7.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


7.1A 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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.

7.1B 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 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 problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving process.

7.1C 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 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.

7.1D 
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, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

7.1E 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 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.

7.1F 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
 VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
 IX.A.2. Connect mathematics to the study of other disciplines.

7.1G 
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:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.4. Justify the solution.
 VII.B. Problem Solving and Reasoning – Proportional reasoning
 VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
 VII.C. Problem Solving and Reasoning – Logical reasoning
 VII.C.1. Develop and evaluate convincing arguments.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII. A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII. C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.

7.4 
Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is expected to:


7.4E 
Convert between measurement systems, including the use of proportions and the use of unit rates.
Supporting Standard

Convert
BETWEEN MEASUREMENT SYSTEMS, INCLUDING THE USE OF PROPORTIONS AND THE USE OF UNIT RATES
Including, but not limited to:
 Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Fractions
 Convert units between measurement systems.
 Customary to metric
 Metric to customary
 Multiple solution strategies
 Dimensional analysis using unit rates
 Unit rates
 Scale factor between ratios
 Proportion method
 Conversion graph
Note(s):
 Grade Level(s):
 Grade 4 converted measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
 Grade 5 solved problems by calculating conversions within a measurement system, customary or metric.
 Grade 6 converted units within a measurement system, including the use of proportions and unit rates.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 I.C. Numeric Reasoning – Systems of measurement
 I.C.2. Convert units within and between systems of measurement.
 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.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

7.5 
Proportionality. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships. The student is expected to:


7.5B 
Describe π as the ratio of the circumference of a circle to its diameter.
Supporting Standard

Describe
π AS THE RATIO OF THE CIRCUMFERENCE OF A CIRCLE TO ITS DIAMETER
Including, but not limited to:
 Circle – a twodimensional figure formed by a closed curve with all points equal distance from the center
 Diameter – a line segment whose endpoints are on the circle and passes through the center of the circle
 Radius – a line segment drawn from the center of a circle to any point on the circle and is half the length of the diameter of the circle
 Circumference – a linear measurement of the distance around a circle
 Pi (π) – the ratio of the circumference to the diameter of a circle
 π is represented by the ratio C:d
 π = or π =
 π ≈ 3.14 or
 Relationship between circumference and diameter
Note(s):
 Grade Level(s):
 Grade 7 introduces describing π as the ratio of the circumference of a circle to its diameter.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.2. Form and validate conjectures about one, two, and threedimensional figures and their properties.
 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.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.

7.8 
Expressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is expected to:


7.8C 
Use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas.

Use
MODELS TO DETERMINE THE APPROXIMATE FORMULAS FOR THE CIRCUMFERENCE AND AREA OF A CIRCLE AND CONNECT THE MODELS TO THE ACTUAL FORMULAS
Including, but not limited to:
 Circle – a twodimensional figure formed by a closed curve with all points equal distance from the center
 Diameter – a line segment whose endpoints are on the circle and passes through the center of the circle
 Radius – a line segment drawn from the center of a circle to any point on the circle and is half the length of the diameter of the circle
 Circumference – a linear measurement of the distance around a circle
 Pi (π) – the ratio of the circumference to the diameter of a circle
 Various models to approximate the formulas for the circumference of a circle
 Using a string to measure the length around a circle and another piece of string to measure the length of the diameter of the circle
 The length of the string representing the circumference of the circle will be a little more than three times longer than the length of the string representing the diameter of the circle.
 Using centimeter cubes to measure the length around a circle and using centimeter cubes to measure the length of the radius of the circle
 The number of centimeter cubes needed to represent the radius of the circle is a little more than onesixth of the number of centimeter cubes needed to represent the length of the circumference of the circle.
 Circumference using the diameter of a circle
 Circumference using the radius of a circle
 Generalizations of models used to determine the approximate formulas for circumference of a circle
 The circumference of a circle is a little more than three times the length of the diameter of a circle.
 The circumference of a circle is a little more than three times twice the length of the radius of a circle or a little more than 6 times the radius.
 Connections between models to represent the circumference of a circle and formulas for circumference
 Formulas for circumference from STAAR Grade 7 Mathematics Reference Materials
 Circumference using the diameter of a circle
 C = πd, where C represents the circumference of the circle, d represents the diameter of the circle, and π represents the approximate number of times the diameter wraps the circumference of the circle.
 The ratio of the circumference to the diameter of the circle is a little more than 3 and denoted by π ≈ 3.14.
 Circumference using the radius of a circle
 C = 2πr, where C represents the circumference of the circle, r represents the radius of the circle, and π represents the approximate number of times the radius wraps the circumference of the circle.
 The ratio of the circumference to the radius of the circle is a little more than 6.
 The ratio of the circumference to the radius of the circle is twice as much as the ratio of the circumference to the diameter of the circle.
 The ratio of the circumference to the diameter of the circle is a little more than 3 and denoted by π ≈ 3.14.
 Area – the measurement attribute that describes the number of square units a figure or region covers
 Area is a twodimensional square unit measure.
 Various models to approximate the formula for the area of a circle
 Cutting a circle into equally sized pieces from the center of the circle to the outside of the circle where the length of the noncurved side is the length of the radius of the circle, then laying the equallysized pieces next to each other to create a figure similar to the shape of a rectangle
 The area of the rectangle (formed with pieces of the circle) is a little more than three times the length of the radius squared.
 Tracing a circle on centimeter grid paper, dividing the circle into four equally sized pieces from the center of the circle, forming squares with three of the four pieces of the divided circle using the radius of the circle as the side length of each square, and using the area of the square that extends beyond the circle to fill the last of the four equally sized pieces
 The number of square centimeters needed to represent the area of the entire circle is a little more than the area of three squares with the radius of the circle as one of the side lengths of the square.
 Generalization of models used to determine the approximate formula for area of a circle
 The area of a circle is a little more than three times the length of the radius squared.
 Connections between models to represent the area of a circle and formulas for area of a circle
 Formula for area of a circle from STAAR Grade 7 Mathematics Reference Materials
 Area of a circle
 A = πr^{2}, where A represents the area of the circle, r represents the radius of the circle, and π represents the approximate number of squares, with a side length of r, needed to fill the area of the circle.
 The ratio of the area of the circle to the area of the radius squared is a little more than 3 and denoted by π ≈ 3.14.
Note(s):
 Grade Level(s):
 Grade 7 introduces using models to determine the approximate formulas for the circumference and area of a circle and connecting the models to the actual formulas.
 Grade 8 will solve problems involving the volume of cylinders, cones, and spheres.
 Grade 8 will use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders.
 Grade 8 will determine the volume of cylinders and cones and the surface area of cylinders.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.2. Form and validate conjectures about one, two, and threedimensional figures and their properties.
 III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
 III.C.1. Make connections between geometry and algebraic equations.
 III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.3. Determine indirect measurements of geometric figures using a variety of methods.
 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.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.

