I came across this problem a few years ago and love using it as a Warm Up. Hoo boy, does it elicit major misconceptions my middle school kids have about fractions. (I can’t figure out where this image came from, but I’d like to give proper attribution, so please let me know if you recognize it!)
My 7th graders really struggled with it at first. I told them the dark blue rectangle was one whole and they just couldn’t wrap their head around it. Thinking of the lime green as a whole was more accessible so we ran with that. I love that it is open-ended and kids can take it to different depths.
It’s the only one I’ve found like it, so I’ve been itching to create my own. I came up with these:
I also created some more traditional fraction talk images, inspired by Nat Banting’s site, fractiontalks.com. He has great tips for implementing and extending fraction talks.
I’ve put them all into a google slideshow for easy use. After getting some feedback, I modified them to improve their accessibility for folks with colorblindness.