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 Instructional Focus DocumentGrade 3 Mathematics
 TITLE : Unit 12: Measurement SUGGESTED DURATION : 12 days

#### Unit Overview

Introduction
This unit bundles student expectations that address determining the area of a rectangle or a composite figure, determining the perimeter of a polygon, solving problems involving addition and subtraction of time intervals, and determining weight and liquid volume (capacity) using appropriate units and tools. 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 Kindergarten, students directly compared the liquid volume (capacity) and weight of objects. In Grade 2, students measured length to the nearest whole unit using standard measuring tools, solved problems involving length, determined the area of a rectangle using concrete models, and read time to the nearest one-minute increment using analog and digital clocks. In Grade 3 Unit 02, students were introduced to perimeter by determining the distance around rectangles and squares. In Grade 3 Unit 03, students were introduced to multiplication using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting, and they determined areas with whole number sides using multiplication related to arrays and area models.

During this Unit
Students determine the area of rectangles and squares with whole number side lengths by multiplying the number of rows by the number of unit squares in each row. Students extend their knowledge of area to determining the area of composite figures by decomposing composite figures into non-overlapping rectangles and using the additive property of area to determine the area of the original figure. Students determine the perimeter of polygons with given side lengths as well as by measuring side lengths with both customary and metric measures. They also extend their understanding of perimeter by finding a missing length when given the perimeter of a polygon and the remaining side lengths and by applying geometric attributes to determine a missing side length. Students determine and use appropriate customary and metric units of measure, including distinguishing between fluid ounces for measuring liquid volume (capacity) and ounces for measuring weight, and determine liquid volume (capacity) and weight in problem situations. Although Grade 3 students do not convert between units of measure, relationships between the sizes of units are established in order to select an appropriate unit for efficiency and precision. In this unit, students also solve problems involving addition and subtraction of time intervals in minutes, finding an ending time when given a start time and an interval of time, and finding a start time when given an end time and an interval of time. When solving time problems, students should experience situations that require knowing there are 60 minutes in one hour. Problems may be solved using pictorial models and tools such as analog or digital clocks and/or number lines. Throughout the unit, students should experience appropriate abbreviations for all units of measure.

After this Unit
In Grade 4, students will use models to determine the formulas for perimeter and area of a rectangle and solve problems involving length, area, intervals of time (including elapsed time), liquid volumes, and mass.

Additional Notes
In Grade 3, determining the area of a rectangle and the perimeter of a polygon are identified as STAAR Readiness Standards 3.6C and 3.7B. Decomposing a composite figure and determining area using the additive property of area and determining liquid volume (capacity) and weight using appropriate units and tools are identified as STAAR Supporting Standards 3.6D, 3.7D, and 3.7E. These standards are included in the Grade 3 Texas Response to Curriculum Focal Points (TxRCFP): Describing characteristics of 2-D and 3-D geometric figures, including measurable attributes. Solving problems related to the addition and subtraction of time intervals is identified as STAAR Supporting Standard 3.7C and is include in the Grade 3 Texas Response to Curriculum Focal Points (TxRCFP): Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000. All of these standards are included in STAAR Reporting Category 3: Geometry and Measurement. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): IV.C. Measurement Reasoning – Measurement involving geometry and algebra, VIII. Problem Solving and Reasoning, IX. Communication and Representation, and X. Connections

Research
According to The National Council of Teachers of Mathematics (2004), research has identified several levels for decomposing and recomposing shapes. Level 3 is where students explicitly use measurement, along with visualization, to decompose and recompose shapes in order to determine and compare areas (p. 21). The National Research Council (2001) emphasizes the “pedagogical value in returning geometry to its roots in spatial measure” (p. 281). In STAAR Reporting Category 3 geometry and measurement concepts are used to develop the properties of two-dimensional shapes. Chapin and Johnson (2000), state that “In order to prepare elementary students to use measurement in a variety of ways, we must provide them with many opportunities to engage in meaningful measurement tasks – tasks that promote understanding of concepts and facility with measurement units” (p.195). According to Van de Walle (2006) “volume typically refers to the amount of space that an object takes up” whereas “capacity is generally used to refer to the amount that container will hold” (p. 265). He explains further that, “having made these distinctions [between volume and capacity], they are not ones to worry about. The term volume can also be used to refer to the capacity of a container” (p. 266).

