
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
strikethrough.

Legend:  Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
 Unitspecific 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 twodimensional and threedimensional geometric figures, including measurable attributes
 TxCCRS:

3.1B 
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving 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 twodimensional and threedimensional 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 twodimensional and threedimensional 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 twodimensional and threedimensional 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 twodimensional and threedimensional 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 nonexamples, 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 twodimensional and threedimensional geometric figures, including measurable attributes
 TxCCRS:

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 twodimensional and threedimensional 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 twodimensional 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 twodigit factor by a onedigit factor
 Recognition of area embedded in mathematical and realworld 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
 Area determined when given the side lengths of a rectangle related to number of rows and number of unit squares in each row
 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
 Area determined when given the side lengths of a rectangle related to number of rows and number of unit squares in each row
 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 twodimensional and threedimensional 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 nonoverlapping rectangles to determine the area of the original figure using the additive property of area.
Supporting Standard

Decompose
COMPOSITE FIGURES FORMED BY RECTANGLES INTO NONOVERLAPPING RECTANGLES
Including, but not limited to:
 Composite figure – a figure that is composed of two or more twodimensional 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
 Nonoverlapping 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 twodimensional figures
 Additive property of area – the sum of the areas of each nonoverlapping 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 realworld 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 twodimensional and threedimensional 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 15minute event plus a 30minute 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 15minute event plus a 30minute 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 realworld problem situations
 Onestep and twostep problems
Note(s):
 Grade Level(s):
 Grade 2 read and wrote time to the nearest oneminute 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 realworld 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 realworld 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 realworld 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 twodimensional and threedimensional 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 twodimensional and threedimensional geometric figures, including measurable attributes
 TxCCRS:
 IV.A. Measurement Reasoning – Measurement involving physical and natural attributes
 IX. Communication and Representation
