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 Instructional Focus DocumentGrade 2 Mathematics
 TITLE : Unit 07: Data Analysis SUGGESTED DURATION : 10 days

#### Unit Overview

Introduction
This unit bundles student expectations that address organizing and representing data using bar graphs and pictographs with intervals of one or more, drawing conclusions, making predictions, and writing and solving addition and subtraction problems using information in graphs. According to the Texas Education Agency, mathematical process standards including application, problem-solving, 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 Grade 1, students collected, sorted, organized, and represented data using picture and bar-type graphs, drew conclusions, generated questions, and answered questions from the data.

During this Unit
Students demonstrate prior understanding of the process and purpose of data collection. Students transition data representations from bar-type graphs to bar graphs and from picture graphs to pictographs. A bar graph is a graphical representation to organize data that uses solid bars that do not touch each other to show the frequency (number of times) that each category occurs. Each bar represents a category and each bar within the bar graph is independent from the other bars. Students determine the total frequency of each category, the length of each bar, by associating the end of each bar to the scale marked interval of the axis. Frequency values may be interval values on the axis or in-between interval values on the axis. A pictograph is a graphical representation to organize data that uses a picture or symbol, where each picture or symbol represents one or more than one unit of data, to show the frequency (number of times) that each category occurs. In a pictograph, the value of each picture or symbol is defined by the pictograph key. Students use skip counting or repeated addition to determine the frequency, the total value of all pictures (or symbols), including partial pictures (or partial symbols), within each category. Both vertical and horizontal orientations of bar graphs and pictographs with up to four categories and intervals of one, two, five, or ten are experienced during this unit. Students summarize the factual data and inferential data (existing data used to make predictions about future data) in bar graphs and pictographs to draw conclusions and make predictions. Students also generate and solve one-step word problems based on the information in bar graphs and pictographs with intervals of one.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool Grade 2

After this Unit
In Grade 3, students will summarize data sets with multiple categories using frequency tables, dot plots, pictographs, or bar graphs with scaled intervals. Dot plots and frequency tables will be introduced as new forms of data representation.

In Grade 2, organizing data using bar graphs and pictographs and explaining how the bars in a bar graph and pictures in a pictograph represent the number of data points in a category are subsumed within the Grade 2 Texas Response to Curriculum Focal Points (TxRCFP): Developing proficiency in the use of place value within the base-10 numeration system. Drawing conclusions, making predictions, and writing and solving addition and subtraction problems using information in bar graphs and pictographs are identified in the Grade 2 Texas Response to Curriculum Focal Points (TxRCFP): Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning A2, B1; II. Algebraic Reasoning D1, D2; V. Statistical Reasoning A1, B2, B3, 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
Connecting math to our world today, research suggests that in a technological world that is data-driven, the description and organization of collected information is a fundamental skill that begins in K-2 mathematics. According to Kilpatrick (2001), “The process of organizing and reducing data incorporates mental actions such as ordering, grouping, and summarizing” (p. 289). “First and second graders’ knowledge of how to represent data appears to be constrained by difficulties in sorting and organizing data…conventions like labeling and scaling are crucial to data representation and are strongly connected to the concepts of measurement” (p. 290). Students must be given the opportunity to collect, sort, and create their own visual displays of data. Van de Walle (2006) states, “The focus of explorations at [the K-3 level] should be on using data and graphs to answer questions. This means that the emphasis should be on ways to present data and how to interpret data in the context of real questions” (p. 310). The goal for students at this grade level should be to not only represent collected data with graphic tools, but to be able think through the meaning of the data and reach conclusions about data relationships.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Kilpatrick, J., Swafford, J., and Findell, B. (Eds.) Mathematics Learning Study Committee, Center for Education Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
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
Van de Walle, J., & Lovin, L. (2006). Teaching student-centered mathematics grades k – 3. Boston, MA: Pearson Education, Inc.

