Carroll County Public Schools Elementary Mathematics Instructional Guide (Pre-K) Updated July 2015
Unit 3: Shapes, Patterns and Positional Language (December/January)
Maryland College and Career Readiness
During Unit 3, students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and
vocabulary. They identify, name, and describe basic two-dimensional shapes, such as circles, triangles, rectangles, and squares,
presented in a variety of ways (e.g., with different sizes and orientations). Students will compare and describe attributes of threedimensional figures such as cones, cubes, cylinders, and spheres, as well as, compose and describe structures using threedimensional shapes. Students will also begin their work with simple repeating patterns which will continue throughout the remainder
of the year.
Research
Big Ideas:
What makes shapes alike and different can be determined by an array of geometric properties.
 Shapes can be moved in a plane or in space.
 Shapes can be seen from different perspectives.
 Objects have shape.
Future Implications:
 Shape is a core component in geometry, with spatial reasoning a complementary component. Spatial reasoning
includes spatial orientation (knowing how to get around the world) and spatial visualization (knowing how to build
and manipulate objects mentally, including composing and decomposing objects). Consistent experiences with
shape and spatial relationships help students to develop spatial sense.
 Exploring shapes, comparing shapes, and seeing shapes in the environment acknowledges math in the real world.
Things to Consider:
 One of the most influential factors in geometry curriculum is the Van Hiele theory. The theory is explained in your TSC
book on pages 188-192.
 Children initially form visual templates, or models, of shapes. These templates vary depending on the quality of their
experiences. Children build more accurate templates of shapes if they experience wider varieties of each shape
category. Teachers can extend and develop children’s thinking by providing varied shapes for children to explore
and by discussing the qualities and attributes of those shapes.
Carroll County Public Schools Elementary Mathematics Instructional Guide (Pre-K) Updated July 2015
Unit 3: Shapes, Patterns and Positional Language (December/January)
The chart below highlights the key understandings of this unit along with important questions that teachers should pose to promote
these understandings. The chart also includes key vocabulary that should be modeled by teachers and used by students to show
precision of language when communicating mathematically.
Enduring Understandings
Essential Questions
Students will understand that:

Objects can be described and
compared by their attributes.

Attributes make shapes alike
and different.

Shapes can be found in the
environment.



Patterns can be represented
using shapes, objects, and/or
numbers.
Patterns can be extended by
predicting what comes next in a
sequence of repeating
elements.
Mathematical strategies can be
used to solve problems.
 How can objects be described
and compared?
 What real world objects if
traced around can be used as
examples of two dimensional
shapes?
 What real world objects can be
used as examples of three
dimensional shapes?
 How can a pattern be
represented?
 How can a pattern be
extended?
Key Vocabulary
Shapes
Circle
Cone
Corners
Cube
Cylinder
Faces
Rectangle
Rolls
Round
Shape
Sides
Sphere
Square
Stacks
Straight
Triangle
Positional Words
Above
Behind
Below
Beside
Between
In front of
Next to
Over
On
Under
Patterns
Copy
Core
Extend
Pattern
Repeat
Carroll County Public Schools Elementary Mathematics Instructional Guide (Pre-K) Updated July 2015
Unit 3: Shapes, Patterns and Positional Language (December/January)
Standards for Mathematical Practice
Connections to this Unit
1. Make sense of problems and persevere
in solving them
Have students explain what they know about shapes in the real world
Use these questions to foster this practice:
 What do you know about this shape?
 How can you make sense of this shape?
2. Reason abstractly and quantitatively
Have students recreate 2D or 3D shapes using different media
 Describe the shapes using precise language so others can recreate shapes
3. Construct viable arguments and critique
the reasoning of others
Use these questions to foster this mathematical practice:
 How can you prove this is a _______?
 What is wrong with _______’s thinking?
 What questions do you have for ______ to help you understand this shape?
4. Model with mathematics
Use these questions to foster this mathematical practice:
 What connections/similarities do you see between these two shapes?
