If you would have asked me to draw and explain how to add and subtract fractions when I first started teaching 5th grade before Common Core, I would have had no clue. My response would have been to just find the least common multiple because that was the way I was taught. Now that I have taught 5th grade for 10 years, I know that adding and subtracting fractions should first be introduced using visual fraction models (such as the area model) to build understanding before using a standard algorithm. Thank you Common Core! Also, research shows that it works too!
How to use area models when teaching adding and subtracting fractions?
Using area models is essential for students to have a deep understanding of what it means to add and subtract fractions with unlike denominators. It is also explicitly stated in Common Core standard Numbers and Operations- Fractions 5.NF.2.
Of course, the goal is to have students eventually not rely on drawing pictures but for the first few days of instruction, my students and do it before we move into algorithms. I make it fun by allowing my students to use different colored pencils. What kid doesn’t like to color during math?
Should you teach your students to just multiply the denominators?
Instead of just telling students that multiplying denominators will always give the common denominator, your goal should be for them to notice it themselves. When solving problems, ask students, “What pattern do you notice?” or “Do you see a shortcut to solve these problems?” I love to see the light bulbs go off! Plus having students look for patterns is a key mathematical habit of the mind. Multiplying the denominators will not always result in the smallest denominator, but it isn’t necessary to find the least common denominator to get the problem correct.
I teach a simple mnemonic for remembering that the denominators need to be the same. I tell them that the fractions are friends and want to dress alike on Halloween by having the same denominator. Kids like stories so why not create some during math? Also, mnemonics really help students who have learning difficulties. Research shows that mnemonics in math increases student performance.
Using other methods to find the common denominator
Once students have success with multiplying denominators to get a common denominator, I teach my on-grade level or advanced students that for some problems it is easier to use the larger multiple of the two denominators. If students multiply both denominators they may get a high number which will require them to simplify later. For example, with the problem 1/3 + 1/9, we would only have to change 1/3 into 3/9. My less advanced students will want to just multiply the denominators 3 and 9 and get 27, which is fine too. However, they will need to know how to simplify fractions. If they take a multiple choice exam, most answers are in reduced form so it’s just an extra step that they have to complete if they don’t see their answer on a multiple choice test.
When I teach my students how to use the larger multiple of the two denominators, I use a mnemonic about the fractions being siblings. I tell them that little siblings always want to copy their older siblings. They want to play with the same toy the older sibling is playing with or they want to be just like them. So they must make the small sibling (or number) into the larger one so they can be the same. You can get the free PDF of this mnemonic with images and an explanation by entering your email address above.
Hold off on teaching the least common multiple
So do I teach all my students how to use the larger multiple or least common multiple (LCM)? Nope! Not initially. I only do it for my most advanced students weeks later when I see that they have a solid understanding of creating common denominators. For the others, I don’t think it is necessary. It’s just one more method your students will have to remember. Also, if you teach this shortcut too soon, you will confuse your students. You don’t want to cause math anxiety which impedes the ability to problem solve. I think it’s easier to just teach them that they need to simplify fractions once they have their solution. They have to do this anyway with other problems as well.
Toward the end of the year before SBAC testing, I will teach the LCM method to my striving students if they are ready for it. Also, when I say striving students, I am talking about my students who are about two grade levels behind in math. These are my kiddos who still don’t know their multiplication very well or do not have a strong background in number sense. I want them to have some success with fractions, so I try to make the steps to solving problems simple. Also, I find that teaching the different methods to find the common denominator should be taught over time. If you teach it all at once, you will be sure to confuse your students. Take your time and only teach the different methods to students who are at grade level in math. As teachers we feel like we are not doing enough or cheating our students if we don’t teach all the methods in math. But I am here to tell you that you cheat your students when you make math confusing. Keep it simple! Multiplying the denominators is a method that always works
How to teach Adding and Subtracting Mixed Numbers with Unlike Fractions
Adding and subtracting mixed numbers with unlike fractions is difficult for most students. There are two different ways to do it. First you can change the fractions into like fractions using a common denominator and then change the fraction into an improper fraction. I only recommend this method for your advanced students.
Another method is to decompose or ungroup the fraction. For those who struggle in math, it is best to teach them to regroup the fraction because they can draw the fractions out. This is the method I prefer to teach my students. I will pull my more advanced students and show them both ways, but in my experience, teaching your kids who struggle with math both methods confuses them. So again keep it simple!
I hope I’ve given you some insight on the best way to teach adding and subtracting fractions for true understanding. If you need a resource that shows you how to break down lessons in a sequential order that provides visual models, you can purchase the lesson in my Teachers Pay Teachers store. It covers the following topics:
Improper Fractions with visual models that students color in to determine the mixed number
Decomposing or ungrouping improper fractions
Adding mixed like numbers and changing them if they are a mixed number with an improper fraction (for example changing 3 and 5/4 to 4 and 1/4)
Ungrouping a mixed number (for example changing 4 and 1/4 to 3 and 5/4).
Subtract Mixed Like Fractions with regrouping
Understanding why you need a common denominator
Mnemonic device so students can remember how to find a common denominator
Add and subtract unlike fractions
Choose how to find a common denominator: multiply denominators or use the greater multiple
Subtract fractions from whole number by renaming
Subtract fractions from unlike mixed numbers by decomposing the whole number or by changing the fraction into an improper fraction
All worksheets have the visuals that you need, plus it goes in a sequential order so your lesson plan is already done. It makes teaching Adding and Subtracting Fractions incredibly easy. You got this! Giselle
