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Building a case for blocks as kindergarten mathematics learning tools

Early Childhood Educ J (2016) 44:389–402
DOI 10.1007/s10643-015-0717-2

Building a Case for Blocks as Kindergarten Mathematics
Learning Tools
Cathy Kinzer1 • Kacie Gerhardt2 • Nicole Coca3

Published online: 4 July 2015
Ó Springer Science+Business Media New York 2015

Abstract Kindergarteners need access to blocks as thinking tools to develop, model, test, and articulate their mathematical ideas. In the current educational landscape,
resources such as blocks are being pushed to the side and
being replaced by procedural worksheets and academic ‘‘seat
time’’ in order to address standards. Mathematics research
provides a solid basis for advocating for hands on resources
to explore geometry and number concepts. Through the use
of blocks in standards based mathematical tasks, students
have the opportunity to develop important mathematical
concepts and reasoning strategies. Kindergarten teachers’
instructional actions can be grounded in history, research,
personal wisdom, and professional knowledge regarding

what is appropriate and meaningful for their students in
learning mathematics with thinking tools such as blocks.
Keywords Mathematics Á Standards Á History of blocks Á
Research informed instruction Á Practical Á Research and
Visualize 5- and 6-year-olds in a kindergarten classroom
discussing ideas, solving problems, representing objects, and
observing the shapes, sizes, patterns, and qualities of a
& Cathy Kinzer
Kacie Gerhardt
Nicole Coca

Mathematics Educator, New Mexico State University,
MSC 3CUR, Las Cruces, NM 88003-8001, USA


New York University, New York, NY, USA


Las Cruces Public Schools, Las Cruces, NM, USA

complex block structure that they have constructed collectively. Then, look to the majority of kindergarten classrooms
in the United States. On a typical day, 5- and 6-year-old
children spend less than 30 min—and often no time at all—
in child-initiated exploratory play or other learning activities
with resources such as blocks (Miller and Almon 2009).
This article is the result of a university-school partnership in which university educators participate in early
childhood classrooms, listening to teachers and learning
with young children. Through extensive interaction with
educators, as well as visits to other kindergarten classrooms
in the area, a common concern emerged about the lack of
opportunity for kindergartens to use physical blocks in
their curriculum. Historically, blocks have been an integral
part of kindergarten classrooms as resources for play,

instruction, and learning. However, as academic seat-time
in kindergarten to address literacy and numeracy standards
and carry out the required assessments has increased, the
result has been fewer opportunities for children to develop
visual, spatial, and fine motor skills by using blocks as
mathematics thinking tools. Many teachers in our partnership expressed concern that, while their mandated curriculum includes pictures of blocks on worksheets, there
are currently not many standards-based lessons that used
real blocks—such as geoblocks, pattern blocks, unit blocks,
tree blocks—for actively learning mathematics.
In spite of the lack of support for utilizing physical
blocks in contemporary standards-based curriculum, we
observed how many teachers in our community continue to
incorporate learning centers that include blocks whenever
possible. The learning centers are important because children can play, explore, and informally engage in mathematical ideas in ways that support their mathematical
development; however, they are not enough. Teachers in
our partnership have advocated for ways to bring blocks



back from the margins of the classroom. One teacher
asked, ‘‘The opportunities to learn through using blocks are
disappearing from our kindergarten school day, except
occasionally in our centers! What can we do?’’ Kindergarten teachers hope to make a case for using blocks as
learning tools to address mathematics standards and to be
an integral part of the curriculum. One kindergarten teacher
in our district said,
If we can articulate both the research and the connections to our standards, we will have a solid
foundation for advocacy…. We are teaching lessons
aligned to the mathematics standards, but how that is
done—how students experience and contribute to the
learning—makes all the difference in the world. Initially, children need concrete, hands-on tools for
thinking about and representing mathematical ideas.
They have transitioned from their homes and preschools where they were interested in using different
types of blocks in activities that stimulated language,
creativity, math knowledge, and enjoyment.
Kindergarten educators recognize the need for relevant
interactive learning activities that connect physical objects
with abstract concepts, and they seek methods to use
learning tools in ways that promote conceptual understanding of the standards that they are required to teach. Another
teacher noted,
Blocks support my students’ learning and interest in
doing math. It is more tangible and real for children as
they relate to blocks. Children use 3-D blocks to
compare sizes and shapes and see relationships
between blocks. They explore the features of shapes in
developing spatial sense and connecting to number
concepts like counting the number of sides or edges of a
block. Children value using blocks as learning tools.
The purpose of this article is to consider mathematics
learning opportunities with blocks through research and the
wisdom of teachers in kindergarten classrooms. The hope is
that kindergarten teachers will gain historical, research, and
practice-oriented perspectives as well as instructional
resources that will enable them to advocate for incorporation
of blocks as learning tools in mathematics lessons while
addressing required state or district mathematics standards.

