Final Project - Rubrics

Dear class:

Here are some rubrics that will be used for evaluating the final projects:

Final Project

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Orbits Program - Calculating Earth's Orbit

Dear students:

Here is the earth orbit program.
Complete Program:
Class Notes:

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The Spherical Fly Problem - Graphical Representation

The following problem was posed in my grade 12 physics class today: A physics fly flies only on the surface of a sphere of radius 1m.  If Φ(t) = f(t) and θ(t) = g(t) (spherical coordinates), find the velocity of the fly after 5s. At first, Φ(t) was given as t and θ(t) was set to 3t.


A visualization of the problem was prepared in Python Visual.

Here is the Python file (change the extension from .txt to .py) :


Here are some screen shots from the program:

Φ(t) = 3t and θ(t) = t

Accident: Φ(t) = TurboBoost!!!(many powers of 2) and θ(t) = 3t






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The "Limited Market Game"

On the way home a few weeks ago, a CBC radio report mentioned the competition between Air Canada and West Jet to offer flight service to small and large markets throughout the country.  There was mention of a possible price war on several newly opened routes.  Considering the complexity of running an airline, such a prospect is mathematically fascinating because many factors determine the profitabilty of an airline and this can be considered on a route by route basis with reference to prices, number of passengers, the size of the planes, the population base, the capital expenditures and other factors.


Inspired by this news report, a "Limited Market Game" was created for a recent lesson in my Grade 10 MPM2D mathematics class.  At the heart of the game is a quadratic relation that often arises in mathematics texts.  The simple Profit formula for businesses is the difference between Revenues and Expenses.  The revenues are based on the number of customers multiplied by the price. At the grade 10 level approximation, the number of customers decreases linearly as the price increases, giving rise to a quadratic relation.   The expenses can also be based on some quadratic relationship involving the number of customers.

In a typical math class, the formula is presented and the class finds the maximum possible profit based on the price.  The students are not necessarily engaged in this process.  I wanted to find a way to make the process more engaging.  In the Limited Market Game, the rules are quite simple.  Each group or "company" must consult upon and select a price for their "product" in the range of $0 to $100. The prices set by the groups determine the number of customers that each company gets.  This, further, affects the Revenues and Expenses, using the simple relationships described above. The point that makes the game interesting is that there are 1000000 imaginary customers, each of whom will purchase a product from one of the companies, based on a price-linked probability model.  Thus, the profitability of a company will be determined by all of the prices, not just the individual company's price.

It is up to the students, each turn to analyse their results and the results of the other companies and make price decisions for the next month.  After five months, the profits for each company are tallied and a winner is announced.  Astute students will start to see patterns in the data and make wiser choices as the game goes on.  Even so, there is no guarantee as the overall market is subject to the whims of all of the companies in the class.  After playing the game in MPM2D and in SPH4U, we had rich discussions about the dynamics of play and investigated special cases using the game's spreadsheet.  It turns out that everyone can make a profit if they cooperate and set their prices moderately high.  This price fixing mechanism is present in certain sectors of the economy and can lead to further discussions.  It is easy to see that chaos ensues if a price fixing scheme unravels.  Thereafter, a price war can arise and every player can potentially lose money.

Evidently, this game would potentially serve as an engaging activity to start units in mathematics, science, business, social studies or other courses.  It mixes mathematical equations with human group dynamics in a way that is possible to analyse within the span of a one hour lesson.

Limited Market Game - Screenshot

Limited Market Game - Screenshot

The raw spreadsheet file generated for this lesson is available below. The first sheet hosts the actual game. There are two parameters at the top - the population and difficulty level.  Other parameters have not yet been made explicit. These are in the formulas used to calculate customers, revenues and expenses. The groups set their prices and these are placed in column A for all to see.  The students can then make predictions about the results.  To calculate the results for a particular month, the prices are copied to column C.  The results are immediately displayed in the spreadsheet table. The profits for that month are then copied and pasted to the chart below to keep track of five months worth of results.  Many of the quantities mentioned in the game are completely arbitrary and may be more interesting if adjusted.

Subsequent sheets in the spreadsheet file host some analysis of the game that will be mentioned in another post.

Limited Market Game

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Metric CEB Press Progress Report

Recently, Mark Amo-Boateng visited our host manufacturing facility in Ma'anshan, Anhui to coordinate efforts to build a metric version of the CEB press.  The engineers there successfully assembled the steel components of the CEB press. There are several technical challenges that still need to be met in order to press the first brick.  Even so, it is a great pleasure to announce that there has been clear progress!


Mark Amoboateng, Project Collaborator

Mark Amoboateng, Project Collaborator

Metric CEB Press

OSE Metric CEB Press - Anhui, China

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Proposed Themes and Logos for South London Youth Group

The youth at our weekly south London youth classes have been proposing graphics and names to associate with the group.  Here is one example.  More will be posted as they become available.

