§111.1. Implementation of Texas Essential Knowledge and Skills for Mathematics, Elementary, Adopted 2012.
Source: The provisions of this §111.1 adopted to be effective September 10, 2012, 37 TexReg 7109.
§111.2. Kindergarten, Adopted 2012.

K.Intro.1  The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on computational thinking, mathematical fluency, and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century. 

K.Intro.2  The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will 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. Students will select appropriate tools such as real objects, manipulatives, algorithms, paper and pencil, and technology and techniques such as mental math, estimation, number sense, and generalization and abstraction to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, computer programs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication. 

K.Intro.3  For students to become fluent in mathematics, students must develop a robust sense of number. The National Research Council's report, "Adding It Up," defines procedural fluency as "skill in carrying out procedures flexibly, accurately, efficiently, and appropriately." As students develop procedural fluency, they must also realize that true problem solving may take time, effort, and perseverance. Students in Kindergarten are expected to perform their work without the use of calculators. 

K.Intro.4  The primary focal areas in Kindergarten are understanding counting and cardinality, understanding addition as joining and subtraction as separating, and comparing objects by measurable attributes. 

K.Intro.4A  Students develop number and operations through several fundamental concepts. Students know number names and the counting sequence. Counting and cardinality lay a solid foundation for number. Students apply the principles of counting to make the connection between numbers and quantities. 

K.Intro.4B  Students use meanings of numbers to create strategies for solving problems and responding to practical situations involving addition and subtraction. 

K.Intro.4C  Students identify characteristics of objects that can be measured and directly compare objects according to these measurable attributes. 

K.Intro.5  Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples. 


Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


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.


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.


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
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
 Techniques
 Mental math
 Estimation
 Number sense
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.


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.


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.


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.


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.


Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system. The student is expected to:


Count
FORWARD TO AT LEAST 20 WITH AND WITHOUT OBJECTS
Including, but not limited to:
 Counting numbers (1 – 20+)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Number word sequence has a correct order.
 Count forward orally by ones.
 With objects starting with one
 Onetoone correspondence – each object counted is matched accurately with a number word in correct sequence
 Tagging with synchrony, meaning when one object is touched it is matched with the correct word
 Arrangement and order of counting objects does not matter as long as the proper number sequence is used.
 Conservation of set – if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change
 Cardinality – the last counting number identified represents the number of objects in the set regardless of which object was counted last
 Cardinal number – a number that names the quantity of objects in a set
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
 Ex:
 Without objects starting with any counting number
 Proper number counting sequence
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
Count
BACKWARD FROM AT LEAST 20 WITH AND WITHOUT OBJECTS
Including, but not limited to:
 Counting numbers (1 – 20+)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Number word sequence has a correct order.
 Count backward orally by ones.
 With objects starting from any given counting number
 Objects provided must match the number count (e.g., if counting backwards from 18, then provide 18 counters; etc.).
 Onetoone correspondence – each object counted is matched accurately with a number word in correct sequence
 Tagging with synchrony, meaning when one object is touched it is matched with the correct word
 Arrangement and order of counting objects does not matter as long as the proper number sequence is used.
 Conservation of set – if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change
 Cardinality – the last counting number identified represents the number of objects in the set regardless of which object was counted last
 Cardinal number – a number that names the quantity of objects in a set
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
 Ex:
 Without objects starting with any counting number
 Proper number counting sequence
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
Note(s):
 Grade Level(s):
 Grade 1 will recite numbers forward and backward from any given number between 1 and 120.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 Developing an understanding of addition and subtraction
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.2. Interpret the relationships between the different representations of numbers.


Read, Write, Represent
WHOLE NUMBERS FROM 0 TO AT LEAST 20 WITH AND WITHOUT OBJECTS OR PICTURES
Including, but not limited to:
 Whole numbers (0 – 20+)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Numeric form
 Numerals represented using the digits 0 – 9
 With objects
 Number of objects in a set communicated orally
 Number of objects in a set written in numerals
 Number presented orally represented with a set of objects
 Number presented in writing represented with a set of objects
 Numbers presented out of sequence (e.g., represent 15; represent 9; represent 2; represent 17; etc.)
 Arrangement and order of counting objects does not matter as long as the proper number is used.
 Conservation of set – if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change
 Relationship between number words and numerals to quantities
 Quantity in terms of “How many?”
 Concrete models begin to develop recognition of magnitude (relative size) of number.
 With pictures
 Number of objects in a picture communicated orally
 Number of objects in a picture written in numerals
 Number presented orally represented with a set of pictures
 Number presented in writing represented with a set of pictures
 Numbers presented out of sequence (e.g., represent 15; represent 9; represent 2; represent 17; etc.)
 Arrangement and order of pictures does not matter as long as the proper number is used.
 Conservation of set – if the same number of pictures are counted and then rearranged, the quantity of pictures in the set does not change
 Relationship between number words and numerals to quantities
 Quantity in terms of “How many?”
 Pictorial models begin to develop recognition of magnitude (relative size) of number.
 Without objects or pictures
 Number presented in written form communicated orally
 Number presented orally written in numerals
 Numbers presented out of sequence (e.g., write 15; write 9; write 2; write 17; etc.)
 Quantity in terms of “How many?”
Note(s):
 Grade Level(s):
 Kindergarten students read, write, and represent whole numbers numerically.
 Kindergarten students should be exposed to the word form of numbers along with the numeric form.
 Grade 1 students will begin reading numbers both in numeric and word form.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers


Count
A SET OF OBJECTS UP TO AT LEAST 20
Including, but not limited to:
 Set of objects (1 – 20+)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Number word sequence has a correct order.
 Arrangement and order of counting objects does not matter as long as the proper number is used.
 Onetoone correspondence – each object counted is matched accurately with a number word in correct sequence
 Tagging with synchrony, meaning when one object is touched it is matched with the correct word
Demonstrate
THE LAST NUMBER SAID TELLS THE NUMBER OF OBJECTS IN THE SET REGARDLESS OF THEIR ARRANGEMENT OR ORDER
Including, but not limited to:
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Cardinality – the last counting number identified represents the number of objects in the set regardless of which object was counted last
 Cardinal number – a number that names the quantity of objects in a set
 Conservation of set – if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change
 Ex:
Note(s):
 Grade Level(s):
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 TxCCRS:
 I.A. Numeric Reasoning –Number representations and operations
 I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.2. Interpret the relationships between the different representations of numbers.


