G.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


G.1A 
Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:
 Mathematical problem situations within and between disciplines
 Everyday life
 Society
 Workplace
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 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.

G.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.

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.
 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.

G.1C 
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select
TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:
 Appropriate selection of tool(s) and techniques to apply in order to solve problems
 Tools
 Real objects
 Manipulatives
 Paper and pencil
 Technology
 Techniques
 Mental math
 Estimation
 Number sense
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 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.

G.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Graphs
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 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.

G.1E 
Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Representations of mathematical ideas
 Organize
 Record
 Communicate
 Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
 Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 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.

G.1F 
Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Mathematical relationships
 Connect and communicate mathematical ideas
 Conjectures and generalizations from sets of examples and nonexamples, patterns, etc.
 Current knowledge to new learning
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 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.

G.1G 
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:
 Mathematical ideas and arguments
 Validation of conclusions
 Displays to make work visible to others
 Diagrams, visual aids, written work, etc.
 Explanations and justifications
 Precise mathematical language in written or oral communication
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 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.

G.2 
Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to:


G.2B 
Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines.

Use
THE DISTANCE FORMULA TO VERIFY GEOMETRIC RELATIONSHIPS
Including, but not limited to:
 Distance formula: d =
 Equation of a line
 Slopeintercept form, y = mx + b
 Pointslope form, y – y_{1} = m(x – x_{1})
 Standard form, Ax + By = C
 Relationships of special segments and points in circles
 Center of circle
 Circle – set of all points equidistant from a given point called the center of the circle
 Center of a circle – point equidistant from all points on the circle
 Chord of a circle
 Chord of a circle – line segment that joins two points on the circle
 Diameter and radius of a circle
 Diameter – a line segment whose endpoints are on the circle and passes through the center of the circle
 Radius – line segment drawn from the center of a circle to any point on the circle and is half the length of the diamter of the circle
 Tangent to a circle
 Tangent to a circle – line, ray, or line segment perpendicular to the radius and intersecting the circle at exactly one point, the point of tangency
Note(s):
 Grade Level(s)
 Grade 8 introduced and applied the Pythagorean Theorem to determine the distance between two points on a coordinate plane.
 Grade 8 introduced slope as or .
 Algebra I addressed determining equations of lines using pointslope form, slope intercept form, and standard form.
 Algebra I wrote equations of lines that contain a given point and are parallel or perpendicular to a given line.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxCCRS
 III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
 III.C.1. Make connections between geometry and algebraic equations.
 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.

G.5 
Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. The student is expected to:


G.5A 
Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools.

Investigate
PATTERNS TO MAKE CONJECTURES ABOUT GEOMETRIC RELATIONSHIPS, INCLUDING SPECIAL SEGMENTS AND ANGLES OF CIRCLES CHOOSING FROM A VARIETY OF TOOLS
Including, but not limited to:
 Conjecture – statement believed to be true but not yet proven
 Investigations should include good sample design, valid conjecture, and inductive/deductive reasoning.
 Patterns include numeric and geometric properties.
 Utilization of a variety of tools in the investigations (e.g., compass and straightedge, paper folding, manipulatives, dynamic geometry software, technology)
 Special segments and angles of circles
 Central angle – angle whose vertex is the center of the circle and whose sides are radii of the circle
 Measure of a central angle is equal to the measure of the intercepted arc.
 Inscribed angle – angle whose vertex is on the circle and whose sides are chords of the circle
 Measure of an inscribed angle is the measure of the intercepted arc.
 Inscribed angle with semicircle intercepted arc is a right angle.
 Measure of an inscribed angle is the measure of the central angle that shares the same intercepted arc.
 Chord of a circle – line segment that joins two points on the circle
 Two chords are congruent if and only if their corresponding intercepting arcs are congruent.
 Diameter of a circle bisects a chord if and only if the diameter and chord are perpendicular.
 Products of the lengths of the segments of intersecting chords are equal.
 Vertical angles formed by intersecting chords are equal in measure.
 Adjacent angles formed by intersecting chords are supplementary.
 Measure of the angle formed by intersecting chords is the sum of the measures of the intercepted arcs.
 Secant to a circle – line, ray, or line segment that intersects the circle in exactly two points
 SecantSecant
 Product of the length of the secant segment and its external segment is equal to the product of the other secant segment and its external segment from the same point outside the circle.
 Measure of the angle formed by two secants intersecting at a point outside the circle is the difference of the measures of the intercepted arcs.
 Tangent to a circle – line, ray, or line segment perpendicular to the radius and intersecting the circle in exactly one point, the point of tangency
 TangentTangent
 Intersecting tangent segments are equal in length from the same point outside the circle.
 Measure of angle formed by the intersection of two tangents at a point outside the circle is the difference of the measures of the intercepted arcs.
 Radii
 Tangent line is perpendicular to a radius of the circle at the point of tangency.
 Combinations of chords, secants, and tangents
 ChordTangent
 Measure of the angle formed by the intersection of a tangent and chord is the measure of the intercepted arc.
 SecantTangent
 Product of the length of a secant segment and its external part is equal to the product of the square of the length of a tangent segment intersecting the secant segment at a point outside the circle.
 Measure of the angle formed by a secant and a tangent intersecting at the same point outside the circle is the difference of the measures of the intercepted arcs.
Note(s):
 Grade Level(s)
 Previous grade levels investigated attributes of geometric figures.
 Grade 8 used informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the AngleAngle criterion for similarity of triangles.
 Geometry introduces analyzing patterns in geometric relationships and making conjectures about geometric relationships which may or may not be represented using algebraic expressions.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 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.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.3. Determine indirect measurements of geometric figures using a variety of methods.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 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.
 VII.C.2. Understand attributes and relationships with inductive and deductive reasoning.

