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 twodimensional shapes and threedimensional solids
 TxCCRS:
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving 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 twodimensional shapes and threedimensional 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 problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving 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 twodimensional shapes and threedimensional 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 twodimensional shapes and threedimensional 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

K.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 whole numbers
 Developing an understanding of addition and subtraction
 Identifying and using attributes of twodimensional shapes and threedimensional 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 nonexamples, 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 twodimensional shapes and threedimensional 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. 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.

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 twodimensional shapes and threedimensional solids
 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.

K.6 
Geometry and measurement. The student applies mathematical process standards to analyze attributes of twodimensional shapes and threedimensional solids to develop generalizations about their properties. The student is expected to:


K.6A 
Identify twodimensional shapes, including circles, triangles, rectangles, and squares as special rectangles.

Identify
TWODIMENSIONAL SHAPES, INCLUDING CIRCLES, TRIANGLES, RECTANGLES, AND SQUARES AS SPECIAL RECTANGLES
Including, but not limited to:
 Identify twodimensional figures
 Twodimensional figure – a flat figure
 Identity not changed by orientation
 Identity not changed by size
 Identity not changed by color
 Identity not changed by texture
 Circle
 A round, flat figure
 No straight outer edges (sides)
 No corners (vertices)
 Triangle
 3 straight outer edges (sides)
 3 corners (vertices)
 Regular triangle – a triangle with outer edges (sides) and corners that appear to be the same or equal
 Irregular triangle – a triangle with outer edges (sides) and/or corners that appear to be different or unequal
 Rectangle
 4 straight outer edges (sides)
 4 square corners (vertices)
 Opposite outer edge (side) lengths that appear to be the same or equal
 Square (special rectangle)
 4 straight outer edges (sides)
 4 square corners (vertices)
 All outer edge (side) lengths that appear to be the same or equal
 Opposite outer edge (side) lengths that appear to be the same or equal
Note(s):
 Grade Level(s):
 Grade 1 will identify twodimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons 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 twodimensional shapes and threedimensional solids
 TxCCRS:
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.1. Recognize characteristics and dimensional changes of two and threedimensional figures.

K.6D 
Identify attributes of twodimensional shapes using informal and formal geometric language interchangeably.

Identify
ATTRIBUTES OF TWODIMENSIONAL SHAPES USING INFORMAL AND FORMAL GEOMETRIC LANGUAGE INTERCHANGEABLY
Including, but not limited to:
 Twodimensional figure – a flat figure
 Attributes of twodimensional figures – characteristics that define a geometric figure (e.g., outer edges [sides], corners [vertices], etc.)
 Properties of twodimensional 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.)
 Connection between informal language and formal language
 Use interchangeably
 “Side” for informal term “edge”
 Side – a straight outer boundary between two vertices (line segment) of a twodimensional figure
 “Vertex” or “vertices” for informal term “corners”
 Vertex (vertices) in a twodimensional figure – a corner where two outer edges (sides) of a twodimensional figure meet
 Circle
 A round, flat figure
 No straight outer edges (sides)
 No corners (vertices)
 Triangle
 3 straight outer edges (sides)
 3 corners (vertices)
 Regular triangle – a triangle with outer edges (sides) and corners that appear to be the same or equal
 Irregular triangle – a triangle with outer edges (sides) and/or corners that appear to be different or unequal
 Rectangle
 4 straight outer edges (sides)
 4 square corners (vertices)
 Opposite outer edge (side) lengths that appear to be the same or equal
 Square (special rectangle)
 4 straight outer edges (sides)
 4 square corners (vertices)
 All outer edge (side) lengths that appear to be the same or equal
 Opposite outer edge (side) lengths that appear to be the same or equal
 Attributes that do not identify a twodimensional figure
 Orientation
 Size
 Color
 Texture
Note(s):
 Grade Level(s):
 Kindergarten transitions to formal geometric language to describe the attributes of twodimensional shapes.
 Grade 1 will identify twodimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons 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 twodimensional shapes and threedimensional solids
 TxCCRS:
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.1. Recognize characteristics and dimensional changes of two and threedimensional figures.

K.6E 
Classify and sort a variety of regular and irregular two and threedimensional figures regardless of orientation or size.

Classify, Sort
A VARIETY OF REGULAR AND IRREGULAR TWODIMENSIONAL FIGURES REGARDLESS OF ORIENTATION OR SIZE
Including, but not limited to:
 Twodimensional 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 twodimensional figures – characteristics that define a geometric figure (e.g., outer edges [sides], corners [vertices], etc.)
 Properties of twodimensional 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 edges (sides) and/or corners that appear to be different or unequal
 Attributes of twodimensional figures
 Side – a straight outer boundary between two vertices (line segment) of a twodimensional figure
 Number of sides
 Length of sides
 Vertex (vertices) in a twodimensional figure – a corner where two outer edges (sides) of a twodimensional figure meet
 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 twodimensional figure
 Orientation
 Size
 Color
 Texture
 Collection of twodimensional figures
 Models and reallife 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”)
Note(s):
 Grade Level(s):
 Grade 1 will classify and sort regular and irregular twodimensional shapes based on attributes using informal geometric language.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Identifying and using attributes of twodimensional shapes and threedimensional solids
 TxCCRS:
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.1. Recognize characteristics and dimensional changes of two and threedimensional figures.
 III.A.2. Form and validate conjectures about one, two, and threedimensional figures and their properties.

K.6F 
Create twodimensional shapes using a variety of materials and drawings.

Create
TWODIMENSIONAL SHAPES USING A VARIETY OF MATERIALS AND DRAWINGS
Including, but not limited to:
 Variety of materials and drawings
 Computer programs to create figures
 Art materials to sketch or create figures
 Twodimensional figure – a flat figure
 Spatial visualization – creation and manipulation of mental representations of shapes
 Attributes of twodimensional figures
 Side – a straight outer boundary between two vertices (line segment) of a twodimensional figure
 Number of sides
 Length of sides
 Vertex (vertices) in a twodimensional figure – a corner where two outer edges (sides) of a twodimensional figure meet
 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 twodimensional figure
 Orientation
 Size
 Color
 Texture
 Create twodimensional figures based on attributes and properties
 Circle
 A round, flat figure
 No straight outer edges (sides)
 No corners (vertices)
 Triangle
 3 straight outer edges (sides)
 3 corners (vertices)
 Regular triangle – a triangle with outer edges (sides) and corners that appear to be the same or equal
 Irregular triangle – a triangle with outer edges (sides) and/or corners that appear to be different or unequal
 Rectangle
 4 straight outer edges (sides)
 4 square corners (vertices)
 Opposite outer edge (side) lengths that appear to be the same or equal
 Square (special rectangle)
 4 straight outer edges (sides)
 4 square corners (vertices)
 All outer edge (side) lengths that appear to be the same or equal
 Opposite outer edge (side) lengths that appear to be the same or equal
Note(s):
 Grade Level(s):
 Grade 1 will create twodimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons.
 Grade 1 will compose twodimensional 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:
 Identifying and using attributes of twodimensional shapes and threedimensional solids
 TxCCRS:
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.1. Recognize characteristics and dimensional changes of two and threedimensional figures.
