By Lisa Englard, Posted June 22, 2015 –

So, how did your students do? I worked with a group of sixth-grade students who have experienced a fairly typical K–grade 5 math education, with emphasis on procedures and skills and some routine applications sprinkled throughout. They were immediately intrigued and engaged with the Animal Cracker Fundraiser task.

The students did a lot of noticing and wondering, and they proposed many good questions. They were also on target with determining the needed information to answer the question we had settled on. But after that, they struggled. I was hoping that students would recognize that they could use the ratio concepts they had learned to figure out how to split the 715 cookies (11 cookies per serving 65 servings) into two groups with a 4:9 ratio. A few did realize that the contents of one small bag and one large bag would total 13 cookies and that 715 ÷ 13 = 55. But they were unsure what the 55 represented and needed some help to reason that this was the number of small and large bags that could be made. When they reached Act 3, they quickly realized that the discrepancy between the 55 bags and the 49 bags in the picture was due to the “about” 65 servings on the label.

In the end, only a few students had reached a solution in the time I had to work with them. Most were engaged but confused. They were used to problems with a question and clearly stated information, complete with units and clues in the wording or topic under study, telling them what they were supposed to do. The messiness of this real-life situation threw them.

Therein lies the beauty, in my opinion, of the three-act math concept. We often give students routine problems to solve, many times with titles like “Use Ratio Tables” on the top of the page; but how often do we ask students to pose their own mathematical questions and reason about the world around them, to wade through the messiness of real life for needed information, to model situations using the math they have learned, to predict and estimate, to be driven to engagement by curiosity? By posing math problems as stories and cutting back the words in favor of a more visual presentation, we can draw students into caring about—and even needing to solve—the problem. Offered regularly, three-act math tasks can present opportunities for students to truly engage in the Common Core’s Mathematical Standards of Practice.

Here is what a three-act lesson looks like from both students’ and teachers’ points of view:

To learn more about teaching with three-act math, start with Dan Meyer’s Ted Talk and his blog.  In the meantime, stop and think about some of those textbook word problems and see if you can rebuild them in a way that supports math reasoning, problem posing, and patient problem solving.

Lisa Englard is a K–grade 8 math specialist in Aventura, Florida, who is passionately devoted to helping children and adults make sense of math. She currently serves on the Teaching Children Mathematics Editorial Panel and works with Student Achievement Partners as a core advocate. Englard blogs at mathspot.net and designs mobile apps for Common Core Math.