 Statistical displays often reveal patterns within data that can be analyzed to interpret information, inform understanding, make predictions, influence decisions, and solve problems in everyday life with degrees of confidence. How does society use or make sense of the enormous amount of data in our world available at our fingertips? How can data and data displays be purposeful and powerful? Why is it important to be aware of factors that may influence conclusions, predictions, and/or decisions derived from data?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Data representations display the counts (frequencies) or measures of data values in an organized, visual format so that the data can be interpreted efficiently.
• What are the parts of a …
• pictograph?
• bar graph?
• How do the title and category labels describe the data being represented in a …
• pictograph?
• bar graph?
• What is the relationship between the data counts and the …
• pictures in a pictograph?
• bars in a bar graph?
• intervals in bar graphs or pictographs?
• How are numbers and counting used when …
• constructing graphs?
• scaling graphs?
• drawing conclusions?
• What types of …
• conclusions can be drawn
• predictions can be made
• questions can be answered
… using data in a graph?
• How does a graph aid in the ability to efficiently …
• draw conclusions
• make predictions
… about the data?
• What is the purpose of an organized, visual format and how does it aid in the ability to efficiently draw conclusions, make predictions, and solve problems?
• 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 graphs and pictographs alike and different?
• Why is it important to be able to use different display representations if they are equivalent in counts or data values?
• Data Analysis
• Data
• Interpretation
• Conclusions
• Predictions
• Statistical Representations
• Pictographs
• Bar 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 they can determine the value a category on a pictograph by counting the number of symbols in the category rather than realizing that each symbol may represent more than one unit of data if indicated in the key.
• Some students may think data in a vertical bar graph or pictograph can be arranged from the top to bottom, not realizing that the bars on a bar graph or symbols in a pictograph are arranged from bottom to top.
• Some students may think data in a horizontal bar graph or pictograph can be arranged from right to left, not realizing that the bars on a bar graph or symbols in a pictograph 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 graph or a pictograph.
• 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.
• Students may think the characteristics of a bar graph are the same as a bar-type graph rather than recognizing that the bar graph uses solid bars that do not touch and a scale on the axis to read the value of the category rather than cells.
• Some students may think a bar in a bar graph that ends between marked intervals greater than one is read based on the closest interval rather than recognizing the unmarked values between marked intervals as with a number line.

Underdeveloped Concepts:

• Some students may struggle with the organization needed to collect and sort data (e.g., keeping track of who they have surveyed, etc.).

#### Unit Vocabulary

• Bar graph – a graphical representation to organize data that uses solid bars that do not touch each other and a scaled axis 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
• Data – information that is collected about people, events, or objects
• Factual data – actual quantities represented in a graph used to interpret data, draw conclusions, and make comparisons
• Graph – a visual representation of the relationships between data collected
• Pictograph – a graphical representation to organize data that uses a picture or symbol, where each picture or symbol may represent one or more than one unit of data, to show the frequency (number of times) that each category occurs

Related Vocabulary:

 Axis/axes Category Comparative language Conclusion Frequency Horizontal Interval Key Label Prediction Scale of the axis Symbols Title Unit of data Vertical
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Center if your district has granted access to that tool.

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 2 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
2.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
2.1A 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1B 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1C 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1D 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1E 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1F 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.1G 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 proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• 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.
2.10 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:
2.10A 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.

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

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
• Limitations
• Up to four categories
• Intervals limited to 1, 2, 5, or 10
• Data representations
• Bar graph – a graphical representation to organize data that uses solid bars that do not touch each other and a scaled axis to show the frequency (number of times) that each category occurs
• Length of the bar in a bar graph represents the number of data points for a given category
• Length of the bar represents the distance from zero on the axis scale
• Axis represented as a number line with scaled intervals of one or more units proportionally displayed
• Value of the data represented by the bar is determined by reading the number on the scaled axis associated with the length of the bar.
• Pictograph – a graphical representation to organize data that uses a picture or symbol, where each picture or symbol may represent one or more than one unit of data, to show the frequency (number of times) that each category occurs
• Number of pictures or symbols in pictograph represents the number of data points for a given category
• Key identifies the value of each picture or symbol
• Value of each picture or symbol may be one or more
• Partial symbols represent the fractional value of the whole picture or symbol
• Value of the data represented by pictures is determined by the total value of pictures and partial-pictures or symbols, as indicated by the key.

Note(s):

• Grade 1 represented data to create picture and bar-type graphs.
• Grade 2 introduces bar graphs and pictographs.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing proficiency in the use of place value within the base-10 numeration system
• TxCCRS:
• 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.
2.10B Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more.

