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 TITLE : Unit 04: Two- and Three-Dimensional Figures SUGGESTED DURATION : 10 days

#### Unit Overview

Introduction
This unit bundles student expectations that address creating, sorting, and classifying two- and three-dimensional figures, as well as composing and decomposing geometric figures based on geometric attributes. 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 Grade 1, students used both formal and informal geometric language to identify two- and three-dimensional figures based on attributes. Students also created, composed, and partitioned two-dimensional figures.

During this Unit
Students analyze attributes of two-dimensional shapes and three-dimensional solids in order to develop generalizations about their properties. Using formal geometric language, students classify and sort polygons with 12 or fewer sides by identifying the number of sides and number of vertices. Students understand that all two-dimensional polygons have a specific name based on the number of sides and vertices in the figure. It is also important that students are exposed to both regular figures where sides are the same length and irregular figures where sides are not the same length. Although students at this grade level are expected to use formal geometric language, the term “right angle” when referring to corners is not an expectation until Grade 4. However, teachers may begin to associate the words “square” and “right” when describing corners of two-dimensional figures. Students use attributes based on formal geometric language to classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), triangular prisms, square pyramids, and triangular pyramids. Students develop spatial visualization skills, meaning the creation and manipulation of mental representations of shapes, as they investigate creating two-dimensional shapes based on given attributes of the figures. Spatial visualization is also reinforced as students compose two-dimensional shapes and three-dimensional solids with given properties or attributes. Students also decompose two-dimensional shapes into equal or unequal parts and use geometric attributes to identify and name the resulting parts.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool Grade 2

After this Unit
In Grade 3, students will continue to use geometric attributes and formal language as they classify and sort two- and three-dimensional figures, including further investigation of two-dimensional shapes classified as quadrilaterals. Students will apply their knowledge of geometric figures as they investigate area of rectangles.

In Grade 2, creating, sorting, and classifying two- and three-dimensional figures, as well as composing and decomposing geometric figures based on geometric attributes are included within the Grade 2 Texas Response to Curriculum Focal Points (TxRCFP): Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts. 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 Reasoning A1; 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
In the primary grades, the instruction of geometry concepts relies heavily on hands-on manipulation of concrete objects. While early experiences with naming shapes is critical to geometry, research by the National Research Council (2001) concludes that rather than limiting geometrical investigations to simply identifying shapes, students who are “encouraged to reflect on and articulate their developing knowledge…subsequently [demonstrate] levels of reasoning well beyond their earlier performance, both in their precision of language and in their use of arguments based on the properties of shapes” (p. 285). Van de Walle (2005) explains that the teaching of geometry involves the gradual attainment of concept levels based on the accurate application of formal geometric vocabulary focused more on properties of figures than on simple identification. He states,As students begin to be able to think about properties of geometric objects without the constraints of a particular object, they are able to develop relationships between and among these properties” (p. 207). The advent of virtual three-dimensional manipulation using technology has increased the need for a well-developed spatial sense and understanding of geometric attributes and properties in order for students to be prepared for the future.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Kilpatrick, J., Swafford, J., and Findell, B. (Eds.) Mathematics Learning Study Committee, Center for Education Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
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
Van de Walle, J., & Lovin, L. (2005). Teaching student-centered mathematics grades 3 – 5. Boston, MA: Pearson Education, Inc.

 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 …
• polygons?
• two-dimensional figures?
• three-dimensional figures?
• How are attributes and properties used to classify geometric figures?
• How are attributes of three-dimensional figures represented in a picture or diagram?
• What relationships exist between …
• two-dimensional figures and three-dimensional figures?
• the sides and vertices in a polygon?
• How are …
• two-dimensional figures and three-dimensional figures
• the attributes of circles and polygons
• figures with curved surfaces and figures with only flat surfaces
… alike and different?
• How can a collection of …
• two-dimensional
• three-dimensional
… figures be sorted and classified in more than one way?
• What strategies can be used to …
• create two-dimensional shapes
• compose two-dimensional shapes
• compose three-dimensional shapes
… when given specific attributes or properties?
• How can a two-dimensional figure be decomposed in more than one way?
• How can the resulting parts of a decomposed two-dimensional figure be described?
• Geometry
• Composition and Decomposition of Figures
• 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

Underdeveloped Concepts:

• Although some students may be able to identify regular figures, they may not be able to identify irregular figures due to limited exposure to a variety of images and lack of understanding regarding the attributes of a given figure (e.g., a student may be able to identify a regular hexagon from exposure to pattern blocks but fail to recognize any closed six-sided figure as a hexagon).
• Although some students may sort or classify a set of figures by size, orientation, texture, or color, they may have difficulty sorting and classifying figures based on geometric attributes.
• Some students may categorize two-dimensional figures incorrectly based on only a few attributes of the figure rather than considering all of the figure’s defining attributes (e.g., a student may say, “If the shape has four sides, it is a square,” although this may not be true because a four-sided figure could also be a rectangle or rhombus).
• Students may have difficulty remembering formal geometric terms or distinguishing formal vocabulary from informal vocabulary (e.g., students may confuse the informal edge and the formal side of a two-dimensional figure with the formal edge of a three-dimensional figure).
• Some students may call a three-dimensional figure by the name of one of its two-dimensional faces (e.g., a student may refer to a cube as a square, etc.).

#### Unit Vocabulary

• Attributes of three-dimensional figures – characteristics that define a geometric figure (e.g., faces, curved surfaces, edges, vertices, etc.)
• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., sides, vertices, etc.)
• Classify – applying an attribute to categorize a sorted group
• Compose figures – to combine smaller geometric figures to form a larger geometric figure
• Decompose figures – to break a geometric figure into two or more smaller geometric figures
• Edge – where the sides of two faces meet on a three-dimensional figure
• Face of a prism – a polygon that forms a surface of a prism
• Irregular figure – a polygon with sides and/or corners that appear to be different or unequal
• Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
• Properties of three-dimensional figures – relationship of attributes within a geometric figure (e.g., a rectangular prism has 6 faces and each pair of opposite faces are the same size and shape, etc.) and between a group of geometric figures (e.g., a cube and a rectangular prism both have 6 faces with opposite faces equal in size and shape; however, a cube has only square faces but a rectangular prism can have square or rectangular faces; etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 sides equal in length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 sides and 4 square corners; however, a square has 4 sides equal in length but a rectangle has only opposite sides equal in length; etc.)
• Regular figure – a polygon with all 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 figure that has measurements including length, width (depth), and height
• Two-dimensional figure – a figure with two basic units of measure, usually length and width
• Vertex (vertices) in a three-dimensional figure – the point (corner) where three or more edges of a three-dimensional figure meet
• Vertex (vertices) in a two-dimensional figure – the point (corner) where two sides of a two-dimensional figure meet

Related Vocabulary:

 7-gon (heptagon) 9-gon (nonagon) 11-gon (hendecagon) 12-gon (dodecagon) Circle Cone Cube Curved surface Cylinder Decagon Flat surface Hexagon Octagon Orientation Pentagon Pyramid Rectangle Rectangular Prism Rectangular Pyramid Rhombus Sphere Square Triangle Triangular Prism Triangular Pyramid
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Center if your district has granted access to that tool.

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 Grade 2 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
2.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
2.1A 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1B 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1C

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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1D 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1E Create and use representations to organize, record, and communicate mathematical ideas.

Create, 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1F 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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. 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.
2.1G 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical 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.
2.8 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:
2.8A Create two-dimensional shapes based on given attributes, including number of sides and vertices.

Create

TWO-DIMENSIONAL SHAPES BASED ON GIVEN ATTRIBUTES, INCLUDING NUMBER OF SIDES AND VERTICES

Including, but not limited to:

• Variety of materials and drawings
• Computer programs
• Art materials
• Two-dimensional figure – a figure with two basic units of measure, usually length and width
• Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
• Spatial visualization – creation and manipulation of mental representations of shapes
• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., sides, vertices, etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 sides equal in length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 sides and 4 square corners; however, a square has 4 sides equal in length but a rectangle has only opposite sides equal in length; etc.)
• 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 – the point (corner) where two 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.).
• May have a box in corner to represent square corner
• Not square corners
• Opposite corners
• Attributes that do not identify two-dimensional figures
• Orientation
• Size
• Color
• Texture
• Regular figure – a polygon with all sides and corners that appear to be the same or equal
• Irregular figure – a polygon with sides and/or corners that appear to be different or unequal
• Create regular and irregular two-dimensional figures based on attributes and properties.
• Circle
• A figure formed by a closed curve with all points equal distance from the center
• No straight sides
• No vertices
• Triangle
• 3 sides
• 3 vertices
• Rectangle
• 4 sides
• 4 vertices
• Opposite sides equal in length
• 4 square corners
• Rhombus
• 4 sides
• 4 vertices
• All sides equal in length
• Opposite corners equal
• Square (a special type of rectangle and a special type of rhombus)
• 4 sides
• 4 vertices
• All sides equal in length
• Opposite sides equal in length
• 4 square corners
• Opposite corners equal
• Pentagon
• 5 sides
• 5 vertices
• Hexagon
• 6 sides
• 6 vertices
• 7-gon (heptagon)
• 7 sides
• 7 vertices
• Octagon
• 8 sides
• 8 vertices
• 9-gon (nonagon)
• 9 sides
• 9 vertices
• Decagon
• 10 sides
• 10 vertices
• 11-gon (hendecagon)
• 11 sides
• 11 vertices
• 12-gon (dodecagon)
• 12 sides
• 12 vertices

Note(s):

• Grade 1 created two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons.
• Grade 1 identified two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language.
• Grade 3 will use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.
2.8B Classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language.

