Conversations to Build Fraction Number Sense

Fractions are one of those concepts that many students struggle with, no matter the grade level—and that’s a problem, because a solid understanding of fractions is essential for success in higher math. In Texas, fractions are considered “readiness” standards, which means they’re heavily emphasized on state assessments. So why are fractions so tricky, and how can we help students truly understand them?

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First, fractions go against everything students know about numbers up to this point. Before third grade, their entire experience is with whole numbers—where bigger numbers mean greater amounts. So when they encounter fractions for the first time, it feels backwards. Eight is bigger than four, right? So how can one-eighth be smaller than one-fourth?

If kids haven’t had lots of experience with fraction manipulatives and representations, like fraction bars or strips, they’ll say one-eighth is bigger every time. Next, many kids don’t understand the symbolic representation. They just don’t really understand what the numerator and denominator mean.

While it’s important to expose students to many different representations and contexts for fraction, here’s one approach I find to be quite relatable. It’s all about “halfness” and candy bars. Talking about fractions in terms of candy bars gives the kiddos a perfect visualization of what the numerator and denominator mean. The denominator is how many pieces in my candy bar, and the numerator is how many I ate. So I have kids practice talking about fractions that way. Then we discuss how much of our candy bar we’ve eaten (this helps kids compare fractions by reasoning about the size of the fractions). Let’s look at how this conversation sounds. I also used a number line on my interactive white board to record their thinking. 

Teacher (Pointing to 2/3): Tell me about this fraction.
Student: There are 3 pieces in my candy bar, and I ate 2 of them.
Teacher: Great! How much of your candy bar did you eat? A lot or a little?
Student: A lot.
Teacher: How do you know?
Student: Because I ate 2 pieces and there’s only 1 left.
Teacher: That’s right. So what part of the number line would your fraction go on?
Student: Right in here (pointing to the space between 1/2 and 1).
Teacher: Right. How about 3/6?
Student: I ate exactly half.
Teacher: How do you know?
Student: Because I ate 3 pieces and there’s 3 pieces left.
Teacher: You’re right!! So it goes where on the number line.
Student: (Points to 1/2).
Teacher: And what about 4/12?
Student: I didn’t eat much at all. There are 12 pieces, and I only ate 4. It would go down here (points to the space between 0 and 1/2).
Teacher: Kiss your brain! So which fraction is the biggest?
Student: 2/3.
Teacher: And the smallest?
Student: 4/12.
Teacher: Perfect!

Lessons like this show the power of mathematical discourse and visual models in helping students make sense of fractions. Using benchmarks like one-half and familiar references such as candy bars allows them to reason, discuss, and truly see the relationships between fractions—building understanding that lasts well beyond the lesson.

Click here to download a file with fraction tiles and number lines.