 Hello, Guest!
 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.

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

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.

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?
• 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:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
2.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

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

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
2.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS

Including, but not limited to:

• Appropriate selection of tool(s) and techniques to apply in order to solve problems
• Tools
• Real objects
• Manipulatives
• Paper and pencil
• Technology
• Techniques
• Mental math
• Estimation
• Number sense

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
2.1D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, 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:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
2.1E Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Representations of mathematical ideas
• Organize
• Record
• Communicate
• Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
• Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
2.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Mathematical relationships
• Connect and communicate mathematical ideas
• Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
• Current knowledge to new learning

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
•  VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
2.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION

Including, but not limited to:

• Mathematical ideas and arguments
• Validation of conclusions
• Displays to make work visible to others
• Diagrams, visual aids, written work, etc.
• Explanations and justifications
• Precise mathematical language in written or oral communication

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing proficiency in the use of place value within the base-10 numeration system
• Using place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Measuring length
• Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
2.6 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 ___
• 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 ___
• 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 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:
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
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 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:
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
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 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:
• I.C. Numeric Reasoning – Systems of measurement
• I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.
• III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
• III.D.1. Find the perimeter and area of two-dimensional figures.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations. 