Organize

A COLLECTION OF DATA WITH UP TO FOUR CATEGORIES USING PICTOGRAPHS AND BAR GRAPHS WITH INTERVALS OF ONE OR MORE

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
• Limitations
• Up to four categories
• Intervals limited to 1, 2, 5, or 10
• Data representations
• Pictograph – a graphical representation to organize data that uses a picture or symbol, where each picture or symbol may represent one or more than one unit of data, to show the frequency (number of times) that each category occurs
• Characteristics of a pictograph
• 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 within each category
• One picture or symbol used to represent all categories
• Partial picture or symbol represents the fractional value of the whole picture or symbol
• Key
• Identifies the value of each picture or symbol
• Every piece of data represented using a one-to-one or scaled correspondence, as indicated by the key
• Value of the data in each category
• Determined by the total value of pictures and partial-pictures or symbols, as indicated by the key
• Represents the frequency for that category
• Bar graph – a graphical representation to organize data that uses solid bars that do not touch each other and a scaled axis to show the frequency (number of times) that each category occurs
• Characteristics of a bar graph
• Titles, subtitles, and labels
• Title represents the purpose of collected data
• Subtitles clarify the meaning of data represented on each axis
• Labels identify each category
• Representation of categorical data
• Bars
• Placed in a horizontal or vertical linear arrangement to represent data
• Solid bars that are equal in width
• Independent bars that do not touch
• Length of the bar represents the distance from zero on the axis scale
• Axis
• Represented as a number line
• Scale intervals proportionally displayed
• Intervals of one or more units
• Every piece of data represented using a one-to-one or scaled correspondence as indicated by the intervals on the axis
• Value of the data represented by the bar
• Determined by reading the number on the scaled axis associated with the length of the bar
• Represents the frequency for that category
• Connection between graphs representing the same data
• Picture graph to pictograph
• Bar-type graph to bar graph
• Pictograph to bar graph
• Bar graph to pictograph
• Same data represented using a pictograph and a bar graph

Note(s):

• Grade 1 used data to create picture and bar-type graphs.
• Graph 3 will summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing proficiency in the use of place value within the base-10 numeration system
• TxCCRS:
• V.B. Statistical Reasoning – Describe data
• V.B.2. Construct appropriate visual representations of data.
2.10C Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one.

Write, Solve

ONE-STEP WORD PROBLEMS INVOLVING ADDITION OR SUBTRACTION USING DATA REPRESENTED WITHIN PICTOGRAPHS AND BAR GRAPHS WITH INTERVALS OF ONE

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 four categories
• Intervals limited to 1
• Operations limited to one-step addition or subtraction
• Data representations
• Pictograph – a graphical representation to organize data that uses a picture or symbol, where each picture or symbol may represent one or more than one unit of data, to show the frequency (number of times) that each category occurs
• Bar graph – a graphical representation to organize data that uses solid bars that do not touch each other and a scaled axis to show the frequency (number of times) that each category occurs
• Write and solve mathematical and real-world problems using data represented within pictographs and bar graphs.

Note(s):

• Grade 3 will solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• TxCCRS:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
• V.B. Statistical Reasoning – Describe data
• V.B.3. Compute and describe the study data with measures of center and basic notions of spread.
2.10D Draw conclusions and make predictions from information in a graph.

Draw

CONCLUSIONS FROM INFORMATION IN A GRAPH

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
• Factual data – actual quantities represented in a graph used to interpret data, draw conclusions, and make comparisons
• Limitations
• Up to four categories
• Intervals limited to 1, 2, 5, or 10
• Data representations
• Pictograph – a graphical representation to organize data that uses a picture or symbol, where each picture or symbol may represent one or more than one unit of data, to show the frequency (number of times) that each category occurs
• Bar graph – a graphical representation to organize data that uses solid bars that do not touch each other and a scaled axis to show the frequency (number of times) that each category occurs
• 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 with numbers
• Comparative language used without numbers
• Changes in orientation do not affect data values

Make

PREDICTIONS FROM INFORMATION IN A GRAPH

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
• Inferential data – existing data used to make predictions about future data
• Limitations
• Up to four categories
• Intervals limited to 1, 2, 5, or 10
• Data representations
• Pictograph – a graphical representation to organize data that uses a picture or symbol, where each picture or symbol may represent one or more than one unit of data, to show the frequency (number of times) that each category occurs
• Bar graph – a graphical representation to organize data that uses solid bars that do not touch each other and a scaled axis to show the frequency (number of times) that each category occurs
• Make predictions based on patterns in the data collected
• Make predictions based on comparisons of quantities in the data collected
• Make predictions about future actions based on the purpose of the data collection

Note(s):