Thursday, March 26, 2015

Does the upside down division method work for everything - just about :)

    The upside down division method can be used to teach just about everything. OK, I exaggerated a little, but I use it to teach kids prime factorization, simplifying algebraic fractions, greatest common factor, least common multiple, and factoring polynomials. Teaching students one way to solve so many different types of problems makes it much easier for them to remember. I am sure that most of you are already very familiar with upside down division. If you are not, it is the cake method many people use for prime factorization, but upside down. See Sarah's post to explain the birthday cake method. The only problem I have with the cake method is if I don't start in just the right place the problem goes off the paper.This is not an issue with upside down division, you can keep dividing all the way down to the bottom of the paper.

    Initially, I teach this when finding prime factorization of numbers. Here is a foldable for their interactive notebooks. I needed to review divisibility rules with my kids before this lesson. 

I love prime factorization because it helps the kids review their multiplication tables with smaller numbers. They should know them but so many of my kids don't.  :(

 I like how this method doesn't take up as much space as the factor trees do.

I have started making more of my notes fill in the blanks. It saves so much time. However, I don't like to have them all written for them.

   I do a quick review of short division with the kids. Many of them have never seen this before.

     We use this method again when simplifying algebraic fractions.

 Here's a foldable we used for simplifying fractions.

I usually draw a fraction bar between the numbers. I forgot to do that on this foldable.

    Before we do upside down division with fractions, we have written fractions in expanded form and simplified to find the answer. They are familar with the exponent rules already.

     Next I use this with Greatest Common Factor and Least Common Multiple. 

I originally had this foldable as one foldable, but I decided to cut it in half and have a separate page for GCF and LCM. The students have already learned the other two methods for finding GCF. They have also covered exponent rules 
as well.

Instead of circling the common factors, the students place a large G over the numbers. It is an added visual for the kids.

Upside Down Division for LCM is also called the Ladder Method. I never knew that until I started writing this post. You learn something everyday:)

On LCM the students draw a large L around the numbers as an added visual.

     Lastly, we factor polynomials using Upside Down Division. 

My Pre-Algebra students always have difficulty with this topic. Using the Upside Down Division makes it so much easier for them to understand.

Download documents from this post here:

I am so happy to have all of this written and saved in one place. I litterally had to search everywhere to consolidate all the pieces. I hope there is something new for you to use.

Til next time,
Jan :D


  1. I am so glad you posted this today! I was getting ready to record a video on factoring polynomials with a GCF, and I happened to catch your pins on Pinterest. I've used the ladder/upside-down division method before, but I liked how you broke it down into factoring out the number, then each variable one at a time. So that's how I worked my examples in the video. I can't wait to see how the kids do with it!

  2. Hi Mickie,
    I can't wait to see how they do as well. I find it helps my Pre-Algebra kids understand it so much better when I break the factoring down this way. It is always good to hear from you. Thanks for stopping by:)

  3. Replies
    1. Thank you ! I hope your students find this helpful.


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