Chapin, S & Johnson, A. (2000). Math matters: Understanding the math you teach. Sausalito, CA: Math Solutions Publications.
National Council of Teachers of Mathematics. (2004). Navigating through problem solving and reasoning in grade 3. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Research Council. (2001). Adding it up: Helping children learn mathematics. Kilpatrick, J., Swafford, J., and Findell, B. (Eds.) Mathematics Learning Study Committee, Center for Education Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J. A. & Lovin, L. H. (2006). Teaching students-centered mathematics: Grades 3-5. Boston: Pearson Education, Inc.

 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)
• Illustrating and analyzing geometric relationships in models and diagrams aid in representing and describing the attributes of geometric figures in order to generalize geometric relationships and solve problem situations.
• How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve a problem involving …
• perimeter?
• area?
• What strategies can be used to determine the …
• perimeter of a polygon?
• missing side length of a polygon when given the perimeter and remaining side lengths?
• area of a rectangle?
• area of a composite figure composed of rectangles?
• What relationships exist between …
• area and perimeter?
• addition and perimeter of a polygon?
• multiplication and area of a rectangle?
• Geometry
• Decomposition of Figures
• Geometric Representations
• Two-dimensional figures
• Composite figures
• Measurement
• Geometric Relationships
• Perimeter
• Area
• Measureable Attributes
• Distance and length
• Measure
• Units of measure
• 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 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 and events have unique measurable attributes that can be defined and described in order to make sense of their relationship to other objects and events in the world.
• How can time be described as a measurement?
• Why is it important to be able to …
• tell time?
• solve problems involving intervals of time?
• In what situations might someone need to solve problems involving addition and subtraction of time intervals?
• Attributes of objects and events can be measured using tools, and their measures can be described using units, in order to quantify a measurable attribute of the object or event.
• What tools can be used to measure time?
• What units of measure are used to describe time?
• What relationships exist between …
• 1 minute and an hour?
• 5 minutes and an hour?
• 15 minutes and an hour?
• 30 minutes and an hour?
• 60 minutes and an hour?
• the numerals, hour hand, minute hand, and second hand on an analog clock?
• the numerals and symbols on a digital clock?
• the markings on an analog clock and a number line?
• What patterns exist in the continuous nature of time?
• How are descriptions of a length of time and descriptions of a time of day similar and different?
• What strategies can be used to …
• add or subtract intervals of time?
• determine an end time when given a start time and an interval of time?
• determine a start time when given an end time and an interval of time?
• How can pictorial models, tools, or number lines aid in solving problems involving addition and subtraction of time intervals?
• What regrouping strategies apply when intervals of time exceed 60 minutes?
• What strategies can be used to determine the reasonableness of the solution in a problem involving the addition and subtraction of time intervals, finding a start time, or finding an end time?
• Measurement
• Measureable Attributes
• Time
• Measure
• Measurement tools
• Units of measure
• 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 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)
• 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.
• How can the measureable attributes of liquid volume (capacity) and weight exist in a single object?
• In what situations might someone need to measure …
• liquid volume (capacity)?
• weight?
• What tools can be used to measure …
• liquid volume (capacity)
• weight
… and how are these tools used?
• What units of measure are used to describe …
• liquid volume (capacity)?
• weight?
• What relationships exist within and between different units of …
• customary liquid volume (capacity)?
• metric liquid volume (capacity)?
• weight?
• What should be considered in order to determine the most appropriate unit to measure …
• liquid volume (capacity)?
• weight?
• Measurement
• Measureable Attributes
• Capacity and liquid volume
• Weight
• Measure
• Measurement tools
• Systems of measurement
• Units of measure
• 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 a composite figure can be decomposed only one way rather than realizing the figure can be decomposed multiple ways.
• Some students may think any measurement described using the label ounce refers to the weight of the object rather than realizing fluid ounces are sometimes referred to as simply ounces.
• Some students may think base-10 regrouping strategies apply to converting minutes to hours rather than realizing the conversion between minutes and hours is based on groups of 60 (e.g., some students may think 115 minutes is 1 hour 15 minutes rather than correctly converting 115 minutes into 1 group of 60 with 55 left or 1 hour 55 minutes).

