# More Fraction Number Lines: More Critiquing Reasoning!

If you missed my post the other day about using number lines to improve fractional reasoning, you might want to take a peek at it before digging into this post!  Just CLICK HERE if you missed it…because I want you to know that the lesson featured today was not the FIRST time my students had worked with this number lines or critiquing reasoning. This lesson is one that should come after they have had some other experiences using number lines and having conversations about them.

### So let’s dig in!

Step one–present students with a number line task.  As I mentioned the other day, even a number line task can be simplistic and obvious.  I am partial to a more “open” number line–where partitions are not already drawn.  When you include those partitions, you’ve done so much of the thinking FOR the students!  Remember, I always ask students to THINK before they pick up their pencil so they have a starting point.

As students worked, I walked around and checked out their work and hunted for misconceptions.  I would make note of how they were organizing their work or strategies they used that I thought might be worth talking about.  In my last post, the next step involved pairing up and having discussions together and coming to consensus.  Today?  Not so much!

### Whole class sharing

My next step was to ask students to come up and place a blue dot on this “class number line” to show where they had marked in in their math journal.  I reminded them to NOT change their answer based on what they see–because they need to trust their gut!
By the time all the dots were up, it was time to have a discussion where we “critiqued the reasoning” and defended our thinking.  We had to use math language and vocabulary with our sharing–so I heard things like…
“The dots on the far left can’t be accurate because they would really be past 0 and into negative numbers.”
and
“I think [pointing to a dot] this isn’t possible because there is no way that you can keep equal parts.”
and
“It was more clear to me when I put in all the whole numbers so I could find where they 1/3 really should go.”
Some students needed some convincing–and we had frequent “turn and talks” throughout to get EVERYONE involved in discussion the ideas people shared.   It was great to see some light bulbs REALLY go off!  After our discussion, I sent the students back to their notebooks to “revise” their thinking if necessary.  SUPER powerful stuff!
This was a very nice and quick warm up for our lesson–and the process can be used not just with number lines but with ANY problem type!  Stay tuned for another post coming soon with more fraction fun!
Want to see the resource that these number line problems are from?  Lots of different problems and options…

Also available bundled with whole numbers to 1,000 and whole numbers to 1,000,000.

Want to pin this for later?  Here you go!