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://tasks.illustrativemathematics.org/content-standards/3/NF/A/1/tasks/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:
And this Illustrative task: https://tasks.illustrativemathematics.org/content-standards/2/G/A/3/tasks/827 It is a 2nd grade CCSS so I gave it to beginning of the year third graders this year.
This task (https://tasks.illustrativemathematics.org/content-standards/6/NS/A/1/tasks/50)is a 6th grade CCSS, these are my students from last year who are now in 6th grade:
This task is 4th grade CCSS: https://tasks.illustrativemathematics.org/content-standards/4/NF/C/5/tasks/154, this is my current 5th graders:
Same group of students on this task: https://tasks.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/855
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…
Have fun math peeps! I would love to chat in the comments or on Twitter about any/all of them!
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
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!