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Reasoning With Shapes and Their Attributes

Unit Details
Subject(s) / Elementary Mathematics
Grade/Course / Third Grade
Unit of Study / Unit 7: Reasoning With Shapes and Their Attributes
Unit Type(s) / ❑Topical X Skills-based❑ Thematic
Pacing / 8 days
Unit Abstract
Unit Abstract
In this unit of study, students will explore shapes and their attributes. They will discover that shapes in different categories may share the same attributes. Students will extend their understanding by drawing and locating shapes that fit specific attributes and determine their category.
Common Core Essential State Standards
Common Core Essential State Standards
Domain: Geometry 3.G.1
Cluster: Reason with shapes and their attributes
Standard: 3.G.1UNDERSTAND 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
Standards for Mathematical Practice
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others. / 4. Model with mathematics.
5.Use appropriate tools strategically.
6. Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Unpacked Standards
“UNPACKED STANDARDS”
3.G.1
In second grade, students identify and draw triangles, quadrilaterals, pentagons, and hexagons. Third graders build on this experience and further investigate quadrilaterals (technology may be used during this exploration). Students recognize shapes that are and are not quadrilaterals by examining the properties of the geometric figures. They conceptualize that a quadrilateral must be a closed figure with four straight sides and begin to notice characteristics of the angles and the relationship between opposite sides. Students should be encouraged to provide details and use proper vocabulary when describing the properties of quadrilaterals. They sort geometric figures (see examples below) and identify squares, rectangles, and rhombuses as quadrilaterals.

Thirdgrade students have built a firm foundation of several shape categories, these categories can be the raw material for thinking about the relationships between classes. Students should classify shapes by attributes and drawing shapes that fit specific categories.
Example: students can form larger, categories, such as the class of all shapes with four sides, or quadrilaterals, and recognize that it includes other categories, such as squares, rectangles, rhombuses, parallelograms, and trapezoids. They also recognize that there are quadrilaterals that are not in any of those subcategories.

The standards do not require the above representation be constructed by students, but the students should be able to draw examples of quadrilaterals that are not in the subcategories.(Progressions for the CCSSM, Geometry, CCSS Writing Team, June 2012, page 13)
Example:

Parallelograms include: squares, rectangles, rhombi, or other shapes that have two pairs of parallel sides. Also, the broad category quadrilaterals include all types of parallelograms, trapezoids and other four-sided figures.
Example:
Draw a picture of a quadrilateral. Draw a picture of a rhombus.
How are they alike? How are they different?
Is a quadrilateral a rhombus? Is a rhombus a quadrilateral? Justify your thinking.
A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are beside each other.
The notion of congruence (“same size and same shape”) may be part of classroom conversation but the concepts of congruence and similarity do not appear until middle school.
TEACHER NOTE: In the U.S., the term “trapezoid” may have two different meanings. Research identifies these as inclusive and exclusive definitions. The inclusive definition states: A trapezoid is a quadrilateral with at least one pair of parallel sides. The exclusive definition states: A trapezoid is a quadrilateral with exactly one pair of parallel sides. With this definition, a parallelogram is not a trapezoid. North Carolina has adopted the exclusive definition. (Progressions for the CCSSM: Geometry, The Common Core Standards Writing Team, June 2012.
Unwrapped Skills and Concepts
“Unpacked” Concepts
(students need to know) / “Unwrapped” Skills
(students need to be able to do) / COGNITION
DOK
3.G.1
· Closed and open figure / I can identify the characteristics of an open or closed figure. / 1
· Properties of a quadrilateral / I can explain the properties of a quadrilateral by using appropriate language. / 2
· Classify shapes by attributes / I can classify shapes by attributes by drawing shapes that fit a particular category. / 2
· Attributes of a parallelogram, trapezoid, rhombus, quadrilateral / I can compare and contrast the attributes of parallelograms, rhombi, trapezoids, and quadrilaterals and explain how they may belong to a larger category. / 3
Essential Questions and Big Ideas
Essential Questions / Corresponding Big Ideas
How can you determine if a figure is closed or open? / Students will draw shapes that are open and closed.
How can you recognize examples of quadrilaterals? / Students can recognize quadrilaterals by their attributes.
How can you determine the category of a shape? / Students will recognize the attributes that define a shape into a particular category.
How can you differentiate shapes and their categories? / Students can differentiate shapes and their categories by using attributes to see that these attributes define shapes into larger category.
Vocabulary
Vocabulary
properties, attributes, features, quadrilateral, open figure, closed figure , three-sided, 2-dimensional, rhombi, rectangles, and squares are subcategories of quadrilaterals, polygon, rhombus/rhombi, rectangle, square, partition, unit fraction, kite, examples, and non-examples
From previous grades: triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle, cone, cylinder, sphere
Language Objectives
Language Objectives
Key Vocabulary
3.G.1 / SWBAT define and give examples of vocabulary specific to this standard: properties, attributes, features, quadrilateral, open figure, closed figure , three-sided, 2-dimensional, rhombi, rectangles, and squares are subcategories of quadrilaterals, polygon, rhombus/rhombi, rectangle, square, partition, unit fraction, kite
From previous grades: triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle, cone, cylinder, sphere
Language Function
3.G.1 / SWBAT identify and explain models of geometric shapes based on their attributes.
3.G.1 / SWBAT identify rhombuses, rectangles, and squares as examples of quadrilaterals.
Language Skill
3.G.1 / SWBAT explain and write the attributes of geometric figures and how they are grouped.
Grammar and Language Structures
3.G.1 / SWBAT share the attributes of a shape.
3.G.1 / SWBAT articulate the differences between quadrilaterals and non-quadrilaterals.
Lesson Tasks
3.G.1 / SWBAT explain categories of shapes and what attributes determine the groups and justify the categories to a partner.
Language Learning Strategies
3.G.1 / SWBAT explain categories of shapes and what attributes determine the groups to a peer.

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