Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

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.

Four Layers

Age 5 to 11
Challenge Level

Can you create more models that follow these rules?

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.

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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?

Triangle Relations

Age 7 to 11
Challenge Level

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

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.

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?

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.

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.

Experiencing Problem Solving

Age 5 to 11

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

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?

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.

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.

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?

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.

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?

Little Boxes

Age 7 to 11
Challenge Level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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?

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.

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?

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?

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?

Tri.'s

Age 7 to 11
Challenge Level

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

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?

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?

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?

All Wrapped Up

Age 7 to 11
Challenge Level

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

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 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?

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?

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.

Two by One

Age 7 to 11
Challenge Level

An activity making various patterns with 2 x 1 rectangular tiles.

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?

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?

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?

Tiling Into Slanted Rectangles

Age 7 to 11
Challenge Level

A follow-up activity to Tiles in the Garden.

Tiles in the Garden

Age 7 to 11
Challenge Level

How many tiles do we need to tile these patios?

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.

Cubes

Age 7 to 11
Challenge Level

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

Eye View

Age 7 to 11
Challenge Level

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

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

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?

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?

More Pebbles

Age 7 to 11
Challenge Level

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

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?

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?

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?

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.