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HISD SCOPE AND SEQUENCEGeometry

1st Cycle 28 Days The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.Aug. 25 – Oct. 2, 2014

Unit # Class Periods

2014-2015 Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)

The student will:


The student will:

Unit 1: Geometry Foundations with Algebra ConnectionsStudents explore geometry topics in connections with algebraic expressions and equations.

2 class periods

(90-minutes each)

or4 class periods

(45-minutes each)

GEOM.1A Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems to verify statements. Ⓢ GEOM.3E Use deductive reasoning to prove a statement.

Ⓢ GEOM.7A Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures.

Ⓡ GEOM.7C Derive and use formulas involving horizontal, vertical, and oblique distances, slope, and midpoint and use in context to applications of distance and midpoint formulas.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1E Create and use representations to organize,

record, and communicate mathematical ideas. GEOM.1F Analyze mathematical relationships to connect

and communicate mathematical ideas.

Coordinate and Transformational GeometryThe student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures. GEOM.2A Determine the coordinates of a point that is a

given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint. [aligns to current GEOM.7A]

GEOM.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. [aligns to current GEOM.7C]

Logical Argument and ConstructionsThe student uses the process skills with deductive reasoning to understand geometric relationships. GEOM.4A Distinguish between undefined terms, definitions,

postulates, conjectures, and theorems. [aligns to current GEOM.1A]

Proof and Congruence

- Aligned to Upcoming State Readiness Standard - State Process Standard Ⓡ - State Readiness Standard Ⓢ - State Supporting Standard© Houston ISD Curriculum 2014 – 2015

Page 1 of 32Last Updated: June 25, 2014





The student will:


The student will:

The student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart. GEOM.6A Verify theorems about angles formed by the

intersection of lines and line segments, including vertical angles, angles formed by parallel lines cut by a transversal, and prove equidistance between the endpoints of a segment and points on its perpendicular bisector, and apply these relationships to solve problems. [aligns to current GEOM.3E]

Unit 2: Parallel and Perpendicular Lines Students analyze relationships among lines that are parallel, perpendicular, or skew and then apply properties of linear equations to parallel and perpendicular lines.

4 class periods

(90-minutes each)

or8 class periods

(45-minutes each)

Part 1: Relationships of Lines 4 (45-min) class periodsⓈ GEOM.2A Apply constructions to explore attributes of geometric figures and to make conjectures about geometric relationships by copying an angle and a segment using various construction techniques such as paper folding, computer programs, compass, and straightedge.Ⓢ GEOM.3A Determine the validity of a conditional statement, its converse, inverse, and contrapositive using everyday situations and geometric properties that have been developed.Ⓢ GEOM.3D Use inductive reasoning by collecting information and finding patterns to formulate conjectures.

Ⓡ GEOM.5A Analyze numeric and geometric patterns to develop algebraic expressions representing geometric properties.

Ⓢ GEOM.5B Analyze numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1D Communicate mathematical ideas, reasoning,

and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. [aligns to current GEOM.4A]


given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint. [aligns to current







The student will:


The student will:

Ⓢ GEOM.7A Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. Ⓢ GEOM.9A Formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models, recognizing when two lines are parallel, perpendicular, skew, or intersecting.

GEOM.7A]

Logical Arguments and ConstructionsThe student uses the process skills with deductive reasoning to understand geometric relationships. GEOM.4B Identify and determine the validity of the

converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse. [aligns to current GEOM.3A]

Logical Arguments and ConstructionsThe student uses constructions to validate conjectures about geometric figures. GEOM.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. [aligns to current GEOM.3D and GEOM.5B]

GEOM.5B Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge. [aligns to current GEOM.2A]

GEOM.5C Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships. [aligns to current GEOM.2A]







The student will:


The student will:

Proof and CongruenceThe student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart. GEOM.6A Verify theorems about angles formed by the

intersection of lines and line segments, including vertical angles, angles formed by parallel lines cut by a transversal, and prove equidistance between the endpoints of a segment and points on its perpendicular bisector, and apply these relationships to solve problems. [aligns to current GEOM.9A]

Part 2: Equations of Parallel and Perpendicular Lines4 (45-min) Class Periods

Ⓡ GEOM.2B Make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.