The Context for Considering Blocks
as Mathematics Learning Tools
Blocks have been an integral part of many young children’s
lives, whether through child-initiated block play, constructions, or guided block-learning experiences. Research
shows that children have powerful intuitive mathematical


Early Childhood Educ J (2016) 44:389–402

competence (Ginsberg 1983). They do not see mathematics
as a separate subject of study until they enter formal
schooling. Children naturally think mathematically as they
compare, quantify, and explore space and shapes in the
world around them. The most powerful opportunities for
learning mathematics in primary grades are those that seek
to build from children’s cultures, languages, and pre-existing informal mathematical experiences. Many kindergarten students can connect with blocks as tools for
exploration and learning because blocks are often part of
their background experiences at home or in preschool.
These prior ways of knowing are powerful resources for
developing learning activities in the kindergarten classroom (Moll et al. 1992). Young children’s early experiences in mathematizing through familiar objects such as
blocks can contribute to collective negotiation not simply
of mathematical knowledge but also social interactions and
communication in the formal setting of kindergarten. In the
following section we discuss the historical landscapes of
blocks as manipulatives that connect to students’ curiosities, ways of knowing, and developing mathematical ideas.

Historical Foundations for Blocks as Mathematics
Learning Resources
Throughout history, humans have utilized natural materials
in the environment such as soap, wood pieces, rocks, and
boxes to build and test their ideas and inventions (Hewitt
2001). The way that blocks became integrated into more
formal educational environments is fundamental to understanding why they are important resources for kindergarten
classrooms today. Many prominent early childhood educators incorporated blocks into the curriculum because the
structure and nature of blocks provide important opportunities for young learners to connect to, and further refine,
their mathematical schemas. That is, blocks and other
manipulatives became foundational in educational contexts
because they are a way of exploring and articulating the
mathematical ideas that children are already beginning to
develop. In the following sections, we will highlight the
history of block use within the educational practices of
several seminal early childhood educators.
Fredrick Froebel (1772–1852), the originator of
kindergarten (‘‘children’s garden’’), utilized blocks in
school as learning objects based on mathematical relationships of size, shape, and geometric structures (Zuckerman 2006). Froebel focused on children’s learning from
the natural environment through structured activities and
wooden materials to develop geometric concepts and spatial reasoning skills in young children through hands-on
design and construction. Following Froebel, Maria
Montessori, a physician in Italy (1870–1952) dedicated her

Early Childhood Educ J (2016) 44:389–402

life to supporting students with special needs through
sensory training and stimulation for deliberate use of ‘‘didactic materials’’ that taught abstract concepts. For example, children constructed individual pieces of a ‘‘pink
tower’’—a graduated building made of blocks. The wooden
blocks in the tower had specific qualities such as dimensions, surface, temperature, and sounds (Montessori 1916/
1964). Froebel and Montessori shared numerous principles
in designing sensory and concept-based modular learning
objects for young learners to engage in three-dimensional
exploration to develop mathematical and science concepts
such as identifying attributes, materials, structures, and
relationships including shape, size, and symmetry that are
present in our geometric world.
Swiss psychologist Jean Piaget formalized many educational theories and built on the ideas of Froebel and
Montessori. Piaget developed the learning schema for children’s logico-mathematical knowledge that includes
important ideas in both arithmetic and spatial knowledge.
Piaget supported learning through active experiences, utilizing concrete materials, interconnecting subject areas, and
peer interactions. According to Piaget, the principle goal of
education is to develop people who are capable of doing new
things, not simply repeating what other generations have
done—people who are creative and inventive discoverers
(Piaget 1976). Many early childhood educators have contended that children should be actively engaged in learning
processes for constructing knowledge, social skills, and
dispositions that engender curiosity and contribute to collective knowledge building. Children’s spatial and geometric learning trajectory is dependent on their opportunities to
develop relevant language while exploring concepts through
spatial activities such as planning and building block cities,
designing homes for animals, studying towers around the
world, and building ramps to study movement of objects
[National Research Council (NRC) 2009].
Pratt (1948/1990) designed unit blocks with mathematical proportions of 1:2:4. These wooden unit blocks provide foundations in geometric properties and empower
students as structural designers as they build, compare,
describe, and analyze block construction. Pratt’s unit
blocks are utilized in home and school settings today (City
and Country and School 2015). These blocks are powerful
tools for creating a mathematical unit, or unitizing, which
occurs in geometry, number, and measurement contexts in
early childhood settings. Children might combine three
blue triangular pattern blocks to make a unit of one yellow
hexagon or make a repeating pattern with wooden blocks
that includes a cube, then a triangular prism, then another
cube and triangular prism, as the unit of the ab pattern. The
activity of combining blocks to make a composite shape or
knowing that ten ones is a unit of ten are very important
math concepts and reasoning processes for young learners


