Hello, Guest!
 TITLE : Unit 10: Operations Using Data Representations SUGGESTED DURATION : 5 days

Unit Overview

Introduction
This unit bundles student expectations that address interpreting, representing, explaining, generating, and solving addition and subtraction situations as well as applying basic fact strategies and properties of operations to solve addition and subtraction problems using the data from picture graphs and bar-type graphs. 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 01, students explored collecting, sorting, and organizing data in up to three categories using picture graphs and bar-type graphs. Students examined the data and drew conclusions to find sums and differences within 10. They also generated and answered questions regarding the data represented in the graphs. In Unit 05, students represented and solved contextual or real-world problem situations involving sums and minuends up to 20 using spoken words, objects, pictorial models, and number sentences. Students also explored, applied, and explained properties of operations and strategies used to solve addition and subtraction problems up to 20.

During this Unit
Students use data represented in bar-type graphs and picture graphs to represent, generate, and solve problem situations involving sums and minuends up to 20 using spoken words, objects, pictorial models, and number sentences. They explore and explain a variety of strategies to solve one-step problems involving addition, subtraction, and comparison of the data. While demonstrating various strategies, students explore and apply properties of operations. While students are not expected to recognize properties by name, they are expected to be able to apply and explain the associative property of addition (if three or more addends are added, they can be grouped in any order, and the sum will remain the same), the commutative property of addition, (if the order of the addends are changed, the sum will remain the same), and additive identity (the sum/difference is not affected when zero is added/subtracted to a number). Students are expected to use a number sentence with the unknown in any position to represent the situation. Students solve problems and are expected to explain that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s). Through the continued use of experiences with addition and subtraction situations, students begin to recognize basic fact relationships, which are essential for developing computational fluency. Thorough understanding of analyzing data and using the problem-solving process in addition and subtraction situations involving sums and minuends up to 20 is critical in setting the foundation for students’ success in mathematics as they progress through future grade levels.

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

After this Unit
In Unit 15, students will review the relationship between addition and subtraction. Repeated exposure to real-world addition and subtraction situations up to 20 further develops students’ understanding of the problem-solving process and solution strategies, including application of basic fact strategies. In Grade 2, students will transition from bar-type graphs to bar graphs and from picture graphs to pictographs. Students will generate and solve one-step word problems based on the information in bar graphs and pictographs.

In Grade 1, interpreting, representing, explaining, generating, and solving addition and subtraction situations as well as applying basic fact strategies and properties of operations are subsumed under the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Solving problems involving addition and subtraction. Representing the data using picture and bar-type graphs in order to draw conclusions, generate questions, and answer questions from the data are subsumed under the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of place value. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning A2, B1; II. Algebraic Reasoning A1, D1, D2; V. Statistical Reasoning A1, B2, C2, C3; 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 the authors of Beyond Arithmetic: Changing Mathematics in the Elementary Classroom (1995), “The speedy recollection of facts should not be confused with real mathematical skill. Good mathematical strategies – not quick memorization – are what really matter in understanding mathematics” (p. 72). The National Council of Teachers of Mathematics (2000) believes students should “collect data using observations, surveys, and experiments” in order to connect what they are learning in mathematics to other contexts (p. 64).