Ⓡ GEOM.7B Apply slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons.



and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.


given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate







The student will:


The student will:

Ⓢ GEOM.9A Formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models, recognizing when two lines are parallel, perpendicular, skew, or intersecting.

systems, including finding the midpoint. [aligns to current GEOM.7A]

GEOM.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. [aligns to current GEOM.7B and GEOM.7C]

GEOM.2C Determine an equation of a line parallel or perpendicular to a given line that passes through a given point. [aligns to current GEOM.7B]


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. [aligns to current GEOM.2B]


intersection of lines and line segments, including vertical angles, angles formed by parallel lines cut by a transversal, and prove equidistance between the endpoints of a segment







The student will:


The student will:

and points on its perpendicular bisector, and apply these relationships to solve problems. [aligns to current GEOM.9A]

Unit 3: Triangle Properties and CongruenceStudents apply and make conjectures about triangle properties and triangle congruence.

5 class periods

(90-minutes each)

or10 class periods

(45-minutes each)

Part 1: Generalizations About Triangles5 (45-min) class periods

Ⓡ GEOM.2B Make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. Ⓢ GEOM.3D Use inductive reasoning by collecting information and finding patterns to formulate conjectures. Ⓢ GEOM.3E Use deductive reasoning to prove a statement.

Ⓢ GEOM.4A Select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) that may be translated from a verbal description in order to solve problems.

Ⓢ GEOM.5B Analyze numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles. Ⓡ GEOM.10B Justify and apply triangle congruence relationships in proofs including flow proofs, transformational proofs, paragraph proofs, coordinate proofs, and two-column proofs.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.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.

GEOM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. [aligns to current GEOM.4A]


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. [aligns to current GEOM.2B GEOM.3D, and GEOM.5B]








The student will:


The student will:

The student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart. GEOM.6A Verify theorems about angles formed by the


GEOM.6B Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions. [aligns to current GEOM.3E and GEOM.10B]

GEOM.6C Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles. [aligns to current GEOM.10B]

Part 2: Triangle Proofs 5 (45-min) class periodsGEOM.1A Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems to verify statements.

Ⓡ GEOM.3C Use logical reasoning and several methods of proof (flow proofs, transformation proofs, coordinate proofs, and two-column proofs) to prove statements are true, and find counter- examples to disprove statements that are false.Ⓢ GEOM.3E Use deductive reasoning to prove a statement.



GEOM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations,







The student will:


The student will:

including symbols, diagrams, graphs, and language as appropriate.



GEOM.4C Verify that a conjecture is false using a counterexample. [aligns to current GEOM.3C]



GEOM.6B Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions. [aligns to current GEOM.3E]




2nd Cycle 25 Days The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.Oct 6 – Nov. 7, 2014

Units # Class Periods


The student will:


The student will:

Unit 4: Triangle Relationships (Constructions)Students perform triangle constructions in order to analyze their attributes.

2 class periods

(90-minutes each)

or4 class periods

(45-minutes each)

Ⓢ GEOM.2A Apply constructions to explore attributes of geometric figures and to make conjectures about geometric relationships by copying an angle and a segment using various construction techniques such as paper folding, computer programs, compass, and straightedge.Ⓡ GEOM.2B Make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.Ⓢ GEOM.3B Construct and justify statements about geometric figures including triangles, quadrilaterals, regular polygons, and circles, and their properties. Ⓢ GEOM.3E Use deductive reasoning to prove a statement.

Ⓢ GEOM.7A Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. Ⓡ GEOM.7B Apply slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons.


GEOM.9B Ⓢ Formulate and test conjectures about the properties and attributes of polygons and their component parts, including diagonals, interior and exterior angles, sides, and vertices, based on explorations and concrete models.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1F Analyze mathematical relationships to connect



given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint. [aligns to current GEOM.7A]

GEOM.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. [aligns to current GEOM.7C]

Coordinate and Transformational GeometryThe student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). GEOM.3D Identify and distinguish between reflectional and

rotational symmetry in a plane figure.







