1. Grade Two PARTNERS for Mathematics Learning Module 5 Partners

2. What is Geometry? “geo” - means earth “metry” – means measure2
What is Geometry?
“geo” - means earth
“metry” – means measure
“Measurement of the earth”
Partners
for Mathematics Learning

3. Geometry … “is grasping space…. that space3
Geometry …
“is grasping space…. that space
in which the child lives, breathes
and moves. The space that the
child must learn to know, explore,
conquer, in order to live, breathe,
and move better in it”
Freudenthal, Mathematics as an Educational Task
How would you define geometry?
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for Mathematics Learning

4.  Geometry can provide a more complete 4
Why Study Geometry?
 Geometry can provide a more complete
appreciation of the world
 Geometry can be found in the structure of
the solar system, in rocks and crystals, in
plants and flowers, even in animals
 Virtually everything that humans create
has geometric forms
Partners
for Mathematics Learning

5. Why Study Geometry?  Spatial reasoning and geometric5
Why Study Geometry?
 Spatial reasoning and geometric
explorations are important forms of
problem solving, a major reason for
studying mathematics
 The ability to look at situations visually,
geometrically, and analytically makes
students better problem solvers
 Geometry plays a major role in other areas
of mathematics such as measurement,
ratio and proportion, and fraction concepts
Partners
for Mathematics Learning

6.  Interpreting 2-D representations of 3-D6
Why Study Geometry?
 Interpreting 2-D representations of 3-D
models: increasingly important as tools
become more visual (such as computer-
aided design)
 Visual skills: central to many occupations
including scientists, architects, artists,
engineers, land developers, etc.
 Home: building a fence, planning a garden,
arranging furniture, decorating with art
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for Mathematics Learning

7.  Children develop skills and conceptual7
We Know That…
 Children develop skills and conceptual
understandings over time through their
experiences
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for Mathematics Learning

8. Children’s Experiences8
Children’s Experiences
 When given appropriate experiences in
mathematics, children can use the
knowledge to make sense of the world
 Think about important
classroom experiences
that you will make part
of your program
Partners
for Mathematics Learning

9. 9
Big Ideas of Geometry
 Shapes or groups of shapes can be classified by
their properties (attributes)
 Two-dimensional shapes are combined to make
three-dimensional shapes
 Shapes can be described in terms of their location
and viewed from different perspectives ;
geometric figures can be moved in a plane without
changing their size or shape
 Coordinate systems can be used to describe
locations precisely
 Area, perimeter, and volume are examples of
measureable attributes in geometry
Partners
for Mathematics Learning

10. Essential Standards  Look at the Essential Standards10
Essential Standards
 Look at the Essential Standards
for 2 nd grade
 What is new to 2 nd grade?
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for Mathematics Learning

11.  Two-dimensional shapes are combined to11
Big Idea for Geometry
 Two-dimensional shapes are combined to
make three-dimensional shapes
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for Mathematics Learning

12. What’s in the Box?  One partner places a shape in the12
What’s in the Box?
 One partner places a shape in the
box without the other partner
seeing the shape
 The other partner feels the shape, without
looking, and describes the shape
 Think about what the teacher would need
to do before this activity to better ensure
the students connect the faces with the
shape

13. 13
What’s in the Box?
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for Mathematics Learning

14. Mystery Bag Grab  Place shapes in a bag14
Mystery Bag Grab
 Place shapes in a bag
 Place a matching set of shapes on the table
 One student reaches into the bag and
“grabs” a shape
 Without removing the shape from the bag,
the student describes the shape by
attributes and indicates the match on the
table
Partners
for Mathematics Learning

15. Geometry Definitions  Look back at the geometry definition15
Geometry Definitions
 Look back at the geometry definition
handout
 Read through the other definitions
 As we go through the module, look for
activities that address these items
 Think about which concepts are developed
in your 2 nd grade classroom
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for Mathematics Learning