Recognize Instantly
THE QUANTITY OF A SMALL GROUP OF OBJECTS IN ORGANIZED AND RANDOM ARRANGEMENTS
Including, but not limited to:
 Group of objects (0 to 10)
 0 – 5 objects
 5 – 10 objects
 Subitizing– the ability to name the number of objects in a set without counting but rather by identifying the arrangement of objects
 Perceptual subitizing – the recognition of a quantity without using any other knowledge to determine the count
 Quantities of 5 or fewer
 Ex:
 Conceptual subitizing – recognition of a quantity based on a spatial arrangement, pattern, parts of the arrangement, etc.
 Ex:
 Organized arrangements
 Organization of objects aids in the instant recognition of the quantity based on the composition and decomposition of the parts.
 Various organized arrangements of objects (e.g., one or two five frame mats, a Rekenrek counting rack, fingers, number cubes, playing cards, dominoes, random number generators, etc.)
 Ex:
 Random arrangements
 Spatial arrangements of objects perceived in a variety of ways to aid in the instant recognition of a quantity based on the composition and decomposition of the parts
 Instant recognition of smaller quantities within the random arrangement aids in determining the total quantity of the random arrangement.
 Ex:
 Various random arrangements of objects
 Ex:
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 recognizes instantly the quantity of structured arrangements.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 TxCCRS:
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.2. Interpret the relationships between the different representations of numbers.


Generate
A SET USING CONCRETE AND PICTORIAL MODELS THAT REPRESENTS A NUMBER THAT IS MORE THAN, LESS THAN, AND EQUAL TO A GIVEN NUMBER UP TO 20
Including, but not limited to:
 Whole numbers (0 – 20)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Quantity represented by concrete models, pictorial models, oral presentations, and symbolic representations
 Concrete and pictorial models begin to develop recognition of magnitude (relative size) of number.
 Concrete models
 Given number presented orally and symbolically
 Counting strategies used to create the set
 Relationship of the set to the given number
 Comparative language
 Describes the relationship between the concrete model and the given number
 Greater than, more than
 Less than, fewer than
 Equal to, same as
 Pictorial models
 Given number presented orally and symbolically
 Counting strategies used to create the set
 Relationship of the set to the given number
 Comparative language
 Describes the relationship between the pictorial model and the given number
 Greater than, more than
 Less than, fewer than
 Equal to, same as
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 will generate a number that is greater than or less than a given whole number up to 120.
 Grade 1 will represent the comparison of two numbers to 100 using the symbols >, <, or =.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 TxCCRS:
 I.A. Numeric Reasoning –Number representations and operations
 I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.


Generate
A NUMBER THAT IS ONE MORE THAN OR ONE LESS THAN ANOTHER NUMBER UP TO AT LEAST 20
Including, but not limited to:
 Whole numbers (0 – 20+)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
 Ex:
 Comparative language
 Describes the relationship between the number generated and the given number
 One more than a given number, including 1 more than 0 and 1 more than 20
 Ex: 21 is 1 more than 20
 Ex: 1 is 1 more than 0
 One less than a given number, including 1 less than 1 and 1 less than 21
 Ex: 19 is 1 less than 20
 Ex: 20 is 1 less than 21
 Quantity represented by concrete models, pictorial models, oral presentations, and symbolic representations
 Concrete and pictorial models begin to develop recognition of magnitude (relative size) of number.
 Counters, linking cubes, beans, calendar, hundreds chart, etc.
 Oral presentations and symbolic representations
 Verbal description, numerical recording using words and numbers
 Ex:
 Quantities presented out of correct sequence (e.g., 1 more than 10; 1 more than 4; 1 less than 18; 1 less than 6; etc.)
Note(s):
 Grade Level(s):
 Grade 1 will generate a number that is greater than or less than a given whole number to 120.
 Grade 2 will generate a number that is greater than or less than a given whole number to 1,200.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 Developing an understanding of addition and subtraction
 TxCCRS:
 I.A. Numeric Reasoning –Number representations and operations
 I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.