Mokros, J., Russell, S., & Econompoulos, K. (1995). Beyond arithmetic: Changing mathematics in the elementary classroom. White Plains, NY: Dale Seymour Publications.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. 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? 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? 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)
• 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 20).
• 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 does the operation(s) in a number sentence determine the context of a problem situation that can be represented by the number sentence?
• How can representing a problem situation using …
• words
• concrete models or objects
• pictorial models
• a number sentence
… aid in problem solving and explaining a problem solving strategy?
• What patterns and relationships can be found within and between the words, concrete objects, pictorial models, and number sentences used to represent a problem situation?
• How does understanding …
• relationships within and between operations
• properties of operations
• basic addition and subtraction facts
… aid in determining an efficient strategy or representation to investigate problem situations?
• What strategies can be used to determine …
• the sum
• the difference
• any unknown
… in an addition or subtraction situation?
• What relationships exist between …
• counting strategies and subtraction?
• What role does the equal sign play in a number sentence?
• 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?
• 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 120; addition or subtraction of data values within 20).
• What are the parts of a …
• picture graph?
• bar-type graph?
• How do the title and category labels describe the data being represented in a …
• picture graph?
• bar-type graph?
• What is the relationship between the data counts and the …
• pictures in a picture graph?
• cells in a bar-type graph?
• How are numbers and counting used when …
• constructing graphs?
• drawing conclusions?
• What types of …
• conclusions can be drawn
… 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, generate questions, and answer questions?
• Different data displays of the same data may appear different because of their unique display characteristics but the representations are equivalent in counts (frequencies) or measures of data values.
• How are bar-type graphs and picture graphs …
• alike?
• different?
• What characteristics aid in determining if data representations show representations with equivalent data sets?
• Which representation is easier to interpret? Why?
• Why is it important to be able to use different display representations if they are equivalent in counts or data values?
• Number and Operations
• Number
• Counting (natural) numbers
• Whole numbers
• Operations
• Subtraction
• Problem Types
• Properties of Operations
• Relationships and Generalizations
• Operational
• Equivalence
• Solution Strategies
• Algebraic Reasoning
• Equivalence
• Representations
• Concrete models
• Pictorial models
• Expressions
• Equations
• Data Analysis
• Data
• Interpretation
• Conclusions
• Statistical Representations
• Picture graphs
• Bar-type 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

Misconceptions:

• Some students may think subtraction is commutative rather than recognizing the minuend as the total amount and the subtrahend as the amount being subtracted (e.g., 5 – 3 is not the same as 3 – 5, etc.).
• Some students may think the equal sign means that an operation must be performed on the numbers on one side and the result of this operation is recorded on the other side of the equal sign rather than understanding that operations and/or individual numbers can be on either side of the equal sign as long as they represent equal quantities.
• Some students may think they can compare the length of the rows/columns of pictures in a picture graph rather than comparing the number of pictures in each row/column, not realizing that the size of the pictures will affect the length of the row/column.
• Some students may think leaving gaps between cells or using cells of differing sizes on a bar-type graph does not affect the data, not realizing that the size and spacing of the cells should be consistent.
• Some students may think data in a vertical bar-type or picture graph can be arranged from the top to bottom, not realizing that the cells on a bar graph or pictures in a picture graph are arranged from bottom to top.
• Some students may think data in a horizontal bar-type or picture graph can be arranged from right to left, not realizing that the cells on a bar graph or pictures in a picture graph are arranged from left to right.
• Some students may think data can only be used in one type of graph rather than realizing the same data can be represented using either a bar-type or picture graph (e.g., if it’s not something easy to draw or find a picture for the data, then the data might be best displayed using a bar-type graph rather than a picture graph, etc.).
• Some students may think if the orientation of the graph changes, then the data itself changes, not realizing that the data being represented remains the same.

Underdeveloped Concepts:

• Some students may not recognize the difference between an addition situation and a subtraction situation based on the context of the problem.
• Some students may confuse the –, +, and = symbols due to not fully understanding the meaning of each symbol.

Unit Vocabulary

• Addend – a number being added or joined together with another number(s)
• Bar-type graph – a graphical representation to organize data that uses bars divided into individual cells, where each cell represents one unit of data, to show the frequency (number of times) that each category occurs
• Categorical data – data that represents the attributes of a group of people, events, or objects
• 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
• Equal sign – a mathematical symbol representing equivalence
• Equation – a mathematical statement composed of equivalent expressions separated by an equal sign
• Expression – a mathematical phrase, with no equal sign or comparison symbol, that may contain a number(s), an unknown(s), and/or an operator(s)
• Fact families – related number sentences using the same set of numbers
• 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
• 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
• Strip diagram – a linear model used to illustrate number relationships
• Subtrahend – a number to be subtracted from a minuend
• Sum – the total when two or more addends are joined
• Survey – to ask a group of people a question in order to collect information about their opinions or answers
• Term – a number and/or an unknown in an expression separated by an operation symbol(s)
• Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}

Related Vocabulary:

 Addition Addition symbol Category Category label Cell Change unknown Combination Comparative language Compare Conclusion Frequency Horizontal Join Minus One-to-one correspondence Operation Part-part-whole Plus Quantity Represent Result unknown Separate Solution Start unknown Strategy Subtraction Subtraction symbol Symbol Title Total Unit of data Unknown Value Vertical
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.
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, 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 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:
1.3B Use objects and pictorial models to solve word problems involving joining, separating, 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.

