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 Instructional Focus DocumentKindergarten Mathematics
 TITLE : Unit 14: Measurable Attributes and Direct Comparisons SUGGESTED DURATION : 8 days

Unit Overview

Introduction
This unit bundles student expectations that address identifying measurable attributes of objects and directly comparing two objects to determine which object has more of or less of the measurable attribute. 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 Units 11 and 12, students explored two- and three-dimensional objects. Students learned the prerequisite skills of describing, comparing, classifying, and sorting objects that will be necessary for discerning measurable attributes of objects.

During this Unit
Students focus on identifying measurable attributes of objects, including length, capacity, and weight. Through repeated direct comparison opportunities, students develop an understanding of conservation (the length, capacity, or weight of an object does not change when the orientation of the object changes). Comparative language is used to describe the differences of the attributes between two objects. Students develop appropriate vocabulary for describing the differences for a specific measureable attribute versus a general term such as bigger. In Kindergarten, the focus of measurement is on direct comparisons using descriptive language rather than quantity. These direct comparisons begin to provide the foundational understanding that measurement involves a comparison of a measureable attribute of an object to a quantity of units of measurement.

After this Unit
In Grade 1, students will explore the continuous nature of linear measurement. Students will select and use non-standard units of measurement for determining length.

In Kindergarten, identifying, directly comparing, and describing measurable attributes, is subsumed within the Kindergarten Texas Response to Curriculum Focal Points (TxRCFP): Identifying and using attributes of two-dimensional shapes and three-dimensional solids. 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 A2; 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
According to Copley (2010), “To lay the foundation for measurement, teachers involve young children in a lot of comparing. In fact, comparison is the core activity and concept that starts children on the path to fully developed understanding and use of measurement” (p. 125). The National Council of Teachers of Mathematics (2003) states, “Recognizing which attributes of physical objects are measurable is the starting point for studying measurement, and very young children begin their exploration of measurable attributes by looking at, touching, and comparing physical things directly” (p. 2).

Copley, J. (2010). The young child and mathematics. Washington, DC: National Association for the Education of Young Children
National Council of Teachers of Mathematics. (2003). Navigating through measurement in pre-kindergarten – grade 2. Reston, VA: National Council of Teachers of Mathematics, 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

 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 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.
• What are some examples of the measureable attribute …
• length?
• capacity (liquid volume)?
• weight?
• How can the measureable attributes of length, capacity (liquid volume), and weight exist in a single object?
• What strategies can be used to compare the …
• length
• capacity (liquid volume)
• weight
… of two objects?
• How can the comparison of the …
• length
• capacity (liquid volume)
• weight
… of two objects be described?
• When might someone need to compare two objects based on the attribute of …
• length?
• capacity (liquid volume)?
• weight?
• Measurement
• Measureable Attributes
• Distance and length
• Capacity and liquid volume
• Weight
• Measure
• Direct comparison
• 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 objects can be compared by simply placing objects next to each other rather than aligning them.
• Some students may think the length, capacity, or weight of an object changes as the orientation of the object changes rather than recognizing that the measureable attributes remain the same when the object is moved.
• Some students may think a general comparison term such as “bigger” accurately describes the comparison of two objects rather than using more appropriate terms specific to the measureable attribute being compared (e.g., longer/shorter for length, heavier/lighter for weight, holds more than/less than for capacity, etc.).
• Some students may think length, height, and distance are separate measureable attributes rather than recognizing all three terms as linear measurements.

Unit Vocabulary

• Capacity – the measurement attribute that describes the maximum amount something can contain
• Compare measurable attributes – to consider a measurable attribute of two objects to determine which object has more or less of the measurable attribute or if the objects have an equal amount of the measurable attribute
• Direct comparison – a comparison using the actual objects being compared, rather than comparing using a measuring tool
• Distance – how far it is from one point to another
• Heft – holding one object in each of your hands to predict and compare which object is heavier or lighter
• Height – how tall something is, such as a person, building, or tree
• Length – the measurement attribute that describes how long something is from end to end
• Measurable attribute – a characteristic of an object that can be measured (length, capacity, weight)
• Weight – the measurement attribute that describes how heavy something is

Related Vocabulary:

 Balance scale Equal to Estimate Farther than, farthest Heavier than, heaviest Less than Lighter than, lightest Longer than, longest More than Same as Shorter than, shortest Spring scale Taller than, tallest
System Resources Other Resources

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

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

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

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

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

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway – Resources Aligned to Kindergarten Mathematics TEKS

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE Legend:

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

Specificity Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific clarifications are in italicized, blue text.
• Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
• A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
TEKS# SE# TEKS SPECIFICITY
K.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
K.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

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

Including, but not limited to:

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

Note(s):

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

Use

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

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
K.1C

Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING ESTIMATION 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
• Estimation

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
K.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

• Mathematical ideas, reasoning, and their implications
• Multiple representations, as appropriate
• Symbols
• Diagrams
• Graphs
• Language

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
K.1E Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
K.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. ConnectionsConnections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
K.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

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

Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing an understanding of whole numbers
• Developing an understanding of addition and subtraction
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• TxCCRS:
• VII.A. Problem Solving and ReasoningMathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII. A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
K.7 Geometry and measurement. The student applies mathematical process standards to directly compare measurable attributes. The student is expected to:
K.7A Give an example of a measurable attribute of a given object, including length, capacity, and weight.

