What Makes a Math Task Truly Low Floor, High Ceiling
Designing Math Tasks That Put Thinking First
In my last post, I discussed the importance of not lowering the ceiling for students — especially students with learning differences — by designing math tasks that are truly rigorous. One of the ways I like to do this is through Low Floor, High Ceiling (LFHC) tasks— tasks that are accessible to all students but do not cap the level of thinking or reasoning. They are purposefully designed for student engagement at different levels and building understanding through discourse.
Before I share a few of my favorite LFHC tasks, I want to clarify what I mean by rigor. Rigor is not harder numbers or more problems. Rigor means thinking and reasoning with and about the math. Students are asked to explain, justify, compare, and discuss their ideas — not just solve and find an answer. Here are the three must-haves for any LFHC task I design or use.
My Non-Negotiables for LFHC Tasks
1. The Math Is More Important Than the Answer
The goal of a LFHC task isn’t to get the answer — it’s to understand the math. When students focus on how and why something works, rather than what the answer is, they are building and developing their mathematical understanding.
2. The Question Is Open-Ended (Sometimes There Is No Right Answer)
LFHC tasks are intentionally open. Some have multiple correct answers. Some have none at all. This eliminates the fear of being wrong and creates a safe space for students to take risks, share ideas, and engage in meaningful discourse.
3. The Task Is Truly Rigorous
Rigor means students are thinking, reasoning, and making sense of the math. LFHC tasks must include opportunities for discussion and conversation — not just quiet work. If students are able to complete the task without talking about the math, the rigor isn’t high enough, or might not be present at all.
My Go-To LFHC Tasks
Which One Doesn’t Belong?
I love this task because there is no wrong answer — only reasoning. Students justify their choice using anything from basic observations to deep mathematical structure. This makes it accessible for hesitant learners while still offering a high ceiling for more advanced thinking.
Pick a Side
This task was created by accident, but it quickly became one of my favorites. Students choose a side and defend their reasoning. The explanations students give provide immediate insight into their understanding. When designed intentionally, the task can have no correct answer, which pushes discourse even further.
Numberless Problems
Numberless problems put students in control of the mathematics. They choose the numbers used to complete the task, which determines how simple or complex the problem is, while still demonstrating their understanding of the concept. This flexibility immediately opens the door for all students and allows them to access the math.
Putting LFHC Into Practice
To build truly inclusive math classes, add Low Floor, High Ceiling tasks to your toolkit. I challenge you to pick one task and try it in your classroom. The engagement and discourse will speak for themselves. You might be surprised by how far your students can rise when given the chance.