Use

OBJECTS AND PICTORIAL MODELS TO SOLVE WORD PROBLEMS INVOLVING JOINING, SEPARATING, AND COMPARING SETS WITHIN 20 AND UNKNOWNS AS ANY ONE OF THE TERMS IN THE PROBLEM

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}
• Sum – the total when two or more addends are joined
• Addend – a number being added or joined together with another number(s)
• Addition of whole numbers within 20
• Subtraction
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• Minuend – a number from which another number will be subtracted
• Subtrahend – a number to be subtracted from a minuend
• Subtraction of whole numbers within 20
• 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
• Unknown in any position
• Concrete models
• Sets of objects within 20
• Base-10 blocks, linking cubes, counters, etc.
• Pictorial models
• Base-10 pictorials, number lines, strip diagrams, etc.
• Strip diagram – a linear model used to illustrate number relationships
• Mathematical and real-world problem situations
• Problems involving action
• Joining action result unknown
• Joining action change unknown
• Joining action start unknown
• Separating action result unknown
• Separating action change unknown
• Separating action start unknown
• Problems with no action
• Part-part-whole whole unknown
• Part-part-whole part unknown
• Additive comparison compare quantity (larger quantity) unknown
• Additive comparison referent (smaller quantity) unknown
• Recognition of addition and subtraction as inverse operations
• Addition can be reversed by subtraction.
• Subtraction can be reversed by addition.
• Fact families – related number sentences using the same set of numbers

Note(s):

• Kindergarten modeled the action of joining to represent addition and the action of separating to represent subtraction in problems with the result unknown.
• Grade 1 introduces comparison problems.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• 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.
1.3D Apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10.

Apply

BASIC FACT STRATEGIES TO ADD AND SUBTRACT WITHIN 20, INCLUDING MAKING 10 AND DECOMPOSING A NUMBER LEADING TO A 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}
• Sum – the total when two or more addends are joined
• Addend – a number being added or joined together with another number(s)
• Addition of whole numbers within 20
• Subtraction
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• Minuend – a number from which another number will be subtracted
• Subtrahend – a number to be subtracted from a minuend
• Subtraction of whole numbers within 20
• 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
• Decompose numbers – to break a number into parts or smaller values
• Compose numbers – to combine parts or smaller values to form a number
• Basic fact strategies for addition
• Counting all
• Count the amount of the first addend and count on the amount of the other addend.
• Counting on
• Begin with the first addend and count on the amount of the other addend.
• Begin with the largest addend and count on the amount of the other addend.
• Plus 1
• Adding 1 related to sequential counting
• Plus 2
• Adding 2 related to skip counting
• Adding zero to a number does not affect the total.
• Making 10
• Composing two addends to form a sum of 10
• Hidden tens
• Decomposing a number leading to a 10
• Plus 10
• Add 1 ten in the tens place and add 0 in the ones place.
• Doubles
• Double plus/minus 1
• Hidden doubles
• Decompose an addend to form a doubles fact.
• In-betweens
• Addends that have exactly one number between them consecutively.
• Double the number between the addends.
• Fact families – related number sentences using the same set of numbers
• Recognition of addition and subtraction as inverse operations
• Commutative property
• Sum does not change when the order of the addends are switched.
• Plus 9
• Basic fact strategies for subtraction
• Counting back
• Begin with the minuend and count back the amount of the subtrahend.
• Counting up
• Begin with the subtrahend and count up to the minuend.
• Minus 1
• Subtracting 1 related to sequentially counting backward once
• Minus 2
• Subtracting 2 related to sequentially counting backward twice
• Subtracting 0 from a number does not affect the total.
• Fact families – related number sentences using the same set of numbers
• Recognition of addition and subtraction as inverse operations
• Decompose the subtrahend
• Decompose the subtrahend to form a known fact.
• Decompose the minuend
• Decompose the minuend to form a known fact.
• Minus 9
• Subtracting 9 is equivalent to subtracting 10 and adding 1.

