THE SHAPE OF GEOMETRY FOR PREK-2
TEACHING AND LEARNING IN THE
COMMON CORE
Lucia M. Flevares & Jamie R. Schiff
SESSION GOALS
1. To explore your knowledge of the design and
implementation of geometry experiences for
students in the PK-2 years, using the Common
Core Standards and the Ohio Pre-Kindergarten
Content Standards for Mathematics
2. To map standards between the primary grades
and back to the Pre-kindergarten years.
3. To share resources for lessons that will help
meet the Common Core geometry goals for the
prekindergarten and early elementary years.
AGENDA FOR THE HOUR

CCSS Geometry Background Knowledge:



What do your teachers/students already know?
What do you still want to know?
Activity: Mapping out the standards
Identifying connections/gaps across grade levels
 Focus on vocabulary


What is new to you?
Learning Progressions
 Back mapping to Pre K


Conclusions
BACKGROUND KNOWLEDGE & POLL
Questions
What do you, and your/ teachers/students already know about
geometry in the early grades and the CCSS?
 What do you still want to know?

Table or Row Discussion

Nominate a person to share out your ideas.
LEARNING PROGRESSIONS
"A learning progression is a
carefully sequenced set of
building blocks that students
must master en route to
mastering a more distant
curricular aim. These building
blocks consist of subskills and
bodies of enabling knowledge"
(Popham, 2007, p. 83)
BACKMAPPING
 “The
process of analyzing desired student
outcomes (or learning objectives) to
identify prerequisite skills and knowledge;
starting with what students will know
and be able to do at the end of a course
and drilling down to what must be
learned first, in order for the outcome to
be successful.”
 teachingtoday.glencoe.com/glossary
ACTIVITY: MAPPING OUT THE STANDARDS

Problem/ challenge: With current students, we must
always keep in mind that their understanding depends
on previous experiences and current experiences then
set the stage for future learning.
Please:
(Re)join your small group
 Read your instructions
 Discuss for 10 minutes

REFERENCES
Popham, W. J. (2007). The lowdown on learning
progressions. Educational Leadership, 64, 83-4.
teachingtoday.glencoe.com/glossary
PREKINDERGARTEN: SPATIAL SENSE


STANDARD STATEMENT: Demonstrate
understanding of the relative positions of
objects with terms such as in/on/under,
up/down, inside/outside, above/ below,
beside/between, in front of/ behind, and next to.
EXAMPLES
Says “My toy fell under the table,” or “I left my ball
outside,” or “Sit down beside me.”
 Navigates an obstacle course when the teacher says “go
under the bridge” and then “go around the climber.”
 Says, “My dad keeps the car inside the garage.”
 Builds simple but meaningful “maps” using blocks and toys
such as trees, cars, houses, and describes relative positions.
(e.g., “The truck is beside the road.” “The dog is behind the
house.”).

PRE-KINDERGARTEN: IDENTIFY AND
DESCRIBE SHAPES
STANDARD STATEMENT: Understand and use
names of shapes when identifying objects.
 EXAMPLES
Recognizes and names basic two-dimensional shapes,
including, circle, square, rectangle, and triangle.
 While playing a game of shape bingo, identify different
shapes that are called out loud.
 While playing with blocks, asks a friend, “Can I have
another square block?”

STANDARD STATEMENT: Names threedimensional objects using informal, descriptive
vocabulary.
 EXAMPLES



Refers to a cube as a “box.”
Calls the cone “ice cream cone.”
Calls a sphere a “ball.”
PRE-KINDERGARTEN: ANALYZE, COMPARE
AND CREATE SHAPES
STANDARD STATEMENT: Compare two-dimensional shapes, in different
sizes and orientations, using informal language.
 EXAMPLES




Locates two-dimensional geometric shapes of differing size and orientation in the
classroom environment.
Answers questions like “How do you know the shape is a triangle?” by describing the
number of “lines” and “points.”
Identifies two-dimensional shapes by feel in a “feely box.”
Identifies a triangle whether sitting on its base or on its point.
STANDARD STATEMENT: Create shapes during play by building, drawing,
etc.
 EXAMPLES



