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Instructional Focus Document
Grade 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.

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.

Additional Notes
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): VIII. Problem Solving and Reasoning, IX. Communication and Representation, and X. Connections.

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?
      • answering questions?
    • 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
      • answer questions
      • 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 Creator 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


TEKS# SE# Unit Level Taught Directly TEKS Unit Level Specificity
 

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.

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.
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:
    • X. Connections
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:
    • VIII. Problem Solving and Reasoning
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:
    • VIII. Problem Solving and Reasoning
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:
    • IX. Communication and Representation
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:
    • IX. Communication and Representation
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:
    • X. Connections
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:
    • IX. Communication and Representation
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 Level(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:
    • IX. Communication and Representation
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 Level(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:
    • IX. Communication and Representation
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 Level(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:
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
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):

  • Grade Level(s):
    • Grade 1 drew conclusions and generated and answered questions using information from picture and bar-type graphs.
    • 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:
    • IX. Communication and Representation
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of each subject in the required curriculum.

School districts shall provide instruction in the knowledge and skills of the foundation and enrichment curriculum in a manner that is linguistically accommodated commensurate with the student’s levels of English language proficiency to ensure that the student learns the knowledge and skills in the required curriculum.


School districts shall provide content-based instruction including the cross-curricular second language acquisition essential knowledge and skills in subsection (c) of the ELPS in a manner that is linguistically accommodated to help the student acquire English language proficiency.

http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4 


Choose appropriate ELPS to support instruction.

ELPS# Subsection C: Cross-curricular second language acquisition essential knowledge and skills.
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ELPS.c.1 The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1B monitor oral and written language production and employ self-corrective techniques or other resources
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.1D speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)
ELPS.c.1E internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment
ELPS.c.1F use accessible language and learn new and essential language in the process
ELPS.c.1G demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one commensurate with grade-level learning expectations
ELPS.c.1H develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations.
ELPS.c.2 The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.2A distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2B recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters
ELPS.c.2C learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
ELPS.c.2D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language
ELPS.c.2F listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment
ELPS.c.2G understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar
ELPS.c.2H understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations
ELPS.c.2I demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs.
ELPS.c.3 The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.3A practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible
ELPS.c.3B expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
ELPS.c.3E share information in cooperative learning interactions
ELPS.c.3F ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments
ELPS.c.3G express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more English is acquired
ELPS.c.3I adapt spoken language appropriately for formal and informal purposes
ELPS.c.3J respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.
ELPS.c.4 The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:
ELPS.c.4A learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words
ELPS.c.4B recognize directionality of English reading such as left to right and top to bottom
ELPS.c.4C develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials
ELPS.c.4D use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text
ELPS.c.4E read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned
ELPS.c.4F use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language
ELPS.c.4G demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs
ELPS.c.4H read silently with increasing ease and comprehension for longer periods
ELPS.c.4I demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text, and distinguishing main ideas from details commensurate with content area needs
ELPS.c.4J demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs
ELPS.c.4K demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade-level needs.
ELPS.c.5 The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:
ELPS.c.5A learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired
ELPS.c.5D edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired
ELPS.c.5E employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
Last Updated 08/01/2018
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