Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 1)
Unit #4 : Geometry (April)
Common Core
Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build
understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes,
they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are
alike and different, to develop the background for measurement and for initial understandings of properties such as
congruence and symmetry.
Research
“In learning the geometry of shapes, students progress through increasingly powerful levels of thinking about shapes. For example, students can
develop rich and more varied visual templates for the shape categories they know, learn about new shape categories, and eventually learn
about the parts and attributes of the shapes. This is especially important if they have not yet received high-quality geometric experiences,
because research suggests that, otherwise, concepts can tend to become inflexible by the end of first grade.
First graders form and tend to initially rely on visual templates, or models, of shape categories. For example, students recognize a square because
“it looks like” other squares. Unfortunately, many students have experienced shapes named as squares only when they have a horizontal base, a
base parallel to the bottom of the page. Therefore, many believe that a square that is rotated 45 degrees from the horizontal is no longer a
square but is a diamond. To ensure that students form accurate and rich mental images, they need to experience a variety of shapes in each
shape category in varied orientations so that their mental models are not overly restricted. Students also need to see examples of shapes beyond
the familiar few. Without these, students develop limited notions. For example, many students come to believe incorrectly that a geometry figure
such as a trapezoid “is not a shape” because it is not a shape for which they know a name (often they know only circle, square, triangle, and
rectangle). Students can learn to recognize not only trapezoids, but also such shapes as rhombuses, hexagons, octagons, and parallelograms.
For several reasons, students must go beyond naming shapes to understanding their attributes. First, such descriptive activity encourages children
to move beyond visual prototypes to the use of mathematical criteria. Second, discussions redirect children’s attention and build strong
concepts, mutually affecting and benefiting mental images. Third, children find these activities interesting, and the activities engage first graders
in mathematical conversations.” (Teaching with Curriculum Focus in Grade 1)
“Children need experiences with a rich variety of both two- and three-dimensional shapes. It is useful for students to be able to identify common
shapes, notice likenesses and differences among shapes, become aware of the properties that different shapes have, and eventually use these
properties to further define and understand their geometric world. As students find out more about shapes over time, they can begin to
appreciate how definitions of special shapes come to be.
The general goal is to explore how shapes are alike and different and use these ideas to create classes of shapes (both physically and mentally).
Some of these classes of shapes have names-rectangles, triangles, prisms, cylinders, and so on. Properties of shapes, such as parallel sides,
symmetry, right angles, and so on, are included at this level but only in an informal, observational manner. Triangles should be more than just
equilateral. Shapes should have curved sides, straight sides, and combinations of these. Along the way, the names of the shapes and their
properties can be introduced casually.” (Van de Walle and Lovin, 2006)
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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 1)
Unit #4 : Geometry (April)
The chart below highlights the key understandings of this cluster 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



Reason with shapes and their
attributes.
Add and subtract within 20.
Represent and interpret data.
Essential Questions




What are the defining
attributes of shapes?
How can we reason about
shapes and their attributes?
How can we efficiently add
and subtract within 20?
How can we represent and
interpret data?
Key Vocabulary
shape
attribute
defining
circle
square
triangle
rectangle
pentagon
hexagon
equal
sides
corners
vertices
halves
half of
fourths
fourth of
quarter
quarter of
*continue basic fact and data
vocabulary
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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 1)
Unit #4 : Geometry (April)
Throughout this unit, students will develop their use of the 8 Mathematical Practices while learning the instructional standards. Specific
connections to this unit and instructional strategies are provided in the following chart.
Standards for Mathematical Practice
1. Make sense of problems and
persevere in solving them
2. Reason abstractly and quantitatively
Unit Connections and Instructional Strategies
-Students use “quick image” cards to show composite shapes for 3-5 seconds for students to copy using
cubes, solid shapes, pattern blocks, or tangrams
-Students need experiences solving problems such as, “create a rectangle out of squares”, or “create a
hexagon out of triangles”. Center cards using pattern blocks or tangrams help develop geometric problem
solving.
-Give students opportunities to build and draw shapes using a variety of materials, including paper,
technology, color tiles, pattern blocks, geoboards, and environmental objects
-Students seek examples and non-examples of a variety of shapes in their environments
3. Construct viable arguments and
critique the reasoning of others
-Students should compare shapes and describe how they are alike and different based on their own
observations (TSCM, pg. 221-222)
-Display a variety of shapes and students should sort them by a particular shape category (for example,
“triangles”) and explain what defining attributes make shapes fit into the triangle category
4. Model with mathematics
-Students should identify shapes in everyday objects or in the classroom, home, or neighborhood
-As students partition shapes into halves and fourths, expect and encourage a variety of representations (for
example, squares can be partitioned into two equal triangles or two equal rectangles)
5. Use appropriate tools strategically
-Provide students with access to a variety of appropriate tools. These may include several kinds of 2D and 3D
shape models, geoboards, paper shapes for partitioning, pattern blocks, and virtual manipulatives.
-Ask questions such as, “Why did you select this tool? How is this tool helping you learn? Will you use a
different tool next time? Why or why not?”
