UIL / TMSCA Number Sense Manual

Since this website will mostly be concerned with discussing some of my personal projects and hobbies, I thought it’d be appropriate for my first post to share one of my first major projects I ever put together: a manual for UIL / TMSCA Number Sense competitions

Number Sense Manual | Bryant Heath | 2007

(Dropbox Mirror)

I wrote it about ten years ago mostly to give me practice with all the nuances of writing in LaTeX and I haven’t really edited it since. I was also frustrated at the time that there were no free resources for prospective students interested in the Texas-based competition, so I made it available for all to download it. After a brief google search, it seems like nothing has changed — most material is either behind a paywall or is incredibly difficult to locate!

One of things I want to work on in the future is to create a sizable pool of Number Sense test questions where I can then formulate freely downloadable practice tests for students to work on. I am also thinking about starting a series of simple, two-minute videos highlighting individual mental math tricks to better showoff the concepts.

The benefits of mental math extend further than just a niche high-school level competition. For example, the ability to quickly and accurately calculate ensures that you have more time answering questions on standardized tests where difficult-to-use on-screen calculators are allowed (GRE, GMAT, etc…). In addition, better approximation methods — which is at the crux of mental math — allows you to save so much time and gives you a great feel of whether a particular approach is to problem or project is feasible.

2 thoughts on “UIL / TMSCA Number Sense Manual”

  1. I have already sent an email about this to bryant.website@gmail.com, so if you could reply to me email, that’d be great.

    I am familiar with the “Remainders of Expressions” and “Finding Remainders of Other Integers” tricks from your Number Sense manual, but I still don’t have an idea to solving a certain question I ran into in a TMSCA Number Sense test. The question is:

    (13^8 – 11) / 7

    It seems in this situation, I’d have to divide 13^8 by 7 in some way, but it is a very big number and I cannot break the 7 down either to find the remainder that way. If you know of an easier way to solve this problem, please do share the process.



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