It’s that moment you’ve been worried about. The time to teach your students to teach adding and subtracting fractions with unlike denominators has come. There are SO many components and skills that really work into needing to complete this task! What’s a teacher to do???

Do you teach them a “trick” like the butterfly method, or cross multiplying? Do you spend days teaching students to find the least common multiple and then how to multiply the numerator and denominator by the same number so they have equivalent fractions that now have common denominators? NO!!! STOP DOING THAT NOW!

Don’t get me wrong, those are exactly the strategies I used to employ when it was time to teach students about dealing with unlike denominators. And, my students who were quick math learners got it. Even a few of the middle of the road kids got the hang of it after a while. But, like with many other topics, my struggling and special education students were LOST. I just chalked it up to the way things had to be. The reason some students were lost is because all of those “tips” and “tricks” have no concrete foundational reading for our young learners. They might be able to learn the rules they are following, but the have no idea WHY they are following those rules. In order for students to truly be able to understand this topic, they NEED to be able to see the why behind the math!

After experimenting from one year to the next, I finally found a way to teach this that ALL students found accessible, and even…fun!

Allow me to walk you through the steps.

Let’s say you are trying to add 1/2 + 1/3.

Step 1: Draw two equal-sized rectangles.

Step 2: Label the rectangle on the left 1/2, draw a vertical line down the middle, and shade 1 of the 2 pieces.

Step 3: Label the rectangle on the right 1/3, draw two lines across horizontally, and shade 1 of the 3 pieces.

So far, this is super easy, and all kids should be able to follow along really well.

Step 4: Take the vertical line from the 1/2 rectangle, and super-impose it over the model of the thirds. Then take the horizontal lines from the 1/3 rectangle and super impose them over the model of 1/2. (this step can take kids a few tries to get the hang of, but they will, and then it will be AMAZING!)

Step 5: Re-label the fractions with their new, equivalent numbers. (1/2 = 3/6; 1/3 = 2/6)

Step 6: Draw a new rectangle below your first two where you will put in all of the new same-sized pieces. Make sure to draw as many parts as the denominators of the fractions above.

Step 7: Shade the pieces from the above fractions into the new rectangle and evaluate the sum of the two fractions.

Here is an anchor chart I put up in my classroom to teach and reinforce this:

When subtracting fractions, Steps 2-5 from above are identical. After you have created your fraction models with equivalent fractions, things are a little different. After all, you ARE subtracting!

Starting with Step 6: Count how many pieces are in the model on the right. Cross out that many pieces in the model on the left.

Step 7: To find the difference, count the number of pieces that have not been crossed out.

Here is the anchor chart I used this year to reinforce subtracting fractions:

After about two days of using this in class, almost every student had had that “ah-ha” moment. They started to ask if they could try doing it without the models. I had them keep using the models for another day for finding the common denominator, but allowed them to skip modeling the answer, and just jump into writing out the addition or subtraction sentence using the new, equivalent fractions. After another day and more begging, I allowed the students to SHOW ME how to find equivalent fractions without the models. It was awesome! Even better, many of them began to realize that they could be using different equivalent fractions because they could see that they could find a smaller common denominator.

At that point, it’s pretty smooth sailing. I spend at least a week and sometimes more on this topic. The last few days can be spent helping those few students who are still struggling to get the hang of it, or understand the models but aren’t ready to move away from them into just using the algorithm. Other students can be challenged with more difficult denominators, or by having them add more than 3 fractions together at the same time.

Coming up with enough math problems to use can be tricky, so here is a paid product I like to use in class to keep students engaged.

How do you know to use 12ths? For example the first problem. I know it’s 12ths but how or what do you tell the learners? I am trying to use this with my special ed caseload.

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Ok, so since you are adding thirds to fourths…the children make thirds vertically (like stripes) and the fourths horizontally (also like stripes). When the two overlap, they make 12ths. If you can get your hands on some transparencies, you could even have them make thirds on a square and fourths on a square and then slide one over the other so they see how they overlap to make 12ths. I hope this helps! Please let me know if you have any other questions I could assist with!

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