Oh the dreaded F word! In math, I’m not sure if there is another F word that scares people more than “FRACTIONS.” But for real, fractions don’t have to be scary. There is a ton we can do to make understanding fractions easier. Read on to learn more!
Tip 1: One thing we can do is focus more on the LANGUAGE of fractions. I see many many many students who can count shaded and unshaded parts but have no idea whatsoever what a unit fraction is. (A unit fraction is one piece of the whole.) These kids can write fractions from a model but when you ask them to name it with words, they will name 3/4 as “3 out of 4.” On the surface, this may not seem to be a big issue. But I have often found that kids who do not use the correct vocabulary (like three fourths) also have no conceptual knowledge of what a fraction actually is. They don’t know that a fourth is one part out of 4 equal parts that make a whole. These students often do not realize that 3/4 is a number rather than two numbers stacked on top of each other. They also do not realize that 1/4+1/4+1/4 is the same as 3/4! I mean, I didn’t understand this until I was an adult teaching elementary school and I’m a smart person…I had two college degrees before I knew this. That’s scary! But we can do better.
Tip 2: Another thing we can do to support our kids in developing number sense with fractions is focus more on the PART/WHOLE relationship. When you say the word “fourth” or “third” or “eighths,” what image comes to mind in your head? Do you see those sized parts? Because many kids DO NOT. They need LOTS of experiences modeling, naming, and working with fractions to be able to really conceptualize them. Another thing we often forget to do is to DEFINE THE WHOLE as well as CHANGE THE SIZE OF THE WHOLE as we practice modeling fractions. All fractions relate to a specific whole, so if you do not define what that whole is, you are basically asking kids to assume. Which isn’t fair. If you want half of the Reese’s, do you want half of the two pack, half of the king size pack, or half of the actual Reese cup? The full size one or the fun size one? See, all of this matters! Not only that, but students need to see that not all fourths are the same size. A fourth of a cup of water is a much different amount than a fourth of a swimming pool’s worth of water. Kids also need to be asked to model what a whole would look like given a unit fraction in addition to the practice partitioning a whole into fractional parts they are more likely getting. Cuesenaire rods and pattern blocks are a great manipulative for this. If red represents one fourth, which bar represents one whole? If the blue triangle is one half, which piece is one whole? What if the blue triangle is one sixth? What piece is the whole now? You can do it with yarn for a linear model, and don’t forget about sets! 3 of the pets at the pet store are dogs. Dogs represent one fifth of the pets at the pet store. How many pets are in the pet store? Exploring part/whole relationships with fractions will also help once that little centimeter cube in base ten blocks no longer represents “one” when students begin to explore decimals as well! Flexibility is important!
Tip 3: Also, I can’t say this enough…EQUIVALENCE, EQUIVALENCE, EQUIVALENCE is HUGE. You may be surprised when you ask students to “show me half” and then “show me another way to make half” what you see. I often see misconceptions arise when I ask students to show fractions another way. Understanding that 50/100=25/50=15/30=6/12=2/4=1/2 is not something that just automatically happens without intentionally planned opportunities for students to explore. Furthermore, if students do not have a solid understanding of fraction equivalence, they do not have the skills they need to be able to compute with fractions, or to simplify…as equivalence is the foundation of all fraction computation. Students without a deep understanding of equivalence are often overwhelmed when asked to work with both fractions and decimals interchangeably as well. There is a reason why comparing and ordering fractions and decimals almost always shows up as an area of weakness on standardized test data. And it is almost always because we could have done a better job teaching fractions. But don’t worry, there is always time to repair the damage that has been done! I have met very few teachers who intentionally mislead kids but I have met a ton of them who do not realize that they are setting their kids up to struggle down the road by not going deep enough into important concepts. Always ask, can you show that number another way?
Tip 4: Use multiple models and real context for solving fraction problems. Learners need to know that fractions are all around them and are not just shapes with certain sections shaded. The more we use real context and a variety of models, the more our students will understand and begin to see and use math in their world. I will never forget how well my students understood fractions in a linear model after I told the story of falling down an entire third of a mountain skiing (they also thought the story was hilarious), or how much they loved figuring out where we can “stop to eat” on that trip to grandma’s house! Also, when they have to fair share a bag of M&Ms with their two siblings to make thirds…they understand that fractions are so much more than shaded shapes and they begin to see fractions EVERYWHERE. This makes your job EASIER! We have got to teach deeply enough. Oversimplifying is often the enemy!
Tip 5: Fractions are not ways to write numbers less than a whole. We have got to stop saying that fractions are part of a whole or less than one whole! They can be, but they are not always. Many fractions are greater than one whole and students need lots of experience working with fractions that are less than one whole as well as fractions that are greater than one whole. This all goes back to that equivalence idea! 1 2/5 is the same as 7/5. If 1/5 is .2 then 7 fifths would be 1.4. That’s all the same number. Fractions have equal areas, but the sections are not always the same shape in an area model (think things you can cut) or even the same object in a set! (think about the Pet Store context I used above.)
Tip 6: Ok last one yall. Teach problem solving with fractions using flexible strategies. Not memorization “tricks” that undermine conceptual understanding. If you are only teaching kids one way to solve a problem, chances are, you are creating gaps in their understanding whether that is your intention or not. If I had 2 1/4 cups of sugar left in a bag, but I used 1 1/2 cups of that sugar to make Kool Aid, and I wanted to know how much sugar was left in the bag…there are numerous ways kids could go about solving this! They could subtract in chunks… 2 1/4 – 1 1/4=1 and then subtract off the last 1/4 to get 3/4. They could ungroup a whole or both wholes to work with improper fractions. So they could think of 2 1/4 as 4/4+4/4+1/4 or 9/4 and then think of the 1 1/2 as 4/4+2/4=6/4. Then 9/4-6/4 is an easy 3/4. They could add up from the part of the sugar we used to the amount we started with to figure out the difference between what was used and what we started with to figure out how much is left in the bag. 1 1/2 and ANOTHER HALF gets me to two wholes. Then I just need ONE MORE FOURTH to get to the original 2 1/4 cup of sugar. So half is 2/4 plus the second half is 1/4 so that makes 3/4 of a cup of sugar left in the bag. I mean we could even shift fractions up or down a number line to make an easier equivalent problem. For 2 1/4- 1 1/2 I could add half to both (the difference would be the same) and then I have 2 3/4-2 and that’s an easy 3/4.
If any of this sounds overwhelming or confusing to you, don’t freak out…REACH OUT! Trust me, I have hated hated hated what I thought was math for so long, and now I love it and it’s my passion. It wasn’t too late for me, and it’s not too late for you. Give us a shout if you are ready to MAKE FRACTIONS FUN! It CAN BE DONE! SumOneCares.com can help!