This PowerPoint demonstrates the K-5th grade learning progressions in the mathematical area of geometry. K-5th grade standards are provided as well.

1. K-5 Learning
Progressions in
Geometry
Jennifer Temple & Megan Waldeck
National University

2. K-5 Progressions Overview
“This progression discusses the most important goals
for elementary geometry according to three categories.
• Geometric shapes, their components (e.g., sides,
angles, faces), their properties, and their categorization
based on those properties.
• Composing and decomposing geometric shapes.
• Spatial relations and spatial structuring” (CCS Writing
Team, 2013).

3. K-2 Progressions Overview
“The Standards for K-2 focus on three major
aspects of geometry. Students (1) build
understandings of shapes and their properties,
becoming (2) able to do and discuss increasingly
elaborate compositions, decompositions, and
iterations of the two, as well as (3) spatial
structures and relations” (CCS Writing Team,
2013).

4. Kindergarten: Take a Look at the Standards
CLUSTER A: Identify and describe shapes. CLUSTER B: Analyze, compare, create, and compose
shapes.
CCSS.MATH.CONTENT.K.G.A.1 CCSS.MATH.CONTENT.K.G.B.4
Describe objects using the names of shapes and
describe the relative position of the object (above,
below, beside, in front of).
Compare two and three dimensional shapes using
informal language to describe their similarities,
differences, attributes and parts.
CCSS.MATH.CONTENT.K.G.A.2 CCSS.MATH.CONTENT.K.G.B.5
Correctly name shapes. Draw shapes and build shapes from components.
CCSS.MATH.CONTENT.K.G.A.3 CCSS.MATH.CONTENT.K.G.B.6
Identify shapes as two or three dimensional. Compose simple shapes to form larger ones.
*Kindergarten has the most geometry standards of any other grade K-5!*

5. K-2 Progressions for Geometry Standards
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6. Kindergarten: Cluster A Progressions
In kindergarten, students learn to
recognize, compare, sort and name
shapes based upon geometric attributes
(number of sides, angels, etc.), not other
attributes, such as color (Gojak & Miles).
Students learn how to describe the relative
position of shapes and objects using terms
such as: above, below, beside, in front of,
behind, and next to (Gojak & Miles).
https://www.teachingchannel.org/video/build-describe-dreme

7. Kindergarten: Cluster B Progressions
Another “important area for kindergartners is
the composition of geometric figures. Students
not only build shapes from components, but
also compose shapes to build pictures and
designs” (CCS Writing Team, 2013).
In kindergarten, students learn to identify two and
three dimensional shapes, even when the shapes
have different orientations. They then learn to
describe certain features of the shapes to justify
their understanding (Gojak & MIles).
Resources: https://www.kindergartenworks.com/guided-
math/dimensional/

8. 1st Grade: Take a Look at the Standards
CLUSTER A: Reason with shapes and their attributes.
CCSS.MATH.CONTENT.1.G.A.1
Distinguish between defining attributes (ex. triangles are closed and three-sided) and non-defining attributes (color,
orientation, overall size); build and draw shapes with defining attributes.
CCSS.MATH.CONTENT.1.G.A.2
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-
dimensional shapes (cubes, right rectangular prisms, right circular cones, & right circular cylinders) to create a composite
shape, & compose new shapes from the composite shape.
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.

9. RECALL: K-2 Progressions
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10. 1st Grade Progressions
Students “continue to develop their sophistication
in describing geometric attributes and properties
and determining how shapes are alike and
different, building foundations for measurement
and initial understandings of properties such as
congruence and symmetry.” (CCS Writing Team,
2013).
● ____ # of sides
● ____ # of corners
● Closed lines
A student might say: “This has to go with the squares,
because all four sides are the same, and these are square
corners. It doesn’t matter which way it’s turned.”

11. 1st Grade Progressions
In regards to composing and decomposing, students
“learn to perceive a combination of shapes as a
single new shape (ex. recognizing that two isosceles
triangles can be combined to make a rhombus, and
simultaneously seeing the rhombus and the two
triangles).” (CCS Writing Team, 2013).
“Students learn to relate geometric figures to equal
parts and name parts as halves and fourths… they must
explore and divide shapes to make the connection that
as they create more parts, the parts get smaller” (Gojak
& MIles).

12. 2nd Grade: Take a Look at the Standards
CLUSTER A: 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. 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.

