Domain: _Geometry_
Standard Code: 4.G.1_ 4.MD.6.7
Name: Class Photo
Teacher Name: _Karan Bleicher , Rick Albright, Rebecca Benoit, Suzanne Marchant
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
What are your mathematical goals for
The student can use models, manipulatives and pictures to create points, lines, line segments, rays, and
the lesson? (i.e., what do you want
students to know and understand about angles.
mathematics as a result of this lesson?) The student will be able to draw, label, and measure angles.
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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 understand angles. Students will identify angles (straight, acute, obtuse,
and right). Students will draw, measure, and label angles in two-dimensional figures.
Tools: geo-boards, uni-fix cubes, protractors, compass, circle protractors, clock face, paper strips,
blocks, etc.
Work: Students will work in small groups of 2 to 4, using concrete, pictorial, and abstract
representations to solve the given task.
Record: Students will record their work on provided template (math journal, grid paper,
manipulatives, etc.)
The teacher takes a class photo from multiple angles (using raisers from a gym, a classroom ladder, a
chair, etc.) Note: make sure the teacher has accident insurance. The teacher shows the photos and
asks students which picture(s) they like best, and why. What is the difference? The teacher will
facilitate a discussion that will help students recognize that the pictures were taken from different
angles.
Note: Students have prior knowledge of identifying and measuring angles. A review may be needed
before this activity. (See the Show Me App for the ipad)
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
As students work independently or in
Why did you choose this tool to depict your stairs?
small groups, what questions will you
What is it that you’re trying to find out?
ask to—
What are we asked to find?
 help a group get started or make
Can we solve this problem using different methods?
progress on the task?
How did you determine your vertex and angle?
 focus students’ thinking on the
What is the measure of the first angle?
key mathematical ideas in the
What is the measure of the second angle?
task?
 assess students’ understanding of What is the measure of the third angle?
key mathematical ideas, problem- What do you notice about the measurement of the entire angle that you constructed?
Explain how your diagram shows each individual angle measurement.
solving strategies, or the
representations?
 advance students’ understanding
Extension: What equation can be used to find the unknown? Why is addition used to write the
of the mathematical ideas?
equation? Can you use a differ type of equation? What operations can we use to find the
unknown?
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?
Ask open-ended questions as students work on the problem solving experience.
The teacher will walk from group to group, asking questions to informally assess students
understanding.
Asking the extension questions can extend the task. (What equation can be used to find the
unknown? Why is addition used to write the equation? Can you use a differ type of equation?
What operations can we use to find the unknown?)
PART 3: SHARING AND DISCUSSING THE TASK
How will you orchestrate the class
1. Concrete Example: Students who solved the task using a concrete manipulative
discussion so that you accomplish your
representation share first, such as stairs built out of uni-fix cubes, blocks, geo-boards, etc.
mathematical goals?
 Which solution paths do you want
2. Pictorial Example: Students who solved the task using a pictorial example will share their
to have shared during the
class discussion? In what order will representation second, such as graph paper, ipad, paper, pencil and ruler.
the solutions be presented? Why?
3. Abstract Example: Students who solved the task using addition or subtraction algorithms.
 What specific questions will you ask
so that students will—
Questions:
1. make sense of the
How did the total angle change from the base to the top as you went up each step?
mathematical ideas that you
want them to learn?
How does the angle change as you go up or down the steps? Do you see a pattern?
2. expand on, debate, and question
the solutions being shared?
What can you tell me about the stairs in your home are built?
3. make connections among the
different strategies that are
How does the rise of the step affect the comfort of using the step?
presented?
4. look for patterns?
5. begin to form generalizations?
When all students are able to explain that the 45-degree angle is a sum of three smaller and
equivalent (15 degree) angles, we know that their understanding of the concept is on the right
track.
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 answer is 15 degrees)
QuickTime™ and a
decompressor
are needed to see this picture.
Mr. Albright is taking a picture
of his fourth-grade class. He
stands on a ladder to get a
better angle. From the top step
of the ladder, he will shoot at
a 45-degree angle. There are 3
evenly spaced steps. From what
angle would the photographer
shoot on the bottom step?
QuickTime™ and a
decompressor
are needed to see this picture.