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Using the Ladder Method in Middle School Math, for GCF, LCM, Factoring

2/25/2016

$Use the ladder method in math class to find GCF & LCM, factor and reduce fractions to lowest terms$

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.

Ways to Use the Ladder Method
As you can see in the anchor chart (sorry it's not as pretty as some!), 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)!

So many uses!

Benefits of Using the Ladder Method

$Use the ladder method in math class to find GCF & LCM, factor and reduce fractions to lowest terms$

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 continued use of the ladder method (for various math concepts) leads middle school math students to make greater connections between numbers.....and finding factors 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.

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. Repeat until all common factors have been 'removed.')
3) Multiply the numbers on the left of the ladder - these are the GCF and go outside the parenthesis in the factored expression.
4) Put the numbers at the bottom of the ladder into the parenthesis.

The short video below demonstrates how to factor a simple expression.

Ladder Method Resources

Ladder Method Fold it Up

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 click the button below, if you'd like to download it.

Download the Ladder Method Fold it Up

Ladder Method Doodle Notes

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

Select the button below to see the Ladder Method Doodle Notes on TPT.

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

To Read Next:

2 Comments

How to Include More Math in Middle School Math Class

2/7/2016

1 Comment

Use the Date to Encourage More Math Thinking in
Middle and Elementary School
Updated 5/2020

$Ideas for using the date to encourage more math thinking in middle and upper elementary school math class.$

How Can You Use Math in Writing the Date?

In 2015, I started adding a little extra math into my classes, homeroom and last period (homeroom students again) - by using the date! I had done this years ago, but hadn't used the idea in a while, so I brought it back to my middle school math classroom in two ways

How to Use Math With the Date, Method 1:

$Using the date to add more math thinking to middle school math$

To include more math in the middle school class, use all the digits in the date to create an equation.

The digits should stay in the same order they are in the date, and any operation signs can be added in between any digits.
The equal sign can also be placed between any digits.
Digits can be used as exponents, as in the example shown, and you can add square roots signs if you can find a way to use them.

How to Use Math With the Date, Method 2:

$Writing the date as a mathematical expression$

The other way I used the date to include more math in the classroom was to write the date so students have to evaluate an expression for each number in the date.

It's been fun to see some students writing these in the corner of their notebooks during class! Others have asked to write their equations or expressions on the board during the last period of the day.

Five Benefits of Using Math Dates

What I love about including math ideas is that they:

Are quick
Can be completed at any time (beginning of class, finished early time, closing of class, or in homeroom)
Help kids to expand their number sense and use some "out of the box" thinking
Help improve students' understanding of equivalent expressions
Can be 'expanded' to challenge students:

Students can create their own expressions
Students can evaluate the expressions (using the bar as a

division sign - a student did this on his own one day!)

If you happen to make a "mistake," students can find it and

correct it:-)

6. EXTRA Math Benefits

Other fabulous benefits of using the Math Dates. You can:

Introduce Math Concepts

Math Dates can be used to introduce notations or concepts students haven't seen before, like the cube root or exponent rules. As you discuss the date in class, a quick overview of a particular concept can help set students up for greater success when it comes time to teach the concept in the course of the curriculum (especially if they've seen it in several different dates!).

Reinforce Math Concepts or Facts

Math Dates can be used to reinforce some basic concepts, like the meaning of exponents. I don't know about your students, but mine often forget that 2 cubed means 2 x 2 x 2, not 2 x 3. Using the exponents in the date keeps bringing that concept back for review.
In 2017, I used the year part of the date to reinforce that 51 is divisible by 3 - this was such a huge help to students who assumed 51 was prime.

If your students are struggling to retain a certain concept, give the math dates a try - work that concept into the date.

Where Can You Find Math Dates Created for You?

Math Dates are an awesome way to get your students thinking!

Try using Math Dates this year - challenging and fun!

Update: I used to post the dates on Instagram every week, but starting this fall (2021) they will be posted in my Facebook group and will be sent to those in my email community. Feel free to join my group or subscribe to my emails:-)

I created Math Dates resources for you to use throughout the year - these have been published by individual months and as a year-long resource on TPT.

I've added a year of dates for upper elementary math as well.

How do you include more math in the middle school classroom?