They are useful for modelling more complex shapes. Is Bitcoin going to keep rising or crash? This particular problem was solved by Euler. Can you find the pattern behind it? Look at the inherent probabilistic nature of the universe with some quantum mechanics.

What is the minimum number of colours needed for any map? Are maths students better than history students?

This chess puzzle asks how many moves a knight must make to visit all squares on a chess board. This topic links to graph theory. With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else?

Why does the house always win? Maths can be used to both make these codes and break them. How probability and game theory can be used to explore the the best strategies for bluffing in poker. How to use modeling to predict booms and busts.

Essential knowledge for future astronauts. Also look at how the Championship compares to the Premier League. How can a running Achilles ever catch the tortoise if in the time taken to halve the distance, the tortoise has moved yet further away?

Use Tracker software to create a Sine wave.

Some nice examples of using polar coordinates to create interesting designs. The use of game theory in psychology and economics.

This topics provides a fascinating introduction to both combinatorial Game Theory and Group Theory. The use of regression in polling predictions. The planets follow a surprising pattern when measuring their distances.

Investigate some rocket science! Look at some of the maths and psychology behind winning this game. ISBN codes and credit card codes are just some examples of how codes are essential to modern life.

A good chance to investigate misconceptions in probability and probabilities in gambling. Look at how infectious Ebola really is. An amazing shape which is a loop with only 1 side and 1 edge. Also look at the finances behind Premier league teams 10 Is there a correlation between Premier League wages and league position?

We can analyse the data to find out. Some classic physics — which generates some nice mathematical graphs. Topology and networks 1 Knots 2 Steiner problem 3 Chinese postman problem — This is a problem from graph theory — how can a postman deliver letters to every house on his streets in the shortest time possible?

Investigate how binary is used — link to codes and computing. Voting systems 11 Flatland by Edwin Abbott — This famous book helps understand how to imagine extra dimension. You can watch a short video on it here 12 Towers of Hanoi puzzle — This famous puzzle requires logic and patience.

A nice starting point for students good at coding — who want to put these skills to the test mathematically. What would happen to the climate in the event of a nuclear war?

The use of networks to solve problems.1 Maths Investigation Ideas for A-level, IB and Gifted GCSE Students All this content taken from my site at killarney10mile.com ± you might find it easier to follow.

Maths investigations for gifted and talented GCSE and sixth form students. Everything from code breaking to Goldbach's Conjecture, the Riemann Hypothesis, Faster than light time travel, Modelling diseases, Predator-prey models, Game theory, visualising the 4th dimension, war maths, Benford&'s law to catch fraudsters and much much more!/5(25).

Im in my second year of IB HL math (grade 12). in case you are not familiar, we cover everything from sequences/series, to logs, to calculus and a bunch of things in between. So I am expected to use similar to 1st year uni math for this exploration. – user Sep 20 '14 at Quick links: downloadable teaching materials for sequences & series syllabus content for the Algebra Topic: SL syllabus (see syllabus section ); HL syllabus (see syllabus section ).

Although it's interesting (and I would say worthwhile) to discuss sequences that are defined by recursive (or iterative) formulas - such as the Fibonacci sequence - the fact is that the only sequences/series.

Sequence Investigation. This is a nice investigation idea from Nrich. The above screen capture is from their Picture Story puzzle. We have successive cubes –.

Student Guides for the Exploration (internal assessment) I have written a page Student Guide for the Exploration - one for HL, and one for SL. Each Student Guide is available as a PDF such that the dates for the different steps can be filled in by you, the teacher, before printing it to distribute to students.