Basic Fractions on a Number Line (Divisible by Two)

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Objective

SWBAT locate and represent halves, fourths and eighths on a number line in amounts up to but not exceeding one whole.

Big Idea

Students create number lines to represent benchmark fractions.

Direct Instruction

5 minutes

I run through the idea of fractions as represented on a number line between 0 and 1.  I keep it as basic as possible and other than pausing to let them answer (they can just speak - no need to raise hands) at certain points, I ask them to listen for just a few minutes.  They know we will practice together.

I talk through creating a number line that shows 1/2 and 2/2, a number line that shows 1/4 -4/4 and a number line that shows 1/8-8/8.

 

Guided Practice

25 minutes

The advantage to using this student page with a number line already present is that students don't get caught up making straight lines, or worrying about whether or not the intervals are even.

I have my students do this activity on blank paper and I ask them the questions orally.

They are going to make the observation that 2/4 and 4/8 are equal to one half and the color coding also helps them see some of the relationships between halves, fourths, and eights.  When they make these observations, at this stage, I repeat it back to them as an acknowledgement but don't add on yet.  This is an abstract concept and when I'm working with the whole group like this, too many side conversations and extensions with something this difficult (for some of them it is) frustrates them.  I will differentiate in the independent practice. There is still a time and place to be straightforward, and this is one of those times.

Differentiated Independent Practice

25 minutes

I ask students to choose if they'd like to review what we just did further independently or if they'd like to try some new fractions.  

I walk around and talk to the students to clear up misconceptions and help them with typical mistakes, such as trying to divide the number line into a certain number of intervals without using the strategy of dividing by halves.  I strongly suggest dividing by halves.  Otherwise it's a constant struggle for them to draw out the correct number of lines and to make them somewhat evenly spaced. For this exercise, I also want them to label the number line with a zero and a one prior to starting to subdivide into unit fractions.

I project Fractions on Number Line - Basics - Differentiated Independent Practice on the board and they draw the number lines in their journals.  I let students with handwriting struggles work these out on the whiteboard first, or sometimes just on the whiteboard.  I don't want the actual drawing of the number line to interfere with their thinking about the concept of fractions.