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Instructional Focus Document
Grade 2 Mathematics
TITLE : Unit 10: Contextual Multiplication and Division SUGGESTED DURATION : 15 days

Unit Overview

Introduction
This unit bundles student expectations that address contextual multiplication and division situations and finding the area of rectangles using concrete models of square units. 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 Grade 1, students skip-counted by twos, fives, and tens to determine the total number of objects up to 120 in a set.

During this Unit
Students model, create, and describe contextual multiplication and division situations. Students use concrete and pictorial models to represent problem situations where equal grouping is involved. Students use repeated addition or skip counting to determine the total number of objects and describe these situations using language such as “3 equal groups of 5 is 15.” Students extend the understanding of equal grouping situations to include determining the area of a rectangle. Students use concrete models of square units to cover a rectangle with no gaps or overlays, count the number of square units, and describe the measurement using a number and the label “square units.” Students discover the relationship between a variety of equal group models and the arrangement of the objects in rows and columns to determine area. Recognizing this relationship is foundational for students’ understanding of arrays and area models and future learning. Students also use concrete and pictorial models to represent problem situations where a given amount is separated into equal-sized groups and the number of groups is unknown (quotative or measurement division) as well as where a given amount is shared equally among a known number of groups and the number of objects in each group is unknown (partitive division). Students describe these situations using language such as “15 separated into 3 equal groups makes 5 in each group” or “15 separated into equal groups of 5 makes 3 groups.” Repeated exposure to modeling and describing equal grouping situations leads students to the inverse relationship between repeated addition (multiplication) and repeated subtraction (division) that is similar to the inverse relationship between addition and subtraction.

After this Unit
In Grade 3, students will transition to the representation of multiplication expressed using a multiplication symbol and a more formalized understanding of multiplication. The transition of representations will begin with place value. Students will for the first time experience expanded notation, merging place value understandings and multiplication representations. For example, students will transfer their understanding of 50 as 5 groups of 10 to 5 × 10. Later in Grade 3, students will begin to formalize multiplication and division as they determine the total number of objects when equal-sized groups of objects are combined or arranged in arrays and determine the number of objects in each group when a set of objects is partitioned or shared equally. Students will transition from repeated addition and repeated subtraction equations to the multiplication and division symbols in equations. Students will use a variety of approaches to represent multiplication facts leading to the recall of multiplication and division facts and the relationships that exists between them.

Additional Notes
In Grade 2, contextual multiplication and division situations and finding the area of rectangles using concrete models of square units are included in the Grade 2 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 B1, C1; II. Algebraic Reasoning D1, D2; III. Geometric and Spatial Reasoning D1; V. Statistical Reasoning A1, C2; 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
Recent research suggests that when teaching contextual multiplication and division, teachers should give students the opportunity to explore combining and decomposing equal groups in an array model to experience pre-multiplication and division. According to the National Research Council (2001), “An array or area model provides the initial support for the crucial understanding of the effects of multiplying by 1, 10, and 100” (p. 207). Students need to have many opportunities to work with equal groups of objects to develop an understanding of multiplication. Van de Walle points out that, “One of the major conceptual hurdles of working with multiplicative structures is that of understanding groups of things as a single entities while also understanding that a group contains a given number of objects….to think of 4 sets of eight requires children to conceptualize each group of eight as a single item to be counted. Experiences with making and counting groups in contextual situations are extremely useful” (146). Fosnot and Dolk concur that the transition from counting items to counting groups in arrays is the concept of unitizing, “for learners, unitizing is a change in perspective. Children have just learned to count ten objects, one by one. Unitizing these ten things as one thing or one group requires almost negating their original idea of number. It is a huge shift in thinking for children” (p. 11). Unitizing underlies the understanding of multiplication and division requiring that children use numbers to count not only objects but also groups and to count them both simultaneously. Multiplication is a complex mathematical shift that Fosnot and Dolk suggest requires, “the construction of new, higher order numbers out of addition… involving the progression from repeated addition to multiplication” (p. 35) and understanding “the structure and or relationship between the parts and the whole” (p.37).

