Low Floor High Ceiling Tasks FTW

Everyone that knows me on social media understands that I’m very passionate about the Open Up Resources 6-8 Math curriculum authored by Illustrative Mathematics. Because it’s awesome extraordinary and curriculum matters!

Today didn’t disappoint.

Low Floor High Ceiling tasks are those that allow all students to dive into the math. The tasks set the stage for achieving learning goals. They provide an entry point that can be accessed by all learners. And the open-endedness allows for extension, too!

I presented this Warm Up task to my Grade 7 students today. It can be downloaded for *free* here.


I read aloud the first prompt. After quiet think time, we talked about what we noticed and wondered about the tape diagrams. Students noticed that…

  • all of the values are variables
  • the top diagram is longer than the second one
  • y is larger than x
  • the top diagram has 4 equal groups… but wait! so does the second diagram!
  • c is the total of all 4 groups of (a+b), and z is the total of x+x+x+x+y

And then I revealed them the second prompt: What are some possible values for a, b, and c in the first diagram? For xy, and z in the second diagram? How did you decide on those values?

I had a few students volunteer to share their solutions, noticeably less students than the Notice and Wonder part of the task. For a couple of solutions, we checked as a class to ensure their values were correct. One student offered that a=4, b=1, so c=20. Great! Another said that if a=1 and b=2, then c=12. Excellent. They all had an entry point into the task!

One student blew my mind with his unexpected thinking. Not many of his peers followed his logic, but he told me… a=c/4–b. What? Then I asked, what b would equal. b=c/4–a. Nice! He concluded that 4(a+b)=c. The distributive property! Our class had just spent time discovering the concept with Grade 6 materials, and he absolutely nailed it! Even if others in the class didn’t completely understand this logic, they could connect with the distributive property work we’d be practicing. I was careful to point this out and talk about how it matched the diagram. Making explicit connections between ideas for your students is so important!

When talking about xy, and z, I had a few more volunteers. There were lots of suggestions for different values, and I appreciated the debate when one student offered that x=1, y=4, and z=8. Another student noticed that y doesn’t look like it’s four times the size of x. How interesting! We collaborated and revised the work, deciding that if x=1, y could be about 2, so z=6.

By taking the time for Low Floor High Ceiling tasks in Math class, most students will find success! When used purposefully and intentionally, they set the stage for the goals of the lesson. Questioning, noticing, and wondering are all healthy behaviors in math class. And your students will have a chance to access the math and soar beyond expectations when given the opportunity! I’m so proud of these mathematicians!


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