The student will:


The student will:



GEOM.5B Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge. [aligns to GEOM.2A]

GEOM.5C Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships. [aligns to GEOM.2A and GEOM.3B]

GEOM.5D Verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems. [aligns to GEOM.3B]

Proof and CongruenceThe student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart.







The student will:


The student will:

GEOM.6D Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians and apply these relationships to solve problems. [aligns to current GEOM.9B]

GEOM.6E prove a quadrilateral is a parallelogram, rectangle, square or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems. [aligns to current GEOM.9B]

Unit 5:TransformationsStudents apply transformations to various geometric figures and make conjectures about coordinate notation after a transformation.

5 class periods

(90-minutes each)

or10 class periods

(45-minutes each)

Ⓡ GEOM.2B Make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

GEOM.5C Ⓢ Apply properties of transformations: reflections, translations, rotations, and glide reflections to make connections between mathematics and the real world, such as tessellations.


Ⓢ GEOM.10A Use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane.

Ⓢ GEOM.11B Apply ratios to solve problems involving similar figures.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1A Apply mathematics to problems arising in

everyday life, society, and the workplace. GEOM.1D Communicate mathematical ideas, reasoning,



given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint. [aligns to current







The student will:


The student will:

GEOM.7A]

Coordinate and Transformational GeometryThe student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). GEOM.3A Describe and perform transformations of figures

in a plane using coordinate notation. [aligns to current GEOM.10A]

GEOM.3B Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane. [aligns to current GEOM.10A]

GEOM.3C Identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane. [aligns to current GEOM.5C and GEOM.10A]


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







The student will:


The student will:

variety of tools. [aligns to current GEOM.2B]

Similarity, Proof, and TrigonometryThe student uses the process skills in applying similarity to solve problems. GEOM.7A Apply the definition of similarity in terms of a

dilation to identify similar figures and their proportional sides and the congruent corresponding angles. [aligns to current GEOM.11B]

GEOM.7B Apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems. [aligns to current GEOM.11B]

Unit 6:Quadrilaterals and PolygonsStudents examine the properties of various quadrilaterals and polygons using algebraic, concrete, and geometric methods.(continued in cycle 3)

3 of 5 class

periods (90-

minutes each)

or6 of 10 class

periods (45-

minutes each)





GEOM.9B Ⓢ Formulate and test conjectures about the properties and attributes of polygons and their component parts, including diagonals, interior and exterior angles, sides, and

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1G Display, explain, and justify mathematical

ideas and arguments using precise mathematical language in written or oral communication.

Coordinate and Transformational GeometryThe student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures. GEOM.2B Derive and use the distance, slope, and midpoint

formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity







The student will:


The student will:

vertices, based on explorations and concrete models. of pairs of lines. [aligns to current GEOM.7B] GEOM.2C Determine an equation of a line parallel or

perpendicular to a given line that passes through a given point. [aligns to current GEOM.7B]

Coordinate and Transformational GeometryThe student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). GEOM.3C Identify the sequence of transformations that will

carry a given pre-image onto an image on and off the coordinate plane. [aligns to current GEOM.5C]










The student will:


The student will:

The student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart. GEOM.6D Verify theorems about the relationships in

triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians and apply these relationships to solve problems. [aligns to current GEOM.9B]





3rd Cycle 27 Days The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.Nov. 10 – Dec. 19, 2014



The student will:


The student will:

Unit 6 (continued):Quadrilaterals and PolygonsStudents examine the properties of various quadrilaterals and polygons using algebraic, concrete, and geometric methods.

2 of 5 class

periods (90-

minutes each)

or4 of 10 class

periods (45-

minutes each)





GEOM.9B Ⓢ Formulate and test conjectures about the properties and attributes of polygons and their component parts, including diagonals, interior and exterior angles, sides, and vertices, based on explorations and concrete models.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1G Display, explain, and justify mathematical ideas

and arguments using precise mathematical language in written or oral communication.

