Number Sense Manual // Revision A

Happy to announce I’ve finally completed the revision to the Number Sense Tricks Manual I originally made a little over ten years ago. Here is the direct download link (you can also get it from my webpage here).

I cleaned up a lot of the LaTeX programming and split up each section into it’s own .tex file making it a lot easier to compile individual sections. I also made the .pdf a lot more navigable by adding referencing and a few hyperlinks to my free Middle and High School practice exams.  Additionally, I double-checked the question/answer pairing and corrected a fair number of problems. Finally, I added about two dozen more tricks that will help with 3rd and 4th column questions on more recent exams which you can find in Section 4 of the manual.

I wanted to get this version out ASAP to help students with their upcoming UIL regional/state meets. Over the summer, I plan on adding a substantial amount of practice problems to each section and doing another run through to make sure I didn’t miss any commonly tested topics. Hope this material is helpful to you!

Number Sense Auto-Generated Practice Tests // Update

Without a doubt, the most trafficked part of this site is my auto-generated number sense practice tests, so I thought I’d give you an update on the project. Here is where we stand at the moment as well as some things I want to implement in the near- to mid-term:

  • The process is almost entirely automated now. The only human component is the transcribing from .pdf to LaTeX code. This should reduce the number of errors you see on practice tests as everything else — from segmenting out a test’s LaTeX code to adding the questions to the appropriate database to generating the practice test itself — is entirely automated and, hence, error free!
  • I have about 6,000 questions in my database. This equates to about 75 complete tests that have been translated in LaTeX code and are being used to generate the practice material.
  • I’m adding at a rate of about 500 questions per week. This means I should hit my goal of having a 10,000 question bank by the beginning of May.
  • As we approach the latter stages of the competition season, I will begin posting practice material more frequently on the repository page, so check back often.
  • I’m going to try to begin making a separate database of regional and state-level type of problems (harder difficulty, multiple steps in order to solve, etc…) in order to gear up for the more challenging exams. I should be able to begin posting that material by late-March.
  • I’m also going to start doing a series of youtube videos detailing step-by-step instructions on how to solve most types of questions asked on the exam. This should help out the more visual learners grasp the concepts.
  • Over the summer, I am going to revise my Number Sense Manual in order to update the LaTeX code, add more sections that are applicable to the current exams, and include much more practice material. Because the manual is sectioned off into types of problems (e.g. multiplying by 11, squaring tricks, roots of polynomials, etc…), students can focus more easily on a particular type of problem they are having difficulty with and do drills to really solidify their understanding.
  • Finally, beginning for the 2017-2018 school year, I’ll make it where students can generate their own practice exams through my website — thus eliminating their dependence on my posting on a weekly basis. You’ll be able to practice as much as you want, whenever you want!

BYU Math Contest + Number Sense Tests // Update

Received word back from the BYU Math Contest organizers that the problems I submitted a few weeks back made the cut and will be used in the problem pool for this years test!

In other news, I crossed the 3,000 question threshold for my automated Number Sense Tests which will mean less test-to-test repetition. My goal is to get a bank of 10,000 questions before I begin work on having user-generated exams via the website so students aren’t beholden to my weekly posts.

Anyways, 2017 is off to a great start!

UIL / TMSCA Auto-Generated Number Sense Test 2 // Future Work

The question pool that my auto-generated Number Sense test relies on has swelled to 1200 questions and is growing at a rate of about 500 questions per week. There might be some weird artifacts — like two Roman Numeral questions or three integral questions within the same exam — but these are attributable to fact that you are randomly selecting problems from the pool and is not indicative of some problem with the program. As a whole, I’d say I am about 90-95% accurate in replicating a competition exam.

Here is the second exam and its answer key. As always, you can find all the practice exams from my repository here.

