CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
3rd Grade
Unit 5: Geometry
November 13, 2012
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Turtle Gunn Toms– tgunn@doe.k12.ga.us
Elementary Mathematics Specialist
CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Third Grade
Unit 5: Geometry
November 13, 2012
Turtle Toms– tgunn@doe.k12.ga.us
Elementary Mathematics Specialist
These materials are for nonprofit educational
purposes only. Any other use may constitute
copyright infringement.
Welcome!
Thank you for taking the time to join us in this
discussion of Unit 5.
At the end of today’s session you should have at least 3
takeaways:
What the research says about developing understanding.
Ideas to support student and teacher understanding.
• The intent of this webinar is to bring awareness to:
the development of foundational geometry
understanding.
the mathematics of Unit 5.
the underlying structure of a task.
We will view task structure by looking at the
culminating task for Unit 5 during this webinar.
What’s Unit 5 all about?
• Geometric properties
• Examples and non-examples of a variety of
plane and solid figures
• Hierarchy of quadrilaterals
• Partitioning plane figures into equal areashalves, thirds, fourths, sixths and eighths.
• Data collection and use
What should students bring from
previous grades?
• Knowledge of triangles, quadrilaterals, pentagons, hexagons,
cubes, cones, cylinders, spheres, rectangular prisms
• Familiarity with angle, face terminology
• Two-dimensions, three dimensions
• Defining attributes of various shapes
• Partitioning into halves, thirds, fourths
• Foundations of area
• Measurement with inches, feet, centimeters, meters
• Line plot, bar graph, picture graph
•
•
•
•
Levels of geometric thinking:
Visual/syncretic- Students recognize shapes, e.g., a
rectangle “looks like a door.”
Descriptive- Students perceive properties of shapes,
e.g., a rectangle has four sides, all its sides are straight,
opposite sides have equal length.
Analytic- Students characterize shapes by their
properties, e.g., a rectangle has opposite sides of equal
length and four right angles.
Abstract- Students understand that a rectangle is a
parallelogram because it has all the properties of
parallelograms.
Students find that some combinations of
properties signal certain classes of figures and
some do not; thus the seeds of geometric
implication are planted. However, only at the next
level, abstraction, do students see relationships
between classes of figures (e.g., understand that
a square is a rectangle because it has all the
properties of rectangles) Competence at this level
affords the learning of higher-level geometry,
including deductive arguments and proof.
Thus, learning geometry cannot progress in the
same way as learning number, where the size
of the numbers is gradually increased and new
kinds of numbers are considered later. In
learning about shapes, it is important to vary the
examples in many ways so that students do not
learn limited concepts that they must later
unlearn.
(http://commoncoretools.me/wpcontent/uploads/2012/
06/ccss_progression_g_k6_2012_06_27.pdf)
Geometric properties
What’s Unit 5 all about?
• Using and sorting examples and non-examples
of a variety of plane and solid figures
Regular vs irregular polygons
• Regular- equal sides, equal angles
• Irregular- unequal sides and/or angles.
Is a rectangle regular or irregular?
What’s Unit 5 all about?
• Hierarchy of quadrilaterals
Subset thinking:
Trapezoid?
In the U.S., that the term “trapezoid” may have two
different meanings. In their study, The Classification of
Quadrilaterals (Information Age Publishing, 2008), Usiskin
et al. call these the exclusive and inclusive definitions:
T(E): a trapezoid is a quadrilateral with exactly one
pair of parallel sides
T(I): a trapezoid is a quadrilateral with at least one
pair of parallel sides.
These different meanings result in different classifications
at the analytic level.
According to T(E), a parallelogram is not a trapezoid;
according to T(I), a parallelogram is a trapezoid.
Both definitions are legitimate.
However, Usiskin et al. conclude, “The preponderance of
advantages to the inclusive definition of trapezoid has caused
all the articles we could find on the subject, and most collegebound geometry books, to favor the inclusive definition.”
Based on the above, Georgia will use the inclusive
definition. A trapezoid is a quadrilateral with at least one
pair of parallel sides.
What’s Unit 5 all about?
• Partitioning plane figures into equal areashalves, thirds, fourths, sixths and eighths.
What’s Unit 5 all about?
• Data collection and use
Picture graph vs pictograph
What’s Unit 5 all about?
• Geometry progression:
(http://commoncoretools.me/wpcontent/uploads/2012/06/ccss_progression_
g_k6_2012_06_27.pdf)
Culminating Task:
Geometry Choice Board
• What is the goal of this task?
• How can you structure the task so
that it works for your classroom?
Culminating Task:
Geometry Choice Board
• What is the goal of this task?
Choice Board
• What might you add?
• How might you increase
student choice/entry points?
Culminating Task: Geometry Choice Board
• How can you structure the task so that it works for
your classroom?
• Intro task- start with task and rubric. Edit either/both
to better fit your students.
• Students work independently/you circulate and ask
questions, take notes
• Set benchmarks along the way to keep students
moving forward, help kids to organize their workflow
Culminating Task: Geometry Choice Board
• Refer students back to rubric all along the way to
help kids to organize their thinking and improve
their work.
• Choose strategically which student ideas offer
opportunities for “mid-stream minilessons”.
• Question more than you answer.
• Listen more than you talk.
• If you are recording your thinking, you are modeling
your expectation for them.
Culminating Task:
• https://www.teachingchannel.org/videos/group-dynamics-in-3rdgrade-math?fd=1
Rubric
• How might the rubric be made more
useful for your students?
• How might the rubric be made more
useful for you?
Horizontal and vertical connections
• Strategies apply everywhere, in multiple contexts
• Integration of content areas ensures connections
and relational thinking
• Multiple steps builds understanding and deeper
thinking
• Work the culminating task collaboratively with
colleagues so you know where your kids need to
go, and what they might have difficulty with
Effective Feedback
• Sharing thinking
Culmination of the unit, not the grade.
Food for thought:
“I’ve learned a lot from watching good teachers. The most important
thing I’ve learned: adopt the mantra “Just the answer isn’t good
enough.” I watched teachers transform passive students into thinkers
because of this simple idea. This expectation, that a teacher sets at any
point in the year, opens up doors to all of the SMP’s (not every one
every day – but many every day). In those classes, because “just the
answer isn’t good enough,” kids made sense of the mathematics they
were doing, reasoned to justify that their answer was correct, critiqued
their work and others’, used tools and made models of the mathematics
that was happening, used some measure of precision as they explained
their thinking, and sometimes found structure (even a few teachers
found this) in their own repeated reasoning.”
From a math coach friend…
Thank You!
Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with
your feedback!
Turtle Gunn Toms
Program Specialist (K-5)
tgunn@doe.k12.ga.us
These materials are for nonprofit educational purposes only. Any
other use may constitute copyright infringement.
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