Coordinate and Transformational GeometryThe student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures. GEOM.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. [aligns to current GEOM.7B]

GEOM.2C Determine an equation of a line parallel or perpendicular to a given line that passes through a given point. [aligns to current GEOM.7B]

Coordinate and Transformational GeometryThe student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). GEOM.3C Identify the sequence of transformations that will

carry a given pre-image onto an image on and off the coordinate plane. [aligns to current GEOM.5C]







The student will:


The student will:



Proof and CongruenceThe student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart. GEOM.6D Verify theorems about the relationships in

triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians and apply these relationships to solve problems. [aligns to current GEOM.9B]


Unit 7: 5 class Part 1: Proportionality with Similar Figures Mathematical Process Standards







The student will:


The student will:

SimilarityStudents solve geometric problems involving similarity, proportionality, and dilation.

periods (90-

minutes each)

or10 class periods

(45-minutes each)

5 (45-min) class periodsⓈ GEOM.8F Use conversions between measurement systems to solve problems in real-world situations.

Ⓢ GEOM.11A Use and extend similarity properties and transformations to explore and justify conjectures about geometric figures including identification of corresponding parts of similar figures.

Ⓢ GEOM.11B Apply ratios to solve problems involving similar figures.

Ⓡ GEOM.11C Develop, apply, and justify triangle similarity relationships, such as mean proportional within triangles, trigonometric ratios, Pythagorean triples, and 45-45-90 and 30-60-90 triangles, using a variety of methods.

The student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.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.

Similarity, Proof, and TrigonometryThe student uses the process skills in applying similarity to solve problems. GEOM.7A Apply the definition of similarity in terms of a

dilation to identify similar figures and their proportional sides and the congruent corresponding angles. [aligns to current GEOM.11B]

GEOM.7B Apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems. [aligns to current GEOM.11B]

Similarity, Proof, and TrigonometryThe student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart. GEOM.8A Prove theorems about similar triangles, including

the Triangle Proportionality theorem, and apply these theorems to solve problems [aligns to current GEOM.11A]

GEOM.8B Identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.







The student will:


The student will:

[aligns to current GEOM.11A]

Similarity, Proof, and TrigonometryThe student uses the process skills to understand and apply relationships in right triangles. GEOM.9A Determine the lengths of sides and measures of

angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems. [aligns to current GEOM.11C]

GEOM.9B Apply the relationships in special right triangles (30º-60º-90º and 45º-45º-90º) and the Pythagorean theorem, including Pythagorean triples, to solve problems. [aligns to current GEOM.11C]

Part 2: Proportionality and Dilation 5 (45-min) class periodsGEOM.1A Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems to verify statements. Ⓢ GEOM.2A Apply constructions to explore attributes of geometric figures and to make conjectures about geometric relationships by copying an angle and a segment using various construction techniques such as paper folding, computer programs, compass, and straightedge.

Ⓡ GEOM.5A Analyze numeric and geometric patterns to develop algebraic expressions representing geometric properties. Ⓢ GEOM.11A Use and extend similarity properties and transformations to explore and justify conjectures about geometric figures including identification of corresponding parts

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1G Display, explain, and justify mathematical ideas




Logical Arguments and ConstructionsThe student uses constructions to validate conjectures about







The student will:


The student will:

of similar figures. Ⓡ GEOM.11C Develop, apply, and justify triangle similarity

relationships, such as mean proportional within triangles, trigonometric ratios, Pythagorean triples, and 45-45-90 and 30-60-90 triangles, using a variety of methods.

geometric figures. GEOM.5B Construct congruent segments, congruent angles,

a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge. [aligns to current GEOM.2A]

GEOM.5C Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships. [aligns to current GEOM.2A]

Similarity, Proof, and TrigonometryThe student uses the process skills with deductive reasoning to prove and apply theorems by utilizing a variety of methods such as coordinate, transformational, axiomatic and formats such as two-column, paragraph, flow chart. GEOM.8A Prove theorems about similar triangles, including

the Triangle Proportionality theorem, and apply these theorems to solve problems [aligns to current GEOM.11A]

GEOM.8B Identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems. [aligns to current GEOM.11A]


angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems. [aligns to







The student will:


The student will:

current GEOM.11C] GEOM.9B Apply the relationships in special right triangles

(30º-60º-90º and 45º-45º-90º) and the Pythagorean theorem, including Pythagorean triples, to solve problems. [aligns to current GEOM.11C]

Unit 8: Pythagoras and Special Right TrianglesStudents apply the Pythagorean theorem to various real-world situations and develop a pattern for special right triangles.

