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 twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving 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 twodimensional shapes and threedimensional 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 problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving 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 twodimensional shapes and threedimensional 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 twodimensional shapes and threedimensional 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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 twodimensional shapes and threedimensional 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 nonexamples, 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 twodimensional shapes and threedimensional 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 twodimensional shapes and threedimensional 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.

1.7 
Geometry and measurement. The student applies mathematical process standards to select and use units to describe length and time. The student is expected to:


1.7A 
Use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement.

Use
MEASURING TOOLS TO MEASURE THE LENGTH OF OBJECTS TO REINFORCE THE CONTINUOUS NATURE OF LINEAR MEASUREMENT
Including, but not limited to:
 Length – the measurement attribute that describes a continuous distance from end to end
 Linear measurement – the measurement of length along a continuous line or curve
 Starting point and ending point defined
 Continuous line may bend or curve, but not break
 Nonstandard measuring tools to reinforce the continuous nature of linear measurement
 Ribbon, yarn, string, adding machine tape, etc.
Note(s):
 Grade Level(s):
 Kindergarten gave an example of a measurable attribute of a given object, including length, capacity, and weight.
 Grade 2 will determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing the understanding of length
 TxCCRS:
 I.C. Numeric Reasoning – Systems of measurement
 I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.

1.7B 
Illustrate that the length of an object is the number of samesize units of length that, when laid endtoend with no gaps or overlaps, reach from one end of the object to the other.

Illustrate
THAT THE LENGTH OF AN OBJECT IS THE NUMBER OF SAMESIZE UNITS OF LENGTH THAT, WHEN LAID ENDTOEND WITH NO GAPS OR OVERLAPS, REACH FROM ONE END OF THE OBJECT TO THE OTHER
Including, but not limited to:
 Length – the measurement attribute that describes a continuous distance from end to end
 Unit of length – the object or unit used to measure length
 Nonstandard units of length
 Color tiles, linking cubes, paper clips, measuring rods, toothpicks, craft sticks, etc.
 Linear measurement – the measurement of length along a continuous line or curve
 Starting point and ending point defined
 Equal sized units of length placed end to end along the distance being measured
 Equal sized units of length iterated (repeated) with no gaps or overlaps
 Length measured using onedimensional units of length (e.g., if measuring with a color tile, measure with the edge, not the area of the color tile; if measuring with a paper clip, measure with either the length or width of the paper clip, not a combination of lengths and widths; etc.)
 Equal sized units of length counted to the nearest whole unit
 Last unit is not counted if the end point falls less than halfway along the unit.
 Last unit is counted if the end point falls halfway, or more than halfway, along the unit.
 Unit of length selected for efficiency
 Smaller unit of length to measure shorter objects or distances
 Larger unit of length to measure longer objects or distances
 Unit of length selected for precision
 Smaller unit of length results in a more precise measurement when measuring to the whole unit.
 Larger unit of length results in a less precise measurement when measuring to the whole unit.
Note(s):
 Grade Level(s):
 Grade 1 introduces illustrating that the length of an object is the number of samesize units of length that, when laid endtoend with no gaps or overlaps, reach from one end of the object to the other.
 Grade 2 will find the length of objects using concrete models for standard units of length.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing the understanding of length
 TxCCRS:
 I.C. Numeric Reasoning – Systems of measurement
 I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.

1.7C 
Measure the same object/distance with units of two different lengths and describe how and why the measurements differ.

Measure
THE SAME OBJECT/DISTANCE WITH UNITS OF TWO DIFFERENT LENGTHS
Including, but not limited to:
 Length – the measurement attribute that describes a continuous distance from end to end
 Unit of length – the object or unit used to measure length
 Nonstandard units of length
 Color tiles, linking cubes, paper clips, measuring rods, toothpicks, craft sticks, etc.
 Equal sized units of length counted to the nearest whole unit
 Last unit is not counted if the end point falls less than halfway along the unit.
 Last unit is counted if the end point falls halfway, or more than halfway, along the unit.
 Linear measurement – the measurement of length along a continuous line or curve
 Starting point and ending point defined
 Equal sized units of length placed end to end along the distance being measured
 Equal sized units of length iterated (repeated) with no gaps or overlaps
 Length measured using onedimensional units of length (e.g., if measuring with a color tile, measure with the edge, not the area of the color tile; if measuring with a paper clip, measure with either the length or width of the paper clip, not a combination of lengths and widths; etc.)
 Equal sized units of length counted to the nearest whole unit
 Last unit is not counted if the end point falls less than halfway along the unit.
 Last unit is counted if the end point falls halfway, or more than halfway, along the unit.
 Measure the same object with different sized units of length.
Describe
HOW AND WHY THE MEASUREMENTS OF THE SAME OBJECT/DISTANCE MEASURED WITH UNITS OF TWO DIFFERENT LENGTHS DIFFER
Including, but not limited to:
 Length – the measurement attribute that describes a continuous distance from end to end
 Unit of length – the object or unit used to measure length
 Nonstandard units of length
 Color tiles, linking cubes, paper clips, measuring rods, toothpicks, craft sticks, etc.
 Compare the measurements of the same object with different sized units of length.
 Description of how the measurements differ
 Measurements described using a number and unit label
 Description of why the measurements differ
 The shorter the unit of length, the more units counted
 The longer the unit of length, the fewer units counted
Note(s):
 Grade Level(s):
 Grade 1 introduces measuring the same object/distance with units of two different lengths and describing how and why the measurements differ.
 Grade 2 will describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing the understanding of length
 TxCCRS:
 I.C. Numeric Reasoning – Systems of measurement
 I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.

1.7D 
Describe a length to the nearest whole unit using a number and a unit.

Describe
A LENGTH TO THE NEAREST WHOLE UNIT USING A NUMBER AND A UNIT
Including, but not limited to:
 Length – the measurement attribute that describes a continuous distance from end to end
 Unit of length – the object or unit used to measure length
 Nonstandard units of length
 Color tiles, linking cubes, paper clips, measuring rods, toothpicks, craft sticks, etc.
 Measurement named using a number and a unit
 Equal sized units of length counted to the nearest whole unit
 Last unit is not counted if the end point falls less than halfway along the unit.
 Last unit is counted if the end point falls halfway, or more than halfway, along the unit.
Note(s):
 Grade Level(s):
 Grade 2 will find the length of objects using concrete models for standard units of length.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing the understanding of length
 TxCCRS:
 I.C. Numeric Reasoning – Systems of measurement
 I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.
