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#### Resources tagged with Investigations similar to A Patchwork Piece:

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### There are 145 results

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

### 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?

### 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?

### 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?

### 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?

### All Wrapped Up

##### Age 7 to 11 Challenge Level:

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

### Triangle Relations

##### Age 7 to 11 Challenge Level:

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

### Christmas 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?

### 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?

### 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?

### 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.

### 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.

### 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?

### More Pebbles

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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?

### 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?

### 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?

### 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.

### 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?

### Tri.'s

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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.

### 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?

### 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.

### 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?

### Magic Constants

##### Age 7 to 11 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 Must Be 2000

##### Age 7 to 11 Challenge Level:

Here are many ideas for you to investigate - all linked with the number 2000.

### Two by One

##### Age 7 to 11 Challenge Level:

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

### 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?

### Sticky Triangles

##### Age 7 to 11 Challenge Level:

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

### Triangle Pin-down

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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.

### Extending Great Squares

##### Age 7 to 11 Challenge Level:

Explore one of these five pictures.

### Polygonals

##### Age 7 to 11 Challenge Level:

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

### Eye View

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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.

### 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.

### 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?

### Division Rules

##### Age 7 to 11 Challenge Level:

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

### 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?

### 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?

### Opening Out

##### Age 5 to 11

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

### 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?

### 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.