Tag Archives: math

Divisibility Rules

I often run into students who need to do a complex operation in algebra or even up through calculus, but they struggle because they are missing a skill from a much simpler time. One of the skills that I see students are missing is being able to quickly determine if a number is divisible by a digit between 2 and 9 in order to simplify and reduce fractions, roots, factor equations, and more. One way to fix this is through practice and learning a few tricks. Even when students are in upper level classes. It’s never too late!

To make this easier for students to learn, it helps to have a list to use, like training wheels while they work to memorize how to find possible factors. To that end, I’ve made a great printable in both color and black and white which explains each rule, then gives two examples and a counterexample so students can see at a glance how to check for divisibility. If you print it two pages per sheet, you can have all of them on one side or print them front and back so you have them just a bit bigger!

How can you use this printable to learn the rules? Well, firstly you can use the chart while doing math work. But sometimes you want a fun way to practice the skill first before you need it. To that end, try these ideas:

  • Get 3-5 (or more!) dice and roll them. Line the dice up to make a number and figure out if that number is divisible by anything between 2 and 9. For example, roll 3 dice and get a 2, a 5, and a 3. Use the number 253 (or 235 or 352 and so on) and figure out if it’s divisible using the chart. If they are successful, they get that number of points (2+5+3=8, so 8 points)
  • Using similar rules, take a deck of cards out and make numbers by picking cards at random and lining them up. This works best if you take out the aces and face cards, but leave 10. If you put 10 into a number, you can fit zeros in that you don’t normally get with dice. For example, you pick a 5, an 8, a 10, and a 3, so you have the number 58,103 to test divisibility rules on.
  • For some competition, you can have kids race against each other. If that causes too much friction, do several rounds and have the kids try to beat their own previous best scores. This can be a great 5-10 minute warm-up or break time to make the day more interesting and get the body and brain moving.
  • Math War: Each student gets half of the deck of cards. Using their own stack face-down, they flip over 3 cards to create a 3+ digit number using the rules above. In this case, assign face cards a value of 10 and aces a value of 1. Use the divisibility rules to find the largest number between 2 and 9 that is a factor of the number formed by the cards. Whoever has the largest number gets to keep all the cards and everyone lays out 3 more cards until one person has all the cards.

This skill is really useful from middle school on up. I can’t emphasize this enough. Whether students are trying to find a common denominator, write a prime factorization, or just doing mental math in general, being able to quickly determine if a large number can be broken down more easily is a huge skill for students to master. If a student is still struggling with a basic skill, learning advanced material will be that much harder.

This skill is learned in chapter 4 of my pre-algebra class, but you can get this great free resource today just for signing up for my email list below! Please share this post if you know anyone who might want the file for themselves!

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Monday Review: Math Mammoth

by Kristen Lauria

Note: I purchased this curriculum myself and have received no compensation for this review.

This is my first ever post for the blog and I wanted to start off by answering a question I get frequently: What’s a great curriculum for teaching math in the elementary years?  For my children, it’s been Math Mammoth by Maria Miller.

I stumbled across Math Mammoth when I was looking for a mastery-based program for my own kids.  I’d heard of many of the big names in math like Saxon and Singapore, but both of those were spiral-based programs.  I could tell from even an early age that my son wouldn’t be interested in small bites and constant repetition.  He has an intuitive nature when it comes to math and often knew the concepts before I had an opportunity to teach him.

Math Mammoth is a series of worktexts, which are consumable combination workbook/textbook, that the student both learns the material and practices it all in one.  Each year is covered by a book level of the same number (so grade 1 is book 1A/1B) in the Light Blue Series and is split into 2 volumes so that it’s not so overwhelming to the student.  The nice part about just one book is that the student learns and practices together and they can flip back to refer to the instruction when they get confused.  Another nice part is that absentminded kids (like DS) don’t have 2 books to keep track of.

Both my children have worked through this series, with DS in grade 5 now and DD in grade 4.  In the beginning, my DS couldn’t read, so I needed to work through the lesson with him.  By second or third grade he was reading well enough he could work through the program relatively independently, only coming to me when he was struggling to understand.  My DD progressed about the same and they both now work on their own, only occasionally needing more explanation.

For perspective, DD is most decidedly not a math person and has still had success with this program.  The only thing that I think it lacks to some degree is practice for the operations (+ – x ÷, but that is easily outsourced to apps and other programs to practice.  The program also comes with links to an online worksheet generator, so if there is a skill that your child needs more practice on, you can always make custom worksheets (with answer keys!) to give your child that extra reinforcement.

I’ve been exceedingly pleased with this program and am disappointed that there’s not a companion curriculum for middle/high school, but I’ve found other great resources to fill that gap that I’ll review in coming weeks.

The Good:  Very thorough and includes all topics I would want covered in elementary, examples and instruction teach right to the student, colorful and engaging, inexpensive.

The Bad:  Not a ton of review of concepts since it’s mastery based.

Recommended For:  All children, including those children who are naturally adept at math and those that struggle.

Website of publisher:  https/www.mathmammoth.com/

Where to buy: I’d recommend Rainbow Resource Center if you want a printed version or Homeschool Buyer’s Co-op (aff) if you want digital.


Please comment below with what elementary math curriculum has worked for you!