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 (PDF)
A printable factors game plus extensive lesson plan for teaching primes, multiples, and factors.
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.

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