Compare
SETS OF OBJECTS UP TO AT LEAST 20 IN EACH SET USING COMPARATIVE LANGUAGE
Including, but not limited to:
 Whole numbers (0 – 20+)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Quantity represented by concrete models, pictorial models, oral presentations, and symbolic representations
 Concrete and pictorial models begin to develop recognition of magnitude (relative size) of number.
 Counters, linking cubes, beans, calendar, hundreds chart, etc.
 Oral presentations and symbolic representations
 Verbal description, numerical recording using words and numbers
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
 Ex:
 Compare sets – to consider the value of two sets to determine which set is greater or less in value or if the sets are equal in value
 Matching or counting strategies to compare sets
 Onetoone correspondence – each object counted is matched accurately with a number word in correct sequence
 Tagging with synchrony, meaning when one object is touched it is matched with the correct word
 Arrangement and order of counting objects does not matter as long as the proper number sequence is used.
 Conservation of set – if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change
 Cardinality – the last counting number identified represents the number of objects in the set regardless of which object was counted last
 Cardinal number – a number that names the quantity of objects in a set
 Comparative language
 Describes the relationship between the quantities of each set
 Inequality language (greater than, more than, less than, fewer than, etc.)
 Ex: Set A is greater than Set B.
 Ex: Set A contains more than Set B.
 Ex: Set A is less than Set B.
 Ex: Set A contains fewer than Set B.
 Equality language (equal to, same as, etc.)
 Ex: Set A is equal to Set B.
 Ex: Set A contains the same as Set B.
 Compare two sets of objects up to at least 20.
 Recognition of the quantity represented by each set
 Comparative language describing the relationship between 2 sets
 Comparison of two organized sets
 Ex:
 Comparison of two unorganized sets
 Ex:
 Comparison of an organized set to an unorganized set
 Ex:
 Compare more than two sets of objects up to at least 20.
 Recognition of the quantity represented by each set
 Comparative language describing the relationship among more than 2 sets
 Comparison of organized sets and unorganized sets
 Ex:
Note(s):
 Grade Level(s):
 Kindergarten uses comparative language only.
 Grade 1 will use place value to compare whole numbers up to 120 using comparative language.
 Grade 1 introduces representing the comparison of two numbers to 100 using the symbols >, <, or =.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 TxCCRS:
 I.A. Numeric Reasoning –Number representations and operations
 I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.


Use
COMPARATIVE LANGUAGE
Including, but not limited to:
 Comparative language
 Describes the relationship between the value of each numeral
 Inequality language
 Greater than, more than
 Less than, fewer than
 Equality language
To Describe
TWO NUMBERS UP TO 20 PRESENTED AS WRITTEN NUMERALS
Including, but not limited to:
 Whole numbers (0 – 20)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Numerals represent quantities
 Compare numbers – to consider the value of two numbers to determine which number is greater or less or if the numbers are equal in value
 Compare two numbers
 Numerals presented out of sequence (e.g., compare 6 and 12; compare 19 and 5; etc.)
 Transition from comparing numbers by counting objects to comparing numbers without counting.
 Ex:
Note(s):
 Grade Level(s):
 Kindergarten uses comparative language only.
 Grade 1 will use place value to compare whole numbers up to 120 using comparative language.
 Grade 1 introduces representing the comparison of two numbers to 100 using the symbols >, <, or =.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.


Compose, Decompose
NUMBERS UP TO 10 WITH OBJECTS AND PICTURES
Including, but not limited to:
 Whole numbers (0 – 10)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Compose numbers – to combine parts or smaller values to form a number
 Decompose numbers – to break a number into parts or smaller values
 Part to whole relationships
 Parts of a composed or decomposed number identified
 Correct number connected to appropriate parts
 Numeric relationship of one part to the other part
 Numeric relationship of each part to the whole
 Missing part determined
 Composition of a number in more than one way using objects and pictures
 Total of the parts conserved
 Ex:
 Ex:
 Composed parts may be listed in any order (commutative property).
 Ex:
 Relationship of composed parts to create a new set of composed parts
 Ex:
 Decomposition of a number in more than one way using objects and pictures
 Original decomposed number conserved
 Ex:
 Ex:
 Decomposed parts may be listed in any order (commutative property).
 Ex:
 Relationship of decomposed parts to create a new set of decomposed parts
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 will use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers
 Developing an understanding of addition and subtraction
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.2. Interpret the relationships between the different representations of numbers.


Number and operations. The student applies mathematical process standards to develop an understanding of addition and subtraction situations in order to solve problems. The student is expected to:


Model
THE ACTION OF JOINING TO REPRESENT ADDITION
Including, but not limited to:
 Whole numbers
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Addition
 Addend – a number being added or joined together with another number(s)
 Sum – the total when two or more addends are joined
 Addition of whole numbers up to sums of 10
 Connection between the action of joining situations and the concept of addition
 Joining situations in contexts that represent an action (e.g., Kristin had 2 pencils, and her teacher gave her 3 more pencils; etc.)
 Appropriate language for joining situations
 Addend, sum, start amount, change amount, result amount
 Connection between quantities and numbers in problem situations to objects and drawings used
 Concrete models to represent contextual joining situations (linking cubes, number path, counters, five frames, beaded number line, Rekenrek, etc.)
 Physical joining of concrete objects
 Ex: Linking cubes
 Ex: Number path
 Ex: Counters and five frames
 Ex: Beaded number line
 Ex: Rekenrek
 Pictorial models to represent contextual joining situations
 Simple sketches representing concrete models without unnecessary details
 Physical joining of pictorial representations by circling or connecting
 Ex:
 Acting out to represent contextual joining situations
Model
THE ACTION OF SEPARATING TO REPRESENT SUBTRACTION
Including, but not limited to:
 Whole numbers
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Subtraction
 Minuend – a number from which another number will be subtracted
 Subtrahend – a number to be subtracted from a minuend
 Difference – the remaining amount after the subtrahend has been subtracted from the minuend
 Subtraction of whole numbers up to minuends of 10
 Including 0 as the subtrahend
 Including 0 as the difference
 Connection between the action of separating and the concept of subtraction
 Separating situations in contexts that represent an action (e.g., Mark had 5 books, and then he gave 2 books away; etc.)
 Appropriate language for separating situations
 Start amount, change amount, result amount, difference, removed, separated from, taken away from, etc.
 Connection between quantities and numbers in problem situations to objects and drawings used
 Concrete models to represent contextual separating situations (linking cubes, number path, counters, five frames, beaded number line, Rekenrek, etc.)
 Physical separation of concrete objects
 Ex: Linking cubes
 Ex: Number path
 Ex: Counters and five frames
 Beaded number line
 Rekenrek
 Pictorial models to represent contextual separating situations
 Simple sketches representing concrete models without unnecessary details
 Physical separation of pictorial representations by crossing out or circling
 Ex:
 Acting out to represent contextual separating situations
Note(s):
 Grade Level(s):
 Grade 1 will use objects and pictorial models to solve word problems involving joining, separating, partpartwhole relationships, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] – 3.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of addition and subtraction
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 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.2. Create and use representations to organize, record, and communicate mathematical ideas.