16. 2-Dimensional to 3-Dimensional16
2-Dimensional to 3-Dimensional
Polyhedron means “many faces”
Edge--3-D term
Formed where
two faces
coincide Face—3-D term
A flat surface on
Vertex—a point A polyhedron
where two or more (Faces are polygons)
edges meet
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for Mathematics Learning

17. Three-Dimensional Shapes17
Three-Dimensional Shapes
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for Mathematics Learning

18. Types of Prisms  These are three-  They are prisms18
Types of Prisms
 These are three-
dimensional shapes
whose sides are all
formed by polygons
 They are prisms
because ends (or
bases) are congruent
and sides are
parallelograms
Partners
for Mathematics Learning

19. Types of Pyramids Pyramids19
Types of Pyramids
Pyramids
 Are pointed polyhedrons with a polygon as a base
 Have triangle faces that meet at a point or vertex
 Are named by their bases
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for Mathematics Learning

20. Tracing Faces  Choose one of the prisms  Trace each face20
Tracing Faces
 Choose one of the prisms
or pyramids
 Trace each face
 How would this activity help students relate
the faces of three-dimensional objects to
two-dimensional shapes?
Partners
for Mathematics Learning

21. Questions To Ask Students21
Questions To Ask Students
 What shape do you have and how
do you know?
 What are the faces of your shape?
 Are any of the faces the congruent?
 Are any of the faces the same shape?
 Are any of the faces different?
 How many faces does your shape have?
 Can you draw around each of them?
Partners
for Mathematics Learning

22. Stamping Faces  The teacher chooses several 3-22
Stamping Faces
 The teacher chooses several 3-
dimensional shapes
 On separate pages stamp all the faces of
each shape
 In a center, students match the faces with
the shapes
Partners
for Mathematics Learning

23. Other Ideas?  What are other ways we can help students23
Other Ideas?
 What are other ways
we can help students
relate the shapes of the
faces of 3-dimenstional
to 2-dimenstional
shapes?
Partners
for Mathematics Learning

24. 24
Creating 3-D Shapes
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for Mathematics Learning

25. Making Polyhedra  Use the 2-dimensional  What Essential Standards25
Making Polyhedra
 Use the 2-dimensional
shapes to create
3-dimensional shapes
 What Essential Standards
does this activity address?
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for Mathematics Learning

26. 26
Making Shapes
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for Mathematics Learning

27. 27
Sorting Polyhedra
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for Mathematics Learning

28. 28
Making Boxes
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for Mathematics Learning

29. Match Me  This square is one of the faces of a29
Match Me
 This square is one of the faces of a
3-D shape
 What 3-D shapes could this be?
 What 3-D shapes do not have a square
face?
Partners
for Mathematics Learning

30. Geometric Match Me Cards30
Geometric Match Me Cards
 For each card, decide which three-
dimensional shapes match the description
 As you work with a partner think about
 The prior knowledge needed for this activity
 Discussion questions
 Extensions
Partners
for Mathematics Learning

31. Comparing Shapes  How do the activities in this31
Comparing Shapes
 How do the activities in this
module address the second
Essential Standard?
 What’s in the Box?
 Tracing Faces
 Stamping Faces
 Creating 3-D Shapes
 Sorting Polyhedra
 Geometric Match Me
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for Mathematics Learning

32. Shapes on the Geoboard  How are these shapes alike?32
Shapes on the Geoboard
 How are these shapes alike?
 How are they different?
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for Mathematics Learning

33. Shapes on the Geoboard  How are these shapes alike?33
Shapes on the Geoboard
 How are these shapes alike?
 How are they different?
Partners
for Mathematics Learning

34. Sorting Triangles  Look at the triangles  How could they be sorted?34
Sorting Triangles
 Look at the triangles
 How could they be sorted?
Partners
for Mathematics Learning

35. Vocabulary Opportunities35
Vocabulary Opportunities
 Students become familiar with and develop
understanding of vocabulary through many
opportunities to hear and use words and
their meanings in context, discussions, and
writing
 Class chart
 Frayer model
 Math journal
 Other ideas?
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for Mathematics Learning

36. 36
Frayer Model
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for Mathematics Learning

