Engaging Students in Three Acts

  • Engaging Students in Three Acts

    By Lisa Englard, Posted June 8, 2015 – 

    I recently had a chance to work with a group of students who had performed poorly on a progress monitoring assessment. I offered them this variation of the Four Digits problem:

    Use the digits 1, 2, 3, and 4, once each, with operations, exponents, and parentheses, to write expressions for all the numbers from 1 to 50.

    I expected that they would struggle and was prepared to support and encourage them. But something amazing happened; the students were so engaged with the task that they refused any help from me and couldn’t stop! They worked collaboratively, hooted whenever they solved a particularly challenging one, and begged me to give them more time to work on it. Impressed with their perseverance, productive struggle, and reasoning, I finally asked the obvious question, “What happened on the assessment?”

    They told me, “There were too many words.”

    The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) reminds us that the ability to apply understanding and skills to solve real-world and mathematical problems is a necessary component of rigor. The Standards for Mathematical Practice (SMPs) describe how mathematically proficient students make sense of problems, persevere, reason, construct and critique arguments, model, use tools, attend to precision, and look for structure and repeated reasoning. NCTM’s Principles to Actions (2014) advises teachers to offer appropriately challenging tasks, and it guides us in facilitating meaningful discourse. But how can we accomplish all this when so many of our students opt out as soon as they see a word problem? How can we engage students in needing to know the solution to a challenging problem without turning them off with “too many words”?

    Dan Meyer, offers a solution: A math problem can be approached through a framework of storytelling, presented in three acts, with a visual introduction that both generates curiosity and avoids the demands of language. Imagine that—instead of a wordy textbook problem with all the necessary facts, numbers, and, of course, a prescribed question to answer—you showed your students the following:

    Animal Cracker Fundraiser Task

    Act 1

    Ask: What story can you tell from these pictures? What do you wonder about this situation? What do you notice?

    2015-06-08 art1

    2015-06-08 art2

    Discuss the possibilities. Consider what questions could be asked and answered. Make guesses about right and wrong answers to the questions. What would be an answer that is too high or too low?

    A suggested question: How much money can students earn with this fundraiser?

    Act 2

    After the class has agreed on the question to be answered, have them think about what information, resources, and tools they will need. Be prepared with the following information and present it as students ask for it:

    Students have decided to make an equal number of large and small bags as follows:

    2015-06-08 art3

    2015-06-08 art4

    Act 3

    This is the resolution, the payoff for the hard work of Act 2. Here, once again in visual form, is what really happened:

    2015-06-08 art5

    49 small bags @ $.50 each = $24.50

    49 large bags @ $1.00 each = $49.00

    $24.50 + $49.00 = $73.50

    The answer prompts conversation: Was the answer what you expected? Why or why not? What did we learn from this process?

    Finally, offer a sequel by flipping the known and the unknown: How might students price the cookies if they need to raise $100 for the trip?

    Your Turn 

    Now it’s your turn. Try presenting the problem in three acts to your students, and let us know what happens. In the next post, we will continue the conversation about engaging students in three acts.  

    We want to hear from you! Post your comments below or share your thoughts on Twitter @TCM_at_NCTM using #TCMtalk.

    2015-06 Englard AULisa 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.


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    Pamela Cintas - 9/16/2015 9:35:40 PM
    Lisa - I teach a 4th grade high-ability class and gave my students the "Four Digits" problem that you mentioned. My students have done such an outstanding job and they are excited and engaged. They have almost all the numbers figured out except six. They are stuck on the number 34. The students have researched factorials. Can they use factorials to solve this problem? Your input would be appreciated.

    Shelly Gilbert - 7/10/2015 12:22:18 PM
    Thanks, Lisa. I am getting plans ready for the year and this idea is getting me excited.

    Drew Polly - 6/21/2015 10:53:15 AM
    With the school year over we didn't have the chance to try this yet, but last week at curriculum planning I talked to some teachers about this approach of 3 acts. We are in the midst of designing some of these and other multi-step performance tasks for next year. Great ideas!