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 Instructional Focus DocumentKindergarten Mathematics
 TITLE : Unit 15: Numeracy SUGGESTED DURATION : 12 days

Unit Overview

Introduction
This unit bundles student expectations that address numeracy concepts as they are applied to operational situations involving addition and subtraction and graphing situations. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Units 08, 09, and 10, students developed concepts about numeracy, which included counting, subitizing, number relationships, composing and decomposing numbers, and part-whole relationships. Students developed ideas about reading, writing, and representing numbers. Other concepts about numbers were developed including comparing and describing sets of objects. Students applied this knowledge about numbers and number relationships in addition and subtraction situations and explored and explained different strategies for solving these problem situations. Students also applied their understanding of number and number relationships to data analysis situations involving real-object and picture graphs.

During this Unit
Students apply their knowledge of mathematical relationships to counting, problem solving, and graphing. Students increase their foundational understandings of the mathematical relationships that exist within numbers. Counting is no longer simply rote. It now involves an understanding of the relationship between the numbers in the counting sequence. Students acquire a mathematical understanding of how numbers increase by one during the forward count or decrease by one during the backward count. Because of this understanding, students are able to count forward and backward easily without the use of objects. The understanding of this relationship will also apply when reciting numbers by ones or tens beginning with any given number and when generating a number that is one more or one less than a given number. Students transition to reading, writing, and representing numerals without objects or pictures. Students also transition from one-to-one correspondence to working with number relationships. These mathematical relationships are applied when students generate and compare sets of objects or compare written numerals using comparative language. Students use the subitizing skills of instantly recognizing quantities as they compose and decompose numbers. An understanding of cardinality and conservation supports their work with addition and subtraction. This understanding that the last number names the set and that the arrangement of the set does not matter, allows students to perform operations with numbers with greater accuracy. Students demonstrate an understanding that joining represents addition situations while separating represents subtraction situations. Students are able to explain the strategies used to solve problems with sums and minuends to 10. Numeracy concepts extend into graphing. Students draw conclusions about data in both real-object and picture graphs.

After this Unit
In Grade 1, students will continue to develop their understanding of numbers and number relationships. Students will be introduced to the concept of place value and will use this knowledge when composing and decomposing larger numbers to 120. The operations of addition and subtraction will also be further developed as use knowledge about number relationships and place value to develop addition and subtraction fact strategies.

In Kindergarten, reciting numbers up to at least 100 by ones and tens by any given starting number, reading, writing, and representing numbers, cardinality, subitizing, and comparing and describing sets of objects are foundational concepts that are included in the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of whole numbers. Counting forward and backward with and without objects, composing and decomposing numbers, and generating numbers and sets of objects that are more than, less than, or equal to an original quantity are also identified within the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of whole numbers as well as the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of addition and subtraction. Modeling, representing, and explaining strategies used to solve addition and subtraction problems are also included in the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of addition and subtraction. Drawing conclusions from graphs is included under the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Grade Level Connections. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I.A. Numeric Reasoning – Number representation, I.B. Numeric Reasoning – Number operations, VIII. Problem Solving and Reasoning, IX. Communication and Representation, and X. Connections.

Research
According to Chapin (2006), “A major milestone occurs in the early grades when students interpret number in terms of part and whole relationships. A part-whole understanding of number means that quantities are interpreted as being composed of other numbers” (p. 17). This understanding of part-whole relationships is foundational for other areas of mathematics and for other grade levels. NCTM (2010) further states, “The foundational ideas of number and numeration link to and support children’s understanding of other, sometimes more sophisticated or complex topics. These topics include addition and subtraction, multiplication, rational number, early algebraic thinking, and other advanced ideas” (p. 43).

Chapin, S & Johnson, A. (2000). Math matters: Understanding the math you teach. Sausalito, CA: Math Solutions Publications.
National Council of Teachers of Mathematics. (2010). Developing essential understanding of number and numeration pre-k – grade 2. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013

 Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place. How is numeracy like literacy? What are some examples of numeracy in everyday life, society, and the work place? How does context influence understanding of a quantity? Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• A thorough understanding of counting involves integrating different skills or characteristics of numbers and is foundational and essential for continued work with numbers (counting numbers through 20).
• What relationships exist between numbers in the proper counting sequence?
• What strategies can be used to keep track of the count when counting a set of objects?
• Why are tracking strategies important in counting a set of objects?
• How does starting the count with a different object affect the count?
• How does rearranging the set of objects affect the count?
• The ability to recognize and represent numbers in various forms develops the understanding of equivalence and allows for working flexibly with numbers in order to communicate and reason about the value of the number (whole numbers through 20; decomposition within 10).
• What are some ways a number can be represented?
• Why can a number vary in representation but the value of the number stay the same?
• Why is it important to be able to recognize and create a variety of representations for a quantity?
• How could representing a number using …
• concrete models
• pictorial models
… improve understanding and communicating about the value of a number and the equivalence of the representations?
• Number
• Composition and Decomposition of Numbers
• Number
• Counting (natural) numbers
• Whole numbers
• Number Recognition and Counting
• Sequence
• Cardinality
• Conservation of set
• Hierarchical inclusion
• Magnitude
• Number Representations
• Standard form
• Relationships
• Numerical
• Equivalence
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place. How is numeracy like literacy? What are some examples of numeracy in everyday life, society, and the work place? How does context influence understanding of a quantity? Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• A thorough understanding of counting involves integrating different skills or characteristics of numbers and is foundational and essential for continued work with numbers (whole numbers through 20).
• What relationships exist between numbers in the proper counting sequence?
• What strategies can be used to keep track of the count when counting a set of objects?
• Why are tracking strategies important in counting a set of objects?
• How does starting the count with a different object affect the count?
• How are counting skills used to generate numbers that are greater or less than a given number?
• The ability to recognize and represent numbers in various forms develops the understanding of equivalence and allows for working flexibly with numbers in order to communicate and reason about the value of the number (whole numbers through 20).
• What are some ways a number can be represented?
• Why can a number vary in representation but the value of the number stay the same?
• Why is it important to be able to recognize and create a variety of representations for a quantity?
• How could representing a number using …
• concrete models
• pictorial models
… improve understanding and communicating about the value of a number and the equivalence of the representations?
• Quantities are compared to determine magnitude of number and equality or inequality relations (whole numbers through 20).
• Why is it important to identify the unit or attribute being described by numbers before comparing the numbers?
• How can …
• numeric representations
• concrete representations
• pictorial representations
… aid in comparing numbers?
• How can the comparison of two numbers be described and represented?
• Number
• Compare
• Comparative language
• Number
• Counting (natural) numbers
• Whole numbers
• Number Recognition and Counting
• Sequence
• Cardinality
• Conservation of set
• Hierarchical inclusion
• Magnitude
• Number Representations
• Standard form
• Relationships
• Numerical
• Equivalence
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place. How is numeracy like literacy? What are some examples of numeracy in everyday life, society, and the work place? How does context influence understanding of a quantity? Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• A thorough understanding of counting involves integrating different skills or characteristics of numbers and is foundational and essential for continued work with numbers (whole numbers through 20).
• What relationships exist between numbers in the proper counting sequence?
• How are counting skills used to generate numbers that are greater or less than a given number?
• What relationships exist between numerals and the quantities?
• Quantities are compared to determine magnitude of number and equality or inequality relations (whole numbers through 20).
• Why is it important to identify the unit or attribute being described by numbers before comparing the numbers?
• How can …
• numeric representations
• concrete representations
• pictorial representations
… aid in comparing numbers?
• How can the comparison of two numbers be described and represented?
• Number
• Compare
• Comparative language
• Number
• Counting (natural) numbers
• Whole numbers
• Number Recognition and Counting
• Hierarchical inclusion
• Magnitude
• Number Representations
• Standard form
• Relationships
• Numerical
• Equivalence
