By definition, a low floor, high ceiling math task is a math activity where all group members, despite background and skills, can begin and then work on at their own level of engagement. Tasks present possibilities for the students to do much more challenging mathematics as it unfolds. In order to make these powerful tasks meaningful, there are some things for teachers to keep in mind. Remember, it IS possible to present these great problems as a part of your whole group instruction!
What does this mean for you?
 ALL students must have the opportunity to participate in fun, engaging, “real” math! So often our more struggling students are given only lowerlevel math opportunities to help build their basic skills. Unfortunately, this means they are rarely exposed to the kind of math that helps them develop true thinking skills.
 The differentiation needed for this type of math task is different than simply reducing number size or problem complexity. Instead, consider the following:

Strategic Grouping:

As teachers, we know some students are excellent group members. We don’t want students DOING the math for their partners, but we do want to make sure students learn how to coach and support each other. Having diverse work groups helps with this.


Access to Manipulatives and Tools:

When students solve quality problems, they need different levels of support. Some students can do much higherpowered math when they have tools to help. Whether that be a calculator, counters, multiplication charts, or number lines–these tools can provide access to the problems that might not occur without them. Creating a climate where students learn how and when to access tools independently is a key part of building your math community.


Teacher Coaching:

Another way to build in differentiation is to recognize that not all students need the same amount or type of coaching. Learning to ask questions to help get students “unstuck”, being an astute “kid watcher”, and being careful to not do the thinking for students is so important. That being said, some students will certainly need more guidance and explicit help as they go through the tasks. As a teacher, work to ask more questions rather than “tell” more information. Try to get students to tell you what they DO know and build on that.


Gradual Release/scaffolding:

Similarly, as teachers, we can find ways to break these tasks into smaller chunks for students who need it. Much like learning to ask questions to get students “unstuck”, being able to take a task and break it into more manageable “bites” is one way to provide access. Sometimes meeting students who are stuck in a small group to talk through their issues can be just enough to let them return to their other groups and to be active contributors.
Ready for more?
3. Creativity/different paths to the solution
The beauty of these more complex tasks is that there are multiple entry points and multiple paths for students to take. Some may be more traditional. Some may be more efficient. In the end, however, all are successful. Helping students to realize that math is more than getting a correct answer is a pretty powerful life lesson. In fact, it frees many students to know that creativity and new thinking are valued. Math is not black and white, and valuing the creative process teaches students to embrace these different strategies.
4. Engaging content and powerful math talk
One of my favorite things about using these low floor, high ceiling math tasks is that students LOVE the topics and are truly engaged. Whether they tackle the Football Feast problem. Or the animal “Shelter Situation”. Or the “Amusement Park Challenge”. These problems address realworld math that is IMPORTANT to students this age. I always laugh at some of the problems in math series and wonder, “What fourth graders did they interview to decide to write a problem about THAT?”. A good task should get students immediately engaged and excited to dig in.
When students work in teams and share their thinking, there is a tremendous opportunity to grow understanding. Using accountable talk stems (I post mine in the front of my room) provides students with the language needed to be successful as they work together to share their ideas with the class.
Goals of Using a Low Floor, High Ceiling Math Task?
Using open ended math tasks is such a great way to accomplish a number of important math goals:
 Gets students tackling problems that have more than one solution
 Helps students learn to make sense of a complex problem
 Allows students to choose from multiple strategies or entry points
 Encourages math talk and discourse
 Allows students to see realworld applications of math
 Helps students see the interconnectedness of math concepts
 Immerses students in the Standards for Mathematical Practice along with the math content
 Provides an excellent forum for partner and small group work
 Naturally differentiate as students take “just right” approaches to solving them
 Encourages creative thinking and strategies
 Allows teachers to serve as coaches as they watch and interact with students as they solve them
 Encourages students (and teachers) to focus on the PROCESS over the solution
Convinced? Give a low floor, high ceiling task a try!
Here are a few options for you. Just click the images to learn more!
Want to check out another post about openended math challenges? CLICK HERE to read it!
Want to try a great sample problem for FREE? Click HERE or the image below! Enjoy–and have fun with math.