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 TITLE : Unit 07: Number Relationships up to 99 SUGGESTED DURATION : 10 days

#### Unit Overview

Introduction
This unit bundles student expectations that address relationships and patterns in numbers including the sum of a multiple of 10 and a one-digit number, reciting numbers, skip counting, and numbers that are 10 more and 10 less than a given number. 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 Kindergarten, students recited numbers by tens up to 100. In Grade 1 Unit 06, students explored place value in order to understand numbers up to 99.

During this Unit
Students delve deeper into the place value system. Various representations (e.g., linking cubes, straw bundles, base-10 blocks, place value disks, hundreds charts, beaded number lines, and open number lines) are used to discover numerical patterns in the number system. Students use place value patterns to determine the sum up to 99 of a multiple of 10 and a one-digit number, as well as determine a number that is 10 more or 10 less than a given number. Students continue to develop the understanding of cardinal numbers, meaning numbers that name the quantity of objects in a set, and hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases, as they recite numbers up to 99 forward and backward by ones and tens in addition to skip counting by 2s, 5s, and 10s.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool Grade 1

After this Unit
In Unit 09, students will continue to explore place value and numerical relationships in larger numbers up to 120, as well as the relationship between skip counting patterns up to 120 and counting a collection of coins up to 120¢.

In Grade 1, reciting numbers is identified within the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of place value. Determining the sum of a multiple of 10 and a one-digit number, determining numbers that are 10 more or 10 less than a given number, and skip counting are also identified within Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of place value in addition to the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Solving problems involving addition and subtraction. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning A1, 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 Teaching Children Mathematics, even students in grades two through five do not understand how the digits in a two-digit number relate to a picture of that many single objects. Drawing students’ attention to these connections in the early grades will help lead to later success (Ross, 2002). Research suggests that students’ abilities to understand various representations of numbers and to make connections among those representations are essential to success with mathematics (Hiebert & Carpenter, 2006).

Hiebert, J. & Carpenter, T. (2006). “Learning and Teaching with Understanding.” Handbook of Research on Mathematics, 65-97.
Ross, Sharon. (2002). “Place Value: Problem Solving and Written Assessment.” Teaching Children Mathematics 8(7): 419-23.
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 numerical patterns and operational relationships in a variety of problem situations leads to efficient, accurate, and flexible representations and solution strategies (sums of a multiple of 10 and a one-digit number up to 99).
• 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 …
• concrete models or objects
• pictorial models
… aid in problem solving and explaining a problem solving strategy?
• How does understanding …
• relationships within and between operations
• properties of operations
… aid in determining an efficient strategy or representation to investigate problem situations?
• What strategies can be used to determine the sum of a multiple of 10 and a one-digit number?
• What patterns and relationships exist when adding a multiple of 10 and a one-digit number?
• When using addition to solve a problem situation, why can the order of the addends be changed?
• Number and Operations
• Base-10 Place Value System
• Number
• Counting (natural) numbers
• Whole numbers
• Operations
• Relationships
• 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.

 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)
• Recognizing and understanding numerical patterns and relationships leads to efficient, accurate, and flexible representations (skip counting by twos, fives, and tens up to 99; 10 more or 10 less than up to 99).
• What patterns can be found when skip counting by …
• twos?
• fives?
• tens?
• How are patterns in place value relationships used to determine a number that is …
• 10 more
• 10 less
… than a given number?
• Algebraic Reasoning
• Patterns and Relationships
• Skip counting
• Multiples
• 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.

 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)
• 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 forward and backward between 1 and 99).
• What patterns can be found between each grouping of ten when reciting numbers in sequence …
• forward by ones?
• backward by ones?
• 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.

#### MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

• Some students may think when increasing or decreasing a number by a multiple of 10, the tens place is increasing or decreasing by 1 rather than understanding that a change of 1 in the tens place means a change by 1 group of 10.
• Some students may think the pattern used to recite numbers backward is different than the pattern used to recite numbers forward rather than applying the same place value relationships to reciting forward or backward (e.g., if, when reciting numbers forward, the digit in the ones place increases by one, then when reciting numbers backward, the digit in the ones place will decrease by one, etc.).
• Some students may think skip counting numbers in sequence is a memorization task rather than understanding that each number represents a group of objects and that each group of objects in the skip counting sequence represents a quantity of one group more than the previous number.

Underdeveloped Concepts:

• Some students may be confused about the counting sequence for the numbers 11 – 15 and recite these numbers as “one-teen, two-teen, three-teen, four-teen, five-teen” rather than “eleven, twelve, thirteen, fourteen, fifteen.”
• Although some students may be able to correctly recite numbers forward from 0 – 99, they may have difficulty beginning with a number other than 0.
• Some students may have difficulty remembering which multiple of 10 follows a number with a 9 in the ones place (e.g., 40 comes after 39, 30 comes after 29, 20 comes after 19, etc.).

#### 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}
• Digit – any numeral from 0 – 9
• Number sentence – a mathematical statement composed of numbers, and/or an unknown(s), and/or an operator(s), and an equality or inequality symbol
• Place value – the value of a digit as determined by its location in a number such as ones, tens, etc.
• Recite – to verbalize from memory
• Skip counting – counting numbers in sequence forward or backward by a whole number other than 1
• Strip diagram – a linear model used to illustrate number relationships
• 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:

 Decrease Greater than, more than Increase Increments Less than, fewer than Multiple of 10 Ones place Relationship Sequence Tens place Total
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 Grade 1 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
1.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
1.1A 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• 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.
1.1B 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• 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.
1.1C

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 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
• Number sense

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• 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.
1.1D 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• 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.
1.1E 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• 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.
1.1F 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
1.1G 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 place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
1.3 Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to:
1.3A Use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99.

