Grade: 3
Units of Study
Unit 11
Trimester 3
Math
Reasoning with Shapes and Their Attributes
Number of Instructional Days: 10 Days (1 Day = 60 Minutes)
Overview
In this unit, students categorize two-dimensional according to their attributes. They
connect these attributes with definitions of shapes. They understand that shapes in
different categories may share attributes, and that the shared attributes can define a
larger category.
Content to be learned
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Understand that shapes in different categories may share attributes, and that
the shared attributes can define a larger category.
Recognize rhombuses, rectangles, and squares as examples of quadrilaterals.
Draw examples of quadrilaterals that are not a rhombus, rectangles, or square.
Categorize shapes according to their attributes.
Mathematical Practices to be integrated
Mathematically proficient students…
3 Construct viable arguments and critique the reasoning of others.
 Justify their categorizations, communicate them to others, and respond to the
arguments of others.
 Construct arguments using concrete referents such as objects, drawings,
diagrams, and actions, attribute blocks, geometry templates, etc…
4 Model with mathematics.
 Apply understanding of categories and attributes to real-world representations
of shapes.
 Build and construct visual models of shapes according to their attributes.
7 Look for and make use of structure.
 Look for patterns in number of sides, attributes of shapes, and side lengths.
 Collaborate to build a collective understanding of the structure of the problem.
Essential Questions
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How can you use attributes to categorize shapes?
What are some attributes of shapes?
What are the attributes of quadrilaterals?
How might you categorize quadrilaterals if they are not a rhombus, rectangle,
or square?
Assessment
Task Name:
Which Shape?
Written Curriculum
Grade-Level Expectations
The Common Core standards for this unit are listed in their complete form, including all
numbering and strand information and exactly as they appear in the CCSS. Any portions of the
standard(s) not addressed in this unit will be marked with a strikethrough to clarify the focus of this
unit’s activities. There will most likely be standards from more than one strand in this section.
Common Core State Standards for Mathematical Content
Geometry 3.G
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Reason with shapes and their attributes.
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.
Common Core State Standards for Mathematical Practice
3 Construct viable arguments and critique the reasoning of others.
Mathematically proficient students . . .
 understand and use stated assumptions, definitions, and previously established
results in constructing arguments.
 make conjectures and build a logical progression of statements to explore the
truth of their conjectures.
 are able to analyze situations by breaking them into cases, and can recognize
and use counterexamples.
 justify their conclusions, communicate them to others, and respond to the
arguments of others.
 reason inductively about data, making plausible arguments that take into
account the context from which the data arose;.
 are able to compare the effectiveness of two plausible arguments, distinguish
correct logic or reasoning from that which is flawed, and—if there is a flaw in an
argument—explain what it is.
 Elementary students can construct arguments using concrete referents such as
objects, drawings, diagrams, and actions. Such arguments can make sense and
be correct, even though they are not generalized or made formal until later
grades. Later, students learn to determine domains to which an argument
applies.
 can listen or read the arguments of others, decide whether they make sense,
and ask useful questions to clarify or improve the arguments.
4 Model with mathematics.
Mathematically proficient students . . .
 can apply the mathematics they know to solve problems arising in everyday
life, society, and the workplace.
 in early grades, this might be as simple as writing an addition equation to
describe a situation.
 in middle grades, a student might apply proportional reasoning to plan a school
event or analyze a problem in the community.
 by high school, might use geometry to solve a design problem or use a function
to describe how one quantity of interest depends on another.
 can apply what they know and are comfortable making assumptions and
approximations to simplify a complicated situation, realizing that these may
need revision later.
 are able to identify important quantities in a practical situation and map their
relationships using such tools as diagrams, two-way tables, graphs, flowcharts
and formulas.
 can analyze those relationships mathematically to draw conclusions.
 routinely interpret their mathematical results in the context of the situation and
reflect on whether the results make sense, possibly improving the model if it
has not served its purpose.
7 Look for and make use of structure.
Mathematically proficient students . . .
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look closely to discern a pattern or structure. Young students, for example,
might notice that three and seven more is the same amount as seven and
three more, or they may sort a collection of shapes according to how many
sides the shapes have. Later, students will see 7 × 8 equals the well
remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive
property. In the expression x2 + 9x + 14, older students can see the 14 as 2
× 7 and the 9 as 2 + 7;
recognize the significance of an existing line in a geometric figure and can use
the strategy of drawing an auxiliary line for solving problems. They also can
step back for an overview and shift perspective;
can see complicated things, such as some algebraic expressions, as single
objects or as being composed of several objects.
see, for example, 5 – 3(x – y)2 as 5 minus a positive number times a square
and use that to realize that its value cannot be more than 5 for any real
numbers x and y.
Clarifying the Standards
Prior Learning
In Second Grade, students described and analyzed shapes by examining their sides
and angles. Students investigated, described, and reasoned about decomposing and
combining shapes to make other shapes. Through building, drawing, and analyzing
two- and three-dimensional shapes, students developed a foundation for
understanding area, volume, congruence, similarity, and symmetry for use in later
grades (2.G.1, 2, and 3).
Current Learning
In Fourth Grade, this is a critical area, which contains content that students need to
have a thorough understanding of in order to go forward and major cluster (tested
majorly). Students describe, analyze, and compare attributes of two-dimensional
shapes. They compare and classify shapes by their sides and angles and connect these
with definitions of shapes. They understand that shapes in different categories may
share attributes, and that the shared attributes can define a larger category.
Future Learning
In Fourth Grade, students will describe, analyze, compare, and classify twodimensional shapes. Through building, drawing, and analyzing two-dimensional
shapes, students will deepen their understanding of properties of two-dimensional
objects and will use them to solve problems involving symmetry. They will develop an
understanding that geometric figures can be analyzed and classified based on their
properties such as having parallel sides, perpendicular sides, particular angle
measures, and symmetry. They will understand concepts of angles and measure
angles (4.MD.5ab; 4.G.1, 2, 3).
Resources and Additional Findings
“Through building, drawing, and analyzing two-dimensional shapes, students
understand attributes and properties of two-dimensional space and the use of those
attributes and properties in solving problems, including applications involving
congruence and symmetry” (Curriculum Focal Points for Prekindergarten through
Grade 8 Mathematics, p. 15).
“As students sort, build, draw, model, trace, measure, and construct, their capacity to
visualize geometric relationships will develop” (Principles and Standards for School
Mathematics, p. 165).
“As students’ ideas about shapes evolve, they should formulate conjectures about
geometric properties and relationships (Principles and Standards for School
Mathematics, p.165-166).
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The standards listed below include all the CCSS-M
linked to this Unit of Study. The list does not
distinguish among MAJOR, SUPPORTING and
ADDITIONAL standards in this Unit of Study.
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