I recently received Smarter Together! Collaboration and Equity in the Elementary Mathematics Classroom as a gift. Although written for elementary teachers, the book offers some great insights and resources applicable to teachers at all grade levels. The authors (in Chapter 7 & Appendix B) provide guidance for adapting existing mathematical tasks to be more “groupworthy” — requires collaboration and multiple abilities/competencies and encourages multiple solution strategies (a key part of Complex Instruction). I found the guiding questions in this book to be extremely useful for adapting mathematical tasks for any purpose — to be more groupworthy, to be more relevant for students, to include a social justice exploration, to fit with your standards/goals, etc. Most teachers that I know construct their own curriculum built from rich mathematical tasks that they find from various sources and adapt them to fit their own needs. From my own experience, I know how much time it takes just to find those sources. In this post, I wanted to share the guiding questions for adapting mathematical tasks provided in Smarter Together! (p. 110-111) and some resources that I’ve found for rich mathematical tasks. If you know of other resources, feel free to share them in the comments section of this post.
1. Questions that help you figure out what mathematical reasoning children will need to do to complete the task.
- Think first about the task’s mathematical demands. Figure out what important mathematical ideas you want your students to be working on. Ask yourself first what ideas the task could get your students thinking about, and then which ones you want to focus on.
- Ask yourself whether this task will challenge all your students mathematically. If not, figure out how you can adapt it so that it will.
- How can you adapt the task so that it affords more than one starting point, requires more than one solution path, and thus makes some mathematical connections visible? What strategies will your students use to succeed with this task? What might they try? What prior knowledge do they bring to this task that will help them succeed?
- What could you add to the task to help students reflect on their mathematical work?
2. Questions to help you figure out how the task’s context supports or distracts from the mathematical thinking you want your students to do.
- How are your students likely to work on this task? What would they be likely to talk about and do? If you think they might focus on parts of the task that do not involve mathematics (e.g. “I want to have sugar cones because they are my favorite.”), try to figure out how you can adapt the task so that it will direct their attention and conversation to the math.
- Think about what decisions students will make. Will they make decisions individually or collectively? Will these decisions require thinking about math?If not, figure out how you can adapt the task so that the thinking and talking will involve math.
3. Questions that help you figure out how you can make the task more groupworthy.
- Does the task allow for multiple entry points and multiple solution strategies? If not, how can you adapt it so that it does? Will students display multiple mathematical competencies?
- Students often approach a group task by dividing up the work in some way that makes sense to them (e.g., “I’ll do the first two problems. Juan can do the next two…”). When they do this, they are less likely to talk about the math, and they don’t get access to the learning that each of the different problems affords. If you think they would be inclined to divide up the work, will this division help all students finish quickly but miss an opportunity to explore important mathematical ideas? Think about how you can structure the task so that everyone in each group must contribute and do mathematical reasoning.
- How does the task provide for individual and group accountability? How will you communicate how you will evaluate both individual and group work and learning?
Resources for rich mathematical tasks
- youcubed.org – Among other great resources, this site includes a number of “low floor high ceiling tasks” – tasks that give all students access to the problem and allow students to work at different depths at different times.
- blog.mrmeyer.com – Dan Meyer’s site includes both is Algebra and Geometry curricula.
- NYC Dept of Education Site – This site contains several rich mathematical tasks for elementary, middle and high school students (e.g. shopping carts task). The full list of tasks if available here or from the drop down menu at the top of the page.
- NRICHmaths.org – Among other resources, this site contains curricula for secondary and beyond, elementary tasks and resources for doing math with young children.
- MARS (Mathematics Assessment Project) – This site contains tasks for “novice”, “apprentice” and “expert” learners for high school and middle school, as well as lesson resources.
- Balanced Assessment Task Bank – These K-12 tasks include scoring rubrics for assessing student performance. More than 300 tasks are available.
- The Math Forum – Hosted by Drexel University, this site includes resources for rich problems, lesson plans and teacher-to-teacher networking.
- samjshah.com – Lots of great stuff here, including some good math problems.
- NCTM.org – If you are an NCTM member, then you have access to K-12 mathematics tasks and lesson here, and you can purchase discounted access to their bank of Real World Math tasks.
NSF funded curricula
- This site contains a list of exemplary NSF-funded mathematics curricula across K-12. If you don’t have access to any of these texts at your school, you might be able to find used, inexpensive copies of older editions online.
Books & other published sources
- Investigations Units – 5 units for middle school investigations.
- About Teaching Mathematics: A K-8 Resource (online pdf) by Marilyn Burns – Tasks are sorted by topic and supported with commentary
- Math Matters: Grades K-8: Understanding the Math You Teach (online pdf) by S. Chapin, A. Johnson & T. Gordon – Digs into the big ideas of K-8 mathematics and includes mathematical activities.
- Get it together: Math problems for groups, grades 4-12 (online pdf) by Tim Erickson – More than 100 problems for groups.
- United we solve: 116 math problems for groups, grades 5-10 by Tim Erickson – The sequel to Get it Together
- Group Solutions: Cooperative logic activities for grades K-4 by Jan Goodman – Group tasks for younger students.