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 Instructional Focus DocumentKindergarten Mathematics
 TITLE : Unit 12: Geometry – Three-Dimensional Solids SUGGESTED DURATION : 9 days

#### Unit Overview

Introduction
This unit bundles student expectations that address identifying three-dimensional solids, identifying the two-dimensional components of three-dimensional objects, and classifying and sorting two- and three-dimensional figures. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Unit 10, students developed the prerequisite skills of sorting and classifying, and in Unit 11, students explored the attributes of two-dimensional shapes.

During this Unit
Students explore three-dimensional solids in the context of real world objects. Students use their knowledge of two-dimensional shapes to identify three-dimensional solids. Two-dimensional shapes found in real-world objects are identified as components of three-dimensional solids. Students also classify and sort a collection of three-dimensional objects and a mixed collection of two- and three-dimensional figures based on their geometric attributes rather than other features such as orientation, color, texture, or size.

After this Unit
In Unit 14, students will apply their geometric knowledge as they explore the measurable attributes of objects.

In Kindergarten, identifying three-dimensional solids, identifying the two-dimensional components of three-dimensional objects, and classifying and sorting two- and three-dimensional figures are subsumed within the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Identifying and using attributes of two-dimensional shapes and three-dimensional solids. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning D1, D2; III. Geometric and Spatial Reasoning A1, A2; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.

Research
According to NCTM (2010), “Kindergarteners should learn to describe the differences between two-dimensional (“flat”) and three-dimensional shapes. Faces of three-dimensional shapes can be identified as specific two-dimensional shapes” (p. 65). Copley (2010) also states, “Manipulating geometric solids helps children learn geometric concepts” (p. 106).

Copley, J. (2010). The young child and mathematics. Washington, DC: National Association for the Education of Young Children
National Council of Teachers of Mathematics. (2010). Focus in kindergarten teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013

 Geometric, spatial, and measurement reasoning are foundational to visualizing, analyzing, and applying relationships within and between scale, shapes, quantities, and spatial relations in everyday life. Why is developing geometric, spatial, and measurement reasoning essential? How does geometric, spatial, and measurement reasoning affect how one sees and works in the world?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Illustrating and analyzing geometric relationships in models and diagrams aid in representing and describing the attributes of geometric figures in order to generalize geometric relationships and solve problem situations.
• What attributes and properties exist in …
• two-dimensional figures?
• three-dimensional figures?
• How are attributes and properties used to …
• identify three-dimensional solids?
• identify two-dimensional components of three-dimensional objects?
• How are …
• two-dimensional figures and three-dimensional figures
• the attributes of circles and other two-dimensional figures
• figures with curved surfaces and figures with only flat surfaces
• real-world examples and models of three-dimensional figures
… alike and different?
• What relationships exist between two-dimensional figures and three-dimensional figures?
• Geometry
• Geometric Attributes and Properties
• Classification
• Geometric Representations
• Two-dimensional figures
• Three-dimensional figures
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Geometric, spatial, and measurement reasoning are foundational to visualizing, analyzing, and applying relationships within and between scale, shapes, quantities, and spatial relations in everyday life. Why is developing geometric, spatial, and measurement reasoning essential? How does geometric, spatial, and measurement reasoning affect how one sees and works in the world?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Illustrating and analyzing geometric relationships in models and diagrams aid in representing and describing the attributes of geometric figures in order to generalize geometric relationships and solve problem situations.
• What attributes and properties exist in …
• two-dimensional figures?
• three-dimensional figures?
• What attributes and properties are …
• used
• not used
… to sort and classify geometric figures? Why?
• How are …
• two-dimensional figures and three-dimensional figures
• the attributes of circles and other two-dimensional figures
• figures with curved surfaces and figures with only flat surfaces
• real-world examples and models of three-dimensional figures
… alike and different?
• What relationships exist between two-dimensional figures and three-dimensional figures?
• How can a collection of two- and three-dimensional figures be sorted and classified in more than one way?
• Geometry
• Geometric Attributes and Properties
• Classification
• Geometric Representations
• Two-dimensional figures
• Three-dimensional figures
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

#### MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

• Some students may think a three-dimensional figure can be named using the name of one of its two-dimensional faces rather than realizing each three-dimensional figure has its own name (e.g., a student may refer to a cube as a square, etc.).
• Some students may think orientation, size, texture, and/or color are defining attributes of geometric figures rather than realizing that these features do not identify or define a shape.