G.12 
Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. The student is expected to:


G.12A 
Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve noncontextual problems.

Apply
THEOREMS ABOUT CIRCLES, INCLUDING RELATIONSHIPS AMONG ANGLES, RADII, CHORDS, TANGENTS, AND SECANTS TO SOLVE NONCONTEXTUAL PROBLEMS
Including, but not limited to:
 Geometric relationships among angles, radii, chords, tangents, and secants
 Measure of the arc is denoted as m.
 Central angle – angle whose vertex is the center of the circle and whose sides are radii of the circle
 Measure of a central angle is equal to the measure of the intercepted arc.
 Inscribed angle – angle whose vertex is on the circle and whose sides are chords of the circle
 Measure of an inscribed angle is the measure of the intercepted arc.
 Inscribed angle with semicircle intercepted arc is a right angle.
 Measure of an inscribed angle is the measure of the central angle that shares the same intercepted arc.
 Radii
 Radius of a circle is perpendicular to a tangent line at the point of tangency.
 Chord of a circle – line segment that joins two points on the circle
 Two chords are congruent if and only if their corresponding intercepting arcs are congruent.
 Diameter of a circle bisects a chord if and only if the diameter and chord are perpendicular.
 Products of the lengths of the segments of intersecting chords are equal.
 Vertical angles formed by intersecting chords are equal in measure.
 Adjacent angles formed by intersecting chords are supplementary.
 Measure of an angle formed by intersecting chords is the sum of the measures of the intercepted arcs.
 Tangent to a circle – line, ray, or line segment perpendicular to the radius and intersecting the circle in exactly one point, the point of tangency
 Intersecting tangent segments are equal in length from the same point outside the circle.
 Measure of angle formed by the intersection of two tangents outside the circle is the difference of the measures of the intercepted arcs.
 Secant to a circle – line, ray, or line segment that intersects the circle in exactly two points
 Product of the length of the secant segment and its external segment is equal to the product of the other secant segment and its external segment from the same point outside the circle.
 Measure of angle formed by two secants intersecting at a point outside the circle is the difference of the measures of the intercepted arcs.
 Combinations of chords, secants, and tangents
 ChordTangent
 Measure of the angle formed by the intersection of a tangent and chord is the measure of the intercepted arc.
 SecantTangent
 Product of the length of a secant segment and its external part is equal to the product of the square of the length of a tangent segment intersecting the secant segment at a point outside the circle.
 Measure of the angle formed by a secant and a tangent intersecting at the same point outside the circle is the difference of the measures of the intercepted arcs.
 Applications to noncontextual mathematical problem situations
 Use of appropriate units of measure
Note(s):
 Grade Level(s)
 Previous grade levels explored characteristics of circles.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 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.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.3. Determine a 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.
 VII.C.2. Understand attributes and relationships with inductive and deductive reasoning.

G.12D 
Describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle.

Describe
RADIAN MEASURE OF AN ANGLE AS THE RATIO OF THE LENGTH OF AN ARC INTERCEPTED BY A CENTRAL ANGLE AND THE RADIUS OF THE CIRCLE
Including, but not limited to:
 Radian measure – ratio of the length of an arc intercepted by a central angle and the radius of the circle
 Comparison of radian measure of a circle and degree measure of a circle
 Generalization of the common conversion factors between degree and radian measure
 Conversions of degrees into radians and radians into degree measures (values in radians can be left in terms of π)
 Radian measure can be described as θ = , where θ is the radian measure of the central angle, ℓ is the length of the arc intercepted by the central angle, and r is the length of the radius of the circle
 Applications of radian measure
Note(s):
 Grade Level(s)
 Geometry lays the foundation for development of radian measurement in Precalculus.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxCCRS
 I.C. Numeric Reasoning – Systems of measurement
 I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.
 I.C.2. Convert units within and between systems of measurement.
 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.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 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.2. Understand attributes and relationships with inductive and deductive reasoning.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 VIII.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.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.

G.12E 
Show that the equation of a circle with center at the origin and radius r is x^{2} + y^{2} = r^{2} and determine the equation for the graph of a circle with radius r and center (h, k), (x  h)^{2} + (y  k)^{2} =r^{2}.

Show
THAT THE EQUATION OF A CIRCLE WITH CENTER AT THE ORIGIN AND RADIUS r: x^{2} + y^{2} = r^{2}
Including, but not limited to:
 Derivation of equation of a circle using the distance formula
Determine
THE EQUATION FOR THE GRAPH OF A CIRCLE WITH RADIUS r AND CENTER (h, k), (x – h)^{2} + (y – k)^{2} = r^{2}
Including, but not limited to:
 General equation for a circle with center (h, k) and radius of length r: (x – h)^{2} + (y – k)^{2} = r^{2}
 Graphs of circles from their equations
 Equations for circles given their graphs
Note(s):
 Grade Level(s)
 Geometry further develops the foundation of conic sections measurement in Precalculus.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxCCRS
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.1. Recognize characteristics and dimensional changes of two and threedimensional figures.
 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.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 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.2. Understand attributes and relationships with inductive and deductive reasoning.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
