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Conversations to Build Fraction Number Sense

In Texas, fractions are considered “readiness” standards, which means they are more heavily tested on the state accountability test. Fractions are traditionally a concept that 5th graders really struggle with. Why is that and how can we help them understand fractions better?

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First, fractions go against what kids know about numbers. Eight is bigger than 4, right? So how come 1/8 is smaller than 1/4? If kids haven’t had lots of experience with fraction manipulatives and representations, like fraction bars or strips, they’ll say 1/8 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 powerful. 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!

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

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5 Comments

  1. how are we able to compare fractions by cross multiplying? this is a question that one of our teachers gave my child for homework to ask me and I have no idea of this and the butterflying thing. Please help asap if you are on now. thanks

  2. I LOVE your materials and articles, however, I’m having a difficult time downloading anything due to my district blocking Dropbox. We have transitioned to only Google. Is there anyway you can have them accessible without using Dropbox? Thank you

    1. Many of my older files are on Google, but I’ve been using DropBox for several years now, and those files are only available on DropBox. Maybe you could access them from home instead of at school? Once you have downloaded the PDF at home, email it to yourself at school so you can print it there. Hope that helps!

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