37. Ways to Build Vocabulary37
Ways to Build Vocabulary
 Because “sense-making” often precedes
vocabulary, provide repeated experiences
with the same terms and concepts
 Teachers use the correct mathematical
terms in “context”
 Explain meanings of vocabulary to students
informally, not with formal definitions
 Through conversations encourage everyone
to agree on “classroom” vocabulary
Partners
for Mathematics Learning

38. Communication and Reasoning38
Process Standards:
Communication and Reasoning
 Why provide opportunities for students to
write and talk about mathematics?
 “…if mathematics were treated as a native
language rather than a foreign language,
using repeated exposure and immersion,
everyone could learn a significant amount
of mathematics”
Zalman Usiskin, 1996
Partners
for Mathematics Learning

39. Revisiting Geometry Valentine Quilt  Symmetry  Congruent  Squares39
Revisiting Geometry
Valentine Quilt
 Symmetry
 Congruent
 Squares
 Triangles
 Fractions
Partners
for Mathematics Learning

40. Geometry “Some students' capabilities with geometric40
Geometry
“Some students' capabilities with geometric
and spatial concepts exceed their number
skills. Building on these strengths fosters
enthusiasm for mathematics and provides a
context in which to develop number and
other mathematics concepts.”
Razel and Eylon 1991

41. “Geometry is a significant branch of41
Geometry
“Geometry is a significant branch of
mathematics, the one most visible in
the physical world.”
Marilyn Burns
Partners
for Mathematics Learning

42.  Look back at the grade 2 Essential  Talk with your neighbor42
Essential Standards
 Look back at the grade 2 Essential
Standards
 Talk with your neighbor
 How has this module addressed
the Essential Standards?
 How will your instructional plans
be different this school year?
Partners
for Mathematics Learning

43. Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell 43
DPI Mathematics Staff
Everly Broadway, Chief Consultant
Renee Cunningham Kitty Rutherford
Robin Barbour Mary H. Russell
Carmella Fair Johannah Maynor
Amy Smith
Partners for Mathematics Learning is a Mathematics-Science
Partnership Project funded by the NC Department of Public Instruction.
Permission is granted for the use of these materials in professional
development in North Carolina Partners school districts.
Partners
for Mathematics Learning

44. PML Dissemination Consultants44
PML Dissemination Consultants
Susan Allman
Julia Cazin
Cara Gordon
Tery Gunter
Shana Runge
Yolanda Sawyer
Ruafika Cobb
Anna Corbett
Gail Cotton
Jeanette Cox
Leanne Daughtry
Lisa Davis
Ryan Dougherty
Shakila Faqih
Patricia Essick
Donna Godley
Barbara Hardy Penny Shockley
Kathy Harris
Julie Kolb
Renee Matney
Tina McSwain
Marilyn Michue
Amanda Northrup
Kayonna Pitchford
Ron Powell
Susan Riddle
Judith Rucker
Partners
for Mathematics Learning
Pat Sickles
Nancy Teague
Michelle Tucker
Kaneka Turner
Bob Vorbroker
Jan Wessell
Daniel Wicks
Carol Williams
Stacy Wozny

45. 2009 Writers Partners Staff Kathy Harris Rendy King Tery Gunter45
2009 Writers
Partners Staff
Kathy Harris
Rendy King
Tery Gunter
Judy Rucker
Penny Shockley
Nancy Teague
Jan Wessell
Stacy Wozny
Amanda Baucom
Julie Kolb
Freda Ballard, Webmaster
Anita Bowman, Outside Evaluator
Ana Floyd, Reviewer
Meghan Griffith, Administrative Assistant
Tim Hendrix, Co-PI and Higher Ed
Ben Klein , Higher Education
Katie Mawhinney, Co-PI and Higher Ed
Wendy Rich, Reviewer
Catherine Stein, Higher Education
Please give appropriate credit to the Partners
for Mathematics Learning project when using the
materials.
Jeane Joyner, Co-PI and Project Director
Partners
for Mathematics Learning

46. Grade Two PARTNERS for Mathematics Learning Module 5 Partners