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 Instructional Focus DocumentGrade 1 Mathematics
 TITLE : Unit 01: Numeracy Using Data Analysis SUGGESTED DURATION : 8 days

#### Unit Overview

Introduction
This unit bundles student expectations that address collecting, sorting, and organizing data, and representing the data using picture and bar-type graphs in order to draw conclusions, generate questions, and answer questions from the data while demonstrating numeracy skills. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Kindergarten, students developed an understanding of numbers up to 20, including the comparison of numbers up to 20. Kindergarten students solved problems involving addition and subtraction of whole numbers within 10. Kindergarten students also collected, sorted, and organized data to create real-object graphs and picture graphs. Students compared and contrasted the different data representations. Students drew conclusions to answer questions using information from the graphs, including identifying the quantities represented in each category and comparing the value of each category as more than, less than, or the same as another category.

During this Unit
Students begin the year demonstrating numeracy using authentic data analysis experiences. Students explore collecting, sorting, and organizing data in up to three categories using previously learned data analysis skills. They use the categorical data collected from surveys or collections of objects to create tally charts, T-charts, picture graphs, and bar-type graphs. Picture graphs and bar-type graphs are designed to represent data involving small quantities since the intervals of these graphs are one-to-one. Recall, students have prior experiences with picture graphs, but bar-type graphs are a new representation for Grade 1. After creating each representation, students compare and contrast the different data representations. Students examine the data to draw conclusions demonstrating their knowledge of number from Kindergarten by determining the value of each category using one-to-one correspondence and comparing data values up to 20 as more than, less than, or equal to. Students extend drawing conclusions by comparing the values of each category and counting on to determine how many more or how many less. Students also draw conclusions to answer questions that involve determining the necessary operation, addition and subtraction, needed to answer a question among the categories with data values within 10 and performing the necessary operation to determine the solution. Students are expected to generate their own questions along with solutions regarding the data represented in the graphs. Although the unit is designed around Grade 1 standards involving data analysis, the intent of the unit is to provide valuable teacher insight into students’ understanding of numeracy, allowing an opportunity for teachers to reinforce the necessary numeracy skills in preparation for upcoming units that involving place value.

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

After this Unit
In Unit 02, students will have the opportunity to demonstrate operational understanding involving numbers within 10. In Unit 04, students will deepen their understandings of whole numbers up to 20 as they are formally introduced to the base-10 place value system. In Unit 05, they will extend their understandings of addition and subtraction to sums and minuends within 20. In Unit 10, students will revisit all operations using data representations by analyzing data in picture graphs and bar-type graphs to draw conclusions and answer questions. The Grade 1 data analysis expectations are a stepping stone to deeper understanding of data analysis and graphical representations that will be used in future grade levels and in real-world situations. In Grade 2, students will extend their understanding of data analysis from picture graphs to pictographs and bar-type graphs to bar graphs.

In Grade 1, collecting, sorting, and organizing data, and 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 B1; II. Algebraic Reasoning 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 research by the National Research Council (2001), “First and second graders’ knowledge of how to represent data appears to be constrained by difficulties in sorting and organizing data” (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).

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 can be collected in response to a question and can be sorted and organized to represent the intent of the question.
• How does the purpose of the question aid in determining a reasonable way to …
• collect the data?
• sort the data?
• organize the data?
• 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 20; addition or subtraction of data values within 10).
• 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
• questions can be answered
… 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 and 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?
• Data Analysis
• Data
• Data Collection
• Sort
• Organize
• 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 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 struggle with the organization needed to collect and sort data (e.g., keeping track of who they have surveyed, etc.).
• Although students may be able to sort a collection of objects, they may not recognize that the collection of objects can be sorted in different ways based on multiple attributes for a given object (e.g., students can be sorted by gender, hair color, types of shoes, etc.).

#### Unit Vocabulary

• 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
• Data – information that is collected about people, events, or objects
• Graph – a visual representation of the relationships between data collected
• 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
• Survey – to ask a group of people a question in order to collect information about their opinions or answers

Related Vocabulary:

 Attribute Category Category label Cell Characteristic Collect Comparative language Compare Conclusion Frequency Horizontal One-to-one correspondence Organize Represent Sort Symbol Tally marks T-chart Title Unit of data 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.
• A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
TEKS# SE# TEKS SPECIFICITY
1.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
1.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE

Including, but not limited to:

• Mathematical problem situations within and between disciplines
• Everyday life
• Society
• Workplace

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
1.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

• Problem-solving model
• Analyze given information
• Formulate a plan or strategy
• Determine a solution
• Justify the solution
• Evaluate the problem-solving process and the reasonableness of the solution

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of place value
• Solving problems involving addition and subtraction
• Analyzing attributes of two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
1.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, 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.
1.8 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:
1.8A Collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts.

Collect, Sort, Organize

DATA IN UP TO THREE CATEGORIES USING MODELS/REPRESENTATIONS

Including, but not limited to:

• 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 represent numbers or ranges of numbers
• Limitations
• Up to three categories
• Data values limited to whole numbers up to 20
• Data collected in the form of responses to a question
• 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
• Data sorted in a variety of ways
• Data organized and represented in a variety of ways
• Data organized using T-charts, sorting mats, etc.
• Data represented by real-world objects, pictures, drawings, or tally marks
• One unit of data represented by each object, picture, drawing, or tally mark

Note(s):

• Kindergarten collected, sorted, and organized data into two or three categories.
• 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.
1.8B 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 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
• 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 20
• Data values limited to addition or subtraction within 10
• 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 20
• Operations limited to one-step addition or subtraction within 10
• 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.