Kenneth Cole

Construct a Box Project

This project has three parts (1) design a box, (2) record accurately its measurements,cut off waste and create the box, and (3) complete all documentation for submission.

1. Design a box draw the blueprint see Box Blueprint paper.

• a) Draw eleven rectangles on a poster board using the following pattern:
  

      
Blueprint for box on 11" by 14" poster board

   
3D view of completed box

• b) Make sure that the top rectangle is congruent to the bottom, the front rectangle is congruent to the back, and the right side rectangle is congruent to the left side.
• c) Rectangles Waste Area 1 and Waste Area 2 must be congruent squares for drawing to make a box.
• d) If you have a different idea for your blue print, you must sketch your idea for the blue print and submit it to Mr. Cole for approval before proceeding with your idea.

2. The following process must be observed in designing your box:

• a) Use a 11 inch by 14 inch poster board.
• b) After the pattern is drawn on one side, label each rectangle as in the blueprint above.
• c) Record all measurements in millimeters on blueprint worksheet and on the back of this form (eleven in all).
• d) Next, after inspection of blueprint and calculations by Mr. Cole, cut off the waste rectangles and squares.
• e) The remaining lines should be folded to form the box.
• f) Tape the edges to form a rectangular solid (box).
• g) On the front of the box record the following information:
  (1) your name and date of submission
  (2) the length, width and height of the box in millimeters
• h) Submit completed box and blueprint worksheet.
  

3. Complete the evaluation and mathematical calculations on back. Submit this form with your box.

• a) Evaluate your own work and have your parent evaluate your work.
• b) Complete the mathematical calculations.
  

The completed project (the blueprint worksheet and your box) is due on (Next Due Date).

MATHEMATICAL RECORDS

AREA OF RECTANGLES:

1. Top rectangle (lw)                                      Area =

2. Bottom rectangle (lw)                                 Area =

3. Front rectangle (lh)                                     Area =

4. Back rectangle (lh)                                     Area =

5. Right side rectangle (wh)                            Area =

6. Left side rectangle (wh)                              Area =

7. Waste 1 square (w²)                                   Area =

8. Waste 2 square (w²)                                   Area =

9. Waste 3 rectangle [355.6mm-(l+w)]w       Area =

10. Waste 4 rectangle [355.6mm-(l+w)]w    Area =

11. Waste 5 rectangle [355.6mm-2(l+w)]h          Area=

hint: (14"= 355.6mm)

DIMENSIONS OF THE BOX:

Length (l) =                   Width (w) =                        Height (h) =

SURFACE AREA OF BOX:

Add the area of the six faces of the box (answers of 1-6 above). S. A. = 2lw + 2lh + 2wh

Surface Area of box =

VOLUME OF BOX:

Multiply the length x width x height. V=lwh

Volume of box =

Introduction to the Box Project

for

Mr. Cole's Emerging Technology Class

For the purpose of this project, we will imagine that Faubion Middle School is The Faubion Candy Factory. Also, Mr. Cole's classroom is now the Design Engineering Division of the factory. Furthermore, you and every one of your fellow classmates are design engineers. Management has presented our division with the following problem.

The warehouse in the 300 wing of the factory has informed us that we have a great surplus of 11"by 14" poster boards, which we must get off our inventory. Therefore management has decided that our division must design a box to make out of these surplus poster boards so that it will hold the most candy possible. Unfortunately, management has also informed us that an industrial spy from the Dowell Candy Factory has infiltrated the Production Division in the MASH Units. Management knows who the spy is and wants to send bad information to that spy. Therefore, management also wants us to design a box from the poster board, which will hold the least amount of candy using the most posterboard.

Since this project is of such extreme importance to the success of our factory this year, the engineer who designs the box with the largest volume from the poster board will be awarded a bonus. Also, the engineer who designs the box with the least volume to surface area ratio will also be given the same bonus. The latter design will be intentionally leaked to the Dowell Candy Factory spy.

Your job will be to draw a blueprint, cut out and create a model of the box from your blueprint, record all the measurements and calculate all areas of the blueprint, and calculate the volume and surface area of the box. After Mr. Cole has inspected your blueprint, you are to cut, fold, and tape your blueprint to create a working model. You then must record all measurements in millimeters, square millimeters and cubic millimeters.

On (the due date) all of the completed boxes will be measured and recorded on a spreadsheet in class. After calculations are completed, on (the next day) prizes for the winning boxes will be awarded. Mr. Cole's spreadsheet records are final. No late entries will be included in the competition.

The Underlying Objectives of This Project

This project involves designing and reading a blueprint, creating a three dimensional object from that blueprint, using and learning formulae for area, volume, and surface area, as well as, understanding and using linear measurements. Concepts introduced in this lesson are recording real data on a spreadsheet and using that spreadsheet to calculate area, surface area, waste area, and volume. Also introduced in this lesson is the idea of maximizing volume, minimizing waste, and minimizing the resulting ratios of the related concepts of surface area and volume. The concepts of maximum and minimum, which are important concepts in more advanced mathematics areas of study such as differential calculus.

After the project is completed. The students are asked to graph the data contained in the spreadsheet. This is easily done using the spreadsheet's graphing capabilities. This also requires the students to choose the graph that is best for analysis of the data. Allow the students time to explore enough of the possibilities so that they can discover their best choice. Have the students to construct and explain a rule relating the sizes of the volume, the surface area, and their ratio to the length, width, and height of boxes (rectangular prisms). By constructing their own rules in this final step, the student will better understand the true nature of mathematics.

My Soap Box

I define the true nature of mathematics as the rules by which the universe operates. I also think that once students truly understand this, mathematics lessons become more fun for them because they understand that the study of mathematics is a game of uncovering those rules. Thus, the study of mathematics is the greatest game of all.

"Mathematics is the language with which God has written the Universe"—Galileo

Spreadsheet of Calculations for Final Day of Project

A few notes on the total waste column on the spreadsheet: If a negative total waste is recorded, the student is disqualified from the contest. The only way to have a negative total waste is for the student to gain area to the original posterboard. This would mean that the student started with a posterboard too large for the project specifications. The area of the original posterboard is almost 100,000 mm².

• Blueprint Worksheet for this project.
• Similar Project at Milby High School in Houston, Texas.
• See how a student designed a Better Box.
• Excel Spreadsheet Calculations Lesson