Resources tagged with: Investigations

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

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.

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.

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.

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?

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?

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?

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?

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?

Cubes

Age 7 to 11 Challenge Level:

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

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?

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?

Redblue

Age 7 to 11 Challenge Level:

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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.

Four Layers

Age 5 to 11 Challenge Level:

Can you create more models that follow these rules?

Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

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.

Move a Match

Age 7 to 11 Challenge Level:

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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.

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.

Halving

Age 5 to 7 Challenge Level:

These pictures show squares split into halves. Can you find other ways?

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?

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?

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.

Two by One

Age 7 to 11 Challenge Level:

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

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?

All Wrapped Up

Age 7 to 11 Challenge Level:

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

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?

Baked Bean Cans

Age 5 to 7 Challenge Level:

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

Hexpentas

Age 5 to 11 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

28 and It's Upward and Onward

Age 7 to 11 Challenge Level:

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

More Pebbles

Age 7 to 11 Challenge Level:

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

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.

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?

Tea Cups

Age 7 to 14 Challenge Level:

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.

Teddy Town

Age 5 to 14 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Homes

Age 5 to 7 Challenge Level:

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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?

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?

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?

Magazines

Age 7 to 11 Challenge Level:

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.

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?

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?

Extending Great Squares

Age 7 to 11 Challenge Level:

Explore one of these five pictures.

Room Doubling

Age 7 to 11 Challenge Level:

Investigate the different ways you could split up these rooms so that you have double the number.

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.

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?

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?

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.

Triangular Hexagons

Age 7 to 11 Challenge Level:

Investigate these hexagons drawn from different sized equilateral triangles.