Underdeveloped Concepts:

• Some students may confuse the terms area and perimeter.
• Some students may struggle aligning the starting point of the distance being measured with the zero mark on a ruler, thinking the starting point should be aligned with the end of the ruler or the number 1 on the ruler.
• Some students may confuse counting the marked intervals on a ruler with measuring the space or distance between the marked units.

#### Unit Vocabulary

• Additive property of area – the sum of the areas of each non-overlapping region of a composite figure equals the area of the original figure
• Area – the measurement attribute that describes the number of unit squares (or square units) a figure or region covers
• Capacity – the measurement attribute that describes the maximum amount something can contain
• Composite figure – a figure that is composed of two or more two-dimensional figures
• Decompose figures – to break a geometric figure into two or more smaller geometric figures
• Liquid volume – the measurement attribute that describes the amount of space that a liquid or dry, pourable material takes up, typically measured using standard units of capacity
• Perimeter – a linear measurement of the distance around the outer edge of a figure
• Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
• Weight – the measurement attribute that describes how heavy an object is, determined by the pull of gravity on the object

Related Vocabulary:

 Analog clock Centimeter Columns Cup Customary unit of measure Digital clock Distance Fluid ounce Foot Gallon Hours Inch Interval of time Kiloliter Kilometer Liter Meter Metric unit of measure Mile Milliliter Millimeter Minutes Ounce Pint Pound Quart Rows Seconds Side length Space/region Square unit Ton Yard
Unit Assessment Items System Resources Other Resources

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

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

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

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

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

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

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway – Resources Aligned to Grade 3 Mathematics TEKS

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

Legend:

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

Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific clarifications are in italicized, blue text.
• Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
3.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
3.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

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:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Solving problems with multiplication and division within 100
• Understanding fractions as numbers and representing equivalent fractions
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• X. Connections
3.1B 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.
Process Standard

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:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Solving problems with multiplication and division within 100
• Understanding fractions as numbers and representing equivalent fractions
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• VIII. Problem Solving and Reasoning
3.1C 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.
Process Standard

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:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Solving problems with multiplication and division within 100
• Understanding fractions as numbers and representing equivalent fractions
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• VIII. Problem Solving and Reasoning
3.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

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:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Solving problems with multiplication and division within 100
• Understanding fractions as numbers and representing equivalent fractions
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• IX. Communication and Representation
3.1E Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

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:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Solving problems with multiplication and division within 100
• Understanding fractions as numbers and representing equivalent fractions
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• IX. Communication and Representation
3.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

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:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Solving problems with multiplication and division within 100
• Understanding fractions as numbers and representing equivalent fractions
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• X. Connections
3.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

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:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• Solving problems with multiplication and division within 100
• Understanding fractions as numbers and representing equivalent fractions
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• IX. Communication and Representation
3.6 Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties. The student is expected to:
3.6C 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.
Readiness Standard

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

Including, but not limited to:

