Using the Ladder Method in Math - Minds in Bloom (2024)

Happy spring! I’m Ellie from Middle School Math Moments, and I’m so happy to have the opportunity to share my ideas with you!

I am always excited to learn something new, and I’ve learned quite a bit in the last few years about how the ladder method can help students with different math concepts (I didn’t learn this method when I was in school)! To be completely honest, I have to say that I LOVE the ladder method, and I’d like to share how I came upon our newest (and probably my favorite) use of the ladder method.

Up until a few weeks ago, we used the ladder method to find prime factorizations, GCF, and LCM. But THEN, we started discussingfactoring, mostly with numerical expressions. It’s 6th grade, it’s the firsttime my students were exposed to factoring, and it was the first time I had taught factoring. Iknow how to factor, but I wasn’t really sure how to best explain it so it wouldbe easy for the students to understand. When I learned to factor something like18x + 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.

So, not knowing what to expect from the students, I started with a video clip from our math series, as well as a PowerPointfrom the series. The PowerPoint explanation/examples connected to theDistributive Property, but not well enough for the students to reallyunderstand the connection. When they tried a few problems on their own, somestudents were still confused. So, I showed them what I remember being taught(find the GCF and divide the terms by it). They thought this was muchsimpler, but it was close to the end of class and we only had time for one or two additional examples before theperiod was over. I knew we’d need to continue the next day, but this was good,because it gave me more time to evaluate the lesson and consider which way to go next. The videoand PowerPoint weren’t great, but the dividing idea seemed to make sense tothem.

Even though the resources I used didn’t work well for my students, I’m so glad I used them, because that lesson, that day, led me to something new! During the instruction many of the students were using the ladder methodto find the GCF (without me telling them to). Looking at their papers as I circulated, I noticed that the numbers at the bottom of the ladderend up being the numbers that go in the parentheses when the GCF is“removed” from the expression. I hadn’t seen the idea of the ladder method being used for factoring, so after school, I searched online to see if I could find it…Icouldn’t. I spoke to a few teachers and they hadn’t seen it before either, butthey really liked it and thought it was a great visual!

Here’s how it works, if we want to factor the expression 18 + 24:

The 18 and 24 are placed side by side on the ladder, and wesee that they can both be divided by 3. So, we divide them both by 3 to get 6and 8; 6 and 8 can both be divided by 2, so we do that and end up with 3 and 4on the bottom of the ladder. Since 3 and 4 have no common factors to divide by, we are done dividing.

When I presented this method to mystudents the next day (being sure to make the Distributive Property connection), they thought it made so much sense and that it was SO easy! It seems to be particularly helpful for students who don’t know all their facts that well (ladder helps them to find the GCF more easily) or for when a GCF might not be as easy to think of (for example, GCF of 42 and 56 is 14 – most students automatically think it’s 7, but the ladder method helps them to determine that it’s 14). It adds a structure that makes the placement of the numbers more clear, and it adds a kind of automatic “checking” component to ensure that they have actually found the GCF (if the numbers at the bottom of the ladder still have a common factor that they can be divided by, then the process is not finished – they haven’t found the GCF, and the expression isn’t completely factored).

Shortly after I started using this method with my students, my daughter’s homework was to factor the GCF out of longer algebraic expressions; we used the ladder method – it worked really well for her!