Currently, the difficultly in the auto-generated tests are comparable to UIL Invitational through District exams. I plan on, separately, creating harder practice tests that replicate Regional and State competitions for those who want more advanced practice. (I didn’t want to discourage novice competitors by incorporating very challenging problems into the question pool that could be randomly incorporated into the practice tests).

As this project moves into the “auto-pilot” phase, I’ve been thinking about what I want to do next. One topic I am very passionate about is personal finance and the journey towards Financial Independence (or more commonly know as FI). One thing that has been helpful to both myself and my friends is a more “real-world” mortgage amortization table that I created which aids a future-homeowner with their decision of finding the right house to buy and the type of loan to buy it with. I’m beginning work on developing python code to generate this table from basic loan/house information as well as output helpful statistics (e.g. the amount of time where a 15-year loan is preferred to a 30-year, assuming a particular market return, etc…).

UIL / TMSCA Number Sense Auto-Generated Practice Tests

Note: If you’re looking for the results of the auto-generated Number Sense practice tests, you can find them in the repository here. If you’re interested in some of the background behind the project, read below:

So I had a couple of free hours this past week so I whipped up some rough python code to auto-generate UIL Number Sense tests based off a database of questions that are sub-divided into 10-question buckets (e.g., I pooled Questions 1-10, 11-20, etc…, and randomly selected ten problems from each bucket and assembled a test in rough order). This would ensure that you don’t wind up with weird results like an integral question as Problem #1 or an easy multiply by 11 question as problem number #75.

You can download the first auto-generated practice test here and the answers here. For the time being, I plan on releasing a new practice test every week and setting up an archive on my website so you can view and download all auto-generated practice tests that have been created.

The formatting is about 98% there — occasionally you’ll have some quirky typesetting based on the conversion to LaTeX — and I only checked randomly selected answers to make sure they are coinciding with the problems asked, so there might be some mistakes on that end. For future tests, I’ll do a quick scan and correct any obviously wrong typeface.

All that’s left now is to write LaTeX stubs for more practice problems and increase my database of questions. I plan on contracting out that work through Fiverr in order to better optimize my time. I’ll be sure to release a “final” version of my python code as well as periodic updates to my questions database on this website so that coaches and students can run the code themselves and generate as many practice tests as they want.

So stay tuned for any updates and, if you are a competitor, check back every week for a new test!

Number Sense Practice Test LaTeX Template

[8/3/2017 Edit]: If you are looking for my archive of auto-generated practice tests, you can find the High School tests here and the Middle School tests here. Below gives you a brief description on how they were produced and my initial stab at creating a template (which I have since refined).


As I mentioned in a prior post, I am extremely interested in creating a pool of free UIL / TMSCA Number Sense practice tests. I spent an hour or so creating a \LaTeX template to produce worksheets and answer keys that are similarly formatted to the actual tests. I used this year’s UIL Sample Test as a reference to see if I could reproduce it. You can see the results yourself by downloading my \LaTeX version here and compare the two. All-in-all I think I was able to keep the formatting consistent, if not improve on some aspects — particular questions concerning fractions where I can use \dfrac{}{} to make the numerator and denominator appear larger in certain circumstances. Here is a quick comparison:

Scan of Current UIL Sample Test

Sample Number Sense Test

My LaTeX Version

LaTeX Number Sense Test

If you’d like to be able to make your own Number Sense Practice Tests, you can download my Questions Template here and the Answers Template here and mess around with improving it using TeXnicCenter or some other \LaTeX IDE. Note: you will have to install the <Exam> Package which you can do by using the MiKTex package installer or by downloading it from CTAN and manually installing the package.

For the future, I plan on publishing two practice tests a month that replicate the difficulty level seen in prior UIL-sanctioned exams. This should start a good a pool of free exams for teachers and students to use and, hopefully, make practicing for the competition accessible to more students. Eventually, I will automate the entire process using Python to piece together entire exams using the UIL Problem Sequencing as a guide and a every expanding pool of questions to choose from. Stay tuned!

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.