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!

Hi Bryant:

My daughter, a 7th grader, has been representing her school in Number Sense since 4th grade. She has started using your Middle School Number Sense tests in 7th grade. I think Number Sense has helped her build a strong base in math. She took the December 02, 2017 SAT and scored a 1390 (math : 730). We thank you very much for providing the Number Sense tests and tricks. Her District Number Sense Competition is on 2-3-2018.

btw my son, a high school senior, has been accepted to Texas Tech Honors College on a presidential scholarship, so he may go there to college in Fall 2018 (I saw that you graduated from TTU).

Hi Bryant, I love your extensive book of number sense tricks and the tests that you post very often. I have a question, though. For the “Finding a Remainder when Dividing by 11” trick, what if you so happen to get a negative number as the remainder. The problem I ran into is “(92×13)/11 has a remainder of” . I got to 1196/11, and got a remainder of -3. Please help.

Thanks

If you receive a negative number when doing remainders (or any sort of modular arithmetic), the quickest way is to add back whatever you are dividing by until you get your first positive number. So with your example, you’d take the calculated -3 and add 11 back to it (since you are dividing by 11), which gives a remainder of 8.

Let’s say you do a similar calculation and wind up with a calculated remainder of -16. You’d add back 11 –> -5, then add back 11 again –> 6. That would be the correct remainder.

If you want to read into more of why this is, I suggest just googling “Modular congruence” and it will bring up a wealth of information.

One last thing, with the example you gave there is a quicker way to run that calculation than doing the multiplication of 92×13 and then doing the divide by 11 remainder trick. Section 1.4.5 “Remainders of Expressions” of my manual gives you a little insight on a faster approach. Basically, “the remainders after algebra is equal to the algebra of the remainders” — so you can find the remainder of 92/11 and then multiply that by the remainder of 13/11 –> 92/11 has a remainder of 4 and 13/11 has a remainder of 2 –> 4×2 = 8 (which is your answer).