Domain: Geometry
Standard Code:
K.G.2-5
Teacher Name: Darle Taylor
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
Introduction of 3 Dimensional Shapes:
What are your mathematical goals for
Students will be introduced to cubes, cones, cylinders, and spheres. Students will be able to name the
the lesson? (i.e., what do you want
students to know and understand about 3 dimensional shapes and tell attributes of each. Students will compare the 3 dimensional shapes to
the 2 dimensional shapes and discuss contrasts with a partner. Students will find examples of the 3
mathematics as a result of this lesson?)
dimensional shapes in the environment as partners in class and individually at home.
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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?
EXPECTATIONS: Students will be able to name the 3 dimensional shapes and work as partners to
find examples of these shapes in the classroom environment, then independently at home to find
examples of these shapes in their home environment.
RESOURCES: 2 dimensional shape manipulatives, 3 dimensional shape manipulatives, paper,
pencils, crayons, clipboard for each partnership, chart or math vocabulary cards showing the 3
dimensional shapes & names, 3D Treasure Hunt take home note. Book: Cubes, Cones, Cylinders, and
Spheres by Tana Hoban.
GROUPING: Whole group, partners, and independently.
RECORD/REPORT: Student partners will report their findings to the whole group during debriefing
and on their partnership paper. Students will bring items or the reporting paper back to school to share
with the class on their assigned day.
LAUNCH: Access prior knowledge by reviewing names of 2 dimensional shapes.
Hand out sets of two and three dimensional shapes to each partnership and give students a few
minutes to discuss attributes (compare & contrast) with their partner. As a whole group discuss
“discoveries” about these new shapes.
Here are some shapes. Some we know and some are new. Look at these shapes and tell your partner
what you think about these shapes. Are these shapes the same in some ways? Are these shapes
different in some ways? What have you noticed about these shapes? Do you know the names of any
of these shapes?
As a whole group discuss the “discoveries” students made, names of the 3 dimensional shapes, and
introduce vocabulary of “flat”/2 dimensional shapes and “solid”/3 dimensional shapes.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
EXPLORE: Students as partners will move around the room with a paper on a clipboard and
As students work independently or in
pencil/crayons to look for items in the classroom environment that are cones, cubes, cylinders, and
small groups, what questions will you
spheres. They record what they find on their paper.
ask to—
 help a group get started or make
Why is the ________ a cone?
progress on the task?
 focus students’ thinking on the
What attributes are the same between the _________ and a cube?
key mathematical ideas in the
task?
 assess students’ understanding of How are a sphere and the _____ the same?
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?
The teacher moves around listening to partner discussions and viewing their “discoveries” on their
clipboard paper.
Assist: Can you find a cube/sphere/cone/cylinder/in the Book Corner/by the Reading table/by
teacher’s desk, etc.?
Additional challenge: Can you find something that has more than one of the 3 dimensional shapes
together on it?
PART 3: SHARING AND DISCUSSING THE TASK
DEBRIEF:
How will you orchestrate the class
discussion so that you accomplish your
Each partnership will report to the whole group one of each of the 3 dimensional shapes they
mathematical goals?
found in the classroom.
 Which solution paths do you want
to have shared during the
class discussion? In what order will Why did you choose the ___________ to be a cone/sphere/cube/cylinder?
the solutions be presented? Why?
What 3 dimensional shape was the ______________?
 What specific questions will you ask
so that students will—
What is the name of the 3 dimensional shape the ______ is like?
1. make sense of the
mathematical ideas that you
Is the ___________ really shaped like a cube/cone/cylinder/sphere?
want them to learn?
2. expand on, debate, and question
What else is shaped like a cone/cylinder/cube/sphere?
the solutions being shared?
3. make connections among the
Read the book Cubes, Cones, Cylinders, and Spheres by Tana Hoban.
different strategies that are
presented?
4. look for patterns?
Students understanding of attributes of the 3 dimensional shapes and use of the shape’s name
5. begin to form generalizations?
during their partnership’s report to the whole group will demonstrate their understanding of the
concept. Students will take home the 3D Treasure Hunt note to look for 3 dimensional shapes
independently at home and report back to the class. Five students are assigned to report each
What will you see or hear that lets you
day of the following week. Students will bring items found or return the 3D Treasure Hunt
know that all students in the class
paper with items drawn or listed on the paper. Whole group will discuss the items found:
understand the mathematical ideas that
you intended for them to learn?
Is this really a cone?
How is this like a sphere?
What makes this item a cylinder?
Why is this item a cube?
What is the name of the 3 dimensional shape this item is like?