#### Unit Vocabulary

• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., outer edges [sides], corners [vertices], etc.)
• Classify – applying an attribute to categorize a sorted group
• Irregular figure – a figure with outer edges (sides) and/or corners that appear to be different or unequal
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 outer edges [sides] that appear to be the same length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 outer edges [sides] and 4 square corners; however, a square has 4 outer edges [sides] that appear to be the same length but a rectangle has only opposite outer edges [sides] that appear to be the same length; etc.)
• Regular figure – a figure with outer edges (sides) and corners that appear to be the same or equal
• Side – a straight outer boundary between two vertices (line segment) of a two-dimensional figure
• Sort – grouping objects or figures by a shared characteristic or attribute
• Three-dimensional figure – a solid figure
• Two-dimensional figure – a flat figure
• Vertex (vertices) in a two-dimensional figure – a corner where two outer edges (sides) of a two-dimensional figure meet

Related Vocabulary:

 Cone Cube Curved surface Cylinder Flat surface Length Orientation/direction Prism Pyramid Sphere Surface
System Resources Other Resources

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway – Resources Aligned to Kindergarten Mathematics TEKS

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE Legend:

• Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
• Student Expectations (TEKS) identified by TEA are in bolded, black text.
• Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Specificity Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific clarifications are in italicized, blue text.
• Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
• A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
TEKS# SE# TEKS SPECIFICITY
K.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
K.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE

Including, but not limited to:

• Mathematical problem situations within and between disciplines
• Everyday life
• Society
• Workplace

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
K.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

• Problem-solving model
• Analyze given information
• Formulate a plan or strategy
• Determine a solution
• Justify the solution
• Evaluate the problem-solving process and the reasonableness of the solution

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
K.1C

Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE TO SOLVE PROBLEMS

Including, but not limited to:

• Appropriate selection of tool(s) and techniques to apply in order to solve problems
• Tools
• Real objects
• Manipulatives
• Paper and pencil
• Technology

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
K.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

• Mathematical ideas, reasoning, and their implications
• Multiple representations, as appropriate
• Symbols
• Diagrams
• Graphs
• Language

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
K.1E

Create and use representations to organize, record, and communicate mathematical ideas.

Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Representations of mathematical ideas
• Organize
• Record
• Communicate
• Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
• Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
K.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Mathematical relationships
• Connect and communicate mathematical ideas
• Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
• Current knowledge to new learning

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. ConnectionsConnections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
K.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION

Including, but not limited to:

• Mathematical ideas and arguments
• Validation of conclusions
• Displays to make work visible to others
• Diagrams, visual aids, written work, etc.
• Explanations and justifications
• Precise mathematical language in written or oral communication

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VII.A. Problem Solving and ReasoningMathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII. A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
K.6 Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:
K.6B Identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world.

Identify

THREE-DIMENSIONAL SOLIDS, INCLUDING CYLINDERS, CONES, SPHERES, AND CUBES, IN THE REAL WORLD

Including, but not limited to:

• Identify three-dimensional figures
• Three-dimensional figure – a solid figure
• Identity not changed by orientation
• Identity not changed by size
• Identity not changed by color
• Identity not changed by texture
• Identification and connection between formal geometric names to three-dimensional solids by examining objects in the real world
• Cylinder
• Can, straw, etc.
• 2 equal, opposite, flat surfaces shaped like circles
• 1 curved surface
• Rolls, slides, stacks
• Cone
• Ice cream cone, party hat, etc.
• 1 flat surface shaped like a circle
• 1 curved surface
• 1 point (vertex)
• Rolls, slides
• Sphere
• Ball, globe, etc.
• 1 curved surface forming a solid round figure
• Rolls
• Cube
• Die, alphabet block, etc.
• 6 square flat surfaces (faces)
• 12 edges
• 8 corners (vertices)
• Slides, stacks
• Distinguish between prisms and pyramids
• A prism has two flat surfaces (faces) opposite each other connected by rectangular side faces.
• A cube is a prism.
• A pyramid has one flat surface (face) opposite a point (vertex) where the triangular side faces meet.

