Up until a few weeks ago, we used the ladder method to find prime factorizations, GCF, and LCM. But THEN, we started discussing factoring, mostly with numerical expressions. It’s 6th grade, it’s the first time my students were exposed to factoring, and it was the first time I had taught factoring. I know how to factor, but I wasn’t really sure how to best explain it so it would be easy for the students to understand. When I learned to factor something like 18x + 24, we “thought of” the GCF and divided both numbers by it. Not having taught factoring before, I thought that something more in-depth was needed.
To write the factored form of 18 + 24, we take the 3 and 2 from the left and multiply them to get 6 (GCF). This GCF goes on the outside of the parentheses in the factored form. The 3 and 4 on the bottom of the ladder are the factors that remain when the GCF is removed from 18 and 24, and these go inside the parentheses, giving us the factored form of 6(3 + 4).
I created a notes page for my students, with steps and several examples, some of which include variables. Feel free to download it and use it! I also created a Fold It Up for the ladder method, which includes the steps for factoring and for finding GCF and LCM (find this in my TPT store).
I am so excited to have discovered this use for the ladder method, and I find it so interesting to once again realize that even when our lesson plans don’t go exactly as expected, or when they “fail” to teach things as clearly as we want, they can still allow us to “stumble” upon fantastic new ways to help our students.
I am a 6th grade math teacher and have been teaching for 23 years. 🙂 Running, reading, and learning are my favorite things (besides being a mom to three fabulous children). I write about math and education on my blog, Middle School Math Moments.
** Font in the images is created by Teaches Third in Georgia.
Roseanne Welte says
This is exactly how I teach factoring to my students – Thanks so much for this. I have can have them put it in their Interactive Notebooks for reference! Love the foldable too!
My daughter is learning this & I’m trying to figure it out but I’m lost. We can get it to work on some but finding the LCM of 2 9 & 4 for instance isn’t giving the correct answer. Does this work on all problems or are we missing a step? Please help!
A super frustrated mom!
This is a little tough since only two and four have a common factor, but you can put 2 on the outside of the ladder, bring the 9 down below the ladder since it can’t be divided by 2; then 2 divided by 2 is 1, so put a 1 under the ladder, and 4 divided by 2 is 2, so put 2 under the ladder. Then on the outside of the ladder you have 2, 9, 1, and 2. You would do 2×9×1×2 = 36. Hope this helps!
I agree…it is the simplest and most NON-THREATENING method and covers factoring, GCF, LCM, lowest term fractions, etc….
Kristen Doyle says
I LOVE this method! It is GENIUS! By far the simplest way to teach these skills, with the lowest chance for errors. My students were so excited, since we just practiced the "other" method for GCF last week and they hated all the work! Thank you!!
Chalk & Apples
Jamie Randall says
I am trying to find this product to utilize the Fold it up. Can you send me a link as my searches are not bringing it up?
Here is the link to this guest bloggers category for Fold It Up resources in their TpT store: https://www.teacherspayteachers.com/Store/Cognitive-Cardio-With-Middle-School-Math-Moments/Category/Fold-It-Ups-144427
We hope that helps!
Jen Shoemate says
So I have a question that I have came across in teaching LCM. I have tried the ladder method using 3 numbers, and my students found one that it doesn’t work with-3,6 and 10. If you use the ladder method, you get 180 however listing the multiples, the LCM is 30. What am I doing wrong? And why doesn’t it work?