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 Instructional Focus DocumentKindergarten Mathematics
 TITLE : Unit 10: Data Analysis with Numbers 10 – 20 SUGGESTED DURATION : 6 days

#### Unit Overview

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

Prior to this Unit
In Unit 05, students began to investigate data analysis situations involving numbers from 0 – 10.

During this Unit
Students extend their knowledge about counting and comparing numbers from 0 – 20 using graphing situations where numbers represent categorical data, meaning data that represents the attributes of a group of people, events, or objects. Data may be collected from posing a question and taking a survey or based on the attributes of a collection of objects or pictures. Students sort and organize the data into two or three categories. The organized data is used to create real-object and picture graphs, and these graphs are examined to understand the components of graphing (e.g., title, labels of categories, what each cell or picture represents, etc.). Both real-object and picture graphs should be constructed side-by-side with horizontal and vertical orientations so that students are provided opportunities to compare and contrast both graphs, discussing their similarities and differences. Students use the data within the graphs to compare categories up to 20 and describe the data using comparative language. Students draw conclusions to answer questions and summarize the data represented in real-object and picture graphs.

After this Unit
In Unit 15, students will revisit the foundations of numbers from 0 – 20 and contextual sums and minuends to 10 as well as incorporating data analysis in real-world problem situations.

In Kindergarten, collecting, sorting, and organizing data to create real-object and picture graphs to draw conclusions is subsumed under the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Grade Level Connections. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B; 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 Copley (2010), “Teachers can introduce children to a variety of data collection methods and model and discuss questions appropriately. They can and should provide many data collection experiences involving children’s own questions” (p. 145). Students should also be actively involved in the construction of graphs. Van De Walle ( 2006) states, “The value of having students actually construct their own graphs is not so much that they learn the techniques but that they are personally involved in the data and that they learn how a graph conveys information. Once a graph is constructed, the most important activity is discussing what it tells the people who see it, especially those who were not involved in making the graph” (p. 318).

Copley, J. (2010). The young child and mathematics. Washington, DC: National Association for the Education of Young Children
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 …
• real-object graph?
• picture graph?
• How do the title and category labels describe the data being represented in a …
• real-object graph?
• picture graph?
• What is the relationship between the data counts and the …
• objects in a real-object graph?
• pictures in a picture graph?
• How are numbers and counting used when …
• constructing graphs?
• drawing conclusions?
• What types of …
• conclusions can be drawn
… using data in a graph?
• What is the purpose of an organized, visual format and how does it aid in the ability to efficiently draw conclusions 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 real-object graphs and picture graphs …
• alike?
• different?
• What characteristics aid in determining if data representations show representations with equivalent data sets?
• 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
• Real-object graphs
• Picture 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 the sorting rule can be changed within the set rather than consistently applying the sorting rule.
• Some students may think data can only be sorted based on the presence or absence of one attribute (e.g., it’s either blue or not blue) rather than recognizing that each sorted group can possess a common attribute (e.g., a group of blue, a group of red, a group of green).
• Some students may think data can only be sorted one way rather than recognizing how someone else may have sorted the data.
• Some students may think the data collected and sorted is different from the data represented in the real-object or picture graph.
• 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 data in a real-object or picture graph can be arranged from the top to bottom, not realizing that the cells on a real-graph or pictures in a picture graph are arranged from bottom to top.
• Some students may think data in a real-object or picture graph can be arranged from right to left, not realizing that the cells on a real-object 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 real-object or picture graph.
• 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.

#### Unit Vocabulary

• 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
• Real-object graph – a graphical representation to organize data that uses concrete or real objects evenly spaced or placed in individual cells, where each object 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 Cell Classify Collect Compare Conclusion Equal to/same as Estimate Greater than/more than Horizontal Interpret Label Less than/fewer than One-to-one correspondence Organize Quantity Relationship Represent Sort Summarize Symbol Tally marks T-chart Title Total 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 Kindergarten 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
K.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
K.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 whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• 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.
K.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 whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• 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.
K.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 whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• 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.
K.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 whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• 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.
K.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 whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• 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.
K.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 whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• 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. ConnectionsConnections 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.
K.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 whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VII.A. Problem Solving and ReasoningMathematical 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.
K.8 Data analysis. The student applies mathematical process standards to collect and organize data to make it useful for interpreting information. The student is expected to:
K.8A Collect, sort, and organize data into two or three categories.

Collect, Sort, Organize

DATA INTO TWO OR THREE CATEGORIES

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 include numbers or ranges of numbers
• Limitations
• Two 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):

• Grade 1 will collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Grade Level Connections (reinforces previous learning and/or provides development for future learning)
• TxCCRS:
• V.B. Statistical Reasoning – Describe data
• V.B.2. Construct appropriate visual representations of data.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
K.8B Use data to create real-object and picture graphs.

Use

DATA

To Create

REAL-OBJECT AND PICTURE 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
• 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
• Limitations
• Two to three categories
• Data values limited to whole numbers up to 20
• Data representations
• Real-object graph – a graphical representation to organize data that uses concrete or real objects evenly spaced or placed in individual cells, where each object represents one unit of data, to show the frequency (number of times) that each category occurs
• 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 real-object and 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
• Objects or pictures
• 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 object or picture used to represent each category
• Every piece of data represented using a one-to-one correspondence
• One unit of data represented by each object or picture
• Value of the data represented by the objects or pictures
• Determined by the total number of objects or pictures in that category
• Represents the frequency of each category
• Connection between graphs representing the same data
• Real-object graph to picture graph
• Picture graph to real-object graph
• Same data represented using a picture graph and a bar-type graph

Note(s):

• Grade 1 will use data to create picture and bar-type graphs.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Grade Level Connections (reinforces previous learning and/or provides development for future learning)
• TxCCRS:
• V.B. Statistical Reasoning – Describe data
• V.B.2. Construct appropriate visual representations of data.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
K.8C Draw conclusions from real-object and picture graphs.

Draw

CONCLUSIONS FROM REAL-OBJECT AND PICTURE 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
• Two to three categories
• Data values limited to whole numbers up to 20
• Data representations
• Real-object graph – a graphical representation to organize data that uses concrete or real objects evenly spaced or placed in individual cells, where each object represents one unit of data, to show the frequency (number of times) that each category occurs
• One unit of data represented by each object or picture
• 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 object or picture
• 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
• Comparisons of data represented
• Comparative language used without numbers (e.g., more than, less than, fewer than, the most, the least, the same as, equal to, etc.)
• Changes in orientation do not affect data values

Note(s):

• Grade 1 will draw conclusions and generate and answer questions using information from picture and bar-type graphs.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Grade Level Connections (reinforces previous learning and/or provides development for future learning)
• TxCCRS:
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.3. Make predictions using summary statistics.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• 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.