If factoring expressions ever felt like one of those math skills your students just don’t get right away, you’re not alone. With the right approach, this topic doesn’t have to be confusing for you or your students. In this post, I’m walking you through a step-by-step video that lays the groundwork with a quick distributive property review, then moves into factoring using the greatest common factor and ladder method. I’ll also share a classroom resource that makes practice meaningful and easy to implement. Let’s dive into a way of teaching factoring expressions that’s clear, supportive, and ready to use.

Watch the Video for Step-by-Step Help for Teaching Factoring Expressions

In this quick YouTube tutorial, we focus on how to help your students make sense of factoring expressions. It begins with a reminder of the distributive property and how factoring is really just the reverse process. Then, we dive into several examples that show how to pull out the greatest common factor and use the ladder method to factor.

Throughout the video, you’ll see how the math builds in complexity, from basic numerical expressions to ones that include variables. You’ll learn how to explain the why behind each step so your students don’t just follow a process. They will understand it. This video is a great resource to boost your confidence as a teacher and give your students clear, structured examples during whole group or small group instruction.

A Tip for Teaching Factoring Expressions

One thing I’ve found really helpful is emphasizing that there’s more than one right way to factor as long as students are pulling out a common factor correctly. Sometimes, they’ll factor by a number that isn’t the greatest common factor. That’s okay at first! It still works. It just may not be fully simplified. Allowing your students to recognize and compare methods helps them internalize the importance of the GCF while also boosting their confidence.

Also, the ladder method introduced in the video is a game-changer. It’s a student-friendly way to find the GCF, especially as numbers get bigger. I recommend teaching it early and often. It’ll come in handy beyond just factoring expressions.

A Helpful Resource for Practicing Factoring Expressions

To go along with the video, I’ve created a classroom-ready lesson that walks your students through factoring expressions using both visual support and gradual release. The resource includes teacher notes to guide your lesson, guided notes, and a practice page where your students apply what they’ve learned.

There’s also an exit ticket to check for understanding, which is perfect for quick data collection or small group planning. This kind of structured approach ensures you’re not just telling your students how to factor. You’re helping them reason through the process, one step at a time.

You can use this Factoring & Distributive Property lesson for whole group instruction, targeted intervention, or even independent practice if your students are ready for it. It’s a solid addition to your unit on expressions or any review leading into equations.

Save for Later

Don’t lose track of this helpful lesson on factoring expressions! Pin this post to your math board so you can come back when you’re ready to teach or review factoring. Clear visuals, structured steps, and flexible resources. That’s everything you need to make this concept stick!

The post Make Factoring Expressions Stick for Your Students appeared first on Cognitive Cardio Math.

When you’re teaching the greatest common factor to 6th graders, it helps to have a clear structure and multiple methods at your fingertips. Whether you’re brand new to teaching this concept or just want a more effective way to deliver it, this post has you covered. I’ve pulled together two videos and a helpful classroom resource that will take the guesswork out of introducing and practicing GCF.

Greatest Common Factor Videos With Three Strategies That Work

In this first video, I explain what the greatest common factor actually means. Then, we walk through three go-to strategies to find it. We look at listing factors, using prime factorization, and my favorite, which is the ladder method. I show you how to help your students decide which method is best for the numbers they’re working with. I also weave in divisibility rules and factor trees to give your students extra tools for breaking down numbers. Each strategy builds a deeper understanding of how numbers connect. This helps to make the greatest common factor more than just a vocabulary term. It becomes something your students can use.

3 Ways to Find the Greatest Common Factor

Solving GCF Word Problems

Once your students understand how to find the GCF, it’s time to show them how to apply it. In the second video, I walk through a word problem that requires using GCF. I model how your students can organize their thinking, use a guess-and-check strategy if they feel stuck, and connect the numbers in the problem back to what they already know about factoring. We also solve the problem using the ladder method, allowing your students to see how math shows up in everyday problem-solving. This is a great way to answer the classic “When are we going to use this?” question.

Help Students Choose What Works With These Three GCF Strategies

When it comes to teaching the greatest common factor, it’s not just about memorizing the steps. It’s about helping your students understand why each method works and when to use it. Let’s take a closer look at the three strategies highlighted in the video and resource.

Listing Factors is a solid place to start with smaller numbers. You should always encourage your students to list pairs in order (starting with 1 and the number itself) and to stop once they meet in the middle. It’s simple and visual, but it can be tricky when working with larger numbers, especially if your students don’t know all their math facts.

Prime Factorization takes things a step further by using factor trees to break numbers into their prime parts. This method gives your students a way to actually see how numbers are built. They learn how to find what factors two numbers have in common. It’s a great strategy for reinforcing prime numbers and multiplication facts, too.