Note(s):

• Grade 1 introduces applying basic fact strategies to add and subtract within 20.
• Grade 2 will recall basic facts to add and subtract within 20 with automaticity.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• 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.
1.3E Explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences.

Explain

STRATEGIES USED TO SOLVE ADDITION AND SUBTRACTION PROBLEMS UP TO 20 USING SPOKEN WORDS, OBJECTS, 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}
• Mathematical and real-world problem situations
• Sum – the total when two or more addends are joined
• Addend – a number being added or joined together with another number(s)
• Addition of whole numbers within 20
• Subtraction
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• Minuend – a number from which another number will be subtracted
• Subtrahend – a number to be subtracted from a minuend
• Subtraction of whole numbers within 20
• Detailed explanation of solution process and strategy
• Counting all
• Counting on
• Plus 1
• Plus 2
• Making 10
• Hidden tens
• Plus 10
• Doubles
• Doubles plus/minus 1
• Hidden doubles
• In-betweens
• Fact families
• Commutative property
• Plus 9
• Subtraction strategies
• Counting back
• Counting up
• Minus 1
• Minus 2
• Fact families
• Decompose the subtrahend
• Decompose the minuend
• Minus 9
• Connection between information in the problem and problem type
• Joining action situations
• Result unknown
• Change unknown
• Start unknown
• Separating action situations
• Result unknown
• Change unknown
• Start unknown
• Part-part-whole situations
• Whole unknown
• Part unknown
• Difference unknown
• Compare quantity (larger quantity) unknown
• Referent (smaller quantity) unknown
• Relationship between quantities of objects used, pictures drawn, and number sentences to the problem situation
• Explanation using spoken words
• Appropriate mathematical language for addition and subtraction situations
• Labels for quantities represented
• Explanation using objects
• Base-10 blocks, linking cubes, counters, etc.
• Explanation using pictorials
• Base-10 pictorials, number lines, strip diagrams, etc.
• Strip diagram – a linear model used to illustrate number relationships
• 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
• Subtraction symbol represents separating
• Minuend – subtrahend = difference
• Difference = minuend – subtrahend
• Equal symbol represents a relationship where expressions on each side of the equal sign represent the same value

Note(s):

• Kindergarten explained the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences.
• Grade 2 will add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• 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.A. Communication and Representation – Language, terms, and symbols of mathematic
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• 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.
1.3F Generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20.

Generate, Solve

PROBLEM SITUATIONS WHEN GIVEN A NUMBER SENTENCE INVOLVING ADDITION OR SUBTRACTION OF NUMBERS WITHIN 20

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}
• Sum – the total when two or more addends are joined
• Addend – a number being added or joined together with another number(s)
• Addition of whole numbers within 20
• Subtraction
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• Minuend – a number from which another number will be subtracted
• Subtrahend – a number to be subtracted from a minuend
• Subtraction of whole numbers within 20
• 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 an equal sign at the beginning or end
• Unknown in any position
• Generate and solve mathematical and real-world problem situations when given an addition number sentence.
• Appropriate mathematical language
• Connection between information in the problem and problem type
• Joining action result unknown
• Joining action change unknown
• Joining action start unknown
• Part-part-whole whole unknown
• Part-part-whole part unknown
• Additive comparison compare quantity (larger quantity) unknown
• Generate and solve mathematical and real-world problem situations when given a subtraction number sentence.
• Appropriate mathematical language
• Connection between information in the problem and problem type
• Subtraction situations
• Separating action result unknown
• Separating action change unknown
• Separating action start unknown
• Part-part-whole part unknown
• Additive comparison referent (smaller quantity) unknown

Note(s):

• Grade 1 introduces generating and solving problem situations when given a number sentence involving addition and subtraction of whole numbers within 20.
• Grade 2 will generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• 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.
1.5 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:
1.5D Represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences.