 Where else do you see this shape?
Allow math conversations related to shapes in other subject areas
5. Use appropriate tools strategically
Allow students to use manipulatives to build 3D shapes
 Trace 3D shapes to discover the 2D counterpart
 Trace toothpicks, straws, Anglegs to help discuss attributes of 2D shapes
6. Attend to precision
Develop precise definitions of vocabulary on anchor charts
 Use vocabulary accurately and often and have children use as well
7. Look for and make use of structure
Make connection between shapes
 How is _________ similar to ___________?
8. Look for and express regularity in
repeated reasoning
Carroll County Public Schools Elementary Mathematics Instructional Guide (Pre-K) Updated July 2015
Unit 3: Shapes, Patterns and Positional Language (December/January)
PK.G.A. –Identify and describe two dimensional shapes (circles, triangles,
rectangles, including a square which is a special rectangle)
Maryland College and Career
Readiness
PK.G.A.1: Match
like twodimensional shapes
and correctly
name the shapes
regardless of their
orientations or
overall size.
Instructional Targets and Resource Support
Teacher Background Reading: TSC Pages 187-195, 217, 221-222
McGraw-Hill 20A-20B, 20E-20H, 26E-26F
Name, recognize and use the attributes of plane geometric
figures (i.e. describe shapes by number of sides and/or corners).
 Describe two-dimensional shapes (circles, triangles,
rectangles, and squares) by the number of sides and corners.
 Identify the shapes circle, triangle, rectangle, and square by
name.
 Understand that a square is a special rectangle.
 Identify triangles, circles, rectangles and squares in the
environment.
PK.G.A.2: Group
the shapes by
like attributes and
distinguish
between examples
and non-examples
of various twodimensional
shapes.
 Match two-dimensional shapes that are the same shape and
size.
 Match triangles, circles, rectangles, and squares in a variety of
orientations or different sizes.
 Distinguish examples and non-examples of the basic shapes.
 Sort two-dimensional shapes into groups based on the
attribute of shape, (by round/curved or straight sides) using
examples and non-examples.
 Describe their groupings by the attributes used (curved or
straight lines) or by the names of the shapes.
Formative
Assessments
Obeservation
Can the
student
identify a
shape by
name (circle,
triangle,
rectangle or
square)?
Can the
student
describe a
shape by the
number of
sides and
corners?
Can the
student
match like
shapes that
are the same
size? different
size? different
orientation?
Can the
student sort
shapes based
on an
attribute?
Can they
name the
attribute or
shape name
used to sort?
Text Support
09 McGraw-Hill
Math Connects
24A – 24D
25A – 25D
Growing with
Mathematics
(pre-k edition)
11-7, 11-8, 11-9,
11-10, 11-13
(k edition)
3-22, 3-28,
7-10, 7-12,
7-13, 7-20,
7-29
Carroll County Public Schools Elementary Mathematics Instructional Guide (Pre-K) Updated July 2015
Unit 3: Shapes, Patterns and Positional Language (December/January)
PK.G.B. –Work with three- dimensional shapes to gain foundations for geometric
thinking
Maryland College and Career
Readiness
PK.G.B.3: Match
and sort threedimensional
shapes.
PK.G.B.4: Use real
world examples
to describe
threedimensional
objects using
correct
mathematical
vocabulary
(cube, sphere,
and cylinder).
Instructional Targets and Resource Support
Teacher Note: This standard should be taught using wooden blocks and concrete
manipulatives from your “Block Center”. Students should have multiple experiences with
free play using these materials to explore three-dimensional shapes. Students are not
expected to name these shapes in the early stages of working with the shapes. During
these beginning stages of working with three-dimensional shapes, students will use real
world names for the shapes such as ice cube for cube or ball for sphere. Teachers should
introduce the correct mathematical names for the three-dimensional shapes as students
work with the shapes.
Compare and describe attributes of three-dimensional figures such
as cones, cubes, cylinders, and spheres.
