Question

三葉蟲

根本看不懂啦＼(￣▽￣;)／

Your report should follow these guidelines, although you may choose how you present it:
How to Write a Mathematics Report
In writing your report, remember that you are writing up a mathematical story and so, like all good
stories, it will need a beginning, a middle and an end. More formally, the main components of this
writing style are: Introduction, Formulating the Problem, Solving the problem, Discussion of Results,
and Conclusion. We will now consider some of the detail in each of these aspects.
Introduction
This is the beginning of the story. Give a brief explanation of what the problem is about what the
goals of the report are and what will be presented. Assume that your reader does not know what the
problem is about or how to solve it.
Formulating the problem
Translate the situation into a maths problem. Explain how you will begin to solve the problem and
break it into simpler stages. Discuss any assumptions made. What quantities are variables and which
values are fixed?
You may use sub-headings if they assist you.
Solving the Problem
Show any calculations and mathematical reasoning that you use. (Assume that your reader does not
know much maths). Do not show the same types of calculations repetitively. Just give one or two
examples of a calculation and then put the rest of the results in a table.
Use diagrams or graphs if they assist you. Make general remarks about what you observe in your
calculation results and, possibly, why. You may want to criticise your work and go on to improve it in
the next section. Explain what you will do next and why.
Discussion of Results - Evaluate and Verify
Summarise your results if necessary and refer to your mathematical reasoning. Justify procedures used.
Interpret your results. First, are they reasonable or does something not look right and need further
investigation or checking? Is there a decision to be made? Here is where you should present the
decision-making process. Evaluate the strengths and limitations of your solutions.
Conclusion
Summarise your findings. Refer to the problem outlined in the introduction. Make sure that you
answer the question that was asked. Make recommendations. No new material should be presented
here.

roach to problem-
and mathematical
ng
Stage 1
Fcrmulate
Formulate - Once you understand what the problem
is asking, you must design a plan to solve the
problem. You translate the problem into a
mathematical representation by first determining the
applicable mathematical principles, concepts,
techniques and technology that are required to make
progress with the problem. Appropriate assumptions,
variables and observations are identified and written
down. In mathematical modelling, formulating a
model involves the process of mathematisation
moving from the real world to the mathematical
world.
Stage 2
Solve
Solve - You are to select and apply mathematical
procedures, concepts and techniques previously learnt
to solve the mathematical problem. Use standard
mathematical techniques to produce a valid solution
regarding the boxes and cartons. Solutions can be
found using algebraic, graphic, arithmetic and/or
numeric methods, with and/or without technology.
No
Is it
solved?
Yes
Stage 3
Evaluate and
verify
Evaluate and verify - Once a possible solution has
been achieved, you need to consider the
reasonableness of your box and carton solutions in
terms of the problem. You evaluate your results and
make a judgment about the boxes and cartons in
relation to the original request. This involves
exploring the strengths and limitations of your
solutions via a decision matrix. Where necessary, this
will require going back through the process to further
refine the solution. You must check that the boxes and
cartons provide a valid solution to the real-world
problem they have been designed to address.
Is the
solution
verified
Yes
Communicate - The development of solutions to
real-world problems must be capable of being
evaluated and used by others and so need to be
communicated clearly and fully. You communicate
findings systematically and concisely using
mathematical and everyday language. You draw
conclusions, discussing the key results and the
strengths and limitations of the solution. You could
offer further explanation, justification, and/or
recommendations, framed in the context of the initial
problem.
Stage 4
Communicate

WHO MOVED THE CHEESE?
Wedges of cheese are manufactured for retail sale in the shape of a sector-based prism, as shown.
SSIMS
The base of each wedge of cheese has a sector angle of Orn1_degrees. A wedge weighs
grams.
Each wedge is wrapped in foil with the seams (where edges meet) being heat-welded closed. The
wedges are then packed into cylindrical boxes, similar to the one shown above, although the wedges
might not fit snugly like these do.
Batches of cylindrical boxes are then packed into cartons to be taken in refrigerated trucks to the shops
from which they will be sold. The weight of cheese in a carton should be close to, but no more than,
19 kg.
As the mathematician with the logistics section of the cheese company, your job is to analyse the
packaging required at each stage of preparing the cheeses for retail sale. Management are most
concerned to know about
How each wedge will be wrapped
How the cylindrical boxes of cheese should be packed into cartons
.
Within your response you should
Apply the "Approach to Problem-Solving and Mathematical Modelling" flowchart to guide
both your working on the task and the structure of your final response
Choose a type of cheese and determine what the volume of a wedge will be given the weight
of each of your wedges
Determine the dimensions of a wedge to meet the weight requirement
Calculate the area of foil needed to wrap each wedge
Determine the net for wrapping each wedge that results in the least area of wasted foil. The net
is to be stamped out of a rectangular piece of foil. Provide the dimensions of the rectangle and
a life-sized (or scaled) diagram of the net.
Calculate the dimensions of the cylindrical boxes that the wedges are to be packed into, in a
single layer
Decide on the best way to pack the cylindrical boxes into cartons to make transport to shops
efficient, manageable and cost effective ). Three alternative packing arrangements are to be
considered and assessed on at least three criteria.
.
.