• Area of rectangles
• Area – the measurement attribute that describes the number of unit squares (or square units) a figure or region covers
• Squares as a special type of rectangle
• Products of up to a two-digit factor by a one-digit factor
• Recognition of area embedded in mathematical and real-world problem situations
• Area determined by multiplying the number of rows times the number of unit squares in each row
• Concrete and pictorial models to represent the number of rows and the number of units in each row
• Concrete models
• Color tiles to measure square inches
• Centimeter cubes to measure square centimeters
• Area determined when given a rectangle
• Whole unit side lengths
• Area determined when given the side lengths of a rectangle related to number of rows and number of unit squares in each row
• Whole unit side lengths
• Pictorial models to represent the number of rows and the number of units in each row
• Pictorial models
• Inch grid paper to measure square inches
• Centimeter grid paper to measure square centimeters
• Pictorial representations with grid lines to represent customary or metric square units
• Pictorial representations with partial grid lines to represent customary or metric square units
• Area determined when given a rectangle with grid lines or partial grid lines
• Whole unit side lengths
• Area determined when given the side lengths of a rectangle related to number of rows and number of unit squares in each row
• Whole unit side lengths
• Relationship to area models in multiplication
• Appropriate labels in standard units
• Square units of standard measure in word form only, not to include exponents
• Typically used customary units
• Square inches, square feet, square yards, square miles
• Typically used metric units
• Square millimeters, square centimeters, square meters, square kilometers

Note(s):

• Grade Level(s):
• Grade 2 students used 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 4 will use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l × w).
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• IV.C. Measurement Reasoning – Measurement involving geometry and algebra
• IX. Communication and Representation
• X. Connections
3.6D Decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area.
Supporting Standard

Decompose

COMPOSITE FIGURES FORMED BY RECTANGLES INTO NON-OVERLAPPING RECTANGLES

Including, but not limited to:

• Composite figure – a figure that is composed of two or more two-dimensional figures
• Decompose figures – to break a geometric figure into two or more smaller geometric figures
• Composite figures decomposed in multiple ways
• Composite figures comprised of rectangles, including squares as a special type of rectangle
• Non-overlapping rectangles

To Determine

THE AREA OF THE ORIGINAL COMPOSITE FIGURE USING THE ADDITIVE PROPERTY OF AREA

Including, but not limited to:

• Area – the measurement attribute that describes the number of unit squares (or square units) a figure or region covers
• Appropriate labels in standard units
• Square units of standard measure in word form only, not to include exponents
• Typically used customary units
• Square inches, square feet, square yards, square miles
• Typically used metric units
• Square millimeters, square centimeters, square meters, square kilometers
• Composite figure – a figure that is composed of two or more two-dimensional figures
• Additive property of area – the sum of the areas of each non-overlapping region of a composite figure equals the area of the original figure
• Determine the area of each decomposed part of the original composite figure.
• Add the areas of all decomposed part to determine the total area of the original composite figure.
3.7 Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement. The student is expected to:
3.7B Determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems.
Readiness Standard

Determine

THE PERIMETER OF A POLYGON

Including, but not limited to:

• Perimeter – a linear measurement of the distance around the outer edge of a figure
• Recognition of perimeter embedded in mathematical and real-world problem situations
• Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
• Regular and irregular polygons
• Determine perimeter when given side lengths.
• Whole number side lengths
• Polygons (regular or irregular)
• Add all side lengths in any order to determine perimeter.
• Apply attributes of geometric figures to determine unmarked side lengths.
• Rectangles
• Opposite sides equal in length
• Regular polygons
• All sides equal in length
• Congruent figures
• Figures with equal measure
• Add all side lengths in any order to determine perimeter.
• Determine perimeter by measuring to determine side lengths.
• Ruler, STAAR Grade 3 Mathematics Reference Materials ruler, yardstick, meter stick, measuring tape, etc.
• Whole number side lengths
• Typically used units of measure in words and abbreviations
• Customary
• Inch (in.)
• Foot (ft)
• Yard (yd)
• Mile (mi)
• Metric
• Millimeter (mm)
• Centimeter (cm)
• Meter (m)
• Kilometer (km)
• Add all side lengths in any order to determine perimeter.