7.9 
Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is expected to:


7.9B 
Determine the circumference and area of circles.
Readiness Standard

Determine
THE CIRCUMFERENCE AND AREA OF CIRCLES
Including, but not limited to:
 Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Fractions
 Circle – a twodimensional figure formed by a closed curve with all points equal distance from the center
 Diameter – a line segment whose endpoints are on the circle and passes through the center of the circle
 Radius – a line segment drawn from the center of a circle to any point on the circle and is half the length of the diameter of the circle
 Semicircle – half of a circle
 Quarter circle – onefourth of a circle
 Circumference – a linear measurement of the distance around a circle
 Pi (π) – the ratio of the circumference to the diameter of a circle
 π ≈ 3.14 or
 Formulas for circumference from STAAR Grade 7 Mathematics Reference Materials
 Circumference using the radius of a circle
 C = 2πr, where C represents the circumference of the circle and r represents the radius of the circle, and π is approximately 3.14 or
 Circumference using the diameter of a circle
 C = πd, where C represents the circumference of the circle, d represents the diameter of the circle, and π is approximately 3.14 or
 Area – the measurement attribute that describes the number of square units a figure or region covers
 Area is a twodimensional square unit measure.
 Positive rational number dimensions
 Formula for area of a circle from STAAR Grade 7 Mathematics Reference Materials
 Area
 A = πr^{2}, where A represents the area of the circle, r represents the radius of the circle, and π is approximately 3.14 or
Note(s):
 Grade Level(s):
 Grade 6 determined solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
 Grade 8 will solve problems involving the volume of cylinders, cones, and spheres.
 Grade 8 will use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.1. Find the perimeter and area of twodimensional figures.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.3. Determine a solution.

7.9C 
Determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles.
Readiness Standard

Determine
THE AREA OF COMPOSITE FIGURES CONTAINING COMBINATIONS OF RECTANGLES, SQUARES, PARALLELOGRAMS, TRAPEZOIDS, TRIANGLES, SEMICIRCLES, AND QUARTER CIRCLES
Including, but not limited to:
 Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Fractions
 Twodimensional figure – a figure with two basic units of measure, usually length and width
 Composite figure – a figure that is composed of two or more twodimensional figures
 Rectangles
 Squares
 Parallelograms
 Trapezoids
 Triangles
 Circles
 Semicircles
 Quarter circles
 Any combination of these figures
 Area – the measurement attribute that describes the number of square units a figure or region covers
 Area is a twodimensional square unit measure.
 Positive rational number side lengths
 Formulas for area from STAAR Grade 7 Mathematics Reference Materials
 Triangle
 A = bh, where b represents the length of the base of the triangle and h represents the height of the triangle
 Rectangle or parallelogram
 A = bh, where b represents the length of the base of the rectangle or parallelogram and h represents the height of the rectangle or parallelogram
 Trapezoid
 A = (b_{1} + b_{2})h, where b_{1} represents the length of one of the parallel bases, b_{2} represents the length of the other parallel base, and h represents the height of the trapezoid
 Circle
 A = &pir^{2}, where A represents the area of the circle, r represents the radius of the circle, and π is approximately 3.14 or
 Problem situations could involve using a ruler to determine side lengths when solving problem situations.
Note(s):
 Grade Level(s):
 Grade 6 determined solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.1. Find the perimeter and area of twodimensional figures.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.3. Determine a solution.