in developing an understanding of the base ten number
system (NRC 2009).
Blocks are typically an integral part of the constructivist
curriculum in Reggio Emilia schools that originated after
World War II (North American Reggio Emilio Alliance
2014). This curriculum emanates from students’ interests,
curiosity, and relationships with peers and materials in their
learning environment. Reggio-inspired schools typically
view children as having impressive potential and curiosity.
Children are seen as capable of constructing their own
learning and negotiating a sustained process of shared
learning in their environment. Media and materials such as
blocks are utilized to promote play, discovery, and cognitive and social connections in the processes of learning
(Gandini 2008). Children explore sizes and shapes of
blocks to engage in visualization, problem solving, and
development of collaborative social skills in an environment that connects their creations to reading, science,
mathematics, storytelling, and art. Children in Reggio-inspired settings often view learning as engaging, connected,
and interdisciplinary. This is a way for educators to utilize
blocks in instructional activities or sequences of related
activities that integrate content domains such as numeracy,
literacy, art, history, and science.

Blocks as Mathematical Reasoning Tools
While the preceding examples provide a historical perspective for blocks as resources for mathematics learning,
blocks should continue to serve as powerful objects to
externalize and advance children’s mathematical thinking
in today’s classrooms. Their attributes are particularly
important for uniting concepts that are foundational for
learning. Mathematics Learning in Early Childhood (NRC
2009) research synthesis recommends two foci in mathematics for young children: (a) number, and (b) geometry/
measurement. Individually, these domains are important
for young learners, but the connections between number
and geometry are equally significant, for example, dividing
a rectangle into two equal parts or quantifying categories or
attributes of 3–D shapes. Through the use of blocks, these
mathematical connections between numbers and geometry
become tangible and observable.
In the area of geometry, children can move through
succeeding levels of thought as they learn about geometric
shapes in two and three dimensions (Clements and Battista
1992; van Hiele 1986). Initially, children recognize geometric shapes and form visual schemes for 2-D and 3-D
shapes and spaces. As they develop spatial capacity
through experiences with tools such as blocks, they match
3-D shapes, name common geometric shapes, use relational language, categorize shapes based on properties, and



represent 2-D and 3-D relationships with objects. Children
use spatial structuring as they build in space with blocks.
They fill rectangular containers with layers of cube blocks.
They begin to understand the concepts of perspective,
symmetry, and size through building block configurations.
They can describe why some blocks stack easily (or why
they do not), according to their attributes. These block
activities bolster students’ understanding of geometric
shapes and mathematical reasoning.
According to the Mathematics Learning in Early Childhood
recommendations (NRC 2009), children use four major ideas,
or reasoning processes, in their study of mathematics content.
Blocks are explicitly named as tools for developing mathematical reasoning within these four ideas. Children in kindergarten often compose and decompose numbers and geometric
shapes. For example, several smaller rectangular prisms are
combined to make one large rectangular prism. This idea of
composing and decomposing is very important in learning
about number or quantities and their relationships (e.g.,
knowing that the quantity or total of 9 can be taken apart into the
addends or parts of 7 and 2 or 8 and 1). The second major idea is
unitizing, or creating or discovering, a mathematical unit. To
create a repeating pattern, children have to know the parts that
make up the unit (square rectangle square, repeated) and see it
as a composite whole or unit. Relating and ordering are major
mathematics ideas that are developed with blocks. This is
investigated when children compare two stacks of blocks that
have the same number of blocks but are different in height, or
one stack has more than another stack. Through this process
they observe, compare, and describe differences in measureable
attributes such as length. The fourth major idea in mathematical
reasoning for young learners is looking for patterns and structures and organizing or classifying information. Blocks are
resources for building, describing, and extending unit patterns.
For example, a unit of hexagon and a rhombus can be taken as
the basis for understanding patterns when children are asked,
‘‘What would the pattern look like if we repeated this unit four
times?’’ Or, kindergarten children can be asked to determine
how groups or categories of blocks are similar or different.
These four main ideas in developing mathematical reasoning
guide mathematics learning in kindergarten and build a strong
foundation for mathematics studies in later grades. Children’s
geometric thinking is strengthened through well-designed
activities, use of appropriate physical manipulatives (e.g.,
blocks, computer), and resource-rich learning opportunities that
support their growing geometric and spatial skills.
The historical and research review presented above
leads to the question, How might blocks be a typical
resource to support mathematics learning in kindergarten
classrooms today? In response to current accountability
and high-stakes testing practices, many kindergarten educators have pushed blocks and other useful instructional
resources to the side to meet curriculum requirements.


