Content area project II 
Part (1)  using primary sources to teach Mathematics
Firstly let me start by saying this idea is not new, and yet it is new to me. I had thought about it once, possibly during a discussion with a History teacher about how they teach but then it never entered my mind again. This was most likely before the internet and surprisingly it hadn't once occurred to me to check online if someone else or an organisation had tried and tested the idea. Up until recently it looks like nobody had, but suddenly there are some interesting projects and grants taking place.
Firstly at New Mexico State University, David Pengelley, a professor has been testing this pedagogical approach, this blog post from the American Mathematical Society outlines an extensive approach and specific methodologies for using primary sources in mathematical projects (PSPs).
http://blogs.ams.org/matheducation/2015/01/20/usingprimarysourceprojectstoteachmathematics/#sthash.QOTYfuLF.dpbs
It explores the rationale for implementing original sources into the teaching and learning of undergraduate mathematics, and then describes in detail one method by which faculty may do so, namely through the use of Primary Source Projects (PSPs). It also appears to be catching on with New Washington University about to trial and test a similar approach. (http://www.ecampusnews.com/topnews/newmathteaching035/)
Firstly at New Mexico State University, David Pengelley, a professor has been testing this pedagogical approach, this blog post from the American Mathematical Society outlines an extensive approach and specific methodologies for using primary sources in mathematical projects (PSPs).
http://blogs.ams.org/matheducation/2015/01/20/usingprimarysourceprojectstoteachmathematics/#sthash.QOTYfuLF.dpbs
It explores the rationale for implementing original sources into the teaching and learning of undergraduate mathematics, and then describes in detail one method by which faculty may do so, namely through the use of Primary Source Projects (PSPs). It also appears to be catching on with New Washington University about to trial and test a similar approach. (http://www.ecampusnews.com/topnews/newmathteaching035/)
Since history has no properly scientific value, its only purpose is educative. And if historians neglect to educate the public, if they fail to interest it intelligently in the past, then all their historical learning is valueless except in so far as it educates themselves.
 George M. Trevelyan, British historian
An original excerpt from Euclid's Elements.
"Euclid Vat ms no 190 I prop 47" by Euclid  MS Vaticano, numerato 190, 4to, in 2 volumi. Licensed under Public Domain via Commons  https://commons.wikimedia.org/wiki/File:Euclid_Vat_ms_no_190_I_prop_47.jpg#/media/File:Euclid_Vat_ms_no_190_I_prop_47.jpg
"Euclid Vat ms no 190 I prop 47" by Euclid  MS Vaticano, numerato 190, 4to, in 2 volumi. Licensed under Public Domain via Commons  https://commons.wikimedia.org/wiki/File:Euclid_Vat_ms_no_190_I_prop_47.jpg#/media/File:Euclid_Vat_ms_no_190_I_prop_47.jpg
A primary source project  The Greatest textbook ever written.
In this activity students are two work in groups of 2 or 3 over the course of a 2 week period.
It is essentially an assignment where students will have some in class time and no homework over the period except the assignment to work on.
The task: research and read as much as possible about Euclid's elements. Use the sources below listed below but you are not limited to them.
Present your findings in either a digital video or presentation for class consumption.
Your presentation must include:
Research sources:
(1) A wikipedia overview of Euclid's elements: (https://en.wikipedia.org/wiki/Euclid%27s_Elements)
(2) Euclid's elements in HTML (http://aleph0.clarku.edu/~djoyce/java/elements/elements.html)
(3) Teaching with historical sources in Maths (https://www.math.nmsu.edu/~history/)
Australian Syllabus strands:
This whole approach really does not sit with a specific syllabus outcome area but does align very well with the overarching strand known as Working Mathematically (WM). It states that working mathematically is to develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problemsolving skills and mathematical techniques, communication and reasoning. The specific outcomes are 1WM, 2WM and 3WM below, but given many students may focus on the Pythagorean element in Euclid's work I have listed that outcome as well.
Teacher only resources:
Obviously to mark this activity you would need a clear rubric but one that is also open ended enough to allow for significant discovery by the students. My suggestion would be that before embarking on this task yourself you actually try to complete it yourself and see how challenging it is. By figuring out exactly who and what Euclid did you'll not only be better equipped to guide your students but also to check the accuracy of their work.