Solve
WORD PROBLEMS USING OBJECTS AND DRAWINGS TO FIND SUMS UP TO 10
Including, but not limited to:
 Whole numbers
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Addition
 Addend – a number being added or joined together with another number(s)
 Sum – the total when two or more addends are joined
 Addition of whole numbers with sums up to 10
 Relationship between composing numbers and addition
 Mathematical and realworld problem situations
 Situational language
 Action words indicating joining of quantities
 Partpartwhole relationship of quantities, implied or mental joining
 Connection between quantities and numbers in problem situations to objects and drawings used
 Joining situations in contexts that represent an action (e.g., Kristin had 2 pencils, and her teacher gave her 3 more pencils; etc.)
 Start quantity (addend) given, change quantity (addend) given, result (sum) unknown
 Ex:
 Joining situations in contexts that represent no action (e.g., Kristin had 2 blue pencils and 3 red pencils; etc.)
 Both part quantities (addends) given, whole (sum) unknown
 Ex:
 Addition strategies based on counting
 Count all
 Onetoone correspondence
 Count out one quantity, count out the other quantity, and then count both quantities together.
 Ex:
 Count on strategies
 Onetoone correspondence
 Count on from the first number presented.
 Ex:
 Count on from the largest number.
 Ex:
 Connection to hierarchical inclusion
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
 Ex:
 Adding 1 does not require counting.
 Properties of addition
 Quantities may be joined in any order (commutative property).
 Ex:
 A number keeps its identity when 0 is added to it (additive identity property).
 Ex:
Solve
WORD PROBLEMS USING OBJECTS AND DRAWINGS TO FIND DIFFERENCES WITHIN 10
Including, but not limited to:
 Whole numbers
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Subtraction
 Minuend – a number from which another number will be subtracted
 Subtrahend – a number to be subtracted from a minuend
 Difference – the remaining amount after the subtrahend has been subtracted from the minuend
 Subtraction of whole numbers to find differences within 10
 Including 0 as the subtrahend
 Relationship between decomposing numbers and subtraction
 Mathematical and realworld problem situations
 Situational language
 Action words indicating separation of quantities
 Connection between quantities and numbers in problem situations to objects and drawings used
 Separating situations in contexts that represent an action (e.g., Mark had 5 books, and then he gave 2 books away; etc.)
 Start quantity (minuend) given, change quantity (subtrahend) given, result (difference) unknown
 Ex:
 Subtraction strategies based on counting
 Removing
 Onetoone correspondence
 Count out start quantity, count and remove change quantity, and then count remaining quantity.
 Ex:
 Count backward
 Onetoone correspondence
 Count the whole quantity and then count backward the amount of the change quantity, with the last number in sequence naming the difference.
 Ex:
 Count on
 Onetoone correspondence
 Count on from the change quantity to the whole quantity and then recount the remaining quantity beginning with 1.
 Ex:
 Connection to hierarchical inclusion
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
 Ex:
 Subtracting 1 does not require counting.
 Properties of subtraction
 Commutative property does not apply to subtraction.
 A number keeps its identity when 0 is subtracted from it (additive identity property).
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 will compose 10 with two or more addends with and without concrete objects.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of addition and subtraction
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.


Explain
THE STRATEGIES USED TO SOLVE PROBLEMS INVOLVING ADDING AND SUBTRACTING WITHIN 10 USING SPOKEN WORDS, CONCRETE AND PICTORIAL MODELS, AND NUMBER SENTENCES
Including, but not limited to:
 Whole numbers
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Addition
 Addend – a number being added or joined together with another number(s)
 Sum – the total when two or more addends are joined
 Addition of whole numbers with sums up to 10
 Subtraction
 Minuend – a number from which another number will be subtracted
 Subtrahend – a number to be subtracted from a minuend
 Difference – the remaining amount after the subtrahend has been subtracted from the minuend
 Subtraction of whole numbers to find differences within 10
 Including 0 as the subtrahend
 Including 0 as the difference
 Mathematical and realworld problem situations
 Detailed explanation of the solution process and strategy
 Addition strategies
 Count all
 Count on from the first number presented
 Count on from the largest number
 Subtraction strategies
 Removing
 Count backward
 Count on
 Connection between information in the problem and problem type
 Joining situations in contexts that represent an action (e.g., Kristin had 2 pencils, and her teacher gave her 3 more pencils; etc.)
 Joining situations in contexts that represent no action (e.g., Kristin had 2 blue pencils and 3 red pencils; etc.)
 Separating situations in contexts that represent an action (e.g., Mark had 5 books, and then he gave 2 books away; etc.)
 Relationship between quantities of objects used, pictures drawn and number sentences to the problem situation
 Explanation using spoken words
 Appropriate mathematical language for joining or separating situations
 Labels for quantities represented
 Explanation using objects
 Linking cubes, counters, etc.
 Explanation using pictorials
 Explanation using number sentences
 Number sentence – a mathematical statement composed of numbers, and/or an unknown(s), and/or an operator(s), and an equality or inequality symbol
 Addition symbol represents joining
 Addend + addend = sum
 Sum = addend + addend
 Subtraction symbol represents separating
 Minuend – subtrahend = difference
 Difference = minuend – subtrahend
 Equal symbol indicates the same value being represented on both side(s)
 Ex: 5 + 5 = 10
 Ex: 10 = 2 + 3 + 5
 Ex: 5 – 3 = 2
 Ex: 2 = 5 – 3
 Ex: Joining action result unknown
 Ex: Separating action result unknown
 Ex: Partpartwhole whole unknown
Note(s):
 Grade Level(s):
 Kindergarten introduces number sentences.
 Grade 1 will explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of addition and subtraction
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 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.