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Kindergarten teachers are often part of the substantive
educational accountability systems and focus on testing
that is occurring in many schools. In this realm, classroom
activities and learning experiences are often narrowed to
procedurally ‘‘cover’’ academic standards. The standards
are not always the prominent issue. The high-stakes testing
that is driving educational ‘‘reform’’ has an impact on the
quality of learning experiences in early childhood classrooms. The emphasis on developing academic skills
quickly limits opportunities for creativity, negotiation,
communication, and relational problem solving with
mathematical tools.

Contemporary Perspectives on Blocks as Learning
There are contemporary examples of schools that integrate
blocks in the kindergarten curriculum. The City and Country
School in New York City develops a range of intellectual,
social, mathematics, problem solving, and research skills
through creative block projects (City and Country School
2015). However, a growing number of kindergarten teachers
have determined that their current Common Core State
Standards (CCSS) ‘‘aligned’’ curriculum resources include
more skills-based worksheets that do not involve using
manipulatives or, worse, that students do not engage in rich
problem solving or activities that promote mathematical
reasoning, as they are often told step-by-step how to ‘‘solve
the problem.’’ While the current curriculum presents a
scarcity of mathematics tasks that are interesting on an
individual basis, children are further alienated from opportunities for deep mathematical learning through limited peer
interactions, including sharing individual or collective
mathematics thinking strategies. Children begin to believe
that mathematics is about doing worksheets rather than
engaging in rich activities that include resources for learning
and require students’ mathematical reasoning and communication of important mathematical ideas.
Currently, there is a crisis in kindergarten as teachers
report major factors that inhibit children’s opportunities to
learn through block play or block activities (Miller and
Almon 2009). Early childhood educators are often required
to teach prescribed standards, evaluate student progress,
and utilize most of the day’s schedule to focus on literacy
and numeracy, the two content areas that are assessed by
CCSS standardized tests in later grades. This leaves little or
no time for exploring, creating, or utilizing geometric
objects as thinking tools to promote deeper understanding
of number and geometry concepts. Meeting academic
standards should not come at the price of denying young
children access to engaging and robust mathematics
learning experiences.

Early Childhood Educ J (2016) 44:389–402

Advocacy Research
Blocks provide opportunities for many forms of play and
can support development of mathematics concepts and
processes. Through engaging with blocks, children classify, measure, count, and explore symmetry, shape, and
space (Piaget and Inhelder 1967; Kamii et al. 2004).
Research conducted by Wolfgang et al. (2001) determined
that children who engaged in sophisticated block play
during preschool years were more successful in junior high
and high school and achieved higher mathematics grades
and overall achievement scores.
Exploratory play by young children often reflects the
logic of, and causal structure of, scientific inquiry (Cook
et al. 2011; Schulz and Bonawitz 2007). The inherent
mathematical qualities of blocks support geometric reasoning and mathematical thinking as children explore their
shape and combinatorial aspects (Ginsburg, Inoue, and Seo
1999). Young children use blocks to reason spatially in
three dimensions—a skill that is necessary for future
engagement in mathematics, science, and engineering
disciplines. Spatial thinking is important in many areas,
such as measurement and geometry, and is predictive of
achievement in mathematics and science (Clements and
Sarama 2007; Shea et al. 2001). Using blocks can develop
mathematical and scientific thinking; young children who
engaged in block learning experiences also scored significantly higher than peers without these experiences on
language acquisition assessments (Christakis et al. 2007).
Based on this review, it is clear that blocks can support
academic learning, innovative play, and achievement
across subject domains. In addition to cognitive development, blocks as learning tools promote a range of socioemotional skills and competencies and provide children with
opportunities to interact, design, plan shared goals, negotiate, and develop persistence in solving problems together
(Cartwright 1995).

Professional Wisdom: A Vignette
of a Kindergarten Classroom
In light of current trends that eliminate such valuable handson learning materials, it is imperative that teachers and
administrators understand and articulate the research and the
implications of including thinking tools such as blocks in a
child’s learning day. Through professional knowledge,
educators are empowered to make informed decisions in
planning learning activities for young children. They can
take action based on historical perspectives, research, and
professional wisdom regarding what is appropriate for their
kindergarten students. Young children need access to blocks


