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 Instructional Focus DocumentGrade 1 Mathematics
 TITLE : Unit 11: Two-Dimensional Figures SUGGESTED DURATION : 8 days

Unit Overview

Introduction
This unit bundles student expectations that address distinguishing attributes that define two-dimensional geometric figures and using attributes to identify, classify, sort, compose, and create two-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 Kindergarten, students identified, classified, sorted, and created circles, triangles, rectangles, and squares and identified attributes of these two-dimensional shapes using both informal and formal geometric language.

During this Unit
Students use formal and informal geometric language to describe the attributes that identify and define circles, triangles, rectangles, squares, rhombuses, pentagons, hexagons, and octagons. Students distinguish between attributes that define a two-dimensional figure (sides, vertices) and attributes that do not define a two-dimensional figure (size, color, orientation, texture, etc.) as they sort and classify a collection of two-dimensional shapes. While exploring attributes that define two-dimensional figures, students not only determine the number of vertices and sides, but also examine if the sides appear to be equal in length and if the corners appear to be square. It is important for students to be 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 both formal and informal 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 develop spatial visualization skills, meaning the creation and manipulation of mental representations of shapes, as they create circles, triangles, rectangles, squares, rhombuses, pentagons, hexagons, and octagons using drawings and a variety of materials. Spatial visualization is also reinforced as students compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible.

After this Unit
In Unit 13, students will continue to develop the concept of geometry as they extend their knowledge to include three-dimensional figures. Students will distinguish between attributes that do and do not define three-dimensional figures in order to identify and describe three-dimensional figures.

In Grade 1, distinguishing attributes that define geometric figures and using attributes to identify, classify, sort, compose, and create two-dimensional figures are foundational building blocks to the conceptual understanding of the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Analyzing 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; 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 the article “Young Children’s Concepts of Shape,” teachers should capitalize on geometry skills since “some children’s competence with geometric and spatial concepts exceeds their number skills” (Clements et al. 1999). The National Association for the Education of Young Children believes that “children’s mathematical thinking in geometry allows them to make a connection to number” (2002). Many researchers make connections between geometric concepts and other mathematical concepts. Students with well-developed understandings in geometry are more likely to be successful with the concepts of number, measurement, and fractions due to the development of spatial reasoning and deductive reasoning.

Clements, D. H., Swaminathan, S, Hannibal, M, & Sarama, J. (1999). Young Children’s Concepts of Shape. Journal for Research in Mathematics Education, 30, 192-212.
National Association for the Education of Young Children (NAEYC). (2002). Early Childhood Mathematics: Promoting Good Beginnings. A joint position statement of the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM). Retrieved from www.naeyc.org/about/positions/psmath.asp.
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?
• What attributes and properties are …
• used
• not used
… to sort and classify geometric figures? Why?
• How are attributes and properties used to …
• identify two-dimensional figures?
• classify two-dimensional figures?
• How are the attributes of circles and other two-dimensional figures alike and different?
• What relationship exist between the sides (outer edges) and the vertices (corners) in two-dimensional figures?
• Why is a square considered a special type of rectangle?
• How can a collection of two-dimensional figures be sorted and classified in more than one way?
• What strategies can be used to compose two-dimensional shapes to produce a target shape?
• Geometry
• Composition of Figures
• Geometric Attributes and Properties
• Classification
• Geometric Representations
• Two-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?
• How are attributes and properties used to identify two-dimensional figures?
• How are the attributes of circles and other two-dimensional figures alike and different?
• What relationship exist between the sides (outer edges) and the vertices (corners) in two-dimensional figures?
• Why is a square considered a special type of rectangle?
• What strategies can be used to create two-dimensional shapes when given specific attributes or properties?
• Geometry
• Geometric Attributes and Properties
• Classification
• Geometric Representations
• Two-dimensional figures
• Associated Mathematical Processes
• 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 figure may be categorized 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).
• Some students may think irregular two-dimensional figures have a different name than regular two-dimensional figures rather than recognizing a two-dimensional figure is identified by the number of sides and vertices (e.g., a triangle has 3 sides and 3 vertices regardless of the length of the sides or the size of the vertices, etc.).

Underdeveloped Concepts:

• Although some students may be able to 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.

