Math = Love: Reviewing Prime Factorization at the High School Level

Thursday, February 9, 2017

Reviewing Prime Factorization at the High School Level

My Algebra 1 students are currently working through our unit on radicals.  I already blogged about the dry erase work mat I made for my students to use to organize their work for simplifying radicals. 

Before we could actually begin to simplify radicals, we needed to review how to find the prime factorization of a number.  This is a skill they should have learned before reaching high school, but I wanted to review it to make sure my students had an even footing.  

My students were taught to make factor trees to find the prime factorization.  That's the way I was taught, too.  But, when I was completing my student teaching at Edison Preparatory School, one of the 8th grade teachers invited me to her Algebra 1 class to learn about the birthday cake method for finding prime factorization.  It was LOVE at first sight!  

I show both methods to my students and let them choose the method they prefer. 

Many students prefer the factor tree method because you can start with ANY two numbers that multiply to the given number.  Then, you proceed with finding factors until all of the factors are prime.

The reason I try to steer students away from the factor tree method is that it can get messy.  I have seen too many students do a factor tree like the problem above and write the prime factorization as 2^2 * 3 * 5 instead of 2^3 * 3 * 5.  

The birthday cake method can take a bit longer to get started because you must find a prime number that divides into the given number.  You can start with any prime number that divides into the number, but many of my students choose to use 2, 3, 5, 7, etc in that order. 

I love that the birthday cake method is so streamlined.  Instead of searching for all of my prime factors in a tree, my prime factors are all lined up nicely for me.

To help my students remember their prime numbers, I created a quarter sheet with each of the prime numbers below 100 for my students to glue in their notebooks.  I have a few students repeating Algebra 1 for the second time.  They asked me why I hadn't given them something like this last year!  I guess that means they found it useful!

A few years ago, I created a prime numbers banner poster that my students frequently reference.

After discussing the two methods I presented for finding prime factorization, I gave my students a practice book which gave them a chance to try out both methods.

After giving students a bit of time to work each problem, a student volunteer came to the SMARTBoard to present a solution.  We alternated methods with each solution presentation.

My students were SHOCKED to find out that they always got the same prime factorization even though they took many different paths to get there!

Now that we've been simplifying radicals for awhile, my students have started to realize that we have to keep figuring out some of the same prime factorizations over and over and over.  One of my 8th graders remarked that it would be cool to have something in our notes that gave us every single prime factorization.

I took this idea and ran with it.  Kinda.  I did make them a table to glue in their notebooks for the prime factorization of the numbers between 1 and 100.

I typed the prime numbers in large print in shaded cells.  I typed the composite numbers in small print in unshaded cells.  This means students have room to write in the prime factorization when they find it.  Then, in the future, they can use the prime factorization for that number without making another birthday cake or factor tree.  

Some of my students really took to this and eagerly worked on filling out each box after finishing their quiz.

Hopefully I haven't made any mistakes when filling mine out.  I have to say that it came in handy when I was making answer keys for our adding and subtracting radicals quiz today!

I'll post more about how I'm teaching my students to simplify radicals soon.  I feel like my students have a much greater conceptual understanding of how radicals work than ever before!  

Files are uploaded here


  1. You can also Play with Prime Factorization with my 'Kids Math garden' toy:
    Numbers as plants, seeds and dandelions
    Maths and agriculture:

  2. For years, I have made my middle school students prime factor from 2 to 100. They hate it until they are shown how P.F. can help with all fraction operations. Then they are blown away. I wish that 4th grade would focus on factors and multiples to the exclusion of everything else. That sort of in-depth number theory can really help their conceptual understanding in so many future math classes!
    Keep fighting the good fight!

  3. Somehow in teaching factor trees, students can often miss the forest for the trees (as it were). That's because most examples are shown where you can easily see a starting factor to try. The idea that there is a methodical process that can find any factorization and how that would go tends to get lost.


    It was really eye opening to ask my kids what to do next when there was no obvious starting point.