Proposed Themes and Logos for South London Youth Classes

Proposed Themes and Logos for South London Youth Classes

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Analysis of the Motion of Objects Using Spreadsheets





Equations of Motion Analysis

The above file is a sample spreadsheet for students to use in analysing the equations of motion of an object.


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Hydroponics Experiment

On August 14th, given the short amount of time remaining in the growing season, I decided to conduct an experiment using hydroponics to see if we could harvest something before October 1st.  I watched a few videos online and chose a simple hydroponics starter project. In preparation for the project, I planted some Basil seeds in some pots with some potting soil that I found in the back shed.

On September 2, with my weekend community class, we prepared a tote tub and plant pots as shown in the video and planted the Basil seedlings in coconut husks.  The pots were not net pots but they had a lot of holes in the bottom. Hopefully, this will be sufficient for the plants to grow.  About 300ml of nutrient solution, Mother Earth Blended Natural Super Tea, was placed in the water.  A small air pump for 10 Gallon fish tanks was hooked up to a hose and an air stone which was placed in the tank.

As can be seen in the picture, the flimsy plastic pots were not strong enough to stand up to the rugged plastic. We'll see if this will still work despite the pots' sorry state - the coconut husks and seedlings' roots are still immersed in the nutrient solution.

First Hydroponics Experiment - September 2, 2012

`First Hydroponics Experiment - September 2, 2012



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Reflection - Plan to Build a CEB in China - How did it Go?

The following is a copy of the plan we drew up in order to build an OSE CEB Press in China in May and June of 2012.  We came close to actually staying on schedule for the first few weeks.  Some financial hiccups arose towards the end and took a few extra weeks to negotiate an common agreement of how the finances should be managed.  A large part of the confusion was due to a cultural and language barrier between our team and our manufacturing contacts.  I still think that despite our efforts, they have no idea what 'Open Source' is and they probably think that we are quite strange.


From an email dated May 26, 2012:

Here are some thoughts/suggestions on planning our CEB build. The more details we can consider, the more likely we will be able to meet this schedule.  Any feedback would be appreciated.  I am not sure about the roles that Mark may be interested in taking.

Kind regards,


May 27th-June 1 - Planning / Sourcing

(1)Complete Metric CEB build instructions using newly created CAD images of metric CEB - cut list and fabrication instructions
(2)Source some electronics parts in Zhenjiang
(3)Source most hardware parts in Zhenjiang
(4)Build Electronic Driver board at residence in Zhenjiang
(5)Study CEB build instructions, looking for as many details as possible.

(1)Order Arduino from Taobao:
(2)Secure location for steel cutting, welding, drilling, grinding metal
(3)Secure welders / metal workers
(4) Ask Mark for help getting 4 suitable Chinese bearings for the soil drawer: or order them from this link.
(5) Order magnets: or

Weekend - June 2, 3 - Fabrication of Parts

William and Tony:
(1)Trip to Electronics Shop and Hardware mall (near Heilongjiang) to secure remaining parts - hardware / electronics / tools (if needed)
(2)Supervise the fabrication of the metal parts - all cuts made
(3)Supervise the cutting and welding of the frame, soil loading drawer, hopper, hinges, arms, feet, sensor holders and soil grate (All CEB parts)
(4)Supervise the first step of assembly of the frame

Weekend - June 10 - Fabrication of Parts (William not available June 9)
William and Tony:
(1) Further fabrication of metal parts
(2) Prepare frame as much as possible before receipt of Hydraulics
(3) Design adapter for Chinese main cylinder and Chinese secondary cylinder if necessary
(4) Ask the Hydraulics shop to loan us a solenoid valve (they have several around the showroom) for testing with the electronics
(5) Ask the Hydraulics shop for details on the dimensions of the small hydraulic motor so that we can get a suitable adapter.

Weekend - June 16, 17 - Assembly
William and Tony:
(1) Mount cylinders to the frame
(2) Assemble Hydraulics
(3) Test Electronics board on the Hydraulics
(4) Final arrangements and plans for following weekend - secure assistance from hydraulics people? Secure hydraulics power source
(5) Identify and secure a suitable soil source

Weekend - June 23, 24 - Assembly and Testing
William and Tony:
(1) Final assembly and Testing of CEB.

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Rep Rap - X, Y and Z axes Configured Successfully

Testing the Rep Rap - X, Y and Z Axes

Testing the Rep Rap - X, Y and Z Axes

Recently, progress was made on the Rep Rap: All three axes have been set up with end-stops.  A fair amount of mechanical adjustment and filing was required to get the z-axis working properly.

The following video documents the testing of the axes and the first test print.  The print was unsuccessful - there is more work to do on the extruder.



Test of the X, Y and Z axes of the Rep Rap



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