Fractions. I mean, they’re not just numbers you'd see on a pizza box or spots on a diagram, right? They’re—they’re actual numbers with specific values. Like three fourths doesn’t just mean you’re cutting a pie into pieces; it means something more. It’s a precise value, like 0.75, that sits neatly between 0 and 1 on the number line.And that’s what makes this idea so powerful. When students see that fractions are real numbers, they can start to reason with them just like they would with whole numbers. Let me give you an example. Imagine you’re teaching kids to compare fractions like three-fourths and five-eighths. Understanding that three-fourths is a value closer to 1 than five-eights makes all the difference, especially if they can see it in their minds—or on a number line.Now, the number line—honestly, this is one of my favorite tools for teaching fractions. Think about benchmarks, like 0, one-half, and 1. These are the anchor points that help students estimate and compare fractions confidently. For instance, if a student knows that one-fourth is halfway between 0 and one-half, they can start building that sense of where fractions live on the number line. And you know what? It clicks for them in this fantastic way.Here’s a quick story from my kindergarten class. We were working on visualizing fractions. So, I took out a piece of string and marked 0 on one end and 1 on the other. Then, I asked them, "Where would one-half go?" Of course, some thought the middle, others weren’t so sure. But once we folded the string in half—bam—it made so much sense. They literally saw where one-half belonged, and that helped them understand what fractions represent on a number line.And what’s amazing is seeing how this understanding grows. Students not only start to estimate sizes of fractions, but they also see how they relate to these benchmarks—whether they’re closer to 0, closer to 1, or somewhere in between.So, let’s talk about where it all really begins—unit fractions. A unit fraction, like one-fourth or one-eighth, is just one equal piece when the whole is divided into, well, a certain number of parts. It’s like, kinda like the building block for all other fractions, you know? Every fraction we work with—Three-Fourths or Seven-Eighths—is just a bunch of those unit fractions piled together.But, here’s the thing, it’s not always easy to grasp that right away, especially for younger students. That’s where visual models come in. These are literally game changers. Models like shaded regions, sets of objects, or number lines give students something concrete to latch on to before diving into abstract numbers. Let me explain.Take the number line, for example. Instead of just looking at fractions on a worksheet, students can see how fractions are spaced out as actual numbers in the number system. They can see why one-fourths is smaller than one-half because it's closer to zero. And then, if you add another one-fourth, suddenly you've got your two-fourths sitting exactly at one-half. It’s—it’s like a puzzle that starts making sense.Here’s a story for you. There was this lesson I did where we used a number line to talk about equivalence. I asked the kids to place one-half and two-fourths on the number line and then asked, "Look at where they land—what do you notice?" And their faces lit up when they realized, wait, these are the same! It wasn’t just memorizing rules anymore. They saw it right there on the line, and it stuck.And that’s the goal—to help students see fractions as not just some abstract concept or procedure, but actual numbers they can understand and manipulate.Alright, so let’s dive into instructional strategies for fractions. I mean, teaching fractions—well, it’s not just about getting students to memorize steps or formulas, you know? It’s about helping them build a deep understanding. And honestly, that starts with something as basic as language—precise, intentional vocabulary.Think about it. Words like "numerator" and "denominator"—they might seem obvious to us, but for a lot of kids, they’re just, you know, abstract terms until we really break them down. Like, I’ll say to my students, "The numerator tells us how many parts we have, and the denominator tells us the size of each piece," and I’ll repeat that over and over until, like, it clicks.And here’s a tip: avoid phrases like "the bigger number." I mean, that can confuse a student into thinking, say, one-eighth is bigger than one-third just because 8 is larger than 3. Instead, I’ll use specific language, like, "A larger denominator means the parts get smaller." It seems simple, but trust me, it helps clear up so much confusion.Now let’s talk about multiple representations—oh, these are so critical. A big part of teaching fractions is helping students see the same fraction in different ways. Like, maybe they’ve worked with area models to see fractions as shaded regions. That’s great, but what about number lines? What about sets of objects? Switching between these can really strengthen their understanding.Here’s something I’ve done that worked like magic. I had students fold paper strips to create their own number lines—literally folding the strips into halves, then quarters, then eighths. By the time each strip was sectioned off, they weren’t just seeing fractions—they were making them, understanding them. And guess what? They started connecting the dots between those paper strips and the other models we’d used. It was, honestly, so powerful to watch.But let’s not forget about those, well, misconceptions. Fractions are tricky, and students fall into predictable traps. Take adding fractions—they’ll think one-third plus one-fourth equals two-seventh. I’ve seen it happen over and over. And instead of just correcting them, I’ll ask, "Why do you think this is the answer? Let’s test that thinking." It’s like, by letting them grapple with the concept, they start seeing why their answer doesn’t quite make sense. That moment of struggle, of realization—it’s where the learning happens.You know, I once attended this incredible workshop on differentiating instruction, and one thing really stuck with me. The facilitator said, "Fractions aren’t just math; they’re about relationships." That hit home for me. Fractions don’t live in isolation—they connect to everything else, whether it’s decimals, percentages, or even algebra. And as teachers, it’s our job to show students how those connections work.So, as we wrap up today, let’s remember this: fractions aren’t just a box to check in the curriculum. They’re a journey—a process of discovery for our students, one step at a time. By focusing on vocabulary, using multiple representations, and addressing misconceptions head-on, we can make this journey not just effective but meaningful.And that’s all for today! Thanks for joining me as we unravelled some big ideas about fractions. Until next time, keep teaching, keep learning, and, well, keep making math magical!

Episodes

Fraction Fundamentals