Give

AN EXAMPLE OF A MEASURABLE ATTRIBUTE OF A GIVEN OBJECT, INCLUDING LENGTH, CAPACITY, AND WEIGHT

Including, but not limited to:

• Measurable attribute – a characteristic of an object that can be measured (length, capacity, weight)
• Length – the measurement attribute that describes how long something is from end to end
• Height – how tall something is, such as a person, building, or tree
• Distance – how far it is from one point to another
• Capacity – the measurement attribute that describes the maximum amount something can contain
• Weight – the measurement attribute that describes how heavy something is
• Identify measurable attributes in a variety of objects
• Single measurable attributes of an object
• Multiple measurable attributes of an object

Note(s):

• Grade 1 will use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement.
• Grade 3 will determine liquid volume (capacity) or weight using appropriate units and tools.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Identifying and using attributes of two-dimensional shapes and three-dimensional solids
• 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.A. Geometric and Spatial Reasoning – Figures and their properties
• III.A.2. Form and validate conjectures about one-, two-, and three-dimensional figures and their properties.
K.7B Compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference.

Compare

TWO OBJECTS WITH A COMMON MEASURABLE ATTRIBUTE TO SEE WHICH OBJECT HAS MORE OF/LESS OF THE ATTRIBUTE

Including, but not limited to:

• Measurable attribute – a characteristic of an object that can be measured (length, capacity, weight)
• Length – the measurement attribute that describes how long something is from end to end
• Height – how tall something is, such as a person, building, or tree
• Distance – how far it is from one point to another
• Capacity – the measurement attribute that describes the maximum amount something can contain
• Weight – the measurement attribute that describes how heavy something is
• Compare measurable attributes – to consider a measurable attribute of two objects to determine which object has more or less of the measurable attribute or if the objects have an equal amount of the measurable attribute
• Direct comparison – a comparison using the actual objects being compared, rather than comparing using a measuring tool
• Directly compare the length of two objects.
• Estimation prior to direct comparison
• Identification of the start point and endpoint of each object
• Common base to begin the direct comparison
• Both objects lined up with an even start point
• Direct comparison of the endpoints of both objects
• Conservation of length – the length of an object remains the same regardless of orientation
• Directly compare the capacity of two objects.
• Estimation prior to direct comparison
• Direct comparison of the capacity of each object
• Fill one container with a pourable material, and then transfer the pourable material to the other container to compare their capacities.
If the second container is not yet full, it has a larger capacity than the first container.
If the second container overflows, it has a smaller capacity than the first container.
•  Conservation of capacity – the capacity of an object remains the same regardless of orientation or the material used to fill it
• Directly compare the weight of two objects.
• Estimation prior to direct comparison
• Direct comparison of the weight of each object using a variety of tools
• Heft – holding one object in each of your hands to predict and compare which object is heavier or lighter
• Balance scale
• Place one item in each pan of a balance scale.
The pan that moves lower indicates the heavier object.
The pan that rises higher indicates the lighter object.
If the pans remain balanced, the objects have equal weight.
• Spring scale
• Place objects one at a time in the pan of a spring scale.
The object that pulls the pan down the farthest indicates the heavier object.
• Conservation of weight – the weight of an object remains the same regardless of orientation or the rearrangement of the material

Describe

THE DIFFERENCE IN A COMMON MEASURABLE ATTRIBUTE OF TWO OBJECTS

Including, but not limited to:

• Measurable attribute – a characteristic of an object that can be measured (length, capacity, weight)
• Length – the measurement attribute that describes how long something is from end to end
• Height – how tall something is, such as a person, building, or tree
• Distance – how far it is from one point to another
• Capacity – the measurement attribute that describes the maximum amount something can contain
• Weight – the measurement attribute that describes how heavy something is
• Appropriate language to describe comparison of measurable attributes in two objects
• Comparative language for length
• Longer than, longest
• Taller than, tallest
• Farther than, farthest
• Shorter than, shortest
• Same length as
• Same height as
• Same distance as
• Equal in length
• Equal in height
• Equal in distance
• Comparative language for capacity
• Holds more than
• Holds less than
• Holds the same as
• Holds an equal amount
• Equal capacity as
• Comparative language for weight
• Heavier than
• Lighter than
• The same weight as
• Equal weight as

Note(s):