13. RECALL: K-2 Progressions
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here!

14. 2nd Grade Progressions
In regards to progressions in spatial structuring,
students in 2nd grade “structure an array to
understand two-dimensional regions as truly two-
dimensional” (CCS Writing Team, 2013).
Students will:
● Explore rows and columns within a rectangle
● Draw or place shapes in the rectangle
● Find the total number of squares in the
rectangle
Students need to understand how a rectangle
can be tiled with squares lined up in rows and
columns!

15. 2nd Grade Progressions
“Students explore decompositions of shapes into
regions that are congruent or have equal area... This progression is very similar to one of
the first grade progressions. Both are an
introduction to fractions, but here:
Students will:
● Recognize that equal shares may be
different shapes within the same whole
...For example, two squares can be partitioned into fourths in
different ways. Any of these fourths represents an equal
share of the shape (ex. “the same amount of cake”) even
though they have different shapes” (CCS Writing Team,
2013).

16. 3rd Grade: Take a Look at the Standards
CLUSTER A: Reason with shapes and their attributes.
CCSS.MATH.CONTENT.3.G.A.1
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share
attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g.,
quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw
examples of quadrilaterals that do not belong to any of these subcategories.
CCSS.MATH.CONTENT.3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the
whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as
1/4 of the area of the shape.

17. 3-5 Progressions for Geometry Standards
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18. 3rd Grade Progressions
Students will:
● Use clear, precise language to describe
quadrilaterals in discussions with others.
● Conceptualize a quadrilateral as a closed
figure with four straight sides and notice
characteristics of the angles and the
relationship between opposite sides.
...13).

19. 4th Grade: Take a Look at the Standards
CLUSTER A: Draw and identify lines and angles, and classify shapes by properties of their lines
and angles.
CCSS.MATH.CONTENT.4.G.A.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel
lines. Identify these in two-dimensional figures.
CCSS.MATH.CONTENT.4.G.A.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the
presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right
triangles.

20. RECALL: 3-5 Progressions
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here!

21. 4th Grade Progressions
Students will:
● Classify two-dimensional figures based on
the presence or absence of parallel or
perpendicular lines, or the presence or
absence of angles of a specified size.
● Discuss the relationship among various
quadrilaterals based on the number of
sides opposite sides, side lengths, and
angle measurement
...13).

22. 5th Grade: Take a Look at the Standards
CLUSTER A: Graph points on the coordinate plane to solve
real-world and mathematical problems
CLUSTER B: Classify two-dimensional figures into categories
based on their properties
CCSS.MATH.CONTENT.5.G.A.1 CCSS.MATH.CONTENT.5.G.B.3
Use a pair of perpendicular number lines, called axes, to define
a coordinate system, with the intersection of the lines (the
origin) arranged to coincide with the 0 on each line and a given
point in the plane located by using an ordered pair of numbers,
called its coordinates. Understand that the first number
indicates how far to travel from the origin in the direction of one
axis, and the second number indicates how far to travel in the
direction of the second axis, with the convention that the names
of the two axes and the coordinates correspond.
Understand that attributes belonging to a category of two-
dimensional figures also belong to all subcategories of that
category. For example, all rectangles have four right
angles and squares are rectangles, so all squares have
four right angles.
CCSS.MATH.CONTENT.5.G.A.2 CCSS.MATH.CONTENT.5.G.B.4
Represent real world and mathematical problems by graphing
points in the first quadrant of the coordinate plane, and interpret
coordinate values of points in the context of the situation.
Classify two-dimensional figures in a hierarchy based on
properties.

23. RECALL: 3-5 Progressions
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here!

24. 5th Grade: Cluster A Progressions
Students will:
● Locate coordinates on a coordinate grid by
using an ordered pair of numbers.
● Understand the first number of an ordered
pair indicates how far to travel from the origin
in the direction of one axis and the second
number indicates how far to travel in the
direction of the second axis
● Use specific vocabulary and directions to
explain ordered pair locations
...13).

25. 5th Grade: Cluster B Progressions
Students will:
● Classify two-dimensional figures based on
the presence or absence of parallel or
perpendicular lines, or the presence or
absence of angles of a specified size.
● Discuss the relationship among various
quadrilaterals based on the number of
sides opposite sides, side lengths, and
angle measurement
...13).