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
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:
Ask: What story can you tell
from these pictures? What do you wonder about this situation? What do you notice?
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?
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:
This is the resolution, the
payoff for the hard work of Act 2. Here, once again in visual form, is what
bags @ $.50 each = $24.50
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
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?
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.
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.