Teaching students about fractions can be challenging at times, especially when you have unlike denominators at play. Students need to be able to understand how subtracting fractions with unlike denominators works, and it takes time to build the background skills and knowledge they need to be able to calculate these expressions. Above all, students need time to explore the concept with hands on activities that allow them to work with the fractions in a game environment, which can lower any math anxiety they might have. Here are some ideas for you based on how I teach subtracting fractions with unlike denominators in my classroom.
WHAT DO STUDENTS NEED TO KNOW BEFORE THEY ARE SUBTRACTING FRACTIONS WITH UNLIKE DENOMINATORS?
Here are some prior knowledge skills that students need to have before they can master the skill of subtraction of fractions with unlike denominators:
- Students should be able to tell you that the top numbers of a fraction is the numerator and the bottom numbers of a fraction is the denominator.
- Students should be able to work with equivalent fractions. For example, they should be able to find like fractions for 1/2.
- Students should be able to add and subtract fractions with like denominators.
- Students should be able to find common factors and multiples of numbers.
- It’s helpful if students can find the least common multiple (LCM) of a number, but they can usually get by with just understanding common denominators.
START WITH SMALL, COMMON FRACTIONS
Starting students off with fractions they already know, like 1/2 – 1/4, is a great way to ease students into this topic. Avoid using improper fractions or mixed numbers at this point because they will cause too much frustration. There are three main ways I like to help students explore this concept:
- We use our knowledge of equivalent fractions to find something equivalent to one another. In the example above, students may know that 1/2 = 2/4, so they can convert that and then subtract.
- We use manipulatives. I use money pieces to demonstrate this for students by showing them that I have a half-dollar. If I spend a quarter of it, how much do I have left?
- We use differentiated problems to find common denominators and subtract. My Leveled Problems resource is a lifesaver for me. I just print out the cards, cut them, and we’re ready to learn! This resource is great because I often have kids who get the concept right away and are ready for a challenge, and I have others who need simple problems to work with.
FINDING THE LEAST COMMON DENOMINATOR
If students are really struggling, I sometimes back up and teach finding a common multiple (or denominator) without the subtraction problem. For example, if I want students to solve 2/9 – 1/7, I’d take the 9 and 7 by themselves and just work with those. Let students find success in finding common multiples of denominators, and then use that positive feedback to move back to fractions.
Finding the simplest form of the new fractions is ideal (it keeps the multiplication and subtraction simple), but we can work around that while we practice common multiples. To help my students practice this, I use a student favorite, Solve the Room, to get them out of their seats and interacting with fractions around the room.
ADD IN A WHOLE NUMBER NEXT
Once my students are getting the hang of subtracting two fractions (both less than 1 and improper fractions), the next step I teach is what to do when one of the factors is a whole number. For example, what do I do if I have 3 – 7/8? Money will again come in handy here, because we can use the idea of $3.00 – ($0.25 x 7) to help students contextualize what they’re doing. I also remind students that all whole numbers have a denominator of 1, because money won’t always work as a manipulative.
MIXED NUMBERS ARE NEXT
Mixed numbers can be tricky for students, especially if converting them from improper fractions is still difficult. Once we convert our mixed numbers to improper fractions, we need to find the LCM of the denominators. Then, we can solve. Lots of practice and repetition in this area is necessary for students to feel successful, but sitting at desks working on worksheets is draining for many of our kids.
To help my students practice this, I use these Subtracting Fractions with Unlike Denominators Puzzles. This allows them to solve mixed fraction problems while also having fun creating the puzzles. If I can’t be with a group of kids who is in need of extra support, I write letters on the back of each puzzle piece that go together. This helps students self-check their answers as they work and get their final answer.
PRACTICE MAKES PERFECT
Once many of my students are starting to feel confident in this skill, it’s time to practice while having some fun! I have two games that help my students solve subtraction of fractions problems when they have different denominators. These have mixed number problems in them, so we are practicing all of our skills at this point.
- Students practice solving subtracting fractions with unlike denominators by subtracting the second fraction from the first fraction. Each fraction subtraction problem has students finding the correct answer, and I encourage my students to use the LCM method to do this.
- Students practice solving word problems by subtracting fractions with unlike denominators. This game also has all three different types of fractions (proper, improper, and mixed), and this game allows students to explore subtraction of fractions in the real-world context they need to truly solidify this skill.
I hope these ideas and tips have given you something to work with your students on. Subtracting fractions with unlike denominators can take some time and repetition for students to fully understand, but it’s worth it once you see your students become proud of themselves for understanding this skill.
These resources have saved me from losing my sanity in my classroom, and I know they’ll do the same for you. You can grab all of the resources by clicking the picture below.
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