Here is a quick overview (think of them as Crib notes) thanks to Richard Fitzpatrick (http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf)
"Euclid’s Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Little is known about the author, beyond the fact that he lived in Alexandria around 300 BCE. The main subjects of the work are geometry, proportion, and number theory. Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematicians such as Pythagoras (and his school), Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos. However, Euclid is generally credited with arranging these theorems in a logical manner, so as to demonstrate (admittedly, not always with the rigour demanded by modern mathematics) that they necessarily follow from five simple axioms. Euclid is also credited with devising a number of particularly ingenious proofs of previously discovered theorems: e.g., Theorem 48 in Book 1.
The Elements consists of thirteen books. Book 1 outlines the fundamental propositions of plane geometry, including the three cases in which triangles are congruent, various theorems involving parallel lines, the theorem regarding the sum of the angles in a triangle, and the Pythagorean theorem. Book 2 is commonly said to deal with “geometric algebra”, since most of the theorems contained within it have simple algebraic interpretations. Book 3 investigates circles and their properties, and includes theorems on tangents and inscribed angles. Book 4 is concerned with regular polygons inscribed in, and circumscribed around, circles. Book 5 develops the arithmetic theory of proportion. Book 6 applies the theory of proportion to plane geometry, and contains theorems on similar figures. Book 7 deals with elementary number theory: e.g., prime numbers, greatest common denominators, etc. Book 8 is concerned with geometric series. Book 9 contains various applications of results in the previous two books, and includes theorems on the infinitude of prime numbers, as well as the sum of a geometric series. Book 10 attempts to classify incommensurable (i.e., irrational) magnitudes using the socalled “method of exhaustion”, an ancient precursor to integration. Book 11 deals with the fundamental propositions of threedimensional geometry. Book 12 calculates the relative volumes of cones, pyramids, cylinders, and spheres using the method of exhaustion. Finally, Book 13 investigates the five socalled Platonic solids."
In this activity students are two work in groups of 2 or 3 over the course of a 2 week period.
It is essentially an assignment where students will have some in class time and no homework over the period except the assignment to work on.
The task: research and read as much as possible about Euclid's elements. Use the sources below listed below but you are not limited to them.
Present your findings in either a digital video or presentation for class consumption.
Your presentation must include:
 Images or some other piece of the original source document
 A brief summary of what else was happening in the world at that time (to place Euclid's work in context)
 The most interesting concept or idea that you found in Euclid's work
 An explanation (essentially a translation) of one of Euclid's formulated concepts and how it applies or forms the basis of the Mathematics that we learn today.
Research sources:
(1) A wikipedia overview of Euclid's elements: (https://en.wikipedia.org/wiki/Euclid%27s_Elements)
(2) Euclid's elements in HTML (http://aleph0.clarku.edu/~djoyce/java/elements/elements.html)
(3) Teaching with historical sources in Maths (https://www.math.nmsu.edu/~history/)
Australian Syllabus strands:
This whole approach really does not sit with a specific syllabus outcome area but does align very well with the overarching strand known as Working Mathematically (WM). It states that working mathematically is to develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problemsolving skills and mathematical techniques, communication and reasoning. The specific outcomes are 1WM, 2WM and 3WM below, but given many students may focus on the Pythagorean element in Euclid's work I have listed that outcome as well.
 MA41WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols
 MA42WM applies appropriate mathematical techniques to solve problems
 MA4 3WM recognises and explains mathematical relationships using reasoning
 MA416MG applies Pythagoras’ theorem to calculate side lengths in rightangled triangles, and solves related problem
Teacher only resources:
Obviously to mark this activity you would need a clear rubric but one that is also open ended enough to allow for significant discovery by the students. My suggestion would be that before embarking on this task yourself you actually try to complete it yourself and see how challenging it is. By figuring out exactly who and what Euclid did you'll not only be better equipped to guide your students but also to check the accuracy of their work.