 

Fosnot, C. & Dolk, M. (2001). Young mathematicians at work: Constructing Number Sense. Addition and Subtraction Portsmouth, NH: Heinemann.
Fosnot, C. & Dolk, M. (2001). Young mathematicians at work: Constructing Multiplication and Division, NH: Heinemann.
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
Van de Walle, J, (2004). Elementary and Middle School Mathematics, Boston, MA: Pearson Education, Inc.
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


  • Understanding and generalizing operational relationships leads to more sophisticated representations and solution strategies in order to investigate or solve problem situations in everyday life.
    • What relationships exist within and between mathematical operations?
    • How does generalizing operational relationships lead to developing more flexible, efficient representations and/or solution strategies?
    • Why is understanding the problem solving process an essential part of learning and working mathematically?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Recognizing and understanding operational relationships in a variety of problem situations leads to efficient, accurate, and flexible representations and solution strategies.
    • How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?
    • How can representing a problem situation using …
      • concrete models
      • pictorial models
      … aid in problem solving?
    • What strategies can be used to determine …
      • the total number of objects when equal groups of objects are joined?
      • the number of objects in a group when a set is separated into equal groups?
      • the number of groups when a set of objects is separated into equal groups?
    • What relationships exist between …
      • the number of equal-sized groups, the quantity of objects in each group, and the total number of objects?
      • equal sized groups and multiplication?
      • addition and multiplication?
      • subtraction and division?
      • multiplication and division?
  • Number and Operations
    • Number
      • Counting (natural) numbers
      • Whole numbers
    • Operations
      • Multiplication
      • Division
    • Problem Types
    • Relationships and Generalizations
      • Operational
      • Equivalence
    • Solution Strategies
  • 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.

  • Geometric, spatial, and measurement reasoning are foundational to visualizing, analyzing, and applying relationships within and between scale, shapes, quantities, and spatial relations in everyday life.
    • Why is developing geometric, spatial, and measurement reasoning essential?
    • How does generalizing operational relationships lead to developing more flexible, efficient representations and/or solution strategies?
    • How does geometric, spatial, and measurement reasoning affect how one sees and works in the world?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Objects have unique measurable attributes that can be defined and described in order to make sense of their relationship to other objects in the world.
    • Why is it important to be able to measure area of a rectangle?
    • In what situations might someone need to measure area of a rectangle?
  • Attributes of objects can be measured using tools, and their measures can be described using units, in order to quantify a measurable attribute of the object.
    • What concrete models can be used to measure area?
    • What strategies can be used to measure area using concrete models of square units?
    • Why is it important to …
      • use concrete objects that are square?
      • use the same-sized square units to measure area?
      • not allow gaps between units when measuring area?
      • not allow overlaps of units when measuring area?
    • How can composition or decomposition be used to simplify the measurement process?
    • How can the area of an object be determined when the square units do not fill the rectangle exactly?
    • How can the area of an object be described?
  • Measurement
    • Geometric Relationships
      • Area
    • Measure
      • Measurement tools
      • Units of measure
  • Associated Mathematical Processes
    • 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 word “total” in a problem situation always indicates addition rather than recognizing separating situation that identify the total amount being separated.
  • Some students may think all division situations represent the same type of solution rather than recognizing the difference between partitive division (finding the number in each group) and quotative division (finding the number of groups).
  • Some students may think finding the area of rectangle using concrete models can be accomplished by spreading the square units out within the boundaries of the rectangle rather than realizing the square units must be placed with no gaps or overlaps.