Represent

WORD PROBLEMS INVOLVING ADDITION AND SUBTRACTION OF WHOLE NUMBERS UP TO 20 USING 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}
• Sum – the total when two or more addends are joined
• Addend – a number being added or joined together with another number(s)
• Addition of whole numbers within 20
• Subtraction
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• Minuend – a number from which another number will be subtracted
• Subtrahend – a number to be subtracted from a minuend
• Subtraction of whole numbers within 20
• Represent mathematical and real world problem situations
• Concrete models
• Objects represent the quantities described in the problem situation.
• Base-10 blocks, linking cubes, counters, etc.
• Pictorial models
• Pictures drawn represent the quantities described in the problem situation.
• Base-10 pictorials, number lines, strip diagrams, etc.
• 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
• Numbers represent the quantities described in the problem situation.
• Number sentences, or equations, with an equal sign at the beginning or end
• Unknown in any position
• Oral and written descriptions
• Explanation of relationship between objects, pictorials, and numbers and the information in the problem situation
• Joining action result unknown
• Joining action change unknown
• Joining action start unknown
• Part-part-whole whole unknown
• Part-part-whole part unknown
• Additive comparison compare quantity (larger quantity) unknown
• Subtraction problem types
• Separating action result unknown
• Separating action start unknown
• Separating action change unknown
• Part-part-whole part unknown
• Additive comparison referent (smaller quantity) unknown

Note(s):

• Grade 1 introduces representing word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences.
• Grade 2 will represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Solving problems involving addition and subtraction
• TxCCRS:
• 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.
1.5E Understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).

Understand

THE EQUAL SIGN REPRESENTS A RELATIONSHIP WHERE EXPRESSIONS ON EACH SIDE OF THE EQUAL SIGN REPRESENT THE SAME VALUE(S)

Including, but not limited to:

• Term – a number and/or an unknown in an expression separated by an operation symbol(s)
• Expression – a mathematical phrase, with no equal sign or comparison symbol, that may contain a number(s), an unknown(s), and/or an operator(s)
• Equal sign – a mathematical symbol representing equivalence
• Equation – a mathematical statement composed of equivalent expressions separated by an equal sign
• Multi-step solutions represented with one number sentence, or equation, per step
• All expressions separated by equal signs must be equivalent.
• Equal sign does not necessarily mean “find the answer”
• Equations with operations on both sides of the equal sign
• Equations with the unknown in any position

Note(s):

• Grade 1 introduces an understanding that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).
• Grade 2 will represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Solving problems involving addition and subtraction
• TxCCRS:
• II.A. Algebraic Reasoning – Identifying expressions and equations
• II.A.1. Explain the difference between expressions and equations.
1.5G Apply properties of operations to add and subtract two or three numbers.

Apply

PROPERTIES OF OPERATIONS TO ADD AND SUBTRACT TWO OR THREE NUMBERS

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}
• Sum – the total when two or more addends are joined
• Addend – a number being added or joined together with another number(s)
• Addition of whole numbers within 20
• Subtraction
• Difference – the remaining amount after the subtrahend has been subtracted from the minuend
• Minuend – a number from which another number will be subtracted
• Subtrahend – a number to be subtracted from a minuend
• Subtraction of whole numbers within 20
• Recognition of addition and subtraction as inverse operations
• Fact families – related number sentences using the same set of numbers
• Additive identity – the sum/difference is not affected when zero is added/subtracted to a number
• Commutative property of addition – if the order of the addends are changed, the sum will remain the same
• Subtraction is not commutative even though addition is commutative.
• Associative property of addition – if three or more addends are added, they can be grouped in any order, and the sum will remain the same
• Hidden tens
• Decompose an addend to form a tens fact.
• Hidden doubles
• Decompose an addend to form a doubles fact.
• Modeling properties of operations to add and subtract two or three numbers

Note(s):

• Grade 1 introduces applying properties of operations to add and subtract two or three numbers.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• 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.
1.8 Data analysis. The student applies mathematical process standards to organize data to make it useful for interpreting information and solving problems. The student is expected to:
1.8B Use data to create picture and bar-type graphs.