as thinking tools, particularly in mathematics, to develop,
construct, test, and reflect on their learning. One of the
teachers in our partnership, who has a range of learners in her
inclusion classroom, described this imperative:
As a kindergarten teacher, it is important to provide
young students with many opportunities to explore
and manipulate blocks to deepen their geometry
understanding. By allowing students time to build
with blocks while using guiding questions, they begin
to make important connections between various
shapes that can be composed and decomposed.
This teacher described how her use of blocks in the
classroom arises out of the children’s own understandings
and experiences of shape in the everyday world as this
abstract understanding is concretized through block activities that are integrated across the academic year:
At the beginning of kindergarten, students enter with
their own conceptions about shapes, and through
guided explorations they begin to develop a more
concrete understanding of geometry. Students have a
general idea of shapes in the environment and some
students with preschool experience know the correct
names of shapes. Through songs, literature, classroom discussions, activities, and videos, all students
are exposed to shapes and their attributes. By providing time for them to use blocks they begin to make
a tangible connection to these attributes and are then
able to gain a conceptual understanding of geometry
rather than just an abstract understanding.
This teacher highlighted how pattern blocks and other
2-D resources not only provide an essential connection to
mathematical ideas, but enable students to develop essential vocabulary and social competencies in the classroom:
Throughout the first semester of kindergarten, 2-D
shapes are the focus. Students learn the proper names
of these shapes, how they can be composed and
decomposed, as well as how to describe their attributes, and how to sort and classify these shapes by
their attributes. While students are engaged in various
tasks with blocks, they are able to verbalize their
geometry connections while using correct vocabulary
and mathematical reasoning. When students are
allowed to use blocks they are excited to share their
creations with each other and their teacher. This
excitement provides a wonderful avenue to develop
their vocabulary and geometry concepts as students
describe, and draw or represent, what they have built.
By the second semester, this teacher’s class has made
substantial progress in naming and recognizing shapes
through their work with 3-D shapes, block activities, and



the use of supporting video and literature. The teacher
described how the second semester’s activities build from,
and promote, further study of shapes and their properties:
During the second semester of kindergarten, when 3-D
shapes are introduced in our class, block activities help
reinforce children’s knowledge of shape and the properties and relationships of shapes. They begin to point out
when they find cubes or cylinders in the environment. In
fact, students are also able to identify rectangular and
triangular prisms and consider how to construct equivalent shapes by making connections to geometry videos,
(like the Shape Name Game; Have Fun Teaching.org),
that they have previously viewed in the classroom.
While this kindergarten teacher is addressing the
required state standards, the integration of blocks and other
manipulatives contributes significantly to student learning
and confidence in geometry. For this teacher, a resourcerich approach to geometry includes foundational experiences that are needed to progress to higher levels of geometric thinking:
All students are capable of learning the names of
shapes and can identify them in everyday situations.
However, students that are allowed to explore with
various types of blocks have a deeper understanding
of geometry and are able to verbalize their understanding more articulately. These students have a
greater understanding of spatial relationships and can
see how shapes can be composed and decomposed,
made into a unit or pattern that can repeat, or classified and ordered with more ease than students who
have not had the opportunity to learn geometry
through these interactions and experiences.
While a significant body of literature substantiates this
teacher’s views, the practical implications of using blocks
in ways that align with Common Core State Standards is
worth further discussion.

Early Childhood Educ J (2016) 44:389–402

Another instructional strategy is to integrate literacy
activities that include writing, representing mathematical
concepts, graphing, and so forth. There is a wealth of
children’s educational books that focus on blocks, block
constructions, and geometry to support these activities.
Books recommended by kindergarten teachers include:
Bear in a Square (Blackstone 1998), The Shape of Things
(Dodds 1996), Mouse Shapes (Walsh 2007), When a Line
Bends a Shape Begins (Gowler 1997) and Shapes, Shapes
Shapes (Hoban 1996). These literacy resources connect to
geometry activities. Several examples linking literacy and
numeracy are incorporated in the block learning opportunities that follow.
Blocks provide many opportunities to integrate both the
Common Core Content and Standards for Mathematical
Practices (National Governors Association Center for Best
Practices 2010). When children are solving problems,
modeling, representing ideas, reasoning quantitatively,
developing persistence, constructing, and using blocks as
thinking tools in mathematics, they are experiencing the
mathematics practice standards. In addition to the mathematical concepts and big ideas, children need opportunities
to develop habits of mind or ways of engaging in mathematics as described in the Standards for Mathematical
Practices. These eight practices in the CCSS are mechanisms
for children to develop, refine, and extend their mathematical
thinking. They are the ways in which mathematicians make
sense of complex ideas; for young children, they are avenues
to reasoning and communication in problem solving. Children engage in these mathematical practices when they solve
mathematics problems using various types of blocks. For
example, using of mathematical tools such as blocks to think
about mathematics concepts while solving problems could
include Mathematical Practice Standards 1 and 5. Kindergarten teachers often have these practices displayed as
anchor charts in the classroom:

Eight Mathematical Practices

I can make sense of problems and solve them (persistent problem


I can use numbers, words, and objects to understand problems


I can explain my mathematical thinking to someone else and I
listen to understand others math ideas


I can show/model mathematical problems in different ways


I can use math tools to solve problems and know why I chose


I can figure things out in math so I am accurate. (Mistakes are
opportunities to learn)


I can use what I know to solve new problems


I can look for patterns and organize information to help solve

Block Activities
Many types of blocks can be used in block activities in
standards-based mathematics lessons. When implementing
such activities, the role of the teacher is critical for integrating learning with hands-on experience. A kindergarten
teacher in our partnership remarked, ‘‘I have the essential
role of asking questions that connect the block activities,
math concepts, and children’s thinking.’’ Effective questioning and listening to children’s ideas as they engage in
thinking, reasoning, and making sense of mathematical
ideas are critical to supporting learning.


