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Enhanced TEKS Clarification

Mathematics

Kindergarten

Kindergarten

§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.1The 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.2The 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 problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. 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.3For 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.4The 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.4AStudents 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.4BStudents 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.5Statements 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.

Apply

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

Including, but not limited to:

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

Note(s):

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

Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

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

Including, but not limited to:

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

Note(s):    

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

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, 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 two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • I.B. Numeric Reasoning – Number sense and number concepts
      • I.B.1. Use estimation to check for errors and reasonableness of solutions.
    • V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
      • V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

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

Including, but not limited to:

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

Note(s):    

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

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 two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • VIII.B. Communication and Representation – Interpretation of mathematical work
      • VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
      • VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
    • VIII.C. Communication and Representation – Presentation and representation of mathematical work
      • VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
      • VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.

Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

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

Note(s):    

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

Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

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

Including, but not limited to:

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

Note(s):    

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

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 and backward to at least 20 with and without objects.

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
      • One-to-one 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.).
      • One-to-one 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, and represent whole numbers from 0 to at least 20 with and without objects or pictures.

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 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order.

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.
  • One-to-one 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.

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.

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.

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.

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
    • One-to-one 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 to describe two numbers up to 20 presented as written numerals.

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
        • Equal to, same as

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 and decompose numbers up to 10 with objects and pictures.

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 and the action of separating to represent subtraction.

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
      • Including 0 as an addend 
  • 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, part-part-whole 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 and differences within 10.

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
      • Including 0 as an addend
  • Relationship between composing numbers and addition
  • Mathematical and real-world problem situations
  • Situational language
    • Action words indicating joining of quantities
    • Part-part-whole 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
      • One-to-one correspondence
      • Count out one quantity, count out the other quantity, and then count both quantities together.
      • Ex:
    • Count on strategies
      • One-to-one 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 real-world 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
      • One-to-one correspondence
      • Count out start quantity, count and remove change quantity, and then count remaining quantity.
      • Ex:
    • Count backward
      • One-to-one 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
      • One-to-one 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.

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
      • Including 0 as an addend 
  • 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 real-world 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
      • Sketches, etc.
    • 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: Part-part-whole 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.

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, real-world situations, and everyday life
      • IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world 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.

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 two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:

Identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles.

Identify

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

Including, but not limited to:

  • Identify two-dimensional figures
    • Two-dimensional 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)
    • Ex:
  • 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
    • Ex:
    • Irregular triangle – a triangle with outer edges (sides) and/or corners that appear to be different or unequal
    • Ex:
  • Rectangle
    • 4 straight outer edges (sides)
    • 4 square corners (vertices)
    • Opposite outer edge (side) lengths that appear to be the same or equal
    • Ex:
  • 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
    • Ex:

Note(s):

  • Grade Level(s):
    • Grade 1 will identify two-dimensional 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 two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • III.A. Geometric and Spatial Reasoning – Figures and their properties
      • III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.

Identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world.

Identify

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

Including, but not limited to:

  • Identify three-dimensional figures
    • Three-dimensional figure – a solid figure
    • Identity not changed by orientation
    • Identity not changed by size
    • Identity not changed by color
    • Identity not changed by texture
  • Identification and connection between formal geometric names to three-dimensional solids by examining objects in the real world
    • Cylinder
      • Can, straw, etc.
      • 2 equal, opposite, flat surfaces shaped like circles
      • 1 curved surface
      • Rolls, slides, stacks
      • 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 cube is a prism.
    • 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 three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Identifying and using attributes of two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • III.A. Geometric and Spatial Reasoning – Figures and their properties
      • III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.

Identify two-dimensional components of three-dimensional objects.

Identify

TWO-DIMENSIONAL COMPONENTS OF THREE-DIMENSIONAL OBJECTS

Including, but not limited to:

  • Two-dimensional figure – a flat figure
  • Three-dimensional figure – a solid figure
  • Two-dimensional figures as components of three-dimensional real-world objects
    • Circle
      • Ex: The top and the bottom of a can
      • Ex: The bottom of a party hat
    • Triangle
      • Ex: The ends of a Toblerone® candy box
      • Ex: The ends of a tent
      • Ex: The surfaces of a pyramid
    • Rectangle
      • Ex: A flat surface of a die
      • Ex: A flat surface of a tissue box
      • Ex: The sides and bottom of a tent
    • Square (special rectangle)
      • Ex: The flat surface of an alphabet block

Note(s):

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

Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably.