Determine

A MISSING LENGTH WHEN GIVEN PERIMETER AND REMAINING SIDE LENGTHS IN PROBLEMS

Including, but not limited to:

• Perimeter – a linear measurement of the distance around the outer edge of a figure
• Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
• Determine missing side length when given perimeter and remaining side lengths.
• Whole number side lengths
• Polygons
• Limited to one missing side length in irregular polygons.
• Add all known side lengths and subtract from perimeter to determine the missing side length.
• Apply attributes and properties of geometric figures to determine missing side lengths when given perimeter.
• Regular polygons
• All sides equal in length
• Congruent figures
• Figures with equal measures
• Divide the perimeter by the number of sides to determine one side length
• Add all known side lengths and subtract from perimeter to determine the missing side length(s).

Note(s):

• Grade Level(s):
• Grade 2 determined a solution to a problem involving length, including estimating lengths.
• Grade 4 will use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s).
• Grade 4 will solve problems that deal with measurements of length using addition, subtraction, multiplication, or division as appropriate.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• IV.C. Measurement Reasoning – Measurement involving geometry and algebra
• IX. Communication and Representation
3.7C Determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes.
Supporting Standard

Determine

THE SOLUTIONS TO PROBLEMS INVOLVING ADDITION AND SUBTRACTION OF TIME INTERVALS IN MINUTES USING PICTORIAL MODELS OR TOOLS

Including, but not limited to:

• Addition and subtraction of time intervals in minutes
• Two or more time intervals given
• Such as a 15-minute event plus a 30-minute event equals 45 minutes
• Start time and an interval given
• End time and an interval given
• Conversion of 60 minutes to one hour and one hour to 60 minutes
• Pictorial models and tools
• Analog clock with gears, digital clock, number line, etc.
• Recognition of operations with time embedded in mathematical and real-world problem situations
• One-step and two-step problems

Note(s):

• Grade Level(s):
• Grade 2 read and wrote time to the nearest one-minute increment using analog and digital clocks and distinguished between a.m. and p.m.
• Grade 4 will solve problems that deal with intervals of time, including elapsed time, using addition, subtraction, multiplication, or division as appropriate.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000
• TxCCRS:
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
• X. Connections
3.7D Determine when it is appropriate to use measurements of liquid volume (capacity) or weight.
Supporting Standard

Determine

WHEN IT IS APPROPRIATE TO USE MEASUREMENTS OF LIQUID VOLUME (CAPACITY) OR WEIGHT

Including, but not limited to:

• Liquid volume – the measurement attribute that describes the amount of space that a liquid or dry, pourable material takes up, typically measured using standard units of capacity
• Capacity – the measurement attribute that describes the maximum amount something can contain
• Typically used units of measure in words and abbreviations
• Customary
• Fluid ounce (fl oz)
• Cup (c)
• Pint (pt)
• Quart (qt)
• Gallon (gal)
• Metric
• Milliliter (ml or mL)
• Liter (l or L)
• Kiloliter (kl or kL)
• Recognition of liquid volume (capacity) concepts in mathematical and real-world problem situations
• Situations involving filling a container to its maximum, the amount of material in a container, etc.
• Situations involving liquid volume (capacity) units of measure
• Weight – the measurement attribute that describes how heavy an object is, determined by the pull of gravity on the object
• Typically used units of measure in words and abbreviations
• Customary
• Ounce (oz)
• Pound (lb)
• Ton (T)
• Recognition of weight concepts in mathematical and real-world problem situations
• Situations involving how heavy objects are, how much something weighs, etc.
• Situations involving weight units of measure
• Distinction between liquid ounces and ounces that measure weight
• Fluid ounces are associated with liquid volume (capacity) and ounces are associated with weight.
• Fluid ounces often named as simply ounces
• Distinction between ounces in mathematical and real-world problem situations

Note(s):