Unit Vocabulary

• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., sides [outer edges], vertices [corners], etc.)
• Classify – applying an attribute to categorize a sorted group
• Compose figures – to combine smaller geometric figures to form a larger geometric figure
• Irregular hexagon – a hexagon with sides (outer edges) and/or corners that appear to be different or unequal
• Irregular triangle – a triangle with sides (outer edges) 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 sides [outer edges] 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 sides [outer edges] and 4 square corners; however, a square has 4 sides [outer edges] that appear to be the same length but a rectangle has only opposite sides [outer edges] that appear to be the same length; etc.)
• Regular hexagon – a hexagon with sides (outer edges) and corners that appear to be the same or equal
• Regular triangle – a triangle with sides (outer edges) 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
• Two-dimensional figure – a flat figure
• Vertex (vertices) in a two-dimensional figure – the point (corner) where two sides (outer edges) of a two-dimensional figure meet

Related Vocabulary:

 Circle Hexagon Octagon Orientation Pentagon Rectangle Rhombus Square Square corner Triangle
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 Grade 1 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
1.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
1.1A 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• X. Connections
1.1B 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VIII. Problem Solving and Reasoning
1.1C

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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VIII. Problem Solving and Reasoning
1.1D 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• IX. Communication and Representation
1.1E 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 an understanding of place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• IX. Communication and Representation
1.1F 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• X. Connections
1.1G 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• IX. Communication and Representation
1.6 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:
1.6A Classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language.

Classify, Sort

REGULAR AND IRREGULAR TWO-DIMENSIONAL SHAPES BASED ON ATTRIBUTES USING INFORMAL GEOMETRIC LANGUAGE

Including, but not limited to:

• Two-dimensional figure – a flat 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., sides [outer edges], vertices [corners], etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 sides [outer edges] 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 sides [outer edges] and 4 square corners; however, a square has 4 sides [outer edges] that appear to be the same length but a rectangle has only opposite sides [outer edges] that appear to be the same 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 (outer edges) 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
• Types of two-dimensional figures
• Circle
• A round, flat figure
• No straight sides (outer edges)
• No vertices (corners)
• Triangle
• 3 straight sides (outer edges)
• 3 vertices (corners)
• Regular triangle – a triangle with sides (outer edges) and corners that appear to be the same or equal
• Irregular triangle – a triangle with sides (outer edges) and/or corners that appear to be different or unequal
• Rectangle
• 4 straight sides (outer edges)
• 4 vertices (corners)
• Opposite sides equal in length
• 4 square corners
• Rhombus
• 4 straight sides (outer edges)
• 4 vertices (corners)
• All sides equal in length
• Opposite corners equal
• Square (a special type of rectangle and a special type of rhombus)
• 4 straight sides (outer edges)
• 4 vertices (corners)
• All sides equal in length
• Opposite sides equal in length
• 4 square corners
• Opposite corners equal
• Pentagon
• 5 straight sides (outer edges)
• 5 vertices (corners)
• Hexagon
• 6 straight sides (outer edges)
• 6 vertices (corners)
• Regular hexagon – a hexagon with sides (outer edges) and corners that appear to be the same or equal
• Irregular hexagon – a hexagon with sides (outer edges) and/or corners that appear to be different or unequal
• Octagon
• 8 straight sides (outer edges)
• 8 vertices (corners)
• 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):

• Kindergarten classified and sorted a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size.
• Grade 2 will classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• IX. Communication and Representation
1.6B

Distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape.

Distinguish

BETWEEN ATTRIBUTES THAT DEFINE A TWO-DIMENSIONAL FIGURE AND ATTRIBUTES THAT DO NOT DEFINE THE SHAPE

Including, but not limited to:

• Two-dimensional figure – a flat figure
• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., sides [outer edges], vertices [corners], etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 sides [outer edges] 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 sides [outer edges] and 4 square corners; however, a square has 4 sides [outer edges] that appear to be the same length but a rectangle has only opposite sides [outer edges] that appear to be the same 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 (outer edges) 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 define a two-dimensional figure
• Orientation
• Size
• Color
• Texture

Note(s):

• Kindergarten identified two-dimensional components of three-dimensional objects.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• IX. Communication and Representation
1.6C Create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons.

Create

TWO-DIMENSIONAL FIGURES, INCLUDING CIRCLES, TRIANGLES, RECTANGLES, AND SQUARES, AS SPECIAL RECTANGLES, RHOMBUSES, AND HEXAGONS

Including, but not limited to:

• Variety of materials and drawings
• Computer programs
• Art materials
• Two-dimensional figure – a flat figure
• Spatial visualization – creation and manipulation of mental representations of shapes
• 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 (outer edges) 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
• Create two-dimensional figures based on attributes and properties
• Circle
• A round, flat figure
• No straight sides (outer edges)
• No vertices (corners)
• Triangle
• 3 straight sides (outer edges)
• 3 vertices (corners)
• Regular triangle – a triangle with sides (outer edges) and corners that appear to be the same or equal
• Irregular triangle – a triangle with sides (outer edges) and/or corners that appear to be different or unequal
• Rectangle
• 4 straight sides (outer edges)
• 4 vertices (corners)
• Opposite sides equal in length
• 4 square corners
• Rhombus
• 4 straight sides (outer edges)
• 4 vertices (corners)
• All sides equal in length
• Opposite corners equal
• Square (a special type of rectangle and a special type of rhombus)
• 4 straight sides (outer edges)
• 4 vertices (corners)
• All sides equal in length
• Opposite sides equal in length
• 4 square corners
• Opposite corners equal
• Pentagon
• 5 straight sides (outer edges)
• 5 vertices (corners)
• Hexagon
• 6 straight sides (outer edges)
• 6 vertices (corners)
• Regular hexagon – a hexagon with sides (outer edges) and corners that appear to be the same or equal
• Irregular hexagon – a hexagon with sides (outer edges) and/or corners that appear to be different or unequal
• Octagon
• 8 straight sides (outer edges)
• 8 vertices (corners)

