List of materials with no description.
I once worked for a tutoring agency where the owner was obsessed with something he called "Math Facts". This constituted memorizing the basic arithmetic operations of addition, subtraction, multiplication, and division on integers from 0 to 12. His obsession went so far as to say that students who had not mastered them yet should practice (with flash cards) something like 40 minutes a day until they are mastered. "Mastery" was defined as being able to answer in less than a second, if I recall correctly.
I do not have nearly the same obsession. However, I do admit that being able to do these basic operations quickly is beneficial. Do you really need to know the 12's? Probably not. Is it a problem if there are some that take you longer than a second? No. Do you need to practice for 40 minutes every single day? It wouldn't hurt, but it isn't necessary.
For awhile, I had some students (across elementary and middle school) who needed to practice these "math facts". Although creation of flash cards is very simple (and you can also buy sets for fairly cheap), correctly using flash cards basically requires a second person. Not all of my students have a second person available to practice these "math facts" with.
In response to this need, I wrote an extensive Python program. It was highly versatile, allowing practice for any collection of integers on any subset of the four operations. It could provide detailed feedback from timing on the questions, and had a lot of options.
I am slowly going through the laborious process of converting this to a website option. You can find the current version here. The settings can be tweaked here, which is probably the better link.
As it stands, this code has three uses, although only the first is the intended use:
- To practice math facts.
- To practice arithmetic with negative numbers. Entering -20-20 as the ranges (or something similar) would allow random problems with negative numbers to be generated, with immediate feedback.
- To practice integer arithmetic with larger numbers. This usage may require showing work, so would need separate pen and paper, but also has the benefit of immediate feedback.
A note about the last usage: It is well outside the scope of the project. Thus, it is possible to break the code. I am in the process of optimizing the code to make it more feasible.
Note, in my opinion, part of the appeal of my program is its simplicity. It will never look "flashy". It should also run on basically any device.
In conjunction with the above, I wrote some code that can generate a sheet of 100 problems, which I remember taking many of back when I was in elementary school. There are quite a few sites that have similar such sheets, but I grew frustrated with the availability one day so I wrote this generator. I've tweaked it quite a bit since then.
Note that the intent is for speed problems, so for the four base operations on ranges like 1-12. However, the code supports much larger numbers, specifically at least -99-999. Thus it can at least be used for negative number practice. It shouldn't be used for larger integer problems, since there is not enough space to do actual work.
It also generates an answers document, to make it easier for people to grade these sheets.
Back when I advised students at the University of Chicago REU for mathematics undergraduate students, I and some fellow graduate students created some materials to study for the GRE mathematics subject test. These are still used by students studying for the exam, so the above page will serve as a semi-permanent host for the materials. I am also in the process of improving and expanding the materials.
Donations
This is a soft note that if you find yourself using the resources above a lot, you could consider donating. The more I receive, the more effort I could put into the above. The easiest way to donate is the same way I accept payments, via Zelle to my phone number (612-703-5607) or email (michael@neaton.org).