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Resources tagged with Investigations similar to Clapping Times:

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

Triangle Shapes

Stage: 1 and 2 Challenge Level:

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

Escher Tessellations

Stage: 2 Challenge Level:

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

Halving

Stage: 1 Challenge Level:

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

It's a Fence!

Stage: 1 and 2 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.

The Numbers Give the Design

Stage: 2 Challenge Level:

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

Seven Sticks

Stage: 1 Challenge Level:

Explore the triangles that can be made with seven sticks of the same length.

Fit These Shapes

Stage: 1 and 2 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?

Cutting Corners

Stage: 2 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?

Turning

Stage: 1 Challenge Level:

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Repeating Patterns

Stage: 1 Challenge Level:

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Fencing

Stage: 2 Challenge Level:

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

Stage: 2 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.

Two Squared

Stage: 2 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?

Play a Merry Tune

Stage: 2 Challenge Level:

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

28 and It's Upward and Onward

Stage: 2 Challenge Level:

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

Baked Bean Cans

Stage: 1 Challenge Level:

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

Triple Cubes

Stage: 1 and 2 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.

Redblue

Stage: 2 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?

Little Boxes

Stage: 2 Challenge Level:

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

How Tall?

Stage: 1 and 2 Challenge Level:

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

Four Layers

Stage: 1 and 2 Challenge Level:

Can you create more models that follow these rules?

Newspapers

Stage: 2 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?

Cubes Here and There

Stage: 2 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?

Hexpentas

Stage: 1 and 2 Challenge Level:

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

3 Rings

Stage: 2 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?

Building with Rods

Stage: 2 Challenge Level:

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

Sticks and Triangles

Stage: 2 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?

Triangle Relations

Stage: 2 Challenge Level:

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

Stage: 2 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?

Sort the Street

Stage: 1 Challenge Level:

Sort the houses in my street into different groups. Can you do it in any other ways?

Two on Five

Stage: 1 and 2 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?

Room Doubling

Stage: 2 Challenge Level:

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

Two by One

Stage: 2 Challenge Level:

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

Calcunos

Stage: 2 Challenge Level:

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

Move a Match

Stage: 2 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?

Ice Cream

Stage: 2 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.

Halloween Investigation

Stage: 2 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?

Street Party

Stage: 2 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.

Cuboid-in-a-box

Stage: 2 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?

Bean Bags for Bernard's Bag

Stage: 2 Challenge Level:

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Triangle Pin-down

Stage: 2 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

My New Patio

Stage: 2 Challenge Level:

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

Stairs

Stage: 1 and 2 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.

Magic Constants

Stage: 2 Challenge Level:

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

It Figures

Stage: 2 Challenge Level:

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Sweets in a Box

Stage: 2 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?

Train Carriages

Stage: 1 and 2 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?

Stage: 2 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.

Making Cuboids

Stage: 2 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?

New House

Stage: 2 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?