Use

DATA

To Create

PICTURE AND BAR-TYPE 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
• May include numbers or ranges of numbers
• Data collected in the form of responses to a question with up to three categories
• Survey – to ask a group of people a question in order to collect information about their opinions or answers
• Common characteristics in a collection of objects sorted into up to three categories
• Limitations
• Up to three categories
• Data values limited to whole numbers up to 120
• Data representations
• Picture graph – a graphical representation to organize data that uses pictures or symbols evenly spaced or placed in individual cells, where each picture or symbol represents one unit of data, to show the frequency (number of times) that each category occurs
• Characteristics of picture graphs
• Titles, subtitles, and labels
• Title represents the purpose of collected data
• Subtitle clarifies the meaning of categories
• Labels identify each category below the line
• Representation of categorical data
• Pictures or symbols
• Placed in a horizontal or vertical linear arrangement
• Vertical graph beginning at the bottom and progressing up above the line
• Horizontal graph beginning at the left and progressing to the right of the line
• Spaced approximately equal distances apart or placed in individual cells within each category
• Different picture or symbol used to represent each category
• Every piece of data represented using a one-to-one correspondence
• One unit of data represented by each picture or symbol
• Value of the data represented by the pictures
• Determined by the total number of pictures or symbols in that category
• Represents the frequency of each category
• Bar-type graph – a graphical representation to organize data that uses bars divided into individual cells, where each cell represents one unit of data, to show the frequency (number of times) that each category occurs
• Characteristics of bar-type graphs
• Titles, subtitles, and labels
• Title represents the purpose of collected data
• Subtitle clarifies the meaning of categories
• Labels identify each category below the line
• Representation of categorical data
• Bars composed of individual cells
• Placed in a horizontal or vertical linear arrangement
• Vertical graph beginning at the bottom and progressing up above the line
• Horizontal graph beginning at the left and progressing to the right of the line
• Bars divided into equal-sized cells with no gaps between cells
• Bars equal in width
• Independent bars that do not touch
• May use a different color to represent each category
• Does not include a scaled axis
• Every piece of data represented using a one-to-one correspondence
• One unit of data represented by each shaded cell
• Value of the data represented by the bar
• Determined by the total number of cells in the bar for each category
• Represents the frequency for that category
• Connection between graphs representing the same data
• Picture graph to bar-type graph
• Bar-type graph to picture graph
• Same data represented using a picture graph and a bar-type graph

Note(s):

• Kindergarten used data to create real-object and picture graphs.
• Grade 2 will explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category.
• Grade 2 will organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing an understanding of place value
• TxCCRS:
• V.B. Statistical Reasoning – Design a study
• V.B.2. Construct appropriate visual representations of data.
• 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.
1.8C Draw conclusions and generate and answer questions using information from picture and bar-type graphs.

Draw

CONCLUSIONS USING INFORMATION FROM PICTURE AND BAR-TYPE 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
• Up to three categories
• Data values limited to whole numbers up to 120
• Data values limited to addition or subtraction within 20
• Data representations
• 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 picture or symbol
• Bar-type graph – a graphical representation to organize data that uses bars divided into individual cells, where each cell represents one unit of data, to show the frequency (number of times) that each category occurs
• One unit of data represented by each shaded cell
• 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
• Combined total(s)
• Comparisons of data represented
• Comparative language used without numbers
• Comparative language used with numbers
• Changes in orientation do not affect data values

QUESTIONS USING INFORMATION FROM PICTURE AND BAR-TYPE 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
• Up to three categories
• Data values limited to whole numbers up to 120
• Operations limited to one-step addition or subtraction within 20
• Data representations
• 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 picture or symbol
• Bar-type graph – a graphical representation to organize data that uses bars divided into individual cells, where each cell represents one unit of data, to show the frequency (number of times) that each category occurs
• One unit of data represented by each shaded cell
• Generate and answer questions using data in in picture graphs and bar-type graphs
• Description of data
• Comparison using data values
• Operations using data values

Note(s):

• Kindergarten drew conclusions from real-object and picture graphs.
• Grade 2 will draw conclusions and make predictions from information in a graph.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing an understanding of place value
• TxCCRS:
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.3. Make predictions using summary statistics.
• 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.