I’m going to be honest, the first time I saw some of the “new methods” for adding, subtracting, multiplying, and dividing fractions I was utterly confused. I kept thinking to myself, you have to do what? What happened to simply keeping the first fraction the same, change the division symbol to multiplication, flip the second fraction, and then multiply straight across? Isn’t it easier that way? Well, then my teacher brain started thinking...but why in the world did we do all of that? I honestly had no idea until I began preparing to teach the concept to my own students.
At first, I was at a complete loss for how I was going to have my fifth graders grasp these new methods for solving.Then, I went searching for resources and I was even more disappointed by the lack of options to help guide students in understanding why we need to find a common denominator before adding fractions with unlike denominators or visually what it means to multiply 1/2 x 1/4. I didn’t want activities that simply allowed students to multiply the numerators together then multiply the denominators together. I wanted my students to truly understand the mathematical concept and not simply know the procedural steps for solving. I wanted visuals! I wanted word problems that connected operations with fractions to real world situations! I wanted my students to know more than just the steps!
I knew I needed to create resources that would provide students with the visual support necessary to understand how, for example, if I am combining 1/3 + 1/2 , I can’t simply add those together because I am not comparing parts of equal size. The resources I created can be used in small guided math groups, as homework, center activities, exit cards, or independent practice. I found that for my struggling students, I would sometimes take a page and combine it with manipulatives such as fraction bars so students could have additional tangible and visual support. For my on grade level students many of the visual supports on the resources created were enough to stand on their own.
After using these visual resources, my students understood how when combining or subtracting parts of a whole you must have parts that are of equal size. Operations with fractions took time, but I was happy that my students walked away understanding this big concept.