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Child-friendly versions of the Mathematical Practices
are available online. Standards-based lessons provide
important opportunities for children to develop these
practices and ways of learning mathematics while engaging
in rich tasks utilizing blocks.
It is important for young students to have something
tangible when learning about shapes and their attributes.
Tangible objects allow them to feel the sides and touch the
corners that they are expected to describe in CCSS.
Through access to blocks, children begin to come to their
own conclusions about how shapes are related or different.
To develop clear understanding of geometry, children need
to use these materials extensively with their hands. A
kindergarten teacher noted,
They cannot learn that a building is made of cubes
from a picture of a building made of cubes unless
they have hands-on experience with a ‘‘real cube.’’
They begin to see that shapes can be composed of
other shapes and are enthusiastic in their discoveries
as they connect tangible objects with abstract
Through structured activities, blocks can be a vital part
of the primary mathematics curriculum. The examples of
lessons that follow provide explicit connections to the
CCSS. They are not entire lesson plans; rather, they present
key ideas for early childhood educators to consider in
providing opportunities for kindergarteners to learn
through using blocks as thinking tools to address CCSS for
mathematics. Learning environments should provide
opportunities for children to experience instructional
activities that include blocks, as well as learning centers
that honor children’s ways of making sense of geometric
ideas. This requires understanding the broader policy
landscape and advocating for teaching and learning experiences that are informed through research and the wisdom
of practice to ensure a viable engaging mathematics education that integrates blocks as learning resources for
young children in kindergarten.


also address Counting and Cardinality
Selected Mathematical Practice Standards


MP 1: I can make sense of problems and solve them.
MP 2: I can use numbers, words, and objects to understand problems.
Students are provided a small bag with an assortment of
8–10 pattern blocks. Students utilize work mats or yarn tied
to make a circle. They study the shapes of the pattern blocks
and organize or group them by attributes. Attributes may be
size, shape, color, and number of sides or corners. They put
their categories/groups on separate work mats or encircle
them with yarn. They then describe their categories and ways
of thinking about their shapes to another student or to the
class. Math conversations: ‘‘How did you group the blocks?
What did you notice about the shapes? How are the shapes
alike or different? How many groups did you make?’’
Were students thinking about the attributes of the 2-D
shapes? How did students describe the groups? Did students utilize the vocabulary word wall? What did students
notice about the shapes? Take pictures or make a poster of
several students’ representations for further study.

Connecting Blocks as Learning Tools to Common
Core State Standards for Mathematics
in Kindergarten: Lesson Learning Opportunities

Learning Opportunity: Pattern Block 2-D Design
and Count

How do Blocks Help me in Learning Geometry?
What are the Names, Shapes, and Attributes of 2-D
and 3-D Shapes?

Learning Goals: I can make a design with 5 to 15 pattern
blocks and count the colors and/or geometric shapes.
(K.CC.4.A.B.C) and (K.G.B.5)

Learning Opportunity: Pattern Block Sort
Learning Goals: I can analyze and compare shapes.
(K.G.B.4.1) (Kindergarten Geometry Standards) This can

MP 3: I can explain my mathematical thinking to
someone else.
MP 4: I can model mathematics problems in different



Students select a specified number of pattern blocks from a
tub or bag. They design a shape with that number of pattern
blocks. They count and record on paper how many of each
color and shape they used. They share their strategy and
thinking with a learning partner. The teacher documents
several student responses and asks the class to analyze and
respectfully agree or disagree with the work. Several of the
students’ representations can be used the next day during a
math talk for ten minute math activities.
Learning Opportunity: Pattern Block Pictures
Learning Goals: I can correctly name shapes (regardless of
the orientations/positions or size). (K.G.A.2)

Early Childhood Educ J (2016) 44:389–402

MP 1: I can make sense of problems and solve them.
MP 6: I can figure things out in math so I am accurate.
Students are given a set of pattern and/or attribute blocks
along with a folder or some sort of divider. The divider
will be used to shield blocks from the partner or small
group in which the student is working. One student asks
the other student to cover his/her eyes and then selects a
block and places it behind the divider. The first student
then gives the partner or group clues about the selected
shape by giving statements about its attributes. For
example, if the student selected a triangle, the student
could say, ‘‘This shape has three sides. This shape has
three corners. This shape has straight edges. This shape
looks like a slice of pizza.’’