6. Attend to precision
-Students should have experiences cutting or separating shapes into component parts and reassembling the
parts to form the original shapes using materials such as tangrams, paper shapes, or virtual manipulatives
-Use document camera, flipchart, or overhead to show a set of shapes with a particular attribute in common
(such as three sides), and another set without the attribute. Students work together to define the attribute
that the first set has in common. (TSCM p. 207)
7. Look for and make use of structure
-Provide students with a variety of regular and irregular shapes and give them opportunities to sort, as the
“structure” is the defining attributes of shape categories.
-Students should sort shapes according to one or more attribute
8. Look for and express regularity in
repeated reasoning
-Use concept attainment strategies so that students figure out a “secret shape” (TSCM p. 195)
-Students should hunt for attributes (such as straight sides) in their environments
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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 1)
Unit #4 : Geometry (April)
Common Core State Standards
Reason with shapes and their attributes.
Standard(s)
1.G.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.
1.G.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, and right
circular cylinders) to create a
composite shape, and compose new
shapes from the composite shape.
1.G.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.
Instructional Strategies and Resource Support
TSCM pages 186-200
NCTM Focus in Grade 1 pages 55-70
-Give students opportunities to build and draw shapes using a variety
of materials, including paper, technology, color tiles, pattern blocks,
geoboards, and environmental objects
-Students should compare shapes and describe how they are alike
and different based on their own observations (TSCM, pg. 221-222)
-Students seek examples and non-examples of a variety of shapes in
their environments
-Display a variety of shapes and students should sort them by a
particular shape category (for example, “triangles”) and explain what
defining attributes make shapes fit into the triangle category
-Students should identify shapes in everyday objects or in the
classroom, home, or neighborhood
-Students use “quick image” cards to show composite shapes for 3-5
seconds for students to copy using cubes, solid shapes, pattern
blocks, or tangrams
-Students need experiences solving problems such as, “create a
rectangle out of squares”, or “create a hexagon out of triangles”.
Center cards using pattern blocks or tangrams help develop
geometric problem solving.
-As students partition shapes into halves and fourths, expect and
encourage a variety of representations (for example, squares can be
partitioned into two equal triangles or two equal rectangles)
-Provide students with access to a variety of appropriate tools. These
may include several kinds of 2D and 3D shape models, geoboards,
paper shapes for partitioning, pattern blocks, and virtual
manipulatives.
-Ask questions such as, “Why did you select this tool? How is this tool
helping you learn? Will you use a different tool next time? Why or
why not?”
-Students should have experiences cutting or separating shapes into
component parts and reassembling the parts to form the original
shapes using materials such as tangrams, paper shapes, or virtual
manipulatives
Formative
Assessments
Text
Support
Give the student shapes
A, B, and C. Ask the
student to add a shape
to Set 1. Then ask why
the shape belongs in Set
1. Student should be
able to support their
reasoning.
Scott
Foresman
155I
165A&B
165-168
167A&B
169A&B
169-170
171-172
181-186
185A&B
-Use pattern block
trapezoids, rhombi,
and/or triangles to cover
a pattern block
hexagon. How many
different ways can you
cover it?
-Use cubes to create a
larger cube.
-Give the student a
circle. Ask the student to
fold it to show halves.
Have the child write
his/her name on half of
the circle.
-Circle the rectangle that
shows fourths. Write a
sentence to explain your
thinking.
Math
Connects
395A&B
395-396
405A&B
405-406
457-458
461-462
463-464
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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 1)
Represent and interpret data.
Add and subtract within 20.
Unit #4 : Geometry (April)
1.MD.4 Organize, represent, and
interpret data with up to three
categories; ask and answer questions
about the total number of data
points, how many in each category,
and how many more or less are in one
category than in another.
-Continue to give students opportunities to collect data (for
example, related to science), organize it, and represent that
data.
-Continue to use data representations for problem solving
contexts and interpretation.
-How many students
were surveyed?
-How many more
students like ___ than
___?
1.OA.6 Add and subtract within 20,
demonstrating fluency for addition
and subtraction within 10. Use
strategies such as counting on;
making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10
+ 4 = 14); decomposing a number
leading to a ten (e.g., 13 – 4 = 13 – 3 –
1 = 10 – 1 = 9); using the relationship
between addition and subtraction
(e.g., knowing that 8 + 4 = 12, one
knows 12 – 8 = 4); and creating
equivalent but easier or known sums
(e.g., adding 6 + 7 by creating the
known equivalent 6 + 6 + 1 = 12 + 1 =
13).
*Focus on +/- “Using Doubles” or
“Near Doubles” facts and leftovers
(6+3 and 3+6)
Mastering the Basic Math Facts in Addition and
Subtraction (O’Connell & SanGiovanni)
Chapter 2: Plus 1 and Plus 2
Chapter 3: Adding Zero
Chapter 4: Adding 10
Chapter 5: Doubles
Chapter 6: Making Ten
*Tools on the accompanying CD are useful for
monitoring student progress with each strategy
and subsequent instructional ideas and resources
-Continue to have
students sort basic fact
cards by strategy and
use strategy-focused
timed assessments to
monitor progress toward
fluency in addition and
subtraction facts to 10.
TCM
313-330
Scott
Foresman
251A&B
251-252
309 A&B
309-310
311A&B
311-312
Math
Connects
125A&B
125-126
129A&B
129-134
137-139
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