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#### Resources tagged with Investigations similar to Next Size Up:

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### Four Layers

##### Stage: 1 and 2 Challenge Level:

Can you create more models that follow these rules?

### 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?

##### 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.

### 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?

### 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.

### 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.

### 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?

### 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.

### 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.

### 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?

### 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?

### 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.

### 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?

### Two by One

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### 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?

### Triangle Relations

##### Stage: 2 Challenge Level:

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

### More Pebbles

##### Stage: 2 and 3 Challenge Level:

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

### 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?

### 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?

### 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?

### Three Sets of Cubes, Two Surfaces

##### Stage: 2 Challenge Level:

How many models can you find which obey these rules?

### Building with Rods

##### Stage: 2 Challenge Level:

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

### Polygonals

##### Stage: 2 Challenge Level:

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

### Christmas Presents

##### Stage: 2 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?

### Tri.'s

##### Stage: 2 Challenge Level:

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

### Making Boxes

##### Stage: 2 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?

##### 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?

### 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?

### 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?

### 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?

### 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.

### 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?

### Room Doubling

##### Stage: 2 Challenge Level:

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

### 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.

### Cubes

##### Stage: 1 and 2 Challenge Level:

Investigate the number of faces you can see when you arrange three cubes in different ways.

### 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.

### Egyptian Rope

##### Stage: 2 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?

### 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?

### 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?

### 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?

##### 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.

### 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?

### The Pied Piper of Hamelin

##### Stage: 2 Challenge Level:

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

### Building with Longer Rods

##### Stage: 2 and 3 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

### Counting on Letters

##### Stage: 3 Challenge Level:

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

### More Transformations on a Pegboard

##### Stage: 2 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.