Cube Shaped Boxes and Supermarket Displays

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Cube Shaped Boxes and Supermarket Displays

Introduction

The question:

Boxes made in the shape of a cube are easy to stack to make displays

in supermarkets.

Investigate!

Plan

====

I will carry out this investigation by following these points:

1. Simplify the question by using 2-d shapes.

2. Draw 2-d designs.

3. Draw 3-d designs.

4. Evaluate my work.

Detailed Plan

To investigate each shape I will follow a pattern:

1. I will state which shape I am investigating.

2. Draw the shape or a bird's eye view to show the shape.

3. Draw a difference table to show whether it is a linear or quadratic

formula.

4. Make a guess as to what the formula might be.

5. Check it. If it is right prove it by using the next shape in the

series. If it is not right work out the next part of the formula.

2-d Squares and Rectangles

[IMAGE]To simplify this investigation I will start off with an easy

shape and work my way onto more complex shapes.

[IMAGE]

[IMAGE]

[IMAGE]

To find a formula for this pattern I will draw a difference table.

Number of Layers (N) Number of boxes (B) 1st Difference (1st)

1 2

2

2 4

2

3 6

2

4 8

This shows that each time you add a layer you add two more boxes. I

will try and find a formula for this by multiplying the difference by

the length of the side.

N x 1st =

2

4

6

8

B=

2

4

6

8

As you can see the numbers are the same, meaning the formula for this

pattern is:

B=2N

I shall prove his formula to be right by trying the next shape in the

sequence.

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