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 Instructional Focus DocumentKindergarten Mathematics
 TITLE : Unit 07: Introducing Contextual Sums and Minuends to 10 SUGGESTED DURATION : 10 days

#### Unit Overview

Introduction
This unit bundles student expectations that address modeling, representing, and explaining strategies used to solve addition and subtraction problems involving sums and minuends to 10. 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 Unit 04, students explored conceptual addition and subtraction within 5, the problem-solving process, and the connection between addition and subtraction operations and counting strategies, hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases, and composing and decomposing numbers.

During this Unit
Students extend contextual sums and minuends to 10 to develop the foundation of operations. Students use concrete objects, pictorial models, and acting out a situation to model and represent joining and separating problems. Students use these representations to solve contextual addition and subtraction problems involving sums and minuends up to 10. Students record their solution using a number sentence and orally explain their solution strategy. As students model, represent, and solve addition and subtraction problems, they begin to develop an understanding of the problem solving process that includes understanding the context of the problem situation and the question being asked, forming a plan or strategy, and using the plan or strategy to determine a solution. Although Kindergarten students are not expected to identify problem types by name, they begin to recognize contextual problems that represent joining action result unknown, separating action result unknown, and part-part-whole whole unknown situations.

After this Unit
In Unit 09, students will revisit modeling, representing, and explaining strategies used to solve addition and subtraction problems with sums and minuends up to 10.

In Kindergarten, modeling, representing, and explaining strategies used to solve addition and subtraction problems are subsumed within the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of addition and subtraction. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning A2, B1; II. Algebraic Reasoning D1, D2; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.

Research
According to Copley (2010), “A precursor to change operations, the part-part-whole representation helps children develop an understanding of the relationship between addition and subtraction” (p.59). Carpenter (1999) further states, “The development of understanding of part-whole relationships allows children to be more flexible in their choice of strategy” (p. 28). NCTM (2010) states that “[e]ither addition or subtraction is an appropriate way to express a part-part-whole relationship” (p.26). Fosnot (2001) states, “That subtraction and addition are related is a big idea children need to develop” (p. 90).

Carpenter, T. P, Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999).Children’s mathematics cognitively guided instruction. Portsmouth, NH: Heinemann.
Copley, J. (2010). The young child and mathematics. Washington, DC: National Association for the Education of Young Children
Fosnot, C. T., & Dolk, M. (2001). Young mathematicians at work: Constructing number sense, addition, and subtraction. Portsmouth, NH: Heinemann.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

 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.

#### MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

• Some students may think a problem can only be solved one way rather than realizing a variety of strategies can be used to solve the same problem.
• Some students may think certain key words always indicate the operation to be used to solve a problem rather than using the context of the situation to determine if the situation depicts joining or separating.
• Some students may think every math problem is unique rather than realizing many math problems have the same mathematical structure.
• Some students may think problem solving strategies have no relationship rather than recognizing the relationship between different strategies that can be used to solve a problem.
• Some students might think addition and subtraction are not related rather than recognizing the part-part-whole relationship represented in both addition and subtraction situations.

#### Unit Vocabulary

• Addend – a number being added or joined together with another number(s)
• Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• 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
• 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 Addition symbol Change amount Compose numbers Count all Count backward Count on Decompose numbers Equal symbol Five frame Join Minus Number Number path One-to-one correspondence Part-part-whole mat Plus Problem situation Quantity Remove Result amount Separate Sketch Start amount Subtraction Subtraction symbol Take away Total Unknown Value

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

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE Legend:

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

Specificity Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific clarifications are in italicized, blue text.
• Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
• A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
TEKS# SE# TEKS SPECIFICITY
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:
• 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.
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:
• 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.
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:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
K.1D

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

Communicate

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

Including, but not limited to:

• Mathematical ideas, reasoning, and their implications
• Multiple representations, as appropriate
• Symbols
• Diagrams
• 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.
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:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
K.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Mathematical relationships
• Connect and communicate mathematical ideas
• Conjectures and generalizations from sets of examples and 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.
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:
• 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.
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.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.
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.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
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.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.