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Building Fraction Number Sense

fraction number sense

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

Our 5th graders take their state assessment next week (gulp!), and fractions are considered “readiness” standards for 5th graders in Texas. With our new assessment, that means they’ll be more heavily tested. Fractions are traditionally a concept that 5th graders really struggle with. 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.

Here’s my approach. 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. Period. 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 without all kinds of complicated methods). Let’s look at how this conversation sounds:

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 grab a PNG file with the fraction number line that you can insert into documents and here for a number line and fraction tiles.

3 Comments

  1. Anonymous

    Should not the 2/3 and the 4/12 be the other way around on the number line? 🙂

    Reply
    • Donna Boucher

      Well, yes they should! Thanks for pointing that out, and it’s fixed now. 🙂

      Reply
  2. Anonymous

    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

    Reply

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