4 class periods

(90-minutes each)

or8 class periods

(45-minutes each)

Ⓢ GEOM.1B Recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes. Ⓢ GEOM.3B Construct and justify statements about geometric figures including triangles, quadrilaterals, regular polygons, and circles, and their properties.

GEOM.5D Ⓡ Identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

GEOM.8C Ⓡ Derive, extend, and use the Pythagorean theorem to determine a missing side of a given right triangle and to solve real world problems.

Ⓡ GEOM.11C Develop, apply, and justify triangle similarity relationships, such as mean proportional within triangles, trigonometric ratios, Pythagorean triples, and 45-45-90 and 30-60-90 triangles, using a variety of methods.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1A Apply mathematics to problems arising in

everyday life, society, and the workplace. GEOM.1F Analyze mathematical relationships to connect


Logical Arguments and ConstructionsThe student uses constructions to validate conjectures about geometric figures. GEOM.5C Use the constructions of congruent segments,

congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships. [aligns to GEOM.3B]

GEOM.5D Verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems. [aligns to GEOM.3B]








The student will:


The student will:


GEOM.9B Apply the relationships in special right triangles (30º-60º-90º and 45º-45º-90º) and the Pythagorean theorem, including Pythagorean triples, to solve problems. [aligns to current GEOM.5D and GEOM.11C]

CirclesThe student uses the process skills to understand geometric relationships and apply theorems and equations about circles. GEOM.12E Show that the equation of a circle with center at

the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x – h)2 + (y – k)2 = r2. [aligns to current GEOM.8C]

4th Cycle 28 Days The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.Jan. 6 – Feb. 13, 2015



The student will:


The student will:

Unit 9: Right Triangles and TrigonometryStudents apply properties of triangles to the

4 class periods

(90-minutes each)

or8 class periods

GEOM.5D Ⓡ Identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (30º-60º-90º and 45º-45º-90º) and triangles whose sides are Pythagorean triples.

Ⓡ GEOM.11C Develop, apply, and justify triangle similarity relationships, such as mean proportional within triangles, trigonometric ratios, Pythagorean triples, and 30º-60º-90º and 45º-45º-90º, using a variety of methods.



GEOM.1G Display, explain, and justify mathematical







The student will:


The student will:

study of right-triangle trigonometry.

(45-minutes each)

ideas and arguments using precise mathematical language in written or oral communication.



GEOM.9B Apply the relationships in special right triangles (30º-60º-90º and 45º-45º-90º) and the Pythagorean theorem, including Pythagorean triples, to solve problems. [aligns to current GEOM.5D and GEOM.11C]

Unit 10: Measuring Lengths and AreaStudents concretely and algebraically determine the perimeter and area of various geometric figures or portions of figures.

7 class periods

(90-minutes each)

or14 class periods

(45-minutes each)

Ⓡ GEOM.8A Determine areas of regular polygons, circles, and composite figures using the area of triangles, squares, rectangles, parallelograms, and/or trapezoids.

Ⓢ GEOM.8E Use area models to connect geometry to probability and statistics.Ⓢ GEOM.8F Use conversions between measurement systems to solve problems in real-world situations.

GEOM.11D Describe the effect on perimeter, area,Ⓡ and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.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.

GEOM.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.







The student will:


The student will:

Two-dimensional and Three-dimensional FiguresThe student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. GEOM.10B Determine and describe how changes in the

linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. [aligns to current GEOM.11D]

Two-dimensional and Three-dimensional FiguresThe student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. GEOM.11A Apply the formula for the area of regular

polygons to solve problems using appropriate units of measure [aligns to current GEOM.8A]

GEOM.11B Determine the area of composite two- dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure. [aligns to current GEOM.8A]

Probability The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events. GEOM.13B Determine probabilities based on area to solve

contextual problems. [aligns to current GEOM.8E]




5th Cycle 29 Days The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.Feb. 16 – Apr. 2, 2015



The student will:


The student will:

Unit 11: Surface AreaStudents build and draw three-dimensional figures, deconstruct them to draw a net, and calculate the total and lateral surface areas.