Unit Vocabulary

  • Area – the measurement attribute that describes the number of square units a figure or region covers
  • Square unit – an object or unit, shaped like a square, used to measure area

Related Vocabulary:

  • Column
  • Equal groups/sets
  • Joining
  • Repeated addition
  • Repeated subtraction
  • Row
  • Separating
  • Skip counting
Unit Assessment Items System Resources Other Resources

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

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

 

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

 

Texas Education Agency – Mathematics Curriculum

 

Texas Education Agency – STAAR Mathematics Resources

 

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

 

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

 

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

 

Texas Education Agency Texas Gateway – Resources Aligned to Grade 2 Mathematics TEKS


TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE Legend:

  • Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
  • Student Expectations (TEKS) identified by TEA are in bolded, black text.
  • Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Specificity Legend:

  • Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
  • Unit-specific clarifications are in italicized, blue text.
  • Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
  • A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
TEKS# SE# TEKS SPECIFICITY
2.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
2.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

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

Including, but not limited to:

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

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing proficiency in the use of place value within the base-10 numeration system
    • Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
    • Measuring length
    • Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
  • TxCCRS:
    • 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, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

  • Mathematical ideas, reasoning, and their implications
    • Multiple representations, as appropriate
      • Symbols
      • Diagrams
      • 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
2.6 Number and operations. The student applies mathematical process standards to connect repeated addition and subtraction to multiplication and division situations that involve equal groupings and shares. The student is expected to:
2.6A Model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined.

Model, Create, Describe

CONTEXTUAL MULTIPLICATION SITUATIONS IN WHICH EQUIVALENT SETS OF CONCRETE OBJECTS ARE JOINED

Including, but not limited to:

  • Recognition of combining equivalent sets of objects in contextual situations
  • Recognition of repeated addition of sets of objects in contextual situations
  • Model and describe contextual multiplication situations using concrete objects.
    • Organized to represent equal sized groups
    • Sets up to 10 equal groups of 10
    • Oral description
      • Appropriate labels for number of groups and amount in each group
      • Stated as: “___ equal groups of ___”
    • Written description
      • Recorded as: ____ equal groups of ___
    • Recorded as repeated addition
  • Create and describe contextual multiplication situations.
    • Combination of equally-sized groups
    • Sets up to 10 equal groups of 10
    • Oral description
      • Appropriate labels for number of groups and amount in each group
      • Stated as: “___ equal groups of ___”
    • Written description
      • Recorded as: ____ equal groups of ___
    • Recorded as repeated addition
    • Connection between skip counting (by 2s, 3s, etc.) and counting equivalent sets of objects
    • Comparisons of different equivalent groupings
      • Same number of groups with different amounts in each group
      • Different number of groups with same amount in each group
      • Different number of groups and/or different amount in each group, but same total number of objects

Note(s):

  • Grade Level(s):
    • Grade 2 introduces contextual multiplication situations.
    • Grade 3 will determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 × 10.
    • Grade 3 will introduce the multiplication symbol.
    • 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:
    • I. Numeric Reasoning
    • IX. Communication and Representation
    • X. Connections
2.6B Model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets.

Model, Create, Describe

CONTEXTUAL DIVISION SITUATIONS IN WHICH A SET OF CONCRETE OBJECTS IS SEPARATED INTO EQUIVALENT SETS

Including, but not limited to:

  • Recognition of separating or sharing a set of objects into equivalent sets in contextual situations
    • Partitive division
      • Total amount known
      • Number of groups known
      • Size or measure of each group unknown
    • Quotative division (also known as Measurement division)
      • Total amount known
      • Size or measure of each group known
      • Number of groups unknown
  • Recognition of repeated subtraction of sets of objects in contextual situations
  • Model and describe contextual division situations using concrete objects.
    • Organized to represent equal sized groups
    • Sets up to 10 equal groups of 10
    • Oral description
      • Appropriate labels for number of groups and amount in each group
      • Partitive division stated as: “___ separated into ___ equal groups equals groups of ___,” or “___ separated into ___ equal groups equals ___ in each group”
      • Quotative division stated as: “___ separated into groups of ___ equals ___ equal groups,” or “___separated into ___ in each group equals ___ equal groups”
    • Written description
      • Partitive division recorded as: ___ separated into ___ equal groups equals groups of ___, or ___ separated into ___ equal groups equals ___ in each group
      • Quotative division recorded as: ___ separated into groups of ___ equals ___ equal groups, or ___separated into ___ in each group equals ___ equal groups
    • Recorded as repeated subtraction
  • Create and describe contextual division situations.
    • Separation into equally-sized groups
    • Sets of up to 10 equal groups of 10
    • Oral description
      • Appropriate labels for number of groups and amount in each group
      • Partitive division stated as: “___ separated into ___ equal groups equals groups of ___,” or “___ separated into ___ equal groups equals ___ in each group”
      • Quotative division stated as: “___ separated into groups of ___ equals ___ equal groups,” or “___separated into ___ in each group equals ___ equal groups”
    • Written description
      • Partitive division recorded as: ___ separated into ___ equal groups equals groups of ___, or ___ separated into ___ equal groups equals ___ in each group
      • Quotative division recorded as: ___ separated into groups of ___ equals ___ equal groups, or ___separated into ___ in each group equals ___ equal groups
    • Recorded as repeated subtraction