Number and operations. The student applies mathematical process standards to identify coins in order to recognize the need for monetary transactions. The student is expected to:


Identify
U.S. COINS BY NAME, INCLUDING PENNIES, NICKELS, DIMES, AND QUARTERS
Including, but not limited to:
 U.S. coins by name
 Penny
 Nickel
 Dime
 Quarter
 Attributes of pennies, nickels, dimes, and quarters
 Color
 Penny: copper
 Nickel, dime and quarter: silver
 Size
 Relative sizes
 Largest to smallest: quarter, nickel, penny, dime
 Smallest to largest: dime, penny, nickel, quarter
 Texture
 Smooth edges: penny, nickel
 Ridged edges: dime, quarter
 Informal references
 Heads: front of coin
 Tails: back of coin
 Traditional head designs
 Presidents
 Penny: Abraham Lincoln
 Nickel: Thomas Jefferson
 Dime: Franklin Delano Roosevelt
 Quarter: George Washington
 Traditional tail designs
 Symbols
 Penny: Lincoln Memorial or union shield
 Nickel: Monticello
 Dime: Torch (liberty); olive branch (peace); oak branch (strength and independence)
 Quarter: Presidential coat of arms (eagle with outstretched arms)
 Special designs
 State coins
 U.S. territories
 Commemorative issues
 Concrete and pictorial models
 Views of both sides of coins
Note(s):
 Grade Level(s):
 Kindergarten identifies U.S. coins by name.
 Grade 1 will identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them.
 Grade 1 will write a number with the cent symbol to describe the value of a coin.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Grade Level Connections (reinforces previous learning and/or provides development for future learning)
 TxCCRS:
 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.


Algebraic reasoning. The student applies mathematical process standards to identify the pattern in the number word list. The student is expected to:


Recite
NUMBERS UP TO AT LEAST 100 BY ONES AND TENS BEGINNING WITH ANY GIVEN NUMBER
Including, but not limited to:
 Counting numbers (1 – 100+)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Number word sequence has a correct order
 Recite – to verbalize from memory
 Development of automaticity
 Relationship to counting
 Cardinal number – a number that names the quantity of objects in a set
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 18 is 17 increased by 1; 18 decreased by 1 is 17; etc.)
 Ex:
 Recite numbers forward up to at least 100
 Orally by ones beginning with 1
 Orally by ones beginning with any given number
 Ex: Starting with 43, continue counting forward to at least 100 by ones.
 Orally by tens beginning with 10
 Orally by tens beginning with any given number between 10 and 100
 Beginning number is a multiple of 10.
 Ex: Starting with 60, continue counting forward to at least 100 by tens.
Note(s):
 Grade Level(s):
 Kindergarten introduces reciting numbers by ten.
 Grade 1 will recite numbers forward and backward from any given number between 1 and 120.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of whole numbers


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:


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.


Identify
THREEDIMENSIONAL SOLIDS, INCLUDING CYLINDERS, CONES, SPHERES, AND CUBES, IN THE REAL WORLD
Including, but not limited to:
 Identify threedimensional figures
 Threedimensional figure – a solid figure
 Identity not changed by orientation
 Identity not changed by size
 Identity not changed by color
 Identity not changed by texture
 Identification and connection between formal geometric names to threedimensional solids by examining objects in the real world
 Cylinder
 Can, straw, etc.
 2 equal, opposite, flat surfaces shaped like circles
 1 curved surface
 Rolls, slides, stacks
 Ex:
 Cone
 Ice cream cone, party hat, etc.
 1 flat surface shaped like a circle
 1 curved surface
 1 point (vertex)
 Rolls, slides
 Ex:
 Sphere
 Ball, globe, etc.
 1 curved surface forming a solid round figure
 Rolls
 Ex:
 Cube
 Die, alphabet block, etc.
 6 square flat surfaces (faces)
 12 edges
 8 corners (vertices)
 Slides, stacks
 Ex:
 Distinguish between prisms and pyramids
 A prism has two flat surfaces (faces) opposite each other connected by rectangular side faces.
 A pyramid has one flat surface (face) opposite a point (vertex) where the triangular side faces meet.
 Ex:
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 will identify threedimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Identifying and using attributes of 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.


Note(s):
 Grade Level(s):
 Grade 1 will distinguish between attributes that define a twodimensional or threedimensional figure and attributes that do not define the shape.
 Grade 1 will identify threedimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Identifying and using attributes of 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.


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.


