Fractions on a Number Line - Beyond One Whole

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Objective

SWBAT continue a fraction pattern beyond one whole on a number line and identify the fraction picture that correlates to the number line location.

Big Idea

When the numerator has a greater value than the denominator, the fraction represents a number with a value greater than one whole.

Lesson Updated on February 7, 2015 (Complete Lesson Printout Available Here)

1 minutes

This lesson has been revised and new printable resources have been added.

I am providing this Fractions Beyond One Whole- Teacher Document for those of you who prefer to read off paper rather than reading through each section online.

Opener

8 minutes

I write this on the board:

"Show the following fractions on either a number line or with a shape model:

4/2, 5/4, and 4/3."

A few students had experience with this in previous lessons but most of them have not.  Many students assume that when the numerator and denominator are the same and you have one whole, you're done!  It's the end of the fraction road!

This brief activity informs me about erroneous assumptions and students’ ability to think flexibly.  It also lets me see which children look forward to a reasonable challenge and which students get nervous.  I'm continually trying to teach them that struggle is part of learning. It is completely important and acceptable not to know the answer as long as learning is happening.  Students have great difficulty understanding this as we are just now switching over from a learning environment that focuses on “the right answer” and it’s important to help them make this cognitive shift. 

Here are some examples of what I observed when I gave the pre-assessment:

Guided Instruction

20 minutes

I lead students through a series of examples which demonstrate benchmark fractions (halves, fourths, thirds) that have a value greater than one whole.  I try to talk as little as possible and to instead ask them questions to guide their thinking and prompt conversation.  It is so much more meaningful if they figure this out on their own, rather than if I just demonstrate and tell.

 

This is what I teach:

I repeat this procedure for thirds and, time permitting, tenths.  I love tenths!

Active Engagement

30 minutes

This activity, Fractions Beyond One Whole Independent Practice Page, becomes progressively more difficult.  While students practice the basic skill of identifying and labeling fractions on a number line, including those greater than one whole, I circulate and confer with them.  I also encourage them to work collaboratively with a partner so that they can discuss strategies, reasons, and vocabulary terms.

Some questions I might ask students as they work on this activity are:

  • How many pieces total does it take to make one whole?  Which part of the fraction gives this information?
  • How many pieces are represented by this point on the number line?  How do you know? 
  • What does it mean when the numerator and the denominator are the same?
  • What does it mean when the numerator is smaller than the denominator?  Can you show me an example of a fraction like this on the number line you’re examining right now?  Explain that fraction to me/to your partner.
  • What does it mean when the numerator is larger than the denominator?

These are, of course, just examples of the many types of questions that can be used to re-teach on the spot.  The goal of this activity page is to facilitate conversations that develop students’ ability to apply accurate vocabulary, explain their thinking, and critique the reasoning of others.

Exit Ticket

6 minutes

I have students share their response to the prompt with a partner or write it in their math journal.

How would you explain what you understand about the fraction 3/2 to someone at home?