A couple of days ago, I blogged about equivalent fractions, and I promised a follow-up post about fractions on the number line.
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We’ve been using lots of different representations for fractions, including pattern blocks, Cuisenaire rods, and fraction tiles to explore fractions. To introduce fractions on a number line, I wanted to use a familiar manipulative, Cuisenaire rods, to help the students make a connection between fractions as parts of a whole and fractions on a number line. I wanted to introduce an element of problem-solving, so I didn’t want to directly teach the concept. Instead, I wanted to see if the students could use what they already knew about fractions to develop their own understanding of fractions on a number line.
Students were given the reproducible shown below and a set of rods to work with. First, I asked them to talk with another mathematician about the first number line and to make some observations.
Some students noticed that the number line showed 0, 1, and 2, but that A was between 0 and 1. Still others noted that the A was in the middle between 0 and 1. One student even commented that the A split the space between 0 and 1 into equal parts [smile!]. I referred the class to the number line on the wall and explained that the number line we were looking at was just a small part of the big number line–just the space between 0 and 2. I then gave them a few minutes to work with a partner, using the Cuisenaire rods, to see if they could identify the number represented by the letter A. It was really fun to see them work and hear the great math conversations! It actually wasn’t too long before a couple of partnerships came up with one half. That’s all you need!! I selected one pair of students to come up to the interactive whiteboard and use the Notebook file, which has the same number lines as the reproducible, and the infinite clone Cuisenaire rods to show how they arrived at their solution. I love it when the kids can teach a lesson instead of me.
We went through the same process with each of the other number lines. First students worked in pairs to try to solve the problem and then a pair of students were asked to present. The kids definitely had a much more difficult time with the second number line than the first, but that’s called problem-solving, right?
This is a screenshot of the Notebook file and how we showed our work for the second number line.
Do your students need more practice? Check out my Fractions on a Number Line Scoot game.