Classify, Sort
A VARIETY OF REGULAR AND IRREGULAR TWO AND THREEDIMENSIONAL FIGURES REGARDLESS OF ORIENTATION OR SIZE
Including, but not limited to:
 Twodimensional figure – a flat figure
 Threedimensional figure – a solid figure
 Sort – grouping objects or figures by a shared characteristic or attribute
 Classify – applying an attribute to categorize a sorted group
 Attributes of 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 edge (side) lengths and corners that appear to be the same or equal
 Irregular figure – a figure with outer edge (side) lengths and/or corners that appear to be different or unequal
 Ex:
 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.).
 Ex:
 Attributes that do not identify a two or threedimensional 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”)
 Ex:
 Collection of threedimensional figures
 Reallife objects
 Cylinders, cones, spheres, cubes
 Rectangular prisms, triangular prisms
 Pyramids
 Sort and justify
 Informal language
 Rule used for sorting expressed
 Attributes and properties of geometric figures expressed
 Existence (have) and absence (do not have) of attributes and properties expressed (e.g., figures that have “a common attribute” and figures that do not have “a common attribute”)
 Ex:
 Mixed collection of two and threedimensional figures
 Models and reallife objects
 Sort and justify
 Informal language
 Rule used for sorting expressed
 Attributes and properties of geometric figures expressed
 Existence (have) and absence (do not have) of attributes and properties expressed (e.g., figures that have “a common attribute” and figures that do not have “a common attribute”)
 Ex:
 Ex:
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.


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
 Ex: crayons, chenille sticks, toothpicks, yarn, paint, cutting paper, etc.
 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.).
 Ex:
 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.


Geometry and measurement. The student applies mathematical process standards to directly compare measurable attributes. The student is expected to:


Give
AN EXAMPLE OF A MEASURABLE ATTRIBUTE OF A GIVEN OBJECT, INCLUDING LENGTH, CAPACITY, AND WEIGHT
Including, but not limited to:
 Measurable attribute – a characteristic of an object that can be measured (length, capacity, weight)
 Length – the measurement attribute that describes how long something is from end to end
 Height – how tall something is, such as a person, building, or tree
 Distance – how far it is from one point to another
 Capacity – the measurement attribute that describes the maximum amount something can contain
 Weight – the measurement attribute that describes how heavy something is
 Identify measurable attributes in a variety of objects
 Single measurable attributes of an object
 Ex: A piece of ribbon has the measurable attribute of length.
 Ex: A drinking cup has the measurable attribute of capacity.
 Ex: A toy car has the measurable attribute of weight.
 Multiple measurable attributes of an object
 Ex: A cereal box has the measurable attributes of length, capacity, and weight.
Length: the height of the cereal box Capacity: the amount of cereal it takes to completely fill the cereal box Weight: the heaviness of the cereal box
Note(s):
 Grade Level(s):
 Grade 1 will use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement.
 Grade 3 will determine liquid volume (capacity) or weight using appropriate units and tools.
 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:
 I.C. Numeric Reasoning – Systems of measurement
 I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.2. Form and validate conjectures about one, two, and threedimensional figures and their properties.


Compare
TWO OBJECTS WITH A COMMON MEASURABLE ATTRIBUTE TO SEE WHICH OBJECT HAS MORE OF/LESS OF THE ATTRIBUTE
Including, but not limited to:
 Measurable attribute – a characteristic of an object that can be measured (length, capacity, weight)
 Length – the measurement attribute that describes how long something is from end to end
 Height – how tall something is, such as a person, building, or tree
 Distance – how far it is from one point to another
 Capacity – the measurement attribute that describes the maximum amount something can contain
 Weight – the measurement attribute that describes how heavy something is
 Compare measurable attributes – to consider a measurable attribute of two objects to determine which object has more or less of the measurable attribute or if the objects have an equal amount of the measurable attribute
 Direct comparison – a comparison using the actual objects being compared, rather than comparing using a measuring tool
 Directly compare the length of two objects.
 Estimation prior to direct comparison
 Identification of the start point and endpoint of each object
 Common base to begin the direct comparison
 Both objects lined up with an even start point
 Ex:
 Direct comparison of the endpoints of both objects
 Conservation of length – the length of an object remains the same regardless of orientation
 Ex:
 Directly compare the capacity of two objects.
 Estimation prior to direct comparison
 Direct comparison of the capacity of each object
 Fill one container with a pourable material, and then transfer the pourable material to the other container to compare their capacities.
If the second container is not yet full, it has a larger capacity than the first container. If the second container overflows, it has a smaller capacity than the first container.
 Conservation of capacity – the capacity of an object remains the same regardless of orientation or the material used to fill it
 Ex:
 Directly compare the weight of two objects.
 Estimation prior to direct comparison
 Direct comparison of the weight of each object using a variety of tools
 Heft – holding one object in each of your hands to predict and compare which object is heavier or lighter
 Ex: Place a tennis ball in one hand and a softball in the other to physically compare the weight of the balls.
 Balance scale
 Place one item in each pan of a balance scale.
The pan that moves lower indicates the heavier object. The pan that rises higher indicates the lighter object. If the pans remain balanced, the objects have equal weight.
 Spring scale
 Place objects one at a time in the pan of a spring scale.
The object that pulls the pan down the farthest indicates the heavier object.
 Conservation of weight – the weight of an object remains the same regardless of orientation or the rearrangement of the material
 Ex: If a clay ball is rolled into a snake, the clay ball and the clay snake have the same weight.
Describe
THE DIFFERENCE IN A COMMON MEASURABLE ATTRIBUTE OF TWO OBJECTS
Including, but not limited to:
 Measurable attribute – a characteristic of an object that can be measured (length, capacity, weight)
 Length – the measurement attribute that describes how long something is from end to end
 Height – how tall something is, such as a person, building, or tree
 Distance – how far it is from one point to another
 Capacity – the measurement attribute that describes the maximum amount something can contain
 Weight – the measurement attribute that describes how heavy something is
 Appropriate language to describe comparison of measurable attributes in two objects
 Comparative language for length
 Longer than, longest
 Taller than, tallest
 Farther than, farthest
 Shorter than, shortest
 Same length as
 Same height as
 Same distance as
 Equal in length
 Equal in height
 Equal in distance
 Ex:
 Comparative language for capacity
 Holds more than
 Holds less than
 Holds the same as
 Holds an equal amount
 Equal capacity as
 Ex:
 Comparative language for weight
 Heavier than
 Lighter than
 The same weight as
 Equal weight as
 Ex:
 Ex:
Note(s):
 Grade Level(s):
 Kindergarten introduces comparing measurable attributes of two objects.
 Grade 1 will use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement.
 Grade 3 will determine liquid volume (capacity) or weight using appropriate units and tools.
 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.2. Form and validate conjectures about one, two, and threedimensional figures and their properties.


