City Lots fractions task keeps ALL students thinking

Here’s a 7th grade fractions task called City Lots. My colleagues designed it with two great extensions. I differentiated it by creating resource cards plus I modified the directions to challenge students who need it.

The basic task requires students to determine which of four companies owns the most land. They also have to calculate how much land each company owns based on four quadrants.

The activity was a hit with my 6th grade advanced math students. Most groups began with a strategy of cutting out the shapes to find which company owned the most land. While that was an effective strategy, it’s a difficult way to calculate exactly how much land was owned by each company. That’s where the resource cards came in.

Then the mathematical conversations shifted from cutting shapes to discussing how the property was divided. I asked probing questions such as, “What’s the minimum number of squares do you see?” Many didn’t see one unit divided into four quadrants.

We’re trying to do much more reading and writing in math class, and this task is another opportunity for students to articulate their mathematical thinking in writing.

In terms of time, I presented the task midway into the block. In those 40 minutes, no groups got to the extensions, four groups successfully completed questions 1 and 2 and the others are not far behind. We’ll get to the extensions the next time I see them. I did not hand out the challenge task but at least I was prepared.

I don’t think I’ll have an opportunity to try the challenge task, but if you do I would love to hear how it goes.

Thanks for sharing this resource! I’m going to try it on Thursday with my advanced 6th graders.

I’ve done similar tasks with my students — ones where a larger square is divided into smaller squares, rectangles, and triangles — but I like that this task requires addition of fractions as well as just the identification of the various fractional parts. And the extensions are great! I hope to get to the them and will let you know how it goes if I do!

Yes, please do let me know! There was an incredible amount of mathematical thinking with my students. We continued the task the next class period and two groups presented their strategies to the class. One group was misguided and was corrected by a classmate. I also appreciate the students’ taking risks by sharing their thinking to the rest of the class. They sooo want to be right, but we learn so much more from our mistakes!

Ah dang, I found this page too late into my unit to set aside a whole day for it, but the picture was great to talk about! It was a nice context to start thinking about fraction multiplication since the kids can see what “1/8 of 1/4” looks like etc. and then make sense of why that’s the same as 1/8 x 1/4. Thanks!!

Thanks for sharing this resource! I’m going to try it on Thursday with my advanced 6th graders.

I’ve done similar tasks with my students — ones where a larger square is divided into smaller squares, rectangles, and triangles — but I like that this task requires addition of fractions as well as just the identification of the various fractional parts. And the extensions are great! I hope to get to the them and will let you know how it goes if I do!

Yes, please do let me know! There was an incredible amount of mathematical thinking with my students. We continued the task the next class period and two groups presented their strategies to the class. One group was misguided and was corrected by a classmate. I also appreciate the students’ taking risks by sharing their thinking to the rest of the class. They sooo want to be right, but we learn so much more from our mistakes!

I have been holding onto this activity since you first posted it. I am hoping to try after our break. Thanks for sharing!

Ah dang, I found this page too late into my unit to set aside a whole day for it, but the picture was great to talk about! It was a nice context to start thinking about fraction multiplication since the kids can see what “1/8 of 1/4” looks like etc. and then make sense of why that’s the same as 1/8 x 1/4. Thanks!!