MP 3: I can explain my mathematical thinking to
someone else.
MP 6: I can figure things out in math so I am accurate.
Students use pattern blocks either to create their own pictures or to complete pattern block pictures that the teacher
has provided. Once the pictures are completed, they students describe the picture to a partner by sharing the shapes
that were used. For example, ‘‘I used three squares and four
triangles to make my picture.’’ Once the designing partner
has shared the work, the listening partner asks a question,
such as, ‘‘Did you use any hexagons?’’ This could also be
done with wooden or foam blocks during a free-choice
center. This would address (K.G.A.3): Identify shapes as
two-dimensional (lying in a plane, ‘‘flat’’) or three-dimensional (‘‘solid’’) as well.

Learning Opportunity: Pattern/Attribute Block Share
and Ask
Learning Goals: I can describe attributes of 2D or 3D
shapes. (K.G.B.4)
MP 3: I can explain my mathematical thinking to
someone else.
MP 6: I can figure things out in math so I am accurate.

Learning Opportunity: Guess My Shape
Learning Goals: I can describe attributes of shapes by
analyzing and comparing them. (K.G.B.4)


Students are given pattern and/or attribute blocks to work
in small groups. They are also given the following sentence
frames: ‘‘I have a shape with _______sides. Who has a
shape with _________ sides?’’ or ‘‘I have a shape with
_______ corners. Who has a shape with ________ corners?’’ They fill in the blanks with their own number of
sides or corners, depending on the selected shape. When
asking the ‘‘Who has’’ portion of the question, they do not
have to use the same number of sides or corners as the
selected shape. Thus, they learn to identify and describe the
attributes of shapes. This can be done with other types of
blocks, such as geoblocks and addresses (K.G.A.3).

Early Childhood Educ J (2016) 44:389–402


Learning Opportunity: Making Shapes

Learning Opportunity: Building Block Houses for Animals

Learning Goals: I can use simple shapes to make a larger
shape. (K.G.6)

Learning Goals: I can model shapes in the world by
building shapes from components. (K.G.5) I can actively
engage in groups with peers and in reading activities with
purpose and understanding. (RL.K.10) I can use a combination of drawing, dictating, and writing to compose an
informative text. (W.K.2)

MP 4: I can show/model mathematical problems in
different ways.
MP 5: I can use math tools to solve problems.
Students are given a variety of shapes of blocks and asked to
use two or more blocks to compose larger shapes or shapes
that have different faces and shapes (triangle, rectangle,
square, hexagon), for example, ‘‘Find other unit blocks that
can make a square prism.’’ Over time, students name the new
shapes that kindergatrteners have formed, as well as the
shapes that they used to compose the new shape.
Students construct a block wall or building with equivalent
blocks (e.g., a rectangular prism that is equal to two triangular
prisms). They compose and decompose physical block shapes
to make sense of their attributes, shapes, and sizes in informal
ways. They can make equivalent shape blocks over time.
Kindergatrteners are asked to find all the possible ways to
make this rectangular prism using other blocks.
How did students compose shapes? What did they discover? How did children approach this task? What did
students notice about equivalency?

MP 1: I can make sense of problems and solve them.
MP 4: I can show/model my work in many ways.
The teacher reads a book about animal houses, such as Too
Tall Houses (Marino 2012). Students select a stuffed animal
and build a house for the animal, including a door that fits the
animal. Once the animal house is complete, the student
draws a diagram of the house and writes a description. Students are developing informal measuring skills, representing
3-D buildings in their 2-D drawings and expressing their
mathematical ideas in response to literature.



Early Childhood Educ J (2016) 44:389–402

MP 1: I can make sense of problems and solve them.
MP 4: I can show/model my work in many ways.
Students use unit blocks to build towers or tall structures or
buildings. They research real-world towers and post pictures of these towers, such as the Empire State Building.
They engage in discussion about what defines a tower and
the necessary components of towers, for example, ‘‘What is
the best way to build a foundation that a tower could be
built on?’’ Once the tower is built, each student draws a
diagram of the tower and writes a description. The block
gallery includes students’ ‘‘towers’’ and diagrams and
descriptions for discussion and inquiry.

Learning Opportunity: Building Towers

Learning Opportunity: Building Bridges

Learning Goals: I can model shapes in the world by
building shapes from components. (K.G.5) I can participate
in shared research and writing projects. (W.K.7) I can
participate in collaborative conversations with diverse
partners about kindergarten topics. (SL.K.1) I can use a
combination of drawing, dictating, and writing to compose
an informative text. (W.K.2)

Learning Goals: I can model shapes in the world by
building shapes from components. (K.G.5) I can compare
and contrast adventures and experiences of characters in
familiar stories. (RL.K.9) I can actively engage in group
and reading activities with purpose and understanding.
(RL.K.10) I can participate in collaborative conversations
with diverse partners about kindergarten topics. (SL.K.1) I


