Mochi does Maths!

Ms Carolina's Math class

The Exploration

'Tis the time to finally put in use everything you've learnt about Math in you whole academic life, to make a discovery! No no, It is not about you becoming the first person to develop a new method to calculate integrals, or the first person to discover a new universal constant, if this was the case you would be ready to receive a Nobel prize for your outstanding contributions to Mathematics. 

What is expected from you is to make a discovery for yourself. Explore the Mathematics behind something you love or something you find interesting. It is crucial to be motivated to take on this task.


It's an Essay. 

An essay in Mathematics looks like a regular essay only that some sentences are written in the form of an equation. Every equation you write needs to be part of a sentence, because as you read the essay out loud it needs to make sense. 


There is a different answer to this question depending on the course you are taking. Math Studies SL students will usually apply Mathematics to find conclusions about a certain real life question. Math SL/HL students will be more inclined towards exploring the Mathematics hidden into something.

Common topics to explore are: 

The golden Ratio

Beauty in Mathematics

Understanding Pi

Like shown above, there are multiple places where you can get ideas from.

Evaluation Criteria

Math AA HL

Please find here the information provided by IB.

In the new program, the toolkit consists of a series of activities that will broaden your Mathematical understanding through investigations. For your final assessment, you must produce an essay, of around 7 pages long (around 1200 words) where you explore a topic of your own interest. This exploration needs to reflect deep mathematical understanding of the topics discussed, as well as mastery of the accompanying processes, through error free calculations.

The assessment Criteria are:

You can find more information in the subject guide and other official IB documentation.

Math HL

Your Math IA consists of 20 points distributed in: Communication, Mathematical Presentation, Personal engagement, Reflection, and Use of mathematics. 

Please see HERE for the rubrics and value of each criteria for Math SL and HL (and examples!!). Because the criteria are the same, for both Math SL and HL, it is possible for students in both subjects to ideate together, have discussions and use each other to proofread their essay.

Selecting the topic

To select the topic you must search within your interests. The math exploration has the purpose to allow you to see mathematics within any topic of your choice. An easy way to start could be:

  1. On a piece of paper write down your interests, be specific: Listening to music, singing, sculptures, desserts, dogs, environment. These will make your list of categories.
  2. Then, for each of those categories try writing related topics: Environment: oil spills, animal injuries, deforestation, irresponsible fishing, water accessibility, etc.
  3. Then on a parallel, write down questions relating the subtopics to the categories: 


  • How does the amount of oil spilled affect the marine life in the area of the spill?
  • how is the population of sharks affected by irresponsible or illegal fishing in Japan?
  • How does the GDP of a country relate to water accessibility?
  • What is the trend of deforestation of the amazon jungle?

4.  For each of those questions try to find a link to Mathematics:

  • How does the amount of oil spilled affect the marine life in the area of       the spill? 
     Mathematics: Calculation of affected areas (rates of change, integrals), 
     statistical correlation.
  • how is the population of sharks affected by irresponsible or illegal             fishing in Japan?
     Modeling with calculus, statistical correlation.
  • How does the GDP of a country relate to water accessibility?
     Statistical correlation
  • What is the trend of deforestation of the amazon jungle?
    Modeling with calculus, statistical correlation, rates of change.
5.  At this point you should have an incredible number of options to choose from. Some of them are good, others not so much, just go through them and select the best. You can rank them and choose #1 to start, if that one doesn't work, you have #2 and so on! 

Does this method sound familiar? This is design thinking.

Once you have chosen one, design a main goal and a couple subgoals. Do some research about the topic and start writing that introduction! The introduction should be a paragraph that allows the reader to understand the following points:
  • What is the main goal of the essay? and subgoals?
  • Why did you choose this topic? why is it important to you?
  • What is the methodology you will use? what is the area of Mathematics that you will be           exploring for this essay?
  • Do you have any predictions? Expectations?


I have selected my topic, now what?

Now we try to answer the question, do some math and write!

How much should I write?

The nice thing about Mathematics is that there is no word limit. It is because since a full sentence can be written in the form of an equation there is no way we can predict what is the best number of words for your particular discussion. However, there are some that recommend writing around 1200 words. If you write more or less that that, don't worry.

It is also understood that in Math, you are very likely to use graphs, tables, charts and diagrams that are relevant to the essay and that take a lot of paper space, therefore we cannot say for sure how long the essay should be in terms of pages. Everyone's essay will be different. Just make sure that whatever you write, whatever table or graph you add to your work is relevant to the discussion.

Do I have to have tables and graphs?

No, you don't have to. Unless it is necessary and makes sense for you to attain your goals.

Can I just put all graphs and tables in the Appendix?


It is okay to have an appendix if you so wish, however examiners are not obliged to read it. So if a graph or a table is important, it must be in the body of the essay.

How big should my tables and graphs be?

BIG enough to be read.

SMALL enough to make it visually pleasing. Make sure tables are not split in two different pages, and make sure your graphs are connected to the text, that is make sure the graph is on the same page of the text where you are talking about it.

Can I put pictures of Mochi in my essay?


I recommend avoiding this practice as Mochi is a dog and there are no extra points given for pictures of dogs (Unless said dog is the case study). 


Is my IA complete?: Student Checklist

                                  Student checklist 2

Where do I submit my exploration?

G12 2018-2019

Please add your explorations to this folder. Make sure your file has a name following the example:

Carolina - Draft 1 - Spirals in sunflowers