Classify, Sort

THREE-DIMENSIONAL SOLIDS, INCLUDING SPHERES, CONES, CYLINDERS, RECTANGULAR PRISMS (INCLUDING CUBES AS SPECIAL RECTANGULAR PRISMS), AND TRIANGULAR PRISMS, BASED ON ATTRIBUTES USING FORMAL GEOMETRIC LANGUAGE

Including, but not limited to:

• Three-dimensional figure – a figure that has measurements including length, width (depth), and height
• Sort – grouping objects or figures by a shared characteristic or attribute
• Classify – applying an attribute to categorize a sorted group
• Attributes of three-dimensional figures – characteristics that define a geometric figure (e.g., faces, curved surfaces, edges, vertices, etc.)
• Properties of three-dimensional figures – relationship of attributes within a geometric figure (e.g., a rectangular prism has 6 faces and each pair of opposite faces are the same size and shape, etc.) and between a group of geometric figures (e.g., a cube and a rectangular prism both have 6 faces with opposite faces equal in size and shape; however, a cube has only square faces but a rectangular prism can have square or rectangular faces; etc.)
• Attributes of three-dimensional figures
• Surfaces
• Curved surface
• Flat surface
• Face of a prism – a polygon that forms a surface of a prism
• Number of faces
• Shape of faces
• Edge – where the sides of two faces meet on a three-dimensional figure
• Number of edges
• Vertex (vertices) in a three-dimensional figure – the point (corner) where three or more edges of a three-dimensional figure meet
• Number of vertices
• Curved surface three-dimensional figures
• Cone
• 1 flat surface shaped like a circle
• 1 curved surface
• 1 vertex
• Cylinder
• 2 equal, opposite, flat surfaces shaped like circles
• 1 curved surface
• Sphere
• 1 curved surface with all points on the surface equal distance from the center
• Prisms
• Triangular prism
• 5 faces (2 triangular faces, 3 rectangular faces)
• 9 edges
• 6 vertices
• Rectangular prism
• 6 rectangular faces
• 12 edges
• 8 vertices
• Cube (special rectangular prism or square prism)
• 6 square faces
• 12 edges
• 8 vertices
• Pyramids
• Triangular pyramid
• 4 triangular faces
• 6 edges
• 4 vertices
• Rectangular pyramid (including square pyramid)
• 5 faces (1 rectangular/square face, 4 triangular faces)
• 8 edges
• 5 vertices
• Concrete models (e.g., wood or plastic figures, etc.), real-world objects (e.g., a cereal box, can of beans, etc.), and pictorial models (e.g., drawings, images, etc.)
• Collection of three-dimensional figures
• Sort and justify
• 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):

• Grade 1 classified and sorted regular and irregular two-dimensional shapes based on attributes using informal geometric language.
• Grade 3 will classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.
2.8C Classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices.

Classify, Sort

POLYGONS WITH 12 OR FEWER SIDES ACCORDING TO ATTRIBUTES, INCLUDING IDENTIFYING THE NUMBER OF SIDES AND NUMBER OF VERTICES

Including, but not limited to:

• Two-dimensional figure – a figure with two basic units of measure, usually length and width
• 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., sides, vertices, etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 sides equal in length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 sides and 4 square corners; however, a square has 4 sides equal in length but a rectangle has only opposite sides equal in length; etc.)
• Regular figure – a polygon with all sides and corners that appear to be the same or equal
• Irregular figure – a polygon with sides 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 – the point (corner) where two 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.).
• May have a box in corner to represent square corner
• Not square corners
• Opposite corners
• Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
• Types of polygons
• Triangle
• 3 sides
• 3 vertices
• Rectangle
• 4 sides
• 4 vertices
• Opposite sides equal in length
• 4 square corners
• Rhombus
• 4 sides
• 4 vertices
• All sides equal in length
• Opposite corners equal
• Square (a special type of rectangle and a special type of rhombus)
• 4 sides
• 4 vertices
• All sides equal in length
• Opposite sides equal in length
• 4 square corners
• Opposite corners equal
• Pentagon
• 5 sides
• 5 vertices
• Hexagon
• 6 sides
• 6 vertices
• 7-gon (heptagon)
• 7 sides
• 7 vertices
• Octagon
• 8 sides
• 8 vertices
• 9-gon (nonagon)
• 9 sides
• 9 vertices
• Decagon
• 10 sides
• 10 vertices
• 11-gon (hendecagon)
• 11 sides
• 11 vertices
• 12-gon (dodecagon)
• 12 sides
• 12 vertices
• Concrete models (e.g., wood or plastic figures, etc.) and pictorial models (e.g., drawings, images, etc.)
• Collection of two-dimensional figures
• Sort and justify
• 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):

