Finding the right balance between challenge and accessibility in math education can be a daunting task. This is where low floor, high ceiling math tasks come into play. I design tasks like this to be accessible to all students (low floor) while providing opportunities for deep and extended thinking (high ceiling). Let’s explore how these tasks, combined with scaffolded learning, can enhance problem-solving skills in young learners. Incorporating these into my planning has been a passion of mine for years–and I LOVE the opportunity to help other teachers see their power as well!

Over the years, I’ve figured out that students get most engaged in a few different situations:

• When the topics are “cool” and interesting
• Get this–when they know that it’s ok to NOT get the right answer
• When they can work collaboratively
• If the math ties to something current (holiday, current topic of study)
• When there are logical stopping points along the way where they feel accomplished

Understanding Low Floor, High Ceiling Tasks

So what am I talking about with these big, open-ended tasks?

Low floor, high ceiling tasks are math activities that are easy for all students to tackle but can be extended to challenge even the most advanced learners. In other words, the task allows all students to get started, but then has more challenge that unfolds. These tasks allow for differentiation within the same classroom, making math both inclusive and challenging. They are particularly effective in developing flexible problem-solving skills and let all students feel successful.

As students get to the early intermediate grades, finding “real world” open-ended tasks can keep students super engaged as they explore different problem solving strategies. That’s what I want to talk about more today!

The Importance of Scaffolded Learning with Math Tasks

Scaffolding is a teaching strategy that involves providing support to students as they learn new concepts. Teachers can gradually remove this support as students become more proficient. In the context of low floor, high ceiling tasks, scaffolding can help ensure that all students can engage with the task at their own level. Techniques such as guided questioning, step-by-step instructions, “chunking” problems into sections, and visual aids are great ways to make these amazing problems more accessible to all students.

Other ways to scaffold involve providing “tools” such as manipulatives and calculators to help free students’ brains to tackle the problem solving while getting a quick “assist” on the math.  Similarly, breaking larger tasks into smaller, manageable chunks is another great way to scaffold challenging math tasks.  Once students have a grasp on the first part of the task, you can gradually unfold the task part by part as students are ready.

So often, teachers reserve this kind of rigorous, high quality task for more advanced students.  ALL students deserve access to quality math problems!  We just need to use these techniques to make the problems accessible. Sometimes it’s a matter of changing numbers to make a “Level A” and “Level B” option.  Sometimes we can get our more struggling students started as a small group and then send them off to work.  At other times, strategic pairing makes all the difference.  No matter how we differentiate, we must make sure to give great problem solving tasks to ALL our students.

Productive Challenge

I love to use these more complex, open-ended tasks.  That being said, many of my students begin the year as very beginning-level problem solvers.  Giving them a task that is TOO challenging simply pushes them to shut down completely.  I’m a huge fan of productive struggle, but shutting down completely is NOT productive.  For me, finding the “sweet spot” is part of the art of teaching.

I learned that for some students (and for all at the beginning of the year), I need to break these great tasks up into smaller, manageable pieces.  Later in the year I can give more open-ended tasks, but I start with that scaffold.  Notice that the “scenario” is presented at the top with all that students need to know.  What I do next is divide the problem into three tasks.  I then split the math into those three sections so students do one part at a time.

Check the photo below to see what I mean!

When Do I Use These Math Tasks?

Like I mentioned above, I use these more “scaffolded” tasks earlier in the year to explicitly teach open-ended problem solving.  As the year unfolds, I mix these scaffolded problems in with other that are more sophisticated. Gradual release isn’t just appropriate for a single lesson–but for how our year unfolds as well!  Along that line, as my students develop their problem solving skills, I back off on how much I introduce the tasks, how much I read to them, how much coaching I do, and so on.

I love to use these tasks:

• Between units
• When I have subs
• When the topic matches the season or our curriculum (before our zoo trip this year, my students were SO into the zoo task pictured below!)
• For cooperative work practice
• In centers
• For fast finishers

Powerful Math Lessons

Low floor, high ceiling tasks, combined with scaffolded learning, offer a powerful approach to teaching math. These tasks not only make math accessible to all students but also provide the challenge needed to develop strong problem-solving skills. As teachers, experimenting with different tasks and strategies will help find what works best for your students.

By fostering an environment where every student can succeed and be challenged, teachers can help develop a love for math and a growth mindset in their students. This approach not only supports the development of essential math skills but also encourages lifelong learning and curiosity.

Check out some of these great tasks below!

This first collection is my most scaffolded set–the math needed to solve these is very “third grade”, but the tasks are really broken into manageable chunks. I love that they have a seasonal “flair” but all can certainly be done at any point in the year.

This set is a little more complex.  The math is a little more advanced (better for fourth and up), and the tasks are more “open”.  Students are presented with a situation and they need to figure out how to break it into steps.  There are multiple entry points, but students need to be a bit more independent.  These tasks are perfect for single class periods and can be great supplements to your curriculum.

This final set of tasks is perfect for a little more extended problem solving.  They are differentiated so students can work at different levels, and there are tons of extensions so you can have them extend over several days if you want!

I hope this post has motivated you to incorporate some of these tasks into YOUR math plans!  Want to try one for free?  GRAB THE MATH TASK HERE!

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