• Grade Level(s):
• Kindergarten gave an example of a measurable attribute of a given object, including length, capacity, and weight.
• Grade 3 studies customary measures of weight; however, students should be familiar with the metric units associated with mass as indicated on the STAAR Grade 3 Mathematics Reference Materials.
• Grade 4 will solve problems that deal with measurements of liquid volumes and mass, including conversion, using addition, subtraction, multiplication, or division as appropriate.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• IV.A. Measurement Reasoning – Measurement involving physical and natural attributes
• IX. Communication and Representation
3.7E Determine liquid volume (capacity) or weight using appropriate units and tools.
Supporting Standard

Determine

LIQUID VOLUME (CAPACITY) OR WEIGHT USING APPROPRIATE UNITS AND TOOLS

Including, but not limited to:

• Liquid volume – the measurement attribute that describes the amount of space that a liquid or dry, pourable material takes up, typically measured using standard units of capacity
• Capacity – the measurement attribute that describes the maximum amount something can contain
• Typically used units of measure in words and abbreviations
• Customary
• Fluid ounce (fl oz)
• Cup (c)
• Pint (pt)
• Quart (qt)
• Gallon (gal)
• Metric
• Milliliter (ml or mL)
• Liter (l or L)
• Kiloliter (kl or kL)
• Measurement tools typically used for liquid volume (capacity)
• Measuring cups, measuring containers or jars, eye droppers, beakers, graduated cylinders, etc.
• Pourable material leveled at the top of the measuring tool or container when measuring to whole units
• Measure to determine liquid volume (capacity) in the customary and metric systems
• Measurement determined using equal sized units of liquid volume (capacity) counted to the nearest whole unit
• Last unit is not counted if the amount of pourable material fills less than half of the measuring tool.
• Last unit is counted if the amount of pourable material fills half, or more than half of the measuring tool.
• Measurement determined using scaled measuring tools
• Relationship between reading a scaled measuring tool and a number line
• Appropriate measuring tool selected
• Measuring tool selected for efficiency
• Smaller tool to measure the liquid volume (capacity) of smaller containers
• Larger tool to measure the liquid volume (capacity) of larger containers
• Appropriate unit of liquid volume (capacity) selected
• Unit of liquid volume (capacity) selected for efficiency
• Smaller unit of liquid volume (capacity) to measure the liquid volume (capacity) of smaller containers
• Larger unit of liquid volume (capacity) to measure the liquid volume (capacity) of larger containers
• Unit of liquid volume (capacity) selected for precision
• Smaller unit of liquid volume (capacity) results in a more precise measurement when measuring to the whole unit
• Larger unit of liquid volume (capacity) results in a less precise measurement when measuring to the whole unit
• Weight – the measurement attribute that describes how heavy an object is, determined by the pull of gravity on the object
• Typically used units of measure in words and abbreviations
• Customary
• Ounce (oz)
• Pound (lb)
• Ton (T)
• Measurement tools typically used for weight
• Spring scales, kitchen scales, bathroom scales, etc.
• Measure to determine weight in the in the customary system
• Measurement determined using scaled measuring tools
• Prior to measuring, the needle of the scale should point directly on zero.
• Relationship between reading a scaled measuring tool and a number line
• Appropriate unit of weight selected
• Unit of weight selected for precision
• Smaller unit of weight results in a more precise measurement when measuring to the whole unit
• Larger unit of weight results in a less precise measurement when measuring to the whole unit

Note(s):

• Grade Level(s):
• Kindergarten compared two objects with a common measurable attribute to see which object has more of/less of the attribute and described the difference.
• Grade 4 will solve problems that deal with measurements liquid volumes and mass using addition, subtraction, multiplication, or division as appropriate.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Describing characteristics of two-dimensional and three-dimensional geometric figures, including measurable attributes
• TxCCRS:
• IV.A. Measurement Reasoning – Measurement involving physical and natural attributes
• IX. Communication and Representation
ELPS# Subsection C: Cross-curricular second language acquisition essential knowledge and skills. 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. Choose appropriate ELPS to support instruction. 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.
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