Early Childhood Educ J (2016) 44:389–402

can use a combination of drawing, dictating, and writing to
compose an informative text. (W.K.2)
MP 1: I can make sense of problems and solve them.
MP 4: I can show my work in many ways.
Students use unit blocks to build bridges. After the teacher
has read two or more ‘‘Three Billy Goats Gruff’’ stories
(e.g., Asbjornsen et al. 1957; Carpenter 1998; Galdone
1981), the students compare and contrast the stories. They
build a bridge with unit blocks and then reenact or retell the
story, using figurines. They draw a diagram and write a
description of their bridge.


foundation of unit blocks and connect ramp sections to
build a pathway for rolling balls. They place ramps at
different slopes and test results. They experiment and
determine the effect of rolling different sizes and
weights of balls (e.g., wooden, plastic, golf balls)
down ramps. They are encouraged to try various
strategies, experiment and discover principles for
themselves. If they form misconceptions, the teacher
can ask questions to invoke experimentation and

Learning Opportunity: Constructing Ramps
Learning Goals: I can model shapes in the world by
building shapes from components. (K.G.5) 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, behind,
and next to. (K.G.1) I can actively engage in group and
reading activities with purpose and understanding.
(RL.K.10) I can participate in collaborative conversations with diverse partners about kindergarten topics.
MP 1: I can make sense of problems and solve them.
MP 3: I can explain my thinking and listen to understand
Students investigate constructing and rolling balls
down elevated ramps (sections of wood cove molding).
The teacher reads a book and facilitates discussion
about constructing ramps (e.g., Roll, Slope, and Slide
(Dahl 2006)). Students work with partners to build a



Early Childhood Educ J (2016) 44:389–402

Learning Opportunity: Using Slope and Speed to Knock
Down Towers

Learning Opportunity: Using Angles to Turn Corners
on Ramps

Learning Goals: I can model shapes in the world by
building shapes from components. (K.G.5) 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, behind, and next to.
(K.G.1) I can actively engage in group reading activities
with purpose and understanding. (RL.K.10) I can participate in collaborative conversations with diverse partners
about kindergarten topics. (SL.K.1)

Learning Goals: I can model shapes in the world by
building shapes from components. (K.G.5) 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, behind, and next to.
(K.G.1) I can actively engage in group and reading activities with purpose and understanding. (RL.K.10) I can
participate in collaborative conversations with diverse
partners about kindergarten topics. (SL.K.1)

MP 1: I can make sense of problems and solve them.
MP 3: I can explain my mathematical thinking to
someone else and I listen to understand others.
MP 4: I can show/model mathematics problems in
different ways.
Students investigate ways of knocking down towers placed
at the end of ramps. They can experiment in building
various sizes of towers to study ways the ramp slope affects
results, as well as the influence of various sizes and weights
of balls (e.g., wooden, plastic, golf balls). They are
encouraged to try various strategies, experiment, and discover principles for themselves. The teacher can ask
questions to invoke experimentation and understanding.


MP 1: I can make sense of problems and solve them.
MP 4: I can show/model my work in many ways.
Students investigate strategies of getting balls to turn corners on ramps. They try various ways of building corners
on ramps, using various angles. They can experiment with
various slopes of ramps and diverse structures of walls that
will keep the balls rolling on the ramps. They are
encouraged to try a range of strategies, experiment, and
discover principles for themselves. The teacher and students can ask questions to invoke experimentation and

Early Childhood Educ J (2016) 44:389–402

Acknowledgments The authors appreciate the proffesional contributions of kindergarten teachers Glenda McShannon and Julie
Conflict of interest
of interest.

The authors declare that they have no conflict


General Suggestions for Addressing Kindergarten
Counting and Cardinality Standards with Blocks
as Learning Tools
Over time and through experiences, students will count a
set of blocks, correctly naming each block by the number
of objects that it represents. For each block counted, the
student should be able to match each object with the correct number name (cardinality, keeping track, sequencing,
and one-to-one correspondence). The use of enlarged five
frames and ten frames for counting blocks is helpful.
Create two separate groups of blocks. One group should
have more blocks (up to 10) and one group should have
fewer blocks (up to 10 but fewer than those in the other
group). Students are asked to determine which group has
more blocks and which group has fewer blocks.
Create two separate groups of blocks with an equal
number of blocks (each group should contain no more than
10 blocks). Ask students whether the two groups have a
different number of blocks or are equal, then ask them to
explain their response.
Students can generate block towers with equivalent
shapes. Discuss and ask questions about which is taller,
shorter, or the same quantity of blocks or same height.
They can deconstruct and rebuild the tower, which helps in
counting sequence and decomposing numbers.
Use blocks and categories of blocks to represent quantities. Students can engage in role-play with blocks to
represent the actions of addition and subtraction.
Students can enjoy making a block book to represent the
combinations of ten or an appropriate number.

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