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!

Antelope Island Buffalo Run // 50 Mile Race

So I have been a pretty active runner for the past 15 years, completing in a handful of marathons and one ultramarathon — a 55-kilometer trail race in Iceland last year. Recently, I decided to take a plunge and start running even longer distances as I feel more equipped for endurance rather than speed.

For my first 50-miler, I chose the local Antelope Island Buffalo Run. Antelope Island is a Utah state park that is situated in the middle of the Great Salt Lake. I ran a portion of the east-side of the island a couple of years back for the Layton Marathon and it was incredibly scenic and even caught a glimpse of a buffalo herd! You can check out the coarse map for the 50-mile race below (for perspective, the north/south distance shown of the island is about 12 miles):

Race Course

The start/finish is denoted by the large green dot, major landmarks (e.g. trailhead starts or major aid stations) are shown in yellow and the course itself is in red. There are several out-and-backs and short loops of popular island hikes — the longest of which is about a 20 miler out-and-back on the east-side. What’s nice is that the 100-miler race is just the 50-miler done twice, so I know that I’ll be able to see everything that a 100-miler finisher will see!

As for the elevation profile, it’s not too crazy. I think there is about 3,800 total feet of climbing which is mostly concentrated at the start:

Elevation Profile

(Note: Both the 50-miler and 100-miler profiles are shown above)

The race day is Saturday, March 18th and I’ll have a full 12.5 hours to complete the course before cut-off — this works out to be a 15 min/mile which should be easily do-able. I’ll make some posts later on about some of my preparation to give better insight to what long distance running is all about!

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 $latex \LaTeX&s=1$ 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 $latex \LaTeX&s=1$ 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 $latex \LaTeX&s=1$ 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!

BYU State Math Contest // Submitted Questions

So I came across a math competition hosted by BYU that is open for Utah middle and high school students. After thumbing through their archive of past exams, I tried my hand at producing a handful of problems that I think would be appropriate for the Senior Exam. The questions aren’t too terribly difficult — think AMC 12-type of questions — but ones that I think students would have fun tackling.

Anyways, I submitted the problems directly to the test writers for their consideration for inclusion — hopefully I hear back soon about whether or not they make the cut. If they decide to pass, I’ll post here and would love to get some feedback. I dabbled a little bit in test writing before moving to Utah and it is something I certainly want to get back to doing.

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.