Domain/Standard Code:
4.NBT.6
Author Name:
Merrilee
Page 1
Title of Task: Calves in the Pens
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)
What are your mathematical goals
Students will understand that division is sharing and putting things in equal groups.
for the lesson? (i.e., what do you want
students to know and understand about
mathematics as a result of this lesson?)




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 be expected to TRY. They will know I am more interested in effort then getting the
correct answer.
Students will be allowed to use paper and manipulatives.
Students will have the option of working independently or in pairs.
Students will be prepared to show their thinking.
LAUNCH
Ask the students what they know about farms. Talk about the animals found there, what they eat, and
the farmers’ responsibilities. Emphasize that an organized farm would be much easier to manage. One
method of organization is grouping like things together. Talk about division and what it means. Have
“mini-lessons” (as needed) on putting things in equal groups and divisibility rules.
Domain/Standard Code:
4.NBT.6
Author Name:
Merrilee
Page 2
Title of Task: Calves in the Pens
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK (EXPLORE)
As students work independently or in
What tools will you use to get the answer? What strategies will you use?
small groups, what questions will
you ask to—
How do you know which numbers can be divided by 164 evenly?
 help a group get started or make
progress on the task?
Do you need to know which numbers are divisible by 164?
 focus students’ thinking on the
key mathematical ideas in the
Is there more than one way to put the calves in equal groups? How many combinations
task?
did you find?
 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
Remind the students of divisibility rules.
remain engaged in the task?
 What assistance will you give or
Allow the students to use concrete tools; such as manipulatives to solve the problem.
what questions will you ask a
student (or group) who becomes
For frustrated or hesitant students scaffold by using like examples that are less challenging.
quickly frustrated and requests
more direction and guidance is
Extend the problem for fast finishers. Have them find all the possible grouping combinations or
solving the task?
 What will you do if a student (or give them larger or more challenging numbers.
group) finishes the task almost
immediately? How will you
extend the task so as to provide
additional challenge?
Domain/Standard Code:
4.NBT.6
Author Name:
Merrilee
Page 3
Title of Task: Calves in the Pens
PART 3: SHARING AND DISCUSSING THE TASK (DISCUSS/DEBRIEF)
How will you orchestrate the class
Learners will:
discussion so that you accomplish your
mathematical goals?
Understand that division means sharing or putting items in equal groups.
 Which solution paths do you want
to have shared during the
Students will be able to count using multiples. They will know divisibility rules and
class discussion? In what order will
how to use them to solve problems.
the solutions be presented? Why?
 What specific questions will you ask
Students will understand that in order to have no remainder, the numbers must have a
so that students will—
common multiple.
1. make sense of the
mathematical ideas that you
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?
Domain/Standard Code:
4.NBT.6
Author Name:
Merrilee
Page 4
Title of Task: Calves in the Pens
Learning Task
A farmer has 164 baby calves. He puts the same number of calves in each pen. How
many pens are there? How many calves are in each pen?
Extension: Find all the different grouping combinations.
Solutions
164/1 = 164 pens with 1 calf in each pen
164/2 = 82 pens w/ 2 calves in each pen
164/4 = 41 pens w/ 4 calves in each pen
164/41 = 4 pens w/ 41 calves in each pen
164/82 = 2 pens w/ 82 calves in each pen