Living Math with Factors, Multiples, and Primes

by Jimmie Lanley on August 15, 2009

Living Math Factors Multiples Primes

Our latest arithmetic topic has been factors, multiples, and primes. We used our Singapore math textbook and workbook as a supplement to these activities which formed the meat of the lessons. It wasn’t a very linear study. We skipped around somewhat, revisiting topics from different angles to really cement the understanding.

Paper and Pencil

multiples patterns4 multiples patterns3 multiples patterns2
Identifying multiple patterns I  printed eleven multiplication charts and Sprite labeled each one with a number from 2-12 at the top. Then she highlighted the multiples of that number all over the grid. It was very interesting to see the patterns that emerged. Multiple Matrix is an online version of this activity. Our page is actually from the Living Math book, but you can use any multiplication chart just as easily.

triple venn diagram

multiples Venn diagram

Venn Diagrams for multiples

I love graphic organizers mainly because Sprite and I are so visual. This triple Venn diagram was a great critical thinking application of the arithmetic we were studying. It was one of the last activities we did.



Prime Numbers

For primes, we used a hundred chart and  The Sieve of Eratosthenes to find all the primes (up to 100).

Notebooking Pages

There are two free printable notebooking pages, each in two line styles, over at The Notebooking Fairy–Factors and Multiples Notebooking Pages.

The Notebooking Fairy -- printables and how-tos with a pinch of pixie dustYou can use these to explain what factors and multiples are and to list factors and multiples of a particular number. These are great for math notebooking.

Printable Games

  1. Factor ‘Em In: Exploring Factors and Multiples
    This PDF is an entire lesson plan about multiples. My favorite part is the last page — a game called Multiple Mania. All you need is the printed page, 10 markers per person and a die.
  2. 97 Prime board game (or the same board game in a PDF file)
  3. Factor Finding Game (pictured below) Another simple game that requires only the printed board game, two dice, and 10 markers per person. UPDATE — This link is no longer working. Try the Way Back Machine at for this game.
factor game

factor finding game

Here are two more that I found but didn’t actually use.

Factor Game & Lesson Plan
Click on the PDF lesson link for complete directions, game board, and charts for analyzing how to play the game.

Since I published the blog post, I bought a reproducible game book from Amazon called 25 Super Cool Math Board Games (Grades 3-6). It has a few games that deal with factors and multiples as well as a variety of other basic math skills game. It’s a worthy addition to a math resource bookshelf.

Audio Helps

factors and multiples notebooking

factors & multiples notebooking page

Factors and Multiples Song This PDF has games and worksheets for learning factors and multiples. The best part is the song on the last page sung to the tune of I’ve Been Working on the Railroad.

I find that songs are a great way for Sprite to learn, and this song really helprd her remember the differences between factors and multiples. Plus it’s just fun to be silly and sing about math! The song was really helpful in making this notebooking page about factors and multiples.

Online Games

Illuminations: Factor Game
Play against the computer or with another person. A great strategy game for factors! Read the directions. It’s a bit tricky. We had to play it once through to really understand.
Multiplication Mystery
A simple multiplication grid — place the product where it goes. The computer interface makes it more engaging than paper and pencil.
BBC Education-Maths File-Grid Game
Pythagoras and Hypatia “host” this very classy game. The game is intuitive and knows what to review based on your mistakes. Sprite loved this one! The sound effects for right and wrong answers are hilarious.
Factors and Multiples Game
Follow directions with the 100 chart (provided) or play online.

This post is featured on The Massive Guide for Homeschooling Math. Click to see more great math posts.

The Massive Guide for Homeschooling Math

{ 18 comments… read them below or add one }

BlessedMomma August 16, 2009 at 12:52 am

I love reading your post on Living Math. My two children will be 8 and 11 this fall. My oldest has always struggled with math, so much so that my youngest is now almost caught up with him. We have tried so many math programs and I started seeing that my children were beginning to despise math as much as I did growing up. I soooo don’t want this!

I decided we would try a very relaxed living math type of curriculum this year to try and spark a love of math…..or at least an acceptance.

Do you know of a resources that has some sort of scope and sequence for teaching both children at the same time? I get the general idea of living math, but can’t seem to understand in what order you do what.
.-= BlessedMomma´s last blog ..Julie&Julia Movie Review…….sorta 🙂 =-.