Note(s):

• Grade 1 will identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• III.A. Geometric and Spatial Reasoning – Figures and their properties
• III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.
K.6C Identify two-dimensional components of three-dimensional objects.

Identify

TWO-DIMENSIONAL COMPONENTS OF THREE-DIMENSIONAL OBJECTS

Including, but not limited to:

• Two-dimensional figure – a flat figure
• Three-dimensional figure – a solid figure
• Two-dimensional figures as components of three-dimensional real-world objects
• Circle
• Triangle
• Rectangle
• Square (special rectangle)

Note(s):

• Grade 1 will distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape.
• Grade 1 will identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• III.A. Geometric and Spatial Reasoning – Figures and their properties
• III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.
K.6E Classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size.

Classify, Sort

A VARIETY OF REGULAR AND IRREGULAR TWO- AND THREE-DIMENSIONAL FIGURES REGARDLESS OF ORIENTATION OR SIZE

Including, but not limited to:

• Two-dimensional figure – a flat figure
• Three-dimensional figure – a solid figure
• Sort – grouping objects or figures by a shared characteristic or attribute
• Classify – applying an attribute to categorize a sorted group
• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., outer edges [sides], corners [vertices], etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 outer edges [sides] that appear to be the same length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 outer edges [sides] and 4 square corners; however, a square has 4 outer edges [sides] that appear to be the same length but a rectangle has only opposite outer edges [sides] that appear to be the same length; etc.)
• Regular and irregular figures, regardless of orientation of figure or size
• Regular figure – a figure with outer edges (sides) and corners that appear to be the same or equal
• Irregular figure – a figure with outer edge (side) lengths and/or corners that appear to be different or unequal
• Attributes of two-dimensional figures
• Side – a straight outer boundary between two vertices (line segment) of a two-dimensional figure
• Number of sides
• Length of sides
• Vertex (vertices) in a two-dimensional figure – a corner where two outer edges (sides) of a two-dimensional figure meet
• Number of vertices
• Types of vertices
• Square corners
• Square corners can be determined using the corner of a known square or rectangle (e.g., sticky note, sheet of paper, etc.).
• Not square corners
• Attributes that do not identify a two- or three-dimensional figure
• Orientation
• Size
• Color
• Texture
• Collection of two-dimensional figures
• Models and real-life objects
• Circles, triangles, rectangles, squares
• Sort and justify
• Informal and formal language used interchangeably
• Rule used for sorting expressed
• Attributes and properties of geometric figures expressed
• Existence (have) and absence (do not have) of attributes and properties expressed (e.g., figures that have “a common attribute” and figures that do not have “a common attribute”)
• Collection of three-dimensional figures
• Real-life objects
• Cylinders, cones, spheres, cubes
• Rectangular prisms, triangular prisms
• Pyramids
• Sort and justify
• Informal language
• Rule used for sorting expressed
• Attributes and properties of geometric figures expressed
• Existence (have) and absence (do not have) of attributes and properties expressed (e.g., figures that have “a common attribute” and figures that do not have “a common attribute”)
• Mixed collection of two- and three-dimensional figures
• Models and real-life objects
• Sort and justify
• Informal language
• Rule used for sorting expressed
• Attributes and properties of geometric figures expressed
• Existence (have) and absence (do not have) of attributes and properties expressed (e.g., figures that have “a common attribute” and figures that do not have “a common attribute”)

Note(s):