Note(s):

• Kindergarten identified two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles.
• Kindergarten created two-dimensional shapes using a variety of materials and drawings.
• Grade 2 will create two-dimensional shapes based on given attributes, including number of sides and vertices.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• IX. Communication and Representation
1.6D Identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language.

Identify

TWO-DIMENSIONAL SHAPES, INCLUDING CIRCLES, TRIANGLES, RECTANGLES, AND SQUARES, AS SPECIAL RECTANGLES, RHOMBUSES, AND HEXAGONS

Including, but not limited to:

• Two-dimensional figure – a flat figure
• Names of two-dimensional shapes
• Circle
• Triangle
• Rectangle
• Rhombus
• Square (a special type of rectangle and a special type of rhombus)
• Pentagon
• Hexagon
• Octagon
• Identify two-dimensional shapes in the real-world
• Circle
• Pizza, coin, etc.
• Triangle
• Pizza slice, yield sign, etc.
• Rectangle
• Door, TV screen, etc.
• Rhombus
• Kite, baseball diamond, etc.
• Square (a special type of rectangle and a special type of rhombus)
• Floor tiles, pizza box lid, etc.
• Pentagon
• Cross walk sign, black parts of a soccer ball pattern, etc.
• Hexagon
• Beehive hole, white parts of a soccer ball pattern, etc.
• Octagon
• Stop sign, etc.

Describe

ATTRIBUTES OF TWO-DIMENSIONAL SHAPES USING FORMAL GEOMETRIC LANGUAGE

Including, but not limited to:

• Two-dimensional figure – a flat figure
• Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., sides [outer edges], vertices [corners], etc.)
• Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 sides [outer edges] 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 sides [outer edges] and 4 square corners; however, a square has 4 sides [outer edges] that appear to be the same length but a rectangle has only opposite sides [outer edges] that appear to be the same 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 (outer edges) 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
• Types of two-dimensional figures
• Circle
• A round, flat figure
• No straight sides (outer edges)
• No vertices (corners)
• Triangle
• 3 straight sides (outer edges)
• 3 vertices (corners)
• Regular triangle – a triangle with sides (outer edges) and corners that appear to be the same or equal
• Irregular triangle – a triangle with sides (outer edges) and/or corners that appear to be different or unequal
• Rectangle
• 4 straight sides (outer edges)
• 4 vertices (corners)
• Opposite sides equal in length
• 4 square corners
• Rhombus
• 4 straight sides (outer edges)
• 4 vertices (corners)
• All sides equal in length
• Opposite corners equal
• Square (a special type of rectangle and a special type of rhombus)
• 4 straight sides (outer edges)
• 4 vertices (corners)
• All sides equal in length
• Opposite sides equal in length
• 4 square corners
• Opposite corners equal
• Pentagon
• 5 straight sides (outer edges)
• 5 vertices (corners)
• Hexagon
• 6 straight sides (outer edges)
• 6 vertices (corners)
• Regular hexagon – a hexagon with sides (outer edges) and corners that appear to be the same or equal
• Irregular hexagon – a hexagon with sides (outer edges) and/or corners that appear to be different or unequal
• Octagon
• 8 straight sides (outer edges)
• 8 vertices (corners)

Note(s):

• Kindergarten identified two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles.
• Kindergarten identified attributes of two-dimensional shapes using informal and formal geometric language interchangeably.
• Grade 2 will create two-dimensional shapes based on given attributes, including number of sides and vertices.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• IX. Communication and Representation
1.6F Compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible.

Compose

TWO-DIMENSIONAL SHAPES BY JOINING TWO, THREE, OR FOUR FIGURES TO PRODUCE A TARGET SHAPE IN MORE THAN ONE WAY IF POSSIBLE

Including, but not limited to:

• Two-dimensional figure – a flat figure
• Spatial visualization – creation and manipulation of mental representations of shapes
• Compose figures – to combine smaller geometric figures to form a larger geometric figure
• Compose two-dimensional shapes using a variety of concrete models.
• Compose regular and irregular figures to produce a target shape.
• Multiple compositions if possible

Note(s): 