Data analysis. The student applies mathematical process standards to collect and organize data to make it useful for interpreting information. The student is expected to:


Collect, Sort, Organize
DATA INTO TWO OR THREE CATEGORIES
Including, but not limited to:
 Data – information that is collected about people, events, or objects
 Categorical data – data that represents the attributes of a group of people, events, or objects
 Ex: What is your favorite color?
 Ex: Do you have a brother?
 Ex: Which sporting event do you prefer?
 May include numbers or ranges of numbers
 Ex: How many pets do you have?
 Ex: How many letters are in your name?
 Limitations
 Two to three categories
 Data values limited to whole numbers up to 20
 Data collected in the form of responses to a question
 Survey – to ask a group of people a question in order to collect information about their opinions or answers
 Ex: What type of pet do you have?
 Ex: What is your favorite color of apple?
 Ex: Will you be eating cafeteria lunch or sack lunch today?
 Common characteristics in a collection of objects
 Ex: How many of each color are in a collection of different colored linking cubes?
 Ex: How many of each size are in a collection of real world objects?
 Data sorted in a variety of ways
 Ex: A collection of realworld objects sorted by size, shape, color, etc.
 Data organized and represented in a variety of ways
 Data organized using Tcharts, sorting mats, etc.
 Data represented by realworld objects, pictures, drawings, or tally marks
 One unit of data represented by each object, picture, drawing, or tally mark
 Ex:
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 will collect, sort, and organize data in up to three categories using models/representations such as tally marks or Tcharts.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Grade Level Connections (reinforces previous learning and/or provides development for future learning)
 TxCCRS:
 V.B. Statistical Reasoning – Describe data
 V.B.2. Construct appropriate visual representations of data.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.


Use
DATA
To Create
REALOBJECT AND PICTURE GRAPHS
Including, but not limited to:
 Graph – a visual representation of the relationships between data collected
 Organization of data used to interpret data, draw conclusions, and make comparisons
 Data – information that is collected about people, events, or objects
 Categorical data – data that represents the attributes of a group of people, events, or objects
 Ex: What is your favorite color?
 Ex: Do you have a brother?
 Ex: Which sporting event do you prefer?
 May include numbers or ranges of numbers
 Ex: How many pets do you have?
 Ex: How many letters are in your name?
 Data collected in the form of responses to a question
 Survey – to ask a group of people a question in order to collect information about their opinions or answers
 Ex: What type of pet do you have?
 Ex: What is your favorite color of apple?
 Ex: Will you be eating cafeteria lunch or sack lunch today?
 Common characteristics in a collection of objects
 Ex: How many of each color are in a collection of different colored linking cubes?
 Ex: How many of each size are in a collection of real world objects?
 Limitations
 Two to three categories
 Data values limited to whole numbers up to 20
 Data representations
 Realobject graph – a graphical representation to organize data that uses concrete or real objects evenly spaced or placed in individual cells, where each object represents one unit of data, to show the frequency (number of times) that each category occurs
 Picture graph – a graphical representation to organize data that uses pictures or symbols evenly spaced or placed in individual cells, where each picture or symbol represents one unit of data, to show the frequency (number of times) that each category occurs
 Characteristics of realobject and picture graphs
 Titles, subtitles, and labels
 Title represents the purpose of collected data
 Subtitle clarifies the meaning of categories
 Labels identify each category below the line
 Representation of categorical data
 Objects or pictures
 Placed in a horizontal or vertical linear arrangement
 Vertical graph beginning at the bottom and progressing up above the line
 Horizontal graph beginning at the left and progressing to the right of the line
 Spaced approximately equal distances apart or placed in individual cells within each category
 Different object or picture used to represent each category
 Every piece of data represented using a onetoone correspondence
 One unit of data represented by each object or picture
 Value of the data represented by the objects or pictures
 Determined by the total number of objects or pictures in that category
 Represents the frequency of each category
 Ex:
 Connection between graphs representing the same data
 Realobject graph to picture graph
 Ex:
 Picture graph to realobject graph
 Ex:
 Same data represented using a picture graph and a bartype graph
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 will use data to create picture and bartype graphs.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Grade Level Connections (reinforces previous learning and/or provides development for future learning)
 TxCCRS:
 V.B. Statistical Reasoning – Describe data
 V.B.2. Construct appropriate visual representations of data.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.


