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Welcome to the next part of our series Fractions to the Core
So you've decided to implement a cognitively demanding task
to teach comparing fractions in your classroom
You've spent some time anticipating critical aspects of the lesson
but now it's time to implement it.
You're probably wondering what should I do as students work on this task?
This is where monitoring comes in.
Monitoring is more art than science,
so let's begin by talking about what monitoring isn't.
Monitoring is not about giving students the correct answer.
It's not about telling them the correct solution or
providing a set of procedures that can be memorized.
If you do these you aren't likely to see your students extend their mathematical thinking.
Then what is monitoring about?
It's about pushing student thinking, no matter where it is
and finding ways to challenge them to move forward.
But you can't push until you know what they're thinking.
So, monitoring is really about asking students questions,
listening closely to the answers,
and finding ways to challenge students to extend their thinking.
Imagine you have a student who can't even begin this problem.
Use the questions you anticipated earlier in this video series to monitor.
Ask them to try and easier step first like: Can you place one-half for now?
Even if their thinking is not what you expected,
prove their thinking by asking them to show what they're thinking with fraction bars.
Extend or press them to continue using fraction bars with the other fraction cards
like one fourth.
What about students are doing well with the activity,
but may have placed a few fractions on the number line incorrectly?
You could let them continue with their misconceptions
and see if they can correct them on their own,
or another choice would be ask them to compare with another group or student
and discuss any differences in fraction placement.
That group put two thirds to the right of three fourths and you guys didn't,
can you use fraction bars to figure out who's right?
Other students may need something more challenging.
You can ever variety of questions ready for those students,
Can you make five new fractions that would stump your friend, like 7/2?
Or, Explain your method to someone else.
You could ask them to use a different representation, like a circle or set model.
You could even ask them to a place a faction from this task on a different number line.
One that goes from say, 1/4 to two.
These challenges will help you to see how advance their thinking is
about the placement of fractions.
Again monitoring is an art. There's no correct question to ask.
No matter what the case, if you listen ask, and use questions to extend their thinking,
you're likely to see your students concepts developed more fully over time.
To learn more about the questions you'll use in this task
be sure to view the video in this series about Anticipating.
Also, be sure to watch the next video in a series: Connecting.
Connecting will explain how the information you gather during monitoring
can help you use student work emphasize the key concepts in this CDT.