Domain: Operations and Algebraic Thinking
Title of Task: Reading a Book
Standard Code:
5.OA.1
Author Name: Kercher, Ferrero
(Introduce)__________________________________________________________________________________________
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
Student will write an expression using a variable and solve the problem.
What are your mathematical goals 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 demonstrate understanding of expressions using variables, in various ways including:
1.
Using a manipulative
2.
Drawing a picture or diagram
3.
Relating the problem to a model
4.
Show work using algorithm
5.
Justify and explain any algorithms used
*Resources or tools: Students will be provided a variety of manipulates including:
Pattern blocks, geo-boards, clocks, fraction bars, colored chips, base ten blocks, etc.
*Students will work independently to explore this task.
*Students will have a model, drawing and a written algorithm.
In our literature circles, we need to find out how many days it will take us to read our books, so it is
important to know how many pages we will need to read each day so that we will be on the same page
when we meet in groups.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
As students work independently or in
small groups, what questions will you
1.
What manipulatives could be used to represent the pages, book?
ask to—
2.
Show me what you are thinking.
 help a group get started or make
3.
How can you visually show me what you are thinking?
progress on the task?
4.
Could you prove you answer using the inverse?
 focus students’ thinking on the
5.
Does your answer sound logical?
key mathematical ideas in the
6.
Is there another way you can solve your problem?
task?
 assess students’ understanding of
key mathematical ideas, problemsolving 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?
Struggling or frustrated students:
•
Have you tried some manipulatives?
•
How about drawing a picture?
•
Read the task to me again.
Extensions:
•
How many pages would you need to read if you had 4 days? 5days?
•
What if your book had 125 pages?
PART 3: SHARING AND DISCUSSING THE TASK
Teacher will observe students while working. Make a note of which students should present
How will you orchestrate the class
their data:
discussion so that you accomplish your
•
Model
mathematical goals?
•
Picture
 Which solution paths do you want
•
Algorithm
to have shared during the
Did
you
see any patterns?
class discussion? In what order will
How has another’s explanation improved your understanding?
the solutions be presented? Why?
 What specific questions will you ask
How will you know students have achieved the learning outcome?
so that students will—
•
Students can explain their thinking.
1. make sense of the
•
Students are engaged in task.
mathematical ideas that you
•
Teacher will hear mathematical discourse.
want them to learn?
•
Students will have a written explanation of their thinking.
2. expand on, debate, and question
•
Students will have the algorithm written: 54/n=3. (any other symbols will work.)
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?
Reading a Book
Allen has a 54 page book. He wants to read the book in three
days. If he wants to read the same number of pages each day, how
many pages should he read on the first day?