Jimmie August 16, 2009 at 12:09 pm

That’s one of the things about living math — it’s not necessarily linear. You don’t really have to have an order for teaching the concepts. It can cycle around, and you can teach things as you have a “need” to know them. So when you’re learning about one math concept and other math concepts are tied in, you can add them them at that time.

There are scope and sequence outlines on the web. I find the Curriculum Focal Points at the National Council of Teachers of Math to be very, very helpful. Or you can use your textbook as a guide for what to teach. I do that too. I look for the “next” topic and then look for hands-on, living ways to teach and explore it.

Have you looked at Math on the Level? I don’t own it, but from what I’ve read, it looks like something you could use with both of your boys.


Cindy August 16, 2009 at 1:51 am

Great ideas! I will use some of these with my son!!
.-= Cindy´s last blog ..Boys and Dinosaurs =-.


Shannon August 20, 2009 at 7:27 pm

Your posts and lenses about living math are very inspiring. I am planning on taking more of a leap into living math this year.
.-= Shannon´s last blog ..Backyard Natur-in’ in West Virginia =-.


Dana August 20, 2009 at 8:29 pm

Thanks for some wonderful ideas. I think we will use some of these for our first week of back-to-school math next week. 🙂
.-= Dana´s last blog ..Cliffs of Moher (Final Day in Ireland) =-.


keri August 24, 2009 at 7:08 am

I bookmarked Multiple Matrix… that could help the kids out with reducing fractions.
.-= keri´s last blog ..Sir Isaac Newton =-.


Christie August 25, 2009 at 1:16 am

I LOVE these ideas!! My oldest struggles with this area of math. I think we’ll be spending some fun time doing most of these activities you have listed!! Thank you for the post!
.-= Christie´s last blog ..Preschool Corner–Week 3 =-.


Rachael in NZ September 1, 2009 at 5:28 pm

Thankyou SO much for this Jimmie. All of the links you have put together help will be very helpful for cementing these concepts with my girls. I know they are going to love playing these games!


*Kris* September 14, 2009 at 5:33 am

Great collection of activities–I’ll be picking several of them for Ds#2 this week. What a wonderful submission to the Hands On Homeschool blog carnival. Thank you!
.-= *Kris*´s last blog ..Response to "Unit Studies and Charlotte Mason" =-.


Angie in GA September 24, 2009 at 9:57 am

Can’t wait to check these resources out! Thank you so much for sharing them!! Be Blessed, Angie in GA
.-= Angie in GA´s last blog ..Giotto Inspired Art Lesson =-.


Lainie September 29, 2009 at 5:29 am

Oh Jimmie thank you so much for posting this! I really need to find these today and I thought I remembered you writing about Living Math and to have a whole post on factors– what a blessing!
.-= Lainie@ Mishmash Maggie´s last blog ..A Simple Woman’s Daybook =-.


Michelle December 12, 2009 at 11:07 am

I am loving your living math series! I am bookmarking this page to come back to. I have Family Math and have been wanting to use it more. Thanks for the inspiration and all the wonderful links! *Ü*
.-= Michelle´s last blog ..This One is for the Birds {Kiddo’s Create} Pine Cone Treat =-.


Lisa September 15, 2010 at 4:49 am

HI There,
I would love to make the factor game board but the PDF link does not work. Thoughts? Can you send me the link to print the game? From the picture I am thinking you just put various factors on the game board, you roll the dice and match a factor to that rolled number?

Lisa Gilbert


Jamie November 10, 2010 at 8:07 pm

I recently discovered your blog and wow,oh, wow! We’ve recently been working on factors and multiples so this couldn’t have come at a better time. (DH is also a math teacher so these will come in handy for him as well I’m sure)

Thanks for sharing such an amazing wealth of information and inspiration!


Melissa Telling January 25, 2011 at 12:31 pm

The Sieve of Eratosthenes looked like so much fun that I made up a notebook page with it for my kids to use. It is posted on my Homeschool Launch page.


Kim September 21, 2011 at 6:40 pm

Thank you so much for the Factors and Multiples Song. My daughter had to come up with a catchy phrase to remember the difference between the two and this helped!


Chelsea November 8, 2012 at 9:57 am

I can’t click on your factors and multiples song 🙁 Is there any possibility of you sending that to me?



Marsha Landau October 5, 2013 at 4:51 am

Great website!

For REALLY neat patterns, look at what happens when you do the Sieve of Eratosthenes on the numbers 1-100 when they are set out in rows of 6 rather than 10. Patterns of multiples, location of primes >2, etc. — you’ll like it!


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