How to Easily Teach Adding and Subtracting Unlike Fractions: Using the Fraction List Strategy

As a math interventionist, one topic that I see students struggling with year after year is adding and subtracting fractions with unlike denominators. Earlier in my career, I remember struggling through a fraction unit, trying the 4 square method, multiplication charts, and anything I could remember from my own days in school or find on Pinterest, all without seeing much growth. I knew I needed to do something differently, leading to the creation of my new favorite fraction strategy! Since then, I’ve used this strategy with students year after year and will never go back! 

My middle school students have had a lot of success with this strategy and often prefer it over other faster methods due to how easy it is to understand!

Essential Background Knowledge

Before introducing this strategy, I spend time on two main concepts: equivalent fractions and adding/subtracting fractions with like denominators.

1. Students must understand that equal fractions represent the same amount and are essentially interchangeable. If a student truly understands this concept, the fraction list strategy will make sense to them as an even exchange.
2. Students also need to have a solid understanding of adding fractions as joining parts and subtracting fractions as finding the difference of two parts. This will help simplify the strategy, as students will not need to model addition and subtraction once they find equivalent fractions pictorially.
3. Lastly, It’s also very helpful to get students in the habit of simplifying their answers early on in their fraction journey, but it is not essential for this strategy.

Using the Fraction List Strategy

Using the note page, I introduce the strategy by talking about how fractions need to have a common denominator when we are adding or subtracting them because a denominator means the number of pieces needed to make a whole, and if we have pieces that are different sizes, it’s hard to make a whole exactly because the pieces don’t fit. We talk about how we can replace our fractions with equivalent fractions that mean the same amount, but that will be easier to work with. While working through example problems, I use notes to reinforce the conversations we are having as a class.

We talk through the first example. I model writing the first fraction (1/2) next to the first row of boxes. Then, we make a list of equal fractions by multiplying the top and the bottom of each fraction by the same number and recording our new fractions in the boxes. I always start with multiplying by 2, then 3, then 4, and then 5 to finish the list. It may be helpful to record what you are multiplying by above the new fraction. You’ll end up with a list of equivalent fractions that can be interchanged.

Repeat the process with the next fraction. I write the second fraction (1/3) next to the second row of boxes. Then, we create the list by multiplying by 2, then 3, then 4, and then 5 to finish the list. Again, you’ll end up with a list of equivalent fractions that represent the same value and can be interchanged.

After completing the two lists of equivalent fractions,  we can look for one fraction from the top row and one fraction from the bottom row that share a denominator. I like to have students circle the fractions with like denominators that we are going to use. I explain that we can “trade in” our original fraction for our new fractions, giving us a problem with like denominators. After students have identified the fractions with common denominators from the two lists of equivalent fractions, they will rewrite the original problem using these new fractions. I like to draw arrows to reinforce that the original fraction and the new fraction are equal.

This creates a fraction problem that is easy to solve! While students may struggle to solve 1/2 + 1/3, 3/6 + 2/6 makes more sense to them!  If your students are in the habit of simplifying fractions, ask them if you can simplify your answer, or if you are done!

If your students are struggling with this strategy after some practice, I recommend assessing their understanding of equivalent fractions. A strong foundation in fraction equivalency is essential to many math skills, including adding and subtracting fractions with unlike denominators! 

Next Steps

This strategy is easy to transition to other, faster fraction strategies. For example, when students start to feel confident making fraction lists, they can transition to just making denominator lists, and then using multiplication to get the correct numerator for just the denominator they are going to use. From there, students can use the typical strategy of multiplying the numerator and denominator by the same number to create equivalent fractions that they can use while adding and subtracting unlike fractions.

Are you ready to give your fraction unit a refresh? I can’t wait to hear how this strategy works for you in the comments!