The Ladder Method is typically students’ favorite! It feels less messy than factor trees and works well with large numbers. You pull out common factors on the side and divide both numbers until there’s nothing left to pull out. It’s straightforward, systematic, and pairs beautifully with visual learning styles. Plus, once your students master it, it becomes their go-to method for both GCF and least common multiple later on.

Greatest Common Factor Resource

To go along with the videos, I’ve created a classroom resource packed with everything you need to teach the greatest common factor from start to finish. The resource includes print and digital versions of GCF notes and practice pages, plus two exit tickets that help you assess understanding right away. Each strategy, listing factors, prime factorization, and the ladder method, has its own dedicated lesson page and step-by-step examples.

Your students can also get a chance to try each method on their own with guided support. There’s a Fold It Up activity that helps solidify how to use GCF and when to apply it. Whether you’re teaching a whole group, a small group, or assigning it digitally, this set is built for flexibility and clarity. Your students will walk away knowing how to find the GCF and why it matters.

Help Students Master the Greatest Common Factor

Teaching the greatest common factor in 6th grade math doesn’t have to be complicated. With the right mix of visuals, guided examples, real-life application, and supportive practice, your students can truly understand and use GCF consistently. Whether you start with the videos, the printables, or both, you’ll set them up for success in future algebraic thinking and number sense.

Save for Later

Remember to save this post to your favorite math Pinterest board for quick access to these greatest common factor resources!

The post 3 Ways to Find Greatest Common Factor and Finding GCF Word Problem appeared first on Cognitive Cardio Math.

GCF (greatest common factor) and spending ‘too much time’ on math topics. These are the middle school math ideas I’m thinking about today.

Day 1 of Reviewing How to Find GCF

Day 2 of Reviewing How to Find GCF

GCF Task Cards

The post How to Find GCF and Spending Time in Middle School Math appeared first on Cognitive Cardio Math.

Is it weird that I love using prime factorization??

Every year of teaching math, I have come to appreciate it more and more! Maybe it’s because when I was a student (forever ago!), I didn’t learn how to use prime factorization to find greatest common factors, least common multiples or to reduce fractions. (I will admit to the possibility that I learned and forgot….but I truly think I didn’t learn it!).

In addition to missing this information as a student, I didn’t find it in math teacher manuals until I’d been teaching for more than 20 years.

I’ll share why I love it so much by explaining three ways to use prime factorization: to find GCF, LCM, and lowest terms for fractions.

Using Prime Factorization to find GCF (Greatest Common Factor)

1) First, find the prime factorization of each number.
Using the example in the image:

• 42 is 2 x 3 x 7
• 70 is 2 x 5 x 7

2) Next, identify the factors the numbers have in common

• 24 and 70 both have a 2 and a 7

3) Last, multiply the factors that are in common

• 2 x 7 = 14, so GCF is 14

Why do I like this method? I like using prime factorization to find the greatest common factor because when my students use the ‘listing method, they often miss factors of some numbers; and when they miss factors, they end up missing the GCF.

Using prime factorization, they DON’T miss these factors, so they’re more successful in identifying the GCF.

Love it!

Using Prime Factorization to Find Lowest Terms

In past years, when students reduced fractions, they often chose ANY factor to divide by, (unless they were forced to find the GCF). Then, they would reduce and reduce again, and sometimes they still didn’t reach the lowest terms.

For example, some students would take 54/72 and divide by 2 to get 27/36. Then they might divide by 3 to reach 9/12. Some might stop here and never reach 3/4 as the lowest terms.

To find the lowest terms using prime factorization:
1) First, find the prime factorization of each number.
2) Next, cross out the factors that are in common.

• In the image example, 54 and 72 have one 2 and two 3s in common, so those factors are crossed out

3) The remaining factors are the numerator and denominator of the reduced fraction

• If more than one factor remains in either the numerator or denominator, they should be multiplied

Using Prime Factorization to find Least Common Multiple (LCM or LCD)

Using prime factorization to find the least common multiple is fantastic! Listing multiples can be pretty tedious (though it does reinforce multiplication facts), and although finding the prime factorization might be difficult for students to begin with, it will eventually be quicker than listing multiples.

Once I started talking about prime factorization a lot in math class and thought about it aloud so the students could hear my thought process in breaking down numbers, my students started to find prime factorizations much more quickly than students in the past.

To find LCM with prime factorization:
1) First, find the prime factorization of each number.
2) Next, identify the different factors of each number.

• If a factor is found in both numbers, count it the greatest number of times it appears in either number. For example, in the prime factorizations of 8 and 30 (image above), 2 occurs three times in 8 and only once in 30, so it is used three times in the LCM calculation.

