Challenge Level:

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

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?

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?

The Big Cheese

Age 7 to 11 Challenge Level:

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

Two Squared

Age 7 to 11 Challenge Level:

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?

Fencing

Age 7 to 11 Challenge Level:

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

Double Your Popcorn, Double Your Pleasure

Age 7 to 11 Challenge Level:

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Triangle Shapes

Age 5 to 11 Challenge Level:

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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?

Tessellating Triangles

Age 7 to 11 Challenge Level:

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles 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?

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.

Extending Great Squares

Age 7 to 11 Challenge Level:

Explore one of these five pictures.

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.

Four Layers

Age 5 to 11 Challenge Level:

Can you create more models that follow these rules?

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?

Eye View

Age 7 to 11 Challenge Level:

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

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?

More Pebbles

Age 7 to 11 Challenge Level:

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

Tiles on a Patio

Age 7 to 11 Challenge Level:

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

Fit These Shapes

Age 5 to 11 Challenge Level:

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?

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.

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?

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?

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?

Witch's Hat

Age 11 to 16 Challenge Level:

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

Exploring Number Patterns You Make

Age 7 to 11 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

Sending and Receiving 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?

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?