Student Work with Fractions

I do not have much time to write this morning, however I know how much I love looking at student work, so I thought I would give some of my friends who love doing the same some stuff to look at this morning!

For a future PD I am doing on fraction progression, I wanted some thinking around this Illustrative Math problem: https://www.illustrativemathematics.org/illustrations/833 This is a 3rd grade CCSS, so I had some beginning of the year 4th graders this task to try out. Here are some samples:

IMG_6521 IMG_6522 IMG_6523 IMG_6552 IMG_6553 IMG_6554 IMG_6555 IMG_6556 IMG_6557

And this Illustrative task: https://www.illustrativemathematics.org/illustrations/827 It is a 2nd grade CCSS so I gave it to beginning of the year third graders this year.

IMG_6558 IMG_6559 IMG_6560 IMG_6561 IMG_6562 IMG_6563 IMG_6564

This task (https://www.illustrativemathematics.org/illustrations/50)is a 6th grade CCSS, these are my students from last year who are now in 6th grade:

IMG_6565 IMG_6566 IMG_6567 IMG_6568

This task is 4th grade CCSS: https://www.illustrativemathematics.org/illustrations/154, this is my current 5th graders:

IMG_6476 IMG_6478 IMG_6484

Same group of students on this task: https://www.illustrativemathematics.org/illustrations/855

IMG_6475 IMG_6479 IMG_6483 IMG_6492 IMG_6498IMG_6569 IMG_6570

And then finally, in my class we were comparing fractions. I asked them which was greater 7/8 or 5/6 and how they knew…

IMG_0482 IMG_0479 IMG_0485 IMG_0483 IMG_0481 IMG_0484

Have fun math peeps! I would love to chat in the comments or on Twitter about any/all of them!

-Kristin

One thought on “Student Work with Fractions

  1. Max Ray (@maxmathforum)

    Holy moly so much math!

    The first task caught my eye — it was interesting to me that none of the students interpreted the task they way I eventually did. I ended up thinking of “what could be ‘one whole’ so that each student’s answer would be right?” I wonder how the task was “supposed” to be interpreted.

    Comparing the different students’ reactions and having them discuss could be really fruitful. I thought it was most obvious how both 2 and 2/6 could be right, and it would be interesting to have the students who thought 2 was justifiable debate with those students who thought 2 was unjustifiable.

    The middle option, with 2/3, seemed trickiest… students suggesting that 2 groups of 3 could yield 2/3 seemed like their definition of what a fraction was wasn’t robust enough to deal with this SUPER WEIRD situation. My favorite answer was the rather obvious: it’s 2/3 because 2/3 of the squares are shaded white! Nice one! And those who crossed out the other 3 squares were on to something similar to my thinking… but could they come up with a method that accounted for the extra three squares, dismissing them as “an extra whole that didn’t need to be shown.”

    I wonder if students would feel like
    xxoooo oooooo
    also represents 2/6 or if it can only represent 2/12?

    I wonder how the students would have reacted if the instructions were, Circle one whole unit so that each child’s answer is right. Is that too much giving away? Or does that make the conversation more productive so that everyone is on task?

    I wonder if students were encouraged to come up with a story for the situation, if that could force the units issue as well? Like the first story could be a candy bar that had 6 pieces and Emily got 2 of them. The second story could be 2 blocks next to each other and Raj has painted 2/3 of a block. The third story could be Alejandra bought a half-dozen eggs and 2 of them were broken.

    Cool tasks and thinking to reflect on! Thanks for sharing!

    Like

    Reply

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s