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Happy to announce I’ve finally completed the revision to the Number Sense Tricks Manual I originally made a little over ten years ago.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 Manual // Update

Just wanted to let all the avid Number Sense participants know that I am (finally!) in the process of revising and editing my Number Sense Manual. I’m about halfway done with revamping the LaTeX code which, hopefully, makes it more readable (a lot has changed in 10 years!). Once I’m done with that I plan on adding a few more sections detailing the tricks that can be used to solve some of the more recent exam questions. I also want to expand the content to include popular Middle School tricks since there seems to be a lot of demand for that. I’m hoping to have an updated manual by the end of March – so stay tuned!

Middle School A+ / TMSCA Number Sense Auto-Generated Practice Tests

I’ve been very surprised (and pleased!) by the response of my Auto-Generated High School Number Sense practice exams — we’ve reached upwards of 3,000 total downloads since I began posting about them earlier this year!

As a result of their popularity, several individuals have asked me to produce something similar for the Middle School version of the exam. Since I recently reached my goal of 10,000 questions for my high school competition database, I decided to switch gears and focus on starting up a similar Middle School database. Over the past two weeks, I was able to generate 2,000 questions (sorted in the same way as the high school exam) and I’ve produced my first Auto-generated Exam and Answer Key (which you can download via the links).

I also created a Middle School repository where students can access all the number sense practice exams I generate for free. For the time being, I still intend to publish them on a weekly basis but will ultimately create a button where students can generate a practice test anytime they want a new one. I hope to have this implemented by the end of June — so stay tuned!

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 $latex \LaTeX&s=1$ 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!