A 2nd Example: Find the LCM of 6, 7, and 14
1) Find the prime factorization of each number.

• 6: 2 x 3
• 7: 7
• 14: 2 x 7

2) Identify the different factors of each number.
The factors 2, 3, and 7 occur once at most, so they are each multiplied once to find the LCM of 42.

More Benefits

Besides helping students to find GCF and LCM and reduce fractions more quickly, I love the fact that using prime factorization for these concepts helps students develop a better understanding of relationships between numbers….I see and hear this awareness developing.

Here’s a great benefit – students like it! While some students are comfortable with ways they’ve learned in previous years and are hesitant to use prime factorization, other students have actually come to me during our study period to double check how to use prime factorization in these ways, because they LIKE it and think it’s cool!

I’ve created a note sheet for my students to keep in their notebooks so they can refer to it throughout the year. Feel free to download and use it! 

Grab the Prime Factorization Notes here!

Use the Ladder Method

Of course, I also love how the ladder method can be used to find prime factorizations, as well as GCF, LCM, and lowest terms fractions. Students respond really well to this method and I find that they make fewer mistakes.

Other Resources for GCF, LCM, and Prime Factorization Instruction and Practice

If you’re looking for other resources to help your students practice with GCF, LCM or prime factorization, I have several in my TeachersPayTeachers shop – some print and some digital:

• The Math Wheels are great for notes as you’re teaching or reviewing the greatest common factor and least common multiple.
• Greatest Common Factor Color by Number has 3 print versions, with a digital version coming soon.
• Least Common Multiple Color by Number has 3 print versions, with a digital version coming soon.
• Prime Factorization Footloose, Google Task Cards, and Quiz: 30 task cards in both print and digital versions, plus a Google Form quiz for a quick assessment.
• Prime Factorization Color by Number: Digital practice with the pattern/pictures appearing with students’ correct answers.
• Factors and GCF Footloose: 2 sets of 30 Footloose task cards for students to practice with factors and GCF.

Save this post to your favorite Pinterest board!

The post Three Ways to Use Prime Factorization in Middle School Math appeared first on Cognitive Cardio Math.

Do you use the ladder method in middle school or elementary math, to find GCF, LCM, or for any other math concepts?

If you haven’t had the chance to use the ladder method (or the upside down birthday cake method, as some call it), I highly recommend it.

It can be used for several different concepts and has some great benefits for students.

 

What Concepts Can the Ladder Method Be Used With?

The ladder method can be used for quite a few concepts. As you can see in the anchor chart below (sorry it’s not as pretty as some!), upper elementary and middle school math students can use the ladder method for:

• finding greatest common factor (GCF)
• finding least common multiple (LCM)  
• factoring
• finding lowest terms fractions 
• finding prime factorization
• finding the least common denominator (not pictured, but you can read about it in the linked post)! 

Benefits of Using the Ladder Method

1) What I really love about this method is that the process is the same for each use; the outside numbers are just used differently. 

I love the fact that the continually using the ladder method (for various math concepts) leads middle school math students to make greater connections between concepts. Finding factors also seems to come more easily.

2) In addition to helping math students find GCF and LCM, using the ladder method helps students see the relationships between numbers more clearly. 

It’s very easy to see what factors the numbers have in common and how those factors ‘contribute’ to the LCM or GCF.

Using the Ladder Method for Factoring

When I started using the ladder method for factoring,  students picked up the factoring concept MUCH more quickly than when I hadn’t used it.

The steps to use the ladder method for factoring are:

1. Put the expression into the ladder.
2. Take out the common factors, one at a time (common factors go outside the ladder, then divide each number in the expression by that factor and put the quotient below the numbers in the ladder.) 
3. Repeat until all common factors have been ‘removed.’
4. Multiply the numbers on the left of the ladder – this is the GCF, which goes outside the parenthesis in the factored expression.
5. Put the numbers at the bottom of the ladder into the parenthesis.

You can see this process shown on the Fold It Up below.

Ladder Method Resources

Several years ago, I wrote a guest post about the ladder method on the Minds in Bloom blog, so if you’re interested in reading more, check it out here. 

I shared a ladder method fold-it-up in my guest post, but you can also select the button below, if you’d like to download it.

Download the Fold It Up

Ladder Method Doodle Notes

I’ve also created a fun Doodle Notes page to help students with the Ladder Method!

If you’ve used the ladder method before, I’m sure you understand why I love it:-)

If you haven’t used the ladder method yet, I hope you’ll give it a try!

See the Doodle Notes on TPT

The post Using the Ladder Method in Middle School Math, for GCF, LCM, Factoring appeared first on Cognitive Cardio Math.