Draw
CONCLUSIONS FROM REALOBJECT AND PICTURE GRAPHS
Including, but not limited to:
 Graph – a visual representation of the relationships between data collected
 Organization of data used to interpret data, draw conclusions, and make comparisons
 Data – information that is collected about people, events, or objects
 Categorical data – data that represents the attributes of a group of people, events, or objects
 Limitations
 Two to three categories
 Data values limited to whole numbers up to 20
 Data representations
 Realobject graph – a graphical representation to organize data that uses concrete or real objects evenly spaced or placed in individual cells, where each object represents one unit of data, to show the frequency (number of times) that each category occurs
 One unit of data represented by each object or picture
 Picture graph – a graphical representation to organize data that uses pictures or symbols evenly spaced or placed in individual cells, where each picture or symbol represents one unit of data, to show the frequency (number of times) that each category occurs
 One unit of data represented by each object or picture
 Description of data represented
 Identification of title and category labels
 Explanation of what the graph represents
 Conclusions related to the question that led to the data collection
 Numerical conclusions in the data
 Quantities represented by the data
 Number in each category
 Number in a category(s) may be zero
 Ex:
 Comparisons of data represented
 Comparative language used without numbers (e.g., more than, less than, fewer than, the most, the least, the same as, equal to, etc.)
 Ex:
 Changes in orientation do not affect data values
 Ex:
Note(s):
 Grade Level(s):
 Grade 1 will draw conclusions and generate and answer questions using information from picture and bartype graphs.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Grade Level Connections (reinforces previous learning and/or provides development for future learning)
 TxCCRS:
 V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
 V.C.3. Make predictions using summary statistics.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 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.


Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:


Identify
WAYS TO EARN INCOME
Including, but not limited to:
 Income – money earned
 Ways to earn income
 Job – work performed to complete a task, usually for money
 Jobs are available in the home, school, and community.
 Jobs for adults
 Ex: Teacher, principal, custodian, nurse, bus driver, hair stylist, waiter, mechanic, doctor, lawyer, cashier, etc.
 Jobs for children
 Ex: Household chores, babysitting, mowing the lawn, washing the car, taking care of pets, etc.
 Sale of goods or property (sale of items)
 Ex: Garage sale, resale store, lemonade stand, cookie sale, etc.
Note(s):
 Grade Level(s):
 Grade 1 will define money earned as income.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:


Differentiate
BETWEEN MONEY RECEIVED AS INCOME AND MONEY RECEIVED AS GIFTS
Including, but not limited to:
 Money – coins (pennies, nickels, dimes, and quarters) and paper bills (dollars)
 Money received as income
 Money received for work done
 Money received for selling of items, such as clothes that are too small, old toys, cookies, lemonade, etc.
 Money received for household chores, babysitting, mowing the lawn, washing the car, taking care of pets, etc.
 Money received as gifts
 Money that does not have to be paid back
 Ex: Special occasions and events (e.g., birthdays, holidays, graduation, etc.)
 Money received but not earned
Note(s):
 Grade Level(s):
 Kindergarten introduces money by identifying U.S. coins by name.
 Grade 1 will define money earned as income.
 Grade 1 will identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:


List
SIMPLE SKILLS REQUIRED FOR JOBS
Including, but not limited to:
 Job – work performed to complete a task, usually for money
 Jobs are available in the home, school, and community.
 Skills required for jobs
 Education, knowledge
 Ex: Skills needed by a cafeteria worker include the ability to measure ingredients, count servings, tell time, read recipes, etc.
 Ex: Skills needed by a nurse include the ability to read charts and reports, measure medicine, recognize symptoms, etc.
 Ex: Skills needed to feed the pets include the ability to measure food, read the food label, etc.
 Physical requirements
 Ex: Skills needed by a construction worker include the ability to carry heavy supplies, work with heavy machinery, etc.
 Ex: Skills needed by a waiter include the ability to carry heavy trays of food, stand for long periods of time, etc.
 Ex: Skills needed to mow the lawn include the ability to push the lawn mower, etc.
Note(s):
 Grade Level(s):
 Grade 3 will explain the connection between human capital/labor and income.
 Grade 6 will compare the annual salary of several occupations requiring various levels of postsecondary education or vocational training and calculate the effects of the different annual salaries on lifetime income.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:


Distinguish
BETWEEN WANTS AND NEEDS
Including, but not limited to:
 Distinguish between realworld wants and needs.
 Wants – things you wish for but are not necessary for life
 Ex: Toys, games, movies, entertainment, etc.
 Needs – things that are necessary for life
 Ex: Food, water, shelter, clothing, etc.
 Distinguish between needs that could be considered wants.
 Wants and needs may vary depending on regions, cultures and/or personal situations.
Identify
INCOME AS A SOURCE TO MEET ONE'S WANTS AND NEEDS
Including, but not limited to:
 Income – money earned
 Income is necessary to purchase both wants and needs.
 Items have a cost regardless of whether they are a want or a need.
 Ex: Toys, games, clothing, home, food, water, etc.
 Services have a cost regardless of whether they are a want or a need.
 Ex: Haircut, movies, entertainment, etc.
Note(s):
 Grade Level(s):
 Grade 1 will identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs.
 Grade 1 will consider charitable giving.
 Grade 2 will explain that saving is an alternative to spending.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:

Bibliography: Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from: http://www.thecb.state.tx.us/collegereadiness/crs.pdf
Texas Education Agency. (2013). Introduction to the revised mathematics TEKS – kindergartenalgebra I vertical alignment. Retrieved from: https://www.texasgateway.org/resource/verticalalignmentchartsrevisedmathematicsteks
Texas Education Agency. (2013) Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from: https://www.texasgateway.org/resource/txrcfptexasresponsecurriculumfocalpointsk8mathematicsrevised2013
Texas Education Agency. (2016). Mathematics TEKS – supporting information kindergarten. Retrieved from: https://https://www.texasgateway.org/resource/mathematicstekssupportinginformation