Here is a quick overview (think of them as Crib notes) thanks to Richard Fitzpatrick (http://farside.ph.utexas.edu/Books/Euclid/Elements.pdf)
"Euclid’s Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Little is known about the author, beyond the fact that he lived in Alexandria around 300 BCE. The main subjects of the work are geometry, proportion, and number theory. Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematicians such as Pythagoras (and his school), Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos. However, Euclid is generally credited with arranging these theorems in a logical manner, so as to demonstrate (admittedly, not always with the rigour demanded by modern mathematics) that they necessarily follow from five simple axioms. Euclid is also credited with devising a number of particularly ingenious proofs of previously discovered theorems: e.g., Theorem 48 in Book 1.
The Elements consists of thirteen books. Book 1 outlines the fundamental propositions of plane geometry, including the three cases in which triangles are congruent, various theorems involving parallel lines, the theorem regarding the sum of the angles in a triangle, and the Pythagorean theorem. Book 2 is commonly said to deal with “geometric algebra”, since most of the theorems contained within it have simple algebraic interpretations. Book 3 investigates circles and their properties, and includes theorems on tangents and inscribed angles. Book 4 is concerned with regular polygons inscribed in, and circumscribed around, circles. Book 5 develops the arithmetic theory of proportion. Book 6 applies the theory of proportion to plane geometry, and contains theorems on similar figures. Book 7 deals with elementary number theory: e.g., prime numbers, greatest common denominators, etc. Book 8 is concerned with geometric series. Book 9 contains various applications of results in the previous two books, and includes theorems on the infinitude of prime numbers, as well as the sum of a geometric series. Book 10 attempts to classify incommensurable (i.e., irrational) magnitudes using the socalled “method of exhaustion”, an ancient precursor to integration. Book 11 deals with the fundamental propositions of threedimensional geometry. Book 12 calculates the relative volumes of cones, pyramids, cylinders, and spheres using the method of exhaustion. Finally, Book 13 investigates the five socalled Platonic solids."
Part (2)  using Google Maps to ask  What is the time Mr Map?
Try this as a cool way to grab your classes attention, open the lesson with this link on the projector.
http://www.geogreeting.com/view.html?yGrkDUsCUDroUDswoUwBUwkzb Then allow the students 35 minutes to make their own and save it. Here's a video of it in action ==> 

Australian Syllabus Strands:
Whilst this outcome is just about "interpreting" it could be extended to calculation as it will be in this activity.
The task: Establish via a class discussion why it is important to understand time around the world and why we need a standardised system.
Using directed questions, lead students to linking the concept of the earth as a sphere / circle (360° in one rotation) and one rotation also representing a day broken in to 24 hours. Hence, as a class come to these conclusions and have students record them in their books;
Whilst this outcome is just about "interpreting" it could be extended to calculation as it will be in this activity.
 MA415MG performs calculations of time that involve mixed units, and interprets time zones.
The task: Establish via a class discussion why it is important to understand time around the world and why we need a standardised system.
Using directed questions, lead students to linking the concept of the earth as a sphere / circle (360° in one rotation) and one rotation also representing a day broken in to 24 hours. Hence, as a class come to these conclusions and have students record them in their books;
 The Earth is divided into 24 time zones (one for each hour).
 Twentyfour 15° lines of longitude divide the Earth into its time zones. (360/24 = 15°)
 Time is based on the time in a place called Greenwich, United Kingdom. This is the reference point known as Greenwich Mean Time (GMT) or more recently called Coordinated Universal Time (UTC).
 Like a number line  Places east (to the right) of Greenwich are ahead in time and places west (to the left) of Greenwich are behind in time.
 The cutoff for East and West is the International Date Line, an arbitrary line shown on the map above that has been chosen so that it does not contact any land, only the ocean.
Hence if you are moving east of Greenwich and cross the date line you are now classified as West of Greenwich. (Extension Q  why?)
Give students five locations to find using google maps (http://maps.google.com/) or LatLong (http://www.latlong.net/).
Simple instructions for both are shown in the images at right, respectively. 
Use the worksheet visible to the right with your students.
To check students work there area variety of options. If there is enough time you could pair up students and provide this URL to check: http://www.timeanddate.com/time/map/#!cities=47,42 as it will provide up to the minute times for any city globally but more importantly it also references quickly the GMT/UTC timezone on the bottom of the map. A screenshot from this site is provided underneath. 
