Content reblogged/summarized from this post and this series of posts by Dan Meyer
With the implementation of the new Utah Mathematics States Standards, many teachers are now looking for better tasks that will help them not only teach the content standards but also the eight mathematical practices. One solution to this pressing need is the use of Three-Act Tasks. This is an outline summary of some of the key ideas from this blog post and this series of posts by Dan Meyer:
"Storytelling gives us a framework for certain mathematical tasks that is both prescription enough to be useful and flexible enough to be usable. Many stories divide into three acts, each of which maps neatly onto these mathematical tasks." Dan Meyer
Act 1: Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible.
- Students are presented with an image or video that leads to some interesting mathematical questions
- Students are asked to share the first question that comes to mind
- Teacher narrows in on one or two student questions that will lead students to intended learning outcomes
- Students estimate the answer to the selected question, first creating a boundary of something they know is too high and something they know is too low.
Act 2: The protagonist/student overcomes obstacles, looks for resources, and develops new tools.
- Teacher asks students "What information would be useful?" and students request the information needed. This is in direct contrast to a traditional textbook problem that gives students all the information up front.
- Teacher uses primary sources to provide the information requested by students
- Teacher provides direct instruction. Now that students have the motivation to solve the problem, they are ready for the teacher to instruct them in the skills they need to build a model to help them
- Students build a model and solve the problem
Act 3 and Sequel: Resolve the conflict and set up a sequel/extension.
- Students who finish early are challenged with an enticing sequel (extension) task
- Teacher shows students the answer (a visual, primary source if possible)
- Students cheer!
- Teacher and students find out who had the best estimate and recognize these students
- Teacher and students formalize the math learned
- Students create a title for the lesson that summarizes the mathematics learned
Curious what a Three-Act Task looks like in action? Check out the video below of Dan Meyer leading a Three-Act Task at a workshop in Cambridge.
Are you ready to try a three-act task and wondering where to start? Where to find good tasks? How long these tasks take? How often you should teach a problem-based lesson? How and where to fit it into a unit plan? Robert Kaplinsky, another problem based learning expert, wrote this blog post to answer these and other frequently asked questions regarding implementing problem based learning tasks.