 

Note(s):

  • Grade Level(s):
    • Grade 2 introduces contextual division situations.
    • Grade 3 will determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally.
    • Grade 3 will introduce the division symbol.
    • 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:
    • I. Numeric Reasoning
    • IX. Communication and Representation
    • X. Connections
2.9 Geometry and measurement. The student applies mathematical process standards to select and use units to describe length, area, and time. The student is expected to:
2.9F Use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit.

Use

CONCRETE MODELS OF SQUARE UNITS TO FIND THE AREA OF A RECTANGLE BY COVERING IT WITH NO GAPS OR OVERLAPS, COUNTING TO FIND THE TOTAL NUMBER OF SQUARE UNITS, AND DESCRIBING THE MEASUREMENT USING A NUMBER AND THE UNIT

Including, but not limited to:

  • Area – the measurement attribute that describes the number of square units a figure or region covers
  • Square unit – an object or unit, shaped like a square, used to measure area
  • Concrete models of non-standard square units
    • Flat surface of color tiles, unit cubes, base-10 flats, square sticky notes, etc.
  • Area of a rectangle (including squares as special rectangles)
    • Boundary of rectangle defined
    • Equal sized square units iterated (repeated) in rows and columns inside the boundary of the rectangle being measured
    • Equal sized square units iterated (repeated) in rows and columns with no gaps or overlaps
    • Area measured using two-dimensional square units (e.g., if measuring with a color tile, measure with the square surface of the color tile, not the side of the color tile, etc.)
    • Equal sized square units counted to the nearest whole unit
      • Last square unit in each row/column is not counted if the boundary of the rectangle falls less than half-way through the square unit(s).
      • Last square unit in each row/column is counted if the boundary of the rectangle falls more than half-way through the square unit(s).
    • Measurement determined by counting the number of whole units within the defined boundary
      • Determined by counting each whole unit individually
      • Determined by counting length of one row and it’s iteration (e.g., skip counting the number of units in each row to the last row such as 3 rows of 5 square units would be 5, 10, 15 or using repeated addition 5 + 5 + 5 = 15, etc.)
    • Measurement described using a number and the label square unit(s)
  • Appropriate square unit selected
    • Square unit selected for efficiency
      • Smaller square unit to measure smaller rectangles
      • Larger square unit to measure larger rectangles
    • Square unit selected for precision
      • Smaller square unit results in a more precise measurement when measuring to the whole unit
      • Larger square unit results in a less precise measurement when measuring to the whole unit
  • Inverse relationship between the size of the square unit and the number of square units needed
    • Measure a rectangle with a small square unit and then measure the same rectangle with a large square unit
      • The smaller the square unit, the more square units needed
      • The larger the square unit, the fewer square units needed

Note(s):

  • Grade Level(s):
    • Grade 2 introduces using concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit.
    • Grade 3 will determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row.
    • 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:
    • IV.A Measurement Reasoning – Measurement involving physical and natural attributes
    • 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.
Click here to collapse or expand this section.
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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