6 class periods

(90-minutes each)

or12 class periods

(45-minutes each)

Ⓢ GEOM.6A Describe and draw various three-dimensional figures and draw the intersection of a given plane with various three-dimensional geometric figures.

Ⓢ GEOM.6B Draw and use nets to represent, construct, and deconstruct three- geometric figures.

Ⓢ GEOM.6C Sketch and use orthographic and isometric views of three-dimensional geometric figures to represent, construct, and deconstruct three-dimensional geometric figures and solve problems.

Ⓡ GEOM.8D Determine surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations using formulas and nets. Ⓢ GEOM.8F Use conversions between measurement systems to solve problems in real-world situations.

Ⓢ GEOM.9D Analyze the characteristics of polyhedra and other three-dimensional figures such as prisms, pyramids, cylinders, cones, and spheres, and their component parts (including vertices, edges, faces, and diagonals), based on explorations and concrete models.

GEOM.11D Describe the effect on Ⓡ perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.


record, and communicate mathematical ideas.

Two-dimensional and Three-dimensional FiguresThe student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. GEOM.10A Identify the shapes of two-dimensional cross-

sections of prisms, pyramids, cylinders, cones, and spheres and identify three- dimensional objects generated by rotations of two-dimensional shapes. [aligns to current GEOM.6A]

GEOM.10B Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. [aligns to current GEOM.11D]

Two-dimensional and Three-dimensional FiguresThe student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. GEOM.11C Apply the formulas for the total and lateral

surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. [aligns to current GEOM.8D]

GEOM.11D Apply the formulas for the volume of three-







The student will:


The student will:

dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. [aligns to current GEOM.8D]

Unit 12: VolumeStudents build and draw three-dimensional figures and calculate the area of the base and volume of a figure. Students also analyze what occurs when the measure of the lengths of one or more dimensions is changed by a scale factor greater than one or less than one.

5.5 class periods

(90-minutes each)

or11 class periods

(45-minutes each)

Ⓢ GEOM.6B Draw and use nets to represent, construct, and deconstruct three- geometric figures.

Ⓢ GEOM.6C Sketch and use orthographic and isometric views of three-dimensional geometric figures to represent, construct, and deconstruct three-dimensional geometric figures and solve problems.

Ⓡ GEOM.8D Determine surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations using formulas and nets.Ⓢ GEOM.8F Use conversions between measurement systems to solve problems in real-world situations.

GEOM.11D Describe the effect onⓇ perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.


record, and communicate mathematical ideas.

Two-dimensional and Three-dimensional FiguresThe student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. GEOM.10B Determine and describe how changes in the

linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. [aligns to current GEOM.11D]

Two-dimensional and Three-dimensional FiguresThe student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. GEOM.11C Apply the formulas for the total and lateral

surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. [aligns to current GEOM.8D]

GEOM.11D Apply the formulas for the volume of three-







The student will:


The student will:

dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. [aligns to current GEOM.8D]




6th Cycle 38 Days The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.Apr. 6 – May 28, 2015



The student will:


The student will:

Unit 13: Circles – Sectors and Arc LengthStudents apply properties of circles to determine the area of a sector and the length of an arc; then they connect area of a sector to creating circle graphs.

3 class periods

(90-minutes each)

or6 class periods

(45-minutes each)

GEOM.8A Ⓡ Determine areas of regular polygons, circles, and composite figures using the area of triangles, squares, rectangles, parallelograms, and/or trapezoids.

GEOM.8B Ⓢ Determine areas of sectors and arc lengths of circles using proportional reasoning.

GEOM.8E Ⓢ Use area models to connect geometry to probability and statistics.



