Math Competition Archives

Number Sense Tricks Youtube Channel

Ok, I really took the plunge and started a Youtube Channel that will detail each and every trick outlined in my wildly successful (and free!) Number Sense Tricks Manual.

Please subscribe to the Channel here:
Number Sense Tricks Youtube Channel

I view the videos as a supplement to the Number Sense Manual whereas I will describe less the derivation of each trick and outline more the general thought process when applying the trick under different circumstances. I think having the videos and the Manual sets me a part from other Mental Math channels as you can get exposed to each trick through the Manual, look up the video to see how it can be applied, and go back to the Manual for extra practice.

Anyways, I hope to go through all the tricks by the end of this year. Additionally, I would love to answer student’s questions through videos, so if you have any particular questions you’d like to see answered, e-mail me at:

Re-starting Number Sense Practice Tests

Just wanted to let avid readers of the website (particularly Mental Math enthusiasts) that I have re-started posting practice exams into their appropriate repositories. I plan on posting a new exam about once a week, so check back here often! Here are the links:

High School Practice Exams

Middle School Practice Exams

Updated Number Sense Manual (2018 Revision)

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Happy to announce I’ve finally completed the revision to the Number Sense Tricks Manual I originally made a little over ten years ago.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

First off, thanks to everyone that has made my Auto-Generated Number Sense Practice Tests (both for High School and Middle School) such a success!

In late July, A friend of mine added a better way to track the number of downloads of all the practice exams posted on my website. I’m very happy to report that there were just about 2,000 unique downloads in about a span of 9 weeks! Incredible! I’m very proud to say that I’ve played (albeit a small) part in fostering a love of math with so many students!

Just to give y’all a quick update of the status of the project:

There are about 11,000 question in the Middle School and about 8,000 questions in the High School databases. Collectively, that represents enough problems to total 225 exams!
Now that the databases are pretty robust, I’m going to concentrate on making column-specific drill sheets. Basically, they’ll be full 80-question tests that focus on just questions from Column 1, 2, 3, and 4 of the exam. That way, students can better stretch themselves practicing on questions that they are currently reaching within the time limit.
I’m also going to start making topic-specific drill sheets. This will pair nicely with the work I’ve already done with my Number Sense Manual as I’ll provide even more practice problems for each topic. For instance, if you want to learn how to multiply two numbers close to 100, I’ll have drill sheets specifically highlighting those types of questions.
I’ve decided against making videos of each individual topic for the time being. If you’re looking for better explanations of the tricks outside of my manual, I suggest going to Math Ninja’s Youtube Page as he has already made a ton of videos detailing how to do most of the tricks.

That’s about it! Good luck to all the students and teachers with their competitions during the 2017-2018 school year!

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!

Putnam and Beyond // Putnam Exam

Came across something cool today searching for some test writing material for math contests. As I’ve mentioned previously, I’m trying to get back into the swing of things with creating problems for middle/high-school aged competitions that are medium in difficulty (similar to AMC/AIME type of difficulty). Anyways, I stumbled across this preface to the book Putnam and Beyond, written by my former math instructor at Texas Tech University, Razvan Gelca.

One of my biggest regret after graduating college was how I did not push myself harder to try earnestly at the Putnam Exam. At the time, I overextended myself with my coursework (trying to pull off a Mathematics and Engineering dual-degree, all within four years time) while neglecting some of my extra-curricular activities. If only I knew then what I know now about how classes are, effectively, pretty useless when it comes to the “real-world,” I would have focused more on qualitative accomplishments (like discovering new ideas, the value of research to find answers, etc…) rather than trying to maintain a high GPA. Although I never truly embarrassed myself on the exam (I didn’t ever record the dreaded final score of “zero,” for example), I certainly should have focused my attention more and worked longer hours practicing.

The Putnam Exam is one of the few math contests I feel genuinely strive towards recognizing inventiveness rather than regurgitation of math concepts. This “flicking on of the light bulb” of new ways of approaching problems is really what I cherished most about my Putnam sessions with Dr. Gelca. Although, without much consistent practice since, the math has probably laid dormant in me for a while, I still try to approach problems I come across in my work from multiple perspectives in order to determine the best course of action. There is and will always be high value attached to thinking of things in novel ways.

Anyways, discovering that I was mentioned in the Acknowledgements Section of the book Dr. Gelca was working so hard to compile while I was with him in the mid-2000s made me feel exceptionally proud and provided me a window to reflect on all life lessons I learned during that time.

And if you are math competitor, I highly recommend the book as well (I just ordered a copy myself as I have only a marked-up manuscript in my possession)!

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!

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.