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place. How is numeracy like literacy? What are some examples of numeracy in everyday life, society, and the work place? How does context influence understanding of a quantity? Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• A thorough understanding of counting involves integrating different skills or characteristics of numbers and is foundational and essential for continued work with numbers (whole numbers through 10).
• Why are visualizing and instantly recognizing small quantities beneficial when …
• working with larger quantities of objects?
• composing or decomposing numbers?
• Number
• Composition and Decomposition of Numbers
• Number
• Whole numbers
• Number Recognition and Counting
• Subitizing
• Associated Mathematical Processes
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place. How is numeracy like literacy? What are some examples of numeracy in everyday life, society, and the work place? How does context influence understanding of a quantity? Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy? Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• A thorough understanding of counting involves integrating different skills or characteristics of numbers and is foundational and essential for continued work with numbers (counting numbers forward and backward through 20).
• What relationships exist between numbers in the counting sequence when …
• counting forward from one number to the next number?
• counting backward from one number to the previous number?
• Recognition of patterns in the number word sequence, which are repeated with every grouping of ten, leads to efficient and accurate reciting of numbers (reciting numbers to at least 100).
• What patterns can be found between each grouping of ten when reciting numbers in sequence by …
• ones?
• tens?
• Number
• Number
• Counting (natural) numbers
• Number Recognition and Counting
• Sequence
• Cardinality
• Hierarchical inclusion
• Magnitude
• Algebraic Reasoning
• Patterns and Relationships
• Reciting numbers
• Associated Mathematical Processes
• Problem Solving Model
• Tools and Techniques
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Understanding and generalizing operational relationships leads to more sophisticated representations and solution strategies in order to investigate or solve problem situations in everyday life. What relationships exist within and between mathematical operations? How does generalizing operational relationships lead to developing more flexible, efficient representations and/or solution strategies? Why is understanding the problem solving process an essential part of learning and working mathematically?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Recognizing and understanding operational relationships in a variety of problem situations leads to efficient, accurate, and flexible representations and solution strategies (addition and subtraction of whole numbers through 10).
• What actions can be used to describe a(n) …
• subtraction situation?
• How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?
• How can representing a problem situation using …
• words
• concrete models or objects
• drawings or pictorial models
• a number sentence
… aid in problem solving and explaining a problem solving strategy?
• What strategies can be used for finding sums or differences?
• What relationships exist between …
• counting strategies and addition?
• counting strategies and subtraction?
• addition and subtraction?
• When using addition to solve a problem situation, why can the order of the addends be changed?
• When using subtraction to solve a problem situation, why can the order of the minuend and subtrahend not be changed?
• Operational understandings lead to generalizations that aid in determining the reasonableness of solutions (addition and subtraction of whole numbers through 10).
• When adding two non-zero whole numbers, why is the sum always greater than each of the addends?
• When subtracting two non-zero whole numbers with the minuend larger than the subtrahend, why is the difference always less than the minuend?
• Number and Operations
• Number
• Counting (natural) numbers
• Whole numbers
• Operations
• Subtraction
• Problem Types
• Relationships and Generalizations
• Operational
• Equivalence
• Solution Strategies
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Statistical displays often reveal patterns within data that can be analyzed to interpret information, inform understanding, make predictions, influence decisions, and solve problems in everyday life with degrees of confidence. How does society use or make sense of the enormous amount of data in our world available at our fingertips? How can data and data displays be purposeful and powerful? Why is it important to be aware of factors that may influence conclusions, predictions, and/or decisions derived from data?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Data representations display the counts (frequencies) or measures of data values in an organized, visual format so that the data can be interpreted efficiently (comparison of data values up to 20; addition or subtraction of data values within 10).
• What are the parts of a picture graph?
• How do the title and category labels describe the data being represented in a picture graph?
• What is the relationship between the data counts and the pictures in a picture graph?
• How are numbers and counting used when …
• constructing graphs?
• drawing conclusions?
• What types of …
• conclusions can be drawn
• questions can be answered
… using data in a graph?
• What is the purpose of an organized, visual format and how does it aid in the ability to efficiently draw conclusions and answer questions?
• Data Analysis
• Data
• Interpretation
• Conclusions
• Statistical Representations
• Picture graphs
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Underdeveloped Concepts:

• Some students may still confuse numbers that look similar because they contain the same digits (e.g., 12 and 21).
• Some students may still write numbers with reversals.
• Some students may still be acquiring an understanding of numeracy concepts such as cardinality, subitizing, one-to-one correspondence, conservation, and hierarchical inclusion.
• Some students may still have difficulty with the rote counting sequence.
• Some students may be able to rote count correctly but not understand quantity or mathematical relationships among numbers.
• Although some students may understand numbers that represent smaller quantities, they may still struggle with numbers that represent larger quantities.
• Some students may still have difficulty with teen numbers because the teen numbers do not follow the same pattern as other numbers.
• Some students may not add or subtract correctly because they lack counting skills, cardinality, or conservation of number.
• Some students may be able to solve an addition or subtraction situation but struggle explaining their strategy.
• Although some students may be able to answer obvious questions about a graph (e.g., how many in a category), they may struggle drawing conclusions about the graph (e.g., this category has less than that category).

Unit Vocabulary

• Addend – a number being added or joined together with another number(s)
• 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 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
• Compose numbers – to combine parts or smaller values to form a number
• Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
• Data – information that is collected about people, events, or objects
• Decompose numbers – to break a number into parts or smaller values
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• Graph – a visual representation of the relationships between data collected
• Minuend – a number from which another number will be subtracted
• Number sentence – a mathematical statement composed of numbers, and/or an unknown(s), and/or an operator(s), and an equality or inequality symbol
• One-to-one correspondence – each object counted is matched accurately with a number word in correct sequence
• 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
• 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
• Recite – to verbalize from memory
• Subtrahend – a number to be subtracted from a minuend
• Sum – the total when two or more addends are joined
• Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}

Related Vocabulary:

 Addition Backward Category Change amount Comparative language Compare Conclusion Count all Count backward Count by ones Count by tens Count on Counting order Decrease Digit Equal symbol Equal to, same as Estimate Forward Greater than, more than Increase Join Less than, fewer than Minus Number Numeral Part Plus Quantity Remove Result amount Separate Set Start amount Subtraction Summarize Total Unknown Value Whole
System Resources Other Resources

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway – Resources Aligned to Kindergarten Mathematics TEKS

TEKS# SE# Unit Level Taught Directly TEKS Unit Level Specificity

Legend:

• Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
• Student Expectations (TEKS) identified by TEA are in bolded, black text.
• Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific clarifications are in italicized, blue text.
• Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
K.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
K.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

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

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• X. Connections
K.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

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

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VIII. Problem Solving and Reasoning
K.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, 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:
• VIII. Problem Solving and Reasoning
K.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

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

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• IX. Communication and Representation
K.1E Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Representations of mathematical ideas
• Organize
• Record
• Communicate
• Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
• Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• IX. Communication and Representation
K.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Mathematical relationships
• Connect and communicate mathematical ideas
• Conjectures and generalizations from sets of examples and 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:
• X. Connections
K.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

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

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• IX. Communication and Representation
K.2 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:
K.2A 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.)
• 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.)
• 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 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:
• IX. Communication and Representation
K.2B Read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures.

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):

• 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
• TxCCRS:
• I.A. Numeric Reasoning – Number representation
• IX. Communication and Representation
K.2C 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

Note(s):

• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• TxCCRS:
• IX. Communication and Representation
K.2D 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
• Conceptual subitizing – recognition of a quantity based on a spatial arrangement, pattern, parts of the arrangement, etc.
• 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.)
• 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.
• Various random arrangements of objects

Note(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:
• IX. Communication and Representation
K.2E 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

Note(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 representation
• IX. Communication and Representation
K.2F 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.)
• 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
• One less than a given number, including 1 less than 1 and 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
• 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 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 representation
• IX. Communication and Representation
K.2G 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.)
• 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.)
• Equality language (equal to, same as, etc.)
• 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
• Comparison of two unorganized sets
• Comparison of an organized set to an unorganized set
• 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

Note(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 representation
• IX. Communication and Representation
K.2H 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.

Note(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 representation
• IX. Communication and Representation
K.2I 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
• Composed parts may be listed in any order (commutative property).
• Relationship of composed parts to create a new set of composed parts
• Decomposition of a number in more than one way using objects and pictures
• Original decomposed number conserved
• Decomposed parts may be listed in any order (commutative property).
• Relationship of decomposed parts to create a new set of decomposed parts

Note(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:
• IX. Communication and Representation
K.3 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:
K.3A 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}
• 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
• Pictorial models to represent contextual joining situations
• Simple sketches representing concrete models without unnecessary details
• Physical joining of pictorial representations by circling or connecting
• 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
• 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
• Acting out to represent contextual separating situations

Note(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.B. Numeric Reasoning – Number operations
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
K.3B 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}
• 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
• 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
• 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.
• Count on strategies
• One-to-one correspondence
• Count on from the first number presented.
• Count on from the largest number.
• 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.)
• Adding 1 does not require counting.
• Properties of addition
• Quantities may be joined in any order (commutative property).
• A number keeps its identity when 0 is added to it (additive identity property).

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
• Subtraction strategies based on counting
• Removing
• One-to-one correspondence
• Count out start quantity, count and remove change quantity, and then count remaining quantity.
• 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.
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.
• 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.)
• 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).

Note(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.B. Numeric Reasoning – Number operations
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
K.3C 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}
• 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
• 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
• Subtraction symbol represents separating
• Minuend – subtrahend = difference
• Difference = minuend – subtrahend
• Equal symbol indicates the same value being represented on both side(s)

Note(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.B. Numeric Reasoning – Number operations
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
K.5 Algebraic reasoning. The student applies mathematical process standards to identify the pattern in the number word list. The student is expected to:
K.5A 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.)
• Count forward up to at least 100
• Orally by ones beginning with 1
• Orally by ones beginning with any given number
• Orally by tens beginning with 10
• Orally by tens beginning with any given number between 1 and 100
• Beginning number is a multiple of 10.

Note(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
• TxCCRS:
• IX. Communication and Representation
K.8 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:
K.8C 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
• 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.)
• Changes in orientation do not affect data values

Note(s): 