Download Right Angles

Domain/Standard Code:
Geometry/4.G.2
Page 1
Author Name:
Jennifer Nielsen
Title of Task: ____
Angles around our World
______________________________________________________________________________
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 understand how right triangles are different from other triangles.
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?)




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?




Expectations: Students will understand the difference between right triangles and non-right
triangles.
Students will use manipulatives, art, and smart board hands on work to discover the 90 degree
corner of a right triangle.
Students will work in small groups.
Students will create an art project using angles.
Domain/Standard Code:
Geometry/4.G.2
Page 2
Author Name:
Jennifer Nielsen
Title of Task: ____
Angles around our World
______________________________________________________________________________
How will you introduce students to the
activity so as to provide access to all
students while maintaining the
cognitive demands of the task?
LAUNCH
Introduce various images of angles with various angle sizes, including right, with a smart board
compilation of photos from architecture around the world.
Open a discussion pointing out right angles. “This is a right angle. Why? What makes them different
from the other angles displayed?”
Domain/Standard Code:
Geometry/4.G.2
Page 3
Author Name:
Jennifer Nielsen
Title of Task: ____
Angles around our World
______________________________________________________________________________
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK (EXPLORE)
Walk around the room and monitor independent work and conversations.
As students work independently or in
Ask open ended questions.
small groups, what questions will
Have small groups describe attributes of the various triangles.
you ask to—
Debate: Choose sides/teams/whatever; display on the board a right angle; Have a
 help a group get started or make
side/group “PROVE” that it is a right. What makes a right angle? How do you know it is
progress on the task?
right. Then, choose the other team to “PROVE” an angle is NOT right. Why? What
 focus students’ thinking on the
makes this angle something other than a right angle?” Perpendicular lines would need to
key mathematical ideas in the
be added to the vocabulary or conversation. Allow students to formulate their working
task?
definition, trying to allow them to come up with it on their own.
 assess students’ understanding of
key mathematical ideas, problemsolving strategies, or the
representations?
 advance students’ understanding
of the mathematical ideas?
Continue Monitoring. How does the diagram of a right triangle indicate this is a right? (There is
How will you ensure that students
often times a square in the corner to show exact perpendicular/square corners.)
remain engaged in the task?
 What assistance will you give or
what questions will you ask a
Scaffolding for struggling students.
student (or group) who becomes
quickly frustrated and requests
more direction and guidance is
Allow fast finishers to use class protractors to find the size of other angles; larger and smaller
solving the task?
than
the right angles.
 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?
Domain/Standard Code:
Geometry/4.G.2
Page 4
Author Name:
Jennifer Nielsen
Title of Task: ____
Angles around our World
______________________________________________________________________________
PART 3: SHARING AND DISCUSSING THE TASK (DISCUSS/DEBRIEF)
Which shape is easiest to identify?
How will you orchestrate the class
discussion so that you accomplish your
Where in our room do you notice right angles? Where in the school?
mathematical goals?
 Which solution paths do you want
Where in your world can you see angles?
to have shared during the
class discussion? In what order will
the solutions be presented? Why?
What patterns do you see?
 What specific questions will you ask
so that students will—
1. make sense of the
Is creating an architectural structure stronger then a curve? Why use angles and lines in our
mathematical ideas that you
building of structures?
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:
Geometry/4.G.2
Page 5
Author Name:
Jennifer Nielsen
Title of Task: ____
Angles around our World
______________________________________________________________________________
On this piece of paper provided along with your ruler, pencil, and eventually colored pencils, create
as many triangles as possible. They can be large, small, medium in size; you decide. Angles can
tough each other and you will be coloring them on the interior of each angle to beautify your work.
(We will display these.) You must use a minimum of 5 right angles and 5 angles of other sizes.
Indicate your right angles with a small square in the 90 degree corner, where the perpendicular lines
intersect.
*** Note: I have one of these pages in my class as a model. Or, you could use the one provided on
this site as a copy/paste for a smart board lesson.
Domain/Standard Code:
Geometry/4.G.2
Page 6
Author Name:
Title of Task: ____
Angles around our World
______________________________________________________________________________
Jennifer Nielsen