Use

CONCRETE AND PICTORIAL MODELS TO DETERMINE THE SUM OF A MULTIPLE OF 10 AND A ONE-DIGIT NUMBER IN PROBLEMS UP TO 99

Including, but not limited to:

• Whole numbers (0 – 99)
• 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}
• Sum – the total when two or more addends are joined
• Addend – a number being added or joined together with another number(s)
• Digit – any numeral from 0 – 9
• Sums of a multiple of 10 and a one-digit number up to 99
• Multiples of 10
• 10, 20, 30, 40, 50, 60, 70, 80, 90
• Addition strategy based on patterns and place value
• Solutions recorded with a number sentence
• Number sentence – a mathematical statement composed of numbers, and/or an unknown(s), and/or an operator(s), and an equality or inequality symbol
• Number sentences, or equations, with equal sign at beginning or end
• Concrete models
• Base-10 blocks, linking cubes, place value disks, etc.
• Pictorial models
• Base-10 pictorials, place value disks, number lines, strip diagrams, etc.
• Strip diagram – a linear model used to illustrate number relationships
•  Mathematical and real-world problem situations
• Joining action result unknown problems
• Part-part-whole whole unknown problems

Note(s):

• Grade 2 will solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing an understanding of place value
• Solving problems involving 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.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.
1.5 Algebraic reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to:
1.5A

Recite numbers forward and backward from any given number between 1 and 120.

Recite

NUMBERS FORWARD AND BACKWARD FROM ANY GIVEN NUMBER BETWEEN 1 AND 99

Including, but not limited to:

• Counting numbers (1 – 99)
• 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., 58 is 57 increased by 1; 58 decreased by 1 is 57; etc.)
• Recite numbers forward from any given number between 1 and 99
• 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
• Recite numbers backward from any given number between 1 and 99
• Orally by ones beginning with 99
• Orally by ones beginning with any given number between 1 and 99
• Orally by tens beginning with 99
• Orally by tens beginning with any given number between 1 and 99

Note(s):

• Kindergarten recited numbers up to at least 100 by ones beginning with any given number and by tens beginning with any multiple of 10.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing an understanding of place value
• TxCCRS:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
1.5B

Skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set.

Skip Count

BY TWOS, FIVES, AND TENS TO DETERMINE THE TOTAL NUMBER OF OBJECTS UP TO 99 IN A SET

Including, but not limited to:

• Whole numbers (0 – 99)
• 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}
• Skip counting – counting numbers in sequence forward or backward by a whole number other than 1
• Counting sequence can begin at any number.
• Determine the total number of objects in a set.
• Sets up to 99
• Skip counting by twos, fives, and tens
• More efficient than counting by ones
• Counting the same set of objects using different skip count increments results in the same total.
• Relationships in skip counting by twos
• When counting by twos, one number is skipped.
• When beginning with 0, all numbers counted have a 0, 2, 4, 6, or 8 in the ones place.
• Relationships when skip counting by fives
• When counting by fives, 4 numbers are skipped.
• When beginning with 0, all numbers counted alternate 0 or 5 in the ones place.
• Relationships when skip counting by tens
• When counting by tens, 9 numbers are skipped.
• When beginning with 0, all numbers counted have a 0 in the ones place.
• When beginning with any number, the digit in the ones place remains the same and the digit in the tens place increases by 1.
• When beginning with 0, all numbers counted by ten are also included in the count by twos and the count by fives.
• Relationships represented using concrete or pictorial models
• Hundreds chart, color tiles, number line, real-life objects, etc.

Note(s):

• Grade 1 introduces skip counting by twos, fives, and tens to determine the total number of objects up to 120 in a set.
• Grade 2 will determine whether a number up to 40 is even or odd using pairings of objects to represent the number.
• Grade 3 will represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing an understanding of place value
• Solving problems involving addition and subtraction
• TxCCRS:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
1.5C

Use relationships to determine the number that is 10 more and 10 less than a given number up to 120.

Use

RELATIONSHIPS TO DETERMINE THE NUMBER THAT IS 10 MORE AND 10 LESS THAN A GIVEN NUMBER UP TO 99

Including, but not limited to:

• Whole numbers (1 – 99)
• 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}
• Place value – the value of a digit as determined by its location in a number such as ones, tens, etc.
• Tens place
• Ones place
• Comparative language
• Greater than, more than
• Less than, fewer than
• Relationships based on place value
• 10 more or 10 less
• Adding 10 to a number increases the digit in the tens place by 1.
• Subtracting 10 from a number decreases the digit in the tens place by 1.
• Relationships based on patterns in concrete or pictorial models
• Hundreds chart
• Moving one row down will generate a number that is 10 more than the original number.
• Moving one row up will generate a number that is 10 less than the original number.
• Base-10 blocks
• Adding longs will increase a number by increments of 10.
• Removing longs will decrease a number by increments of 10.

Note(s): 