Adapted from: Smith, Margaret Schwan, Victoria Bill, and Elizabeth K. Hughes. “Thinking Through a Lesson Protocol: Successfully Implementing High-Level Tasks.”
Mathematics Teaching in the Middle School 14 (October 2008): 132-138.
PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK (PREPARE)
Students will be able to estimate and use prior skills to solve a problem. Adding, multiplication,
What are your mathematical goals
estimation, reasoning, rounding etc.
for the lesson? (i.e., what do you want
students to know and understand about
mathematics as a result of this lesson?)
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What are your expectations for
students as they work on and
complete this task?
What resources or tools will
students have to use in their
work that will give them
entry into, and help them
reason through, the task?
How will the students work—
independently, in small groups, or
in pairs—to explore this task?
How will students record and
report their work?
How will you introduce students to the
activity so as to provide access to all
students while maintaining the
cognitive demands of the task?
Students will work individually to create a solution pathway to solve the problem.
Students will have manipulatives, pencil/paper, calculators and diagrams/pictures to use through the
problem.
Students will work individually and compare with partners to ensure the validity of their responses
Students will both diagram (draw) and fill in the sheet to show their knowledge of the concepts.
LAUNCH (5-15 minutes)
http://www.youtube.com/watch?v=npPghp90gIQ
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK (EXPLORE 20-30 minutes)
As students work independently or in
small groups, what questions will
you ask to—
 What do you already know?
 help a group get started or make
 What are you trying to represent in your drawing?
progress on the task?
 focus students’ thinking on the
 What information have you gathered?
key mathematical ideas in the
 What can you relate this too?
task?
 How can you figure out…?
 assess students’ understanding of
 How will you explain...?
key mathematical ideas, problem What would happen if…?
solving strategies, or the
representations?
 advance students’ understanding
of the mathematical ideas?
How will you ensure that students
remain engaged in the task?
 What assistance will you give or
what questions will you ask a
student (or group) who becomes
quickly frustrated and requests
more direction and guidance is
solving the task?
 What will you do if a student (or
group) finishes the task almost
immediately? How will you
extend the task so as to provide
additional challenge?
Extensions: the task is open-ended as students are supposed to find if this is worth it or not for the
fifth grade to watch a movie. How could they get all classes into two showings.
What activity might the classes do all at the same time?
If you added lines into the equation…is the shortest line always the fastest choice?
Is it worth it for the school to offer concessions – which ones should they offer and why?
PART 3: SHARING AND DISCUSSING THE TASK (DISCUSS/DEBRIEF 10-25 minutes)
How will you orchestrate the class
 Estimation – students, halls, etc .
discussion so that you accomplish your
mathematical goals?
 How do you know that your answer is correct?
 Which solution paths do you want
to have shared during the
 Does your answer make sense?
class discussion? In what order will
the solutions be presented? Why?
 Is there a simpler solution to this problem?
 What specific questions will you ask
so that students will—
 Is there a wrong way to solve this?
1. make sense of the
mathematical ideas that you
 In your opinion what is the best deal and why?
want them to learn?
2. expand on, debate, and question
the solutions being shared?
3. make connections among the
different strategies that are
presented?
4. look for patterns?
5. begin to form generalizations?
What will you see or hear that lets you
know that all students in the class
understand the mathematical ideas that
you intended for them to learn?
The 5th grade students at your school have been invited to view a new movie in the Little Theater. The problem is that
only 187 students can fit into the Theater at one time, so there will be 2 showings. The following is a list of class sizes.
Figure the number of students out of each class that can attend each of the scheduled times.
First Hallway
Mrs. Mitchell 28
Mr. Long-Partei 24
Ms. Barrett 28
Mr. Robison 26
Ms. Allred 28
Second Hallway
Mrs. Zachery 30
Mrs. Segura 31
Mrs. VanHouten 29
Mrs. Martin 30
Third Hallway
Mrs. Kingi 31
Mrs. Kohler 26
Mrs. Colburn 30
Mrs. Prince 30
Will all of the classes be able to attend in 2 showings or will it take 3? * Don’t forget to include seats for teachers.
Estimate to show the reasonableness of your answer.
If two classes are gone on a field trip, will all the classes be able to attend on 2 showings?
If 2 classes are gone on a field trip, which classes would fit in the theater for the first showing? Which classes will fit
into the theater for the second showing? Show how you arrived at your answer.
If the classes must attend by hallways, as much as possible, which classes would attend each showing. Show your
answers in fraction form. Then convert each fraction to a decimal.
The movie is only $1.00 per student.
The theater is offering a deal on their concessions.
Drinks: Sm. $3.00 Med. $4.00 Lg. $4.50
Popcorn: Sm. $2.00 med. $2.50 Lg. $3.00
Candy Sm. $2.00 med. $3.00 Lg. $5.00
Special Deal: 1 small drink, popcorn and candy for $6.50
You have $7.50 to spend, what is the best buy for your money, and can you save any money?
There are 3 lines when your class gets to the theater. Line one must wait to order individually for their concessions. It
takes 25 seconds to get through the line and there are 20 students in line.
Line 2 is ordering the special deal and only takes 12 seconds to get through. There are 32 students in this line.
Line 3 is just going into the movie without treats. They take 8 seconds to get through and there are 55 students in line.
Which line would you choose and explain the reasons for your choice.