Rich Math Tasks—Engage Your Students in Meaningful Mathematics

You’ve probably read about rich math tasks and the importance of including these tasks in your daily mathematics instruction. Engaging with rich math tasks is often referred to as “doing” mathematics and involves high-cognitive demand as opposed to more rote, or low-cognitive demand tasks, that typically involve reproducing previously learned facts or formulas. Although not every task needs to be a rich math task, they are essential for building a deep understanding of mathematics concepts and higher reasoning skills. So, what are rich math tasks and why are they so important?

Why Are Rich Math Tasks Important?

Rich math tasks help students think creatively, analyze different approaches, collaborate and discuss ideas, listen to alternate perspectives, make connections, and evaluate findings, basically the skills they need to tackle complex problems in any arena. As the world becomes increasingly more complex, our students will need these skills to tackle the realities of life in the 21st century and confidently master jobs that require critical thinking, ingenuity, and problem solving, some of the top work skills identified by the World Economic Forum.

Rich math tasks provide a manageable way for teachers to differentiate instruction for the range of learners in the classroom. Because rich math tasks are designed to be accessible and challenging for all students, they provide an ideal way to address both the needs of students who are struggling to master concepts, as well as those who are ready to tackle more complex content. Since rich-math tasks are by definition student-centered, they free teachers up to work with those students who need additional guidance as other students work collaboratively towards solving.

Rich math tasks provide teachers with an opportunity to assess students’ mastery of mathematical concepts. As students are working as a class, in groups, and individually, you can see (and hear) who is grappling with basic concepts, where there are misconceptions, what connections they are making to previously learned material, which strategies they rely on to help them make progress, how they use representations to clarify their thinking, and what language they use to describe and defend their ideas. And this will help you determine next steps for the whole class as well as provide you with the data you need to group students effectively.

What Makes a Math Task Rich?

Although there are different definitions of rich math tasks, here are what I consider the essential elements. Not every rich math task will incorporate all of these features, but the richer the task the more of these components it will include.

A rich math task is engaging. Students need to be interested in the task, curious to explore possible solutions, and sufficiently intrigued to persist even though the problem is difficult. Tasks that tap into students’ experiences and cultures, real-world issues, pop culture trends, age-appropriate activities, etc. are more likely to hook students and help them persevere through challenge.

A rich math task is accessible for all students. You’ve most likely heard the term, “low-floor, and high-ceiling” to describe a math task. This means that all of your students will be able to find an entry point (low floor) and all of your students will be able to grapple with some element of complexity (high ceiling), but students will be engaging with the problem at different levels based on their mastery of the underlying mathematical concepts.

A rich math task encourages discussion. When tackling the task, students work together to consider multiple strategies and need to explain and justify their approach and reasoning. It provides students with the opportunity to link their thinking to prior learning, explain why they selected a particular representation or strategy, use mathematical language, and reflect deeply on the underlying mathematical concepts.

A rich math task has multiple solution paths. Students can complete the task successfully in different ways, using multiple strategies and representations (physical, visual, symbolic, verbal, and contextual), changing paths when one approach is not successful. Students consider various ideas, contemplate multiple approaches, collaborate to overcome impasses, and work towards a solution. All the paths may not be as efficient or as elegant, but each leads to a viable result.

A rich math task requires cognitive effort. Although some basic recall might be used to help solve the task, students must engage substantively with the underlying mathematics and use reasoning to develop possible solutions. The task should allow students to build a deeper understanding of concepts and allow them to explore connections and patterns between concepts. Students most likely will experience struggle, but as long as the struggle is productive, research shows that engaging with rich math tasks improves students’ mathematical reasoning.

A rich math task aligns to standards. The mathematical concepts needed to solve the task should be clear and grade-level and developmentally appropriate. While working on the task, students will thoroughly explore and deepen their understanding of the underlying concepts and relate that understanding to previously learned concepts. Rich tasks lay the groundwork for identifying patterns with and connections to new concepts.

How Do I Supports Students in Doing Rich Math Tasks?

The most important thing you can do is to create a learning environment that encourages and supports all students to engage with difficult and challenging mathematics. Here are some of the questions that you might ask yourself when introducing a rich math task.

1. Will my students find this task interesting and will they be eager to work through any challenges that arise?
2. How might I adjust this task to address all of the learning levels in my class?
3. What mathematical concepts (and what are the underlying standards) do I want my students to learn while working on this task?
4. What previous mathematical concepts (and what are the underlying standards) does this task connect to?
5. How will I check to make sure students have learned the underlying concepts?
6. How will I help students who are struggling with the basic mathematical concepts?
7. What are the various representations that students might use to solve this task?
8. What are the various strategies that students might use to solve this task?
9. How can I encourage respectful discussion and disagreement?
10. How will I help students move through struggle productively, without rescuing them?
11. What do I want students to learn in addition to the underlying mathematics concepts from the successful completion of this task?
12. How will I ensure that all students feel successful?

Where Do I Find Rich Math Tasks?

We suggest you start by looking at the curriculum you are using as most include at least some rich math tasks. ORIGO’s Stepping Stones curriculum program includes multiple rich math tasks in every module with ideas for extending those tasks to ensure that every student engages with relevant and rigorous mathematics. We’ve included links to a few of ORIGO’s rich math tasks for grade bands K-2, and 3-6. Each math task is aligned to standards and includes the mathematics concepts highlighted.