Draws a picture of his house using some basic shapes such as a rectangle for the
building and a triangle for the roof and a circle for the sun.
Creates symmetrical block structures.
Draws shapes from memory.
STANDARD STATEMENT: Combine simple shapes to
form larger shapes.
 EXAMPLES



Uses blocks to create larger shape structures.
Manipulates pattern blocks to form larger shapes.
Describes the shapes used to create new shapes.
CCSS KINDERGARTEN

Identify and describe shapes.
CCSS.Math.Content.K.G.A.1 Describe objects in the environment
using names of shapes, and describe the relative positions of these
objects using terms such as above, below, beside, in front of, behind,
and next to.
 CCSS.Math.Content.K.G.A.2 Correctly name shapes regardless of
their orientations or overall size.
 CCSS.Math.Content.K.G.A.3 Identify shapes as two-dimensional
(lying in a plane, “flat”) or three-dimensional (“solid”).


Analyze, compare, create, and compose shapes.
CCSS.Math.Content.K.G.B.4 Analyze and compare two- and threedimensional shapes, in different sizes and orientations, using informal
language to describe their similarities, differences, parts (e.g., number
of sides and vertices/“corners”) and other attributes (e.g., having sides
of equal length).
 CCSS.Math.Content.K.G.B.5 Model shapes in the world by building
shapes from components (e.g., sticks and clay balls) and drawing
shapes.
 CCSS.Math.Content.K.G.B.6 Compose simple shapes to form larger
shapes. For example, “Can you join these two triangles with full sides
touching to make a rectangle?”

CCSS 1ST GRADE



CCSS.Math.Content.1.G.A.1 Distinguish between defining
attributes (e.g., triangles are closed and three-sided) versus
non-defining attributes (e.g., color, orientation, overall size)
; build and draw shapes to possess defining attributes.
CCSS.Math.Content.1.G.A.2 Compose two-dimensional
shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quarter-circles) or three-dimensional shapes
(cubes, right rectangular prisms, right circular cones, and
right circular cylinders) to create a composite shape, and
compose new shapes from the composite shape1.
CCSS.Math.Content.1.G.A.3 Partition circles and
rectangles into two and four equal shares, describe the
shares using the words halves, fourths, and quarters, and
use the phrases half of, fourth of, and quarter of. Describe
the whole as two of, or four of the shares. Understand for
these examples that decomposing into more equal shares
creates smaller shares.
CCSS 2ND GRADE




Reason with shapes and their attributes.
CCSS.Math.Content.2.G.A.1 Recognize and draw
shapes having specified attributes, such as a given
number of angles or a given number of equal faces.1
Identify triangles, quadrilaterals, pentagons,
hexagons, and cubes.
CCSS.Math.Content.2.G.A.2 Partition a rectangle
into rows and columns of same-size squares and count
to find the total number of them.
CCSS.Math.Content.2.G.A.3 Partition circles and
rectangles into two, three, or four equal shares,
describe the shares using the words halves, thirds,
half of, a third of, etc., and describe the whole as two
halves, three thirds, four fourths. Recognize that
equal shares of identical wholes need not have the
same shape.
WHAT’S NEW?

Participant responses


Connections between responses and implementation
Changes/ shifts not merely in terms of phrasings of standards
& vocabulary but in terms of thinking about implementation.
From ODE:
Coherence
 Within & across grades
 Focus:
 Key ideas clearly identified
 Expectation of deep rather than broad learning
 Rigor:
 Deep conceptual understanding
 Skills and fluency
 Application

WHAT’S NEW

Resources and Planning

www.illustrativemathematics.org
 http://ohiorc.org/standards/commoncore/mathematics/
K
and up standards listed;
 Activities

linked to standards
Others you’ve found?
RESOURCES: ILLUSTRATIVE
MATHEMATICS.ORG
SELECT A GRADE…
SELECT A DOMAIN (LIKE GEOMETRY) …
LOOK FOR ILLUSTRATIONS FOR
STANDARDS OR CLUSTERS OF STANDARDS
Look for “see
Illustrations”
SELECT A TASK…
VIEW THE TASK
CONCLUSIONS


What would you share with a fellow educator?
What are you remaining concerns about implementing
the CCSS in K-2?
Our contact info:
 Lucia M. Flevares



flevares.1@osu.edu
Jamie R. Schiff

schiff.64@osu.edu