Identify

ATTRIBUTES OF TWO-DIMENSIONAL SHAPES USING INFORMAL AND FORMAL GEOMETRIC LANGUAGE INTERCHANGEABLY

Including, but not limited to:

  • Two-dimensional figure – a flat figure
  • Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., outer edges [sides], corners [vertices], etc.)
  • Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 outer edges [sides] that appear to be the same length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 outer edges [sides] and 4 square corners; however, a square has 4 outer edges [sides] that appear to be the same length but a rectangle has only opposite outer edges [sides] that appear to be the same length; etc.)
  • 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 two-dimensional figure
      • “Vertex” or “vertices” for informal term “corners”
        • Vertex (vertices) in a two-dimensional figure – a corner where two outer edges (sides) of a two-dimensional figure meet
  • Circle
    • A round, flat figure
    • No straight outer edges (sides)
    • No corners (vertices)
    • Ex:
  • 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
    • Ex:
    • Irregular triangle – a triangle with outer edges (sides) and/or corners that appear to be different or unequal
    • Ex:
  • Rectangle
    • 4 straight outer edges (sides)
    • 4 square corners (vertices)
    • Opposite outer edge (side) lengths that appear to be the same or equal
    • Ex:
  • 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
    • Ex:
  • Attributes that do not identify a two-dimensional figure
    • Orientation
    • Size
    • Color
    • Texture

Note(s):

  • Grade Level(s):
    • Kindergarten transitions to formal geometric language to describe the attributes of two-dimensional shapes.
    • Grade 1 will identify two-dimensional 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 two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • III.A. Geometric and Spatial Reasoning – Figures and their properties
      • III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.

Classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size.

Classify, Sort

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

Including, but not limited to:

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

Note(s):

  • Grade Level(s):
    • Grade 1 will classify and sort regular and irregular two-dimensional 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 two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • III.A. Geometric and Spatial Reasoning – Figures and their properties
      • III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.
      • III.A.2. Form and validate conjectures about one-, two-, and three-dimensional figures and their properties.

Create two-dimensional shapes using a variety of materials and drawings.

Create

TWO-DIMENSIONAL 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.
  • Two-dimensional figure – a flat figure
  • Spatial visualization – creation and manipulation of mental representations of shapes
  • Attributes of two-dimensional figures
    • Side – a straight outer boundary between two vertices (line segment) of a two-dimensional figure
      • Number of sides
      • Length of sides
    • Vertex (vertices) in a two-dimensional figure – a corner where two outer edges (sides) of a two-dimensional figure meet
      • Number of vertices
      • Types of vertices
        • Square corners
          • Square corners can be determined using the corner of a known square or rectangle (e.g., sticky note, sheet of paper, etc.).
            • Ex:
        • Not square corners
  • Attributes that do not identify a two-dimensional figure
    • Orientation
    • Size
    • Color
    • Texture
  • Create two-dimensional figures based on attributes and properties
    • Circle
      • A round, flat figure
      • No straight 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 two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons.
    • Grade 1 will compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible. 
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Identifying and using attributes of two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • III.A. Geometric and Spatial Reasoning – Figures and their properties
      • III.A.1. Recognize characteristics and dimensional changes of two- and three-dimensional figures.

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.

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 two-dimensional shapes and three-dimensional 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 three-dimensional figures and their properties.

Compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference.

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 two-dimensional shapes and three-dimensional solids
  • TxCCRS:
    • III.A. Geometric and Spatial Reasoning – Figures and their properties
      • III.A.2. Form and validate conjectures about one-, two-, and three-dimensional 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, and organize data into two or three categories.

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 real-world objects sorted by size, shape, color, etc.
  • Data organized and represented in a variety of ways
    • Data organized using T-charts, sorting mats, etc.
    • Data represented by real-world 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 T-charts. 
    • 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 real-object and picture graphs.

Use

DATA

To Create

REAL-OBJECT 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
    • Real-object 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 real-object 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 one-to-one 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
    • Real-object graph to picture graph
      • Ex:
    • Picture graph to real-object graph
      • Ex:
    • Same data represented using a picture graph and a bar-type graph
      • Ex:

Note(s):

  • Grade Level(s):
    • Grade 1 will use data to create picture and bar-type 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 real-object and picture graphs.

Draw

CONCLUSIONS FROM REAL-OBJECT 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
    • Real-object 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 bar-type 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.

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:
    • Financial Literacy

Differentiate between money received as income and money received as gifts.

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:
    • Financial Literacy

List simple skills required for jobs.

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 post-secondary 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:
    • Financial Literacy

Distinguish between wants and needs and identify income as a source to meet one's wants and needs.

Distinguish

BETWEEN WANTS AND NEEDS

Including, but not limited to:

  • Distinguish between real-world 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.
      • Ex:
      • Ex:

      • Ex:

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:
    • Financial Literacy

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 – kindergarten-algebra I vertical alignment. Retrieved from:
https://www.texasgateway.org/resource/vertical-alignment-charts-revised-mathematics-teks

Texas Education Agency. (2013) Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from:
https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013

Texas Education Agency. (2016). Mathematics TEKS – supporting information kindergarten. Retrieved from:
https://https://www.texasgateway.org/resource/mathematics-teks-supporting-information

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