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.
I will the do the same for a 4x4x4 cube, 5x5x5 cube and finally a
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It is just an ordinary box. It sits in the corner of the lonesome room, like a cactus on a desert floor, among normal things like a lamp, an alarm clock, and a holy bible. With the box sitting on top of it, I could see the brown perimeter of the bible, like one sees a church steeple in a bank of clouds. The family bible is passed from generation to generation, as evidenced by the cracked leather and brown, rough edges like a cowboy’s face and hands. It is unclear to any stranger why such a boring, plain box would cover something so important. I am surprised this lonely box is not embraced by my family book, intertwining it in its branches and lifting it into the sky as the family tree continually grows. The cardboard box is white; it is square, and insignificantly small, as all individual sand particles are on a beach. It is light, making me wonder if the contents have disappeared over the expanse of two years, never to be seen again. Each side has the words “Priority Mail” in white, atop a background of blue and red. Something about the word “priority” sends shivers down my spine, and a sense of dread crushes me. A price tag dubs the contents $5.25, and an address indicated the box to be sent to Carroll Veterinary Clinic of Hillsville, Virginia. The top of the box looks scarred, almost like it is suffering with the baggage of family hurt. It is easily seen with the eye that the box has only been opened once or twice, and this is why it seems of little value to outsiders. It is no longer protected with tape; the tape has long ago served its purpose and is instead replaced with the less-trustworthy art of flap-folding. Tape is like a sealant of ancient tombs of royalty, while flap-folding is for boxing up unidentifiab...