math IA guide

Topics: Ellipse, Trigonometry, Mathematics Pages: 11 (1382 words) Published: May 19, 2014
IB#Mathematics#Exploration#

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This!exploration!is!your!chance!to!explore!an!area!of!math!you!are!interested!in,!kind!of!like!a!Math! Personal!Project.!!Pay!close!attention!to!the!rubric!the!whole!way!through.! !
It!will!be!carried!out!in!several!stages.!!Below!you!will!find!a!summary!of!dates!on!which!the! different!stages!of!the!process!are!due.!These!dates!are!given!to!you!in!advance!so!that!you!can! balance!your!workload!against!other!subjects!ahead!of!time.! !

The!project!will!be!introduced!on!____________________________. !
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Due#Date#

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Teacher#
Signature#

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!

!

!

Draft!
!

!

!

Final!copy!of!project!is!
submitted.!
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!

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Official#Proposal#Form#!
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1. A clear statement of task.
2. A discussion of the type of
math that will be explored.
3. List of resources/sources.

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!

Student#
Signature#

Task#

The!Math!towards!the!Aim!
completed.!

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• You are strongly advised to set up meetings with your teacher throughout the process.
• If you are not in school on the day of a deadline, you must turn in your task electronically on the due date and hand in a hard copy the first day you come back to school. Alternatively, have someone hand it in for you.

Exploration+Ideas!
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Websites!for!possible!explorations:!
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www.plus.maths.org!!
www.nrich.maths.org!!
http://www.stevenstrogatz.com/publications.html!
http://www.pims.math.ca/resources/publications/piNsky!!!N!!PIMS!–!magazine!for!students! possible!exploration!ideas.!
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Vi!Hart!!http://vihart.com/everything/!!
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Numberphile!–!you!tube!channel!–!may!lead!to!some!interesting!avenues!of!thought!but!be! selective.!
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Notes!from!other!IB!teachers:!
The best papers took general math concepts such as matrices or trig modelling and explored in areas such as cryptography, weather patterns, astronomy, etc. Other









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Ideas
Interesting statistical displays
Conic Sections – hyperbola, ellipses, parabolas, circles
2
Imaginary numbers i = −1 .
Counting problems
Different types of probability distributions (hypergoemetrc, geometric, Poisson) “interesting” statistical displays (think of Florence)
triangulation, wifi and mapping (horizontal and vertical)
transformations – by inversion.

Mathematical SL Proposal:
The Exploration—Initial planning
Name:

1

Mathematical area of interest

2

Your specific topic and aim of exploration

3

Reason for choice (personal engagement is part of Criteria A)

4

Three areas you plan to explore
1.
2.
3.

Due:

5

How will you explore these areas mathematically

1.

2.

3.

6

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Resources / Sources

Mathematical SL Proposal:
The Exploration—Initial planning

Due:

Name: Exemplar 1

1

Mathematical area of interest

Conic Sections – specifically ellipses

2

Your specific topic and aim of exploration

- a carpenters trammel – a tool that draws out ellipses for a carpenter. Also called Trammel of Archimedes or an ellipsograph.
When I’m done I hope to be able to state the settings on a trammel to ensure an ellipse with a major axis length of 5 and a minor axis length of 3.

!
3

Reason for choice (personal engagement is part of Criteria A) - my uncle is a carpenter and he’s made some pretty cool tables. So I’m interested in how this tool makes an ellipse. What are the properties of an ellipse that makes this tool make an ellipse.

4

Three areas you plan to explore
1. Definition of an ellipse, including a proof as to why the trammel produces an ellipse. 2. the parameters within the general ellipse equation and how they affect an ellipse. 3. How settings on the trammel affect the ellipse.

5

How will you explore these areas mathematically

1. I will “make” a trammel with a ruler and pencil to see how the mechanisms work. I have this book that explains the construction of a simplistic model of a trammel.

2. I will explore a GSP...
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