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

Two-dimensional and Three-dimensional FiguresThe student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. GEOM.11A Apply the formula for the area of regular

polygons to solve problems using appropriate units of measure [aligns to current GEOM.8A]

GEOM.11B Determine the area of composite two- dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure. [aligns to current GEOM.8A]

CirclesThe student uses the process skills to understand geometric relationships and apply theorems and equations about circles. GEOM.12B Apply the proportional relationship between the

measure of an arc length of a circle and the circumference of







The student will:


The student will:

the circle to solve problems. [aligns to current GEOM.8B] GEOM.12C Apply the proportional relationship between the

measure of the area of a sector of a circle and the area of the circle to solve problems. [aligns to current GEOM.8B]

GEOM.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. [new content]

Probability The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events. GEOM.13A Develop strategies to use permutations and

combinations to solve contextual problems. [new content] GEOM.13B Determine probabilities based on area to solve

contextual problems. [aligns to current GEOM.8E] GEOM.13C Identify whether two events are independent and

compute the probability of the two events occurring together with or without replacement. [new content]

GEOM.13D Apply conditional probability in contextual problems. [new content]

GEOM.13E Apply independence in contextual problems. [new content]

Unit 14: Circles

6 class periods

GEOM.1C Ⓢ Compare and contrast the structures and implications of Euclidean and non-Euclidean geometries by

Mathematical Process StandardsThe student uses mathematical processes to acquire and







The student will:


The student will:

Students analyze and apply properties of tangents to a circle and the angles and polygons formed within.

(90-minutes each)

or12 class periods

(45-minutes each)

determining that some Euclidean definitions and theorems are not valid in non-Euclidean geometries.Ⓡ GEOM.2B Make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.Ⓢ GEOM.3B Construct and justify statements about geometric figures including triangles, quadrilaterals, regular polygons, and circles, and their properties. Ⓡ GEOM.3C Use logical reasoning and several methods of proof (flow proofs, transformation proofs, coordinate proofs, and two-column proofs) to prove statements are true, and find counter- examples to disprove statements that are false.

GEOM.8B Ⓢ Determine areas of sectors and arc lengths of circles using proportional reasoning.

GEOM.9C Ⓢ Formulate and test conjectures about the properties and attributes of circles, including segments within circles and the lines that intersect the circles, based on explorations and concrete models.

demonstrate mathematical understanding. GEOM.1G Display, explain, and justify mathematical ideas


Logical Argument and ConstructionsThe student uses the process skills with deductive reasoning to understand geometric relationships. GEOM.4C Verify that a conjecture is false using a

counterexample. [aligns to current GEOM.3C] GEOM.4D Compare geometric relationships between

Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle. [aligns to current GEOM.1C]

Logical Argument and ConstructionsThe student uses constructions to validate conjectures about geometric figures. GEOM.5A Investigate patterns to make conjectures about


GEOM.5C Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships.







The student will:


The student will:

[aligns to current GEOM.3B] GEOM.5D Verify the Triangle Inequality theorem using

constructions and apply the theorem to solve problems. [aligns to current GEOM.3B]

CirclesThe student uses the process skills to understand geometric relationships and apply theorems and equations about circles. GEOM.12A Apply theorems about circles, including

relationships among angles, radii, chords, tangents, and secants, to solve non- contextual problems. [aligns to current GEOM.9C]

GEOM.12B Apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems. [aligns to current GEOM.8B]

GEOM.12C Apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems. [aligns to current GEOM.8B]

GEOM.12E Show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x – h)2 + (y – k)2 = r2. [new content]

Unit 15: Bridging Geometry to Algebra IIStudents solve quadratic

3 class periods

(90-minutes each)

or

Ⓢ ALGII.2A Use and apply tools including factoring and properties of exponents to simplify expressions and to transform and solve equations and inequalities.

Ⓡ ALGII.6A Determine the reasonable domain and range values of a quadratic function represented by a table of values, graph, function rule, or a contextual situation, as well as interpret

Mathematical Process StandardsThe student uses mathematical processes to acquire and demonstrate mathematical understanding. GEOM.1G/ ALGII.1G Display, explain, and justify

mathematical ideas and arguments using precise mathematical language in written or oral communication.







The student will:


The student will:

equations through a variety of methods in real-world situations.

6 class periods

(45-minutes each)

and determine the reasonableness of solutions to quadratic equations and inequalities.

Ⓡ ALGII.6B Relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal forms.

Ⓢ ALGII.6C Determine a quadratic function from its roots (real and complex) or a graph.

Ⓢ ALGII.8B Analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula.



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