• Grade 1 classified and sorted regular and irregular two-dimensional shapes based on attributes using informal geometric language.
• Grade 3 will classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.
2.8D Compose two-dimensional shapes and three-dimensional solids with given properties or attributes.

Compose

TWO-DIMENSIONAL SHAPES WITH GIVEN PROPERTIES OR ATTRIBUTES

Including, but not limited to:

• Two-dimensional figure – a figure with two basic units of measure, usually length and width
• Spatial visualization – creation and manipulation of mental representations of shapes
• Compose figures – to combine smaller geometric figures to form a larger geometric figure
• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., sides, vertices, etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 sides equal in length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 sides and 4 square corners; however, a square has 4 sides equal in length but a rectangle has only opposite sides equal in length; etc.)
• Regular figure – a polygon with all sides and corners that appear to be the same or equal
• Irregular figure – a polygon with sides 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 – the point (corner) where two 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.).
• May have a box in corner to represent square corner
• Not square corners
• Opposite corners
• Attributes that do not identify a two-dimensional figure
• Orientation
• Size
• Color
• Texture
• Compose two-dimensional figures using a variety of concrete models.
• Compose regular and irregular figures based on attributes and properties.

Compose

THREE-DIMENSIONAL SOLIDS WITH GIVEN PROPERTIES OR ATTRIBUTES

Including, but not limited to:

• Three-dimensional figure – a figure that has measurements including length, width (depth), and height
• Spatial visualization – creation and manipulation of mental representations of shapes
• Compose figures – to combine smaller geometric figures to form a larger geometric figure
• Attributes of three-dimensional figures – characteristics that define a geometric figure (e.g., faces, curved surfaces, edges, vertices, etc.)
• Properties of three-dimensional figures – relationship of attributes within a geometric figure (e.g., a rectangular prism has 6 faces and each pair of opposite faces are the same size and shape, etc.) and between a group of geometric figures (e.g., a cube and a rectangular prism both have 6 faces with opposite faces equal in size and shape; however, a cube has only square faces but a rectangular prism can have square or rectangular faces; etc.)
• Attributes of three-dimensional figures
• Surfaces
• Curved surface
• Flat surface
• Face of a prism – a polygon that forms a surface of a prism
• Number of faces
• Shape of faces
• Edge – where the sides of two faces meet on a three-dimensional figure
• Number of edges
• Vertex (vertices) in a three-dimensional figure – the point (corner) where three or more edges of a three-dimensional figure meet
• Number of vertices
• Attributes that do not identify a three-dimensional figure
• Orientation
• Size
• Color
• Texture
• Compose three-dimensional figures using a variety of concrete models.
• Compose three-dimensional figures based on attributes and properties.

Note(s):

• Grade 1 composed two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.
2.8E Decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts.

Decompose

TWO-DIMENSIONAL SHAPES

Including, but not limited to:

• Two-dimensional figure – a figure with two basic units of measure, usually length and width
• Spatial visualization – creation and manipulation of mental representations of shapes
• Decompose figures – to break a geometric figure into two or more smaller geometric figures
• Decompose two-dimensional figures by cutting, dividing, or partitioning.
• Such as cutting a square from a rectangle
• Such as dividing a shape in half
• Such as partitioning a rectangle into identical triangles
• Resulting shapes equal or not equal
• Decompose two-dimensional shapes using a variety of concrete models and materials.

Identify

THE RESULTING GEOMETRIC PARTS OF A DECOMPOSED TWO-DIMENSIONAL SHAPE

Including, but not limited to:

• Two-dimensional figure – a figure with two basic units of measure, usually length and width
• Name resulting geometric figures (e.g., a rectangle partitioned into smaller rectangles that may or may not be equal in size or shape; a rectangle partitioned into triangles that may or may not be equal in size or shape; etc.)

Note(s):