 Identify and describe the likeness and differences in threedimensional shapes.
 Sort three-dimensional shapes into groups to show an attribute of
likeness.
 Identify and compare three-dimensional figures by sorting and
describing sides as flat or curved.
 Compare three-dimensional figures with real world objects.
 Match like three-dimensional shapes.
 Use age appropriate language to tell how two three-dimensional
shapes are alike or different.
 Recognize two dimensional shapes within a three-dimensional
shape.(i.e. one side of a cube looks like a square).
 Ability to describe three-dimensional objects using vocabulary
such as shape, corners, edges, and/or similarities to other shapes
(i.e. a cube has six sides and each side looks like a square).
Formative
Assessments
Observation
Can the
student sort
threedimensional
shapes by
an
attribute?
Can the
student
identify
and/or
describe
sides of a
threedimensional
shape as flat
or curved?
Can the
student
match like
threedimensional
shapes that
are the
same size?
different
size?
Can the
student
identify a
twodimensional
shape within
a threedimensional
shape?
Text Support
09 McGraw-Hill
Math Connects
21A – 21D
22A – 22D
Growing with
Mathematics
(pre-k edition)
3-15, 3-16,
3-17, 3-21
(k edition)
3-20, 3-21,
3-23, 3-24,
3-25, 3-26,
3-27
Carroll County Public Schools Elementary Mathematics Instructional Guide (Pre-K) Updated July 2015
Unit 3: Shapes, Patterns and Positional Language (December/January)
PK.G.B. –Work with three- dimensional shapes to gain
foundations for geometric thinking
Maryland College and Career
Readiness
PK.G.B.5: Compose and
describe structures using
three-dimensional
shapes. Descriptions
may include shape
attributes, relative
position, etc.
Instructional Targets and Resource Support
Teacher Note: This standard should be taught using wooden blocks and
concrete manipulatives from your “Block Center”. Students should have
multiple experiences with free play using these materials to explore threedimensional shapes. Students are not expected to name these shapes in
the early stages of working with the shapes. During these beginning
stages of working with three-dimensional shapes, students will use real
world names for the shapes such as ice cube for cube or ball for sphere.
Teachers should introduce the correct mathematical names for the
three-dimensional shapes as students work with the shapes.
 Build structures using manipulatives and blocks.
 Describe their structures including shapes, sizes,
comparisons, positional relationships, etc.
Formative
Assessments
Observation
Can the
student
create a
structure
using
blocks?
Can the
student
describe
their
structure (or
a given
structure)
using shape
names? size
words?
positional
language?
Text Support
Growing with
Mathematics
(k edition)
3-13, 3-28
Carroll County Public Schools Elementary Mathematics Instructional Guide (Pre-K) Updated July 2015
Unit 3: Shapes, Patterns and Positional Language (December/January)
Maryland College and Career
Readiness
Instructional Targets and Resource Support
Teacher Background Reading: TSC Pages 276-280; McGrawHill 34A-34B, 34E-34H, 40C-40D
The instructional targets below should continue to be
developed throughout the year.
 Represent and duplicate simple repeating patterns using
no more than 2 different objects and different actions in
the core of the pattern.
 Extend simple patterns of sound, movement, and concrete
objects by predicting what comes next in a sequence of
repeating elements.
Formative
Assessments
Observation
Can the
student
represent a
repeating
pattern
using 2
different
objects
and/or
actions in
the core?
Can the
student
duplicate a
repeating
pattern
using 2
different
objects
and/or
actions in
the core?
Can the
student
extend a
repeating
pattern?
Text Support
09 McGraw-Hill
Math Connects
37A – 37D
38A – 38D
Growing with
Mathematics
(pre-k edition)
7-11, 7-12,
11-16, 11-18,
11-19, 12-24
(k edition)
3-30, 3-31,
3-32, 3-33,
3-34, 3-37,
3-38,3-39,
3-40, 4-36,
7-32, 7-33,
7-34