Geometry Honors roadmap

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					Geometry Honors
CURRICULUM ROAD MAP
Core Questions
        How is logic used in geometry?
        How can algebra be applied to geometry?
        How can geometry be used to solve real-world problems?
        What relationships hold for figures composed of lines, line segments, or planes?

FIRST QUARTER
UNIT 1                                                                                       BLOCK: 9 periods
How does your point of view affect what you see?                                      TRADITIONAL: 13 periods

KEY CONCEPT                            FOCUS CONTENT                        BENCHMARKS


1. Points, lines, and planes are the   Key Concept 1                        MA.912.G.1.1
   building blocks of geometry.         Points, lines, segments, rays,
                                         planes, and angles                 MA.912.G.2.1
                                        Ruler Postulate, Segment
                                        Addition Postulate                 MA.912.G.7.1
                                        Congruent segments
                                        Distinguishing between             MA.912.G.8.6
                                         sketching, drawing, and
                                         constructing geometric figures     LA.1112.1.6.1
                                        Constructing congruent segments
                                         using a straightedge and compass   LA.1112.1.6.2
                                         or a drawing program
                                        Characterization in Flatland       LA.1112.1.6.5

2. If you know the coordinates of      Key Concept 2
    the endpoints of a segment, you     Midpoint formula
    can find its length and the         Distance formula
    coordinates of its midpoint.

3. There are important                 Key Concept 3
   relationships between some
                                        Protractor Postulate and Angle
   pairs of angles.
                                        Addition Postulate
                                        Constructing congruent angles
                                         and angle bisectors using a
                                         straightedge and compass or a
                                         drawing program
                                        Complementary, supplementary,
                                         and vertical angles


CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 1
UNIT PERFORMANCE ASSESSMENT: Students will work in groups to design a tri-fold brochure about a concept
studied in the unit, and then they will present their brochures to the class.




Geometry Honors         ROADMAP
UNIT 2                                                                                         BLOCK: 12 periods
What does it mean to say, “I proved it”?                                                 TRADITIONAL: 18 periods

KEY CONCEPT                             FOCUS CONTENT                          BENCHMARKS


1. Some versions of a conditional       Key Concept 1                          MA.912.D.6.1
    statement are equivalent to each     Conditional statements
    other and some are not.              Converse, inverse, and               MA.912.D.6.2
                                          contrapositive of conditional
                                          statements                           MA.912.D.6.3
                                         Equivalent statements
                                         Biconditionals                       MA.912.G.8.1

2. Conjectures are often based on       Key Concept 2                          MA.912.G.1.2
   inductive reasoning, can be           Inductive reasoning and
   disproved with one                    counterexamples                      MA.912.G.1.3
   counterexample, and can be            Deductive reasoning
   proved with deductive reasoning.      Proving statements about             MA.912.G.2.2
                                          segments and angles
                                                                               MA.912.G.8.5
3. Special pairs of angles are formed   Key Concept 3
   when a transversal intersects         Parallel and perpendicular lines     LA.1112.1.6.1
   coplanar lines.
                                         Special pairs of angles formed by
                                          coplanar lines and transversals      LA.1112.1.6.5
                                         Using postulates and theorems
                                          about the pairs of angles formed
                                          by parallel lines and transversals
                                         Distinguishing between
                                          postulates and theorems
                                         Constructing parallel and
                                          perpendicular lines (including
                                          perpendicular bisectors) using a
                                          straightedge and compass or a
                                          drawing program
                                         Explaining and justifying the
                                          process used to construct parallel
                                          lines


CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 2 and 3
UNIT PERFORMANCE ASSESSMENT: Students will use logical reasoning and knowledge of parallel lines to
investigate a series of school vandalism incidents.




2                                                                               MANATEE CORE CURRICULUM
SECOND QUARTER
UNIT 3                                                                                       BLOCK: 7 periods
What does it mean for two objects or ideas to be congruent?                           TRADITIONAL: 10 periods

KEY CONCEPT                           FOCUS CONTENT                         BENCHMARKS


1. You can classify and describe      Key Concept 1                         MA.912.G.2.3
    triangles in several different     Classifying triangles
    ways.                              Proving and applying the Triangle   MA.912.G.4.1
                                        Sum Theorem
                                       Triangle Exterior Angle Theorem     MA.912.G.4.4

                                                                            MA.912.G.4.6
2. You can use SSS and SAS to prove   Key Concept 2
    two triangles are congruent.       Corresponding parts of              LA.1112.1.6.1
                                        congruent triangles
                                       SSS and SAS Congruency              LA.1112.1.6.5
                                        Postulates
                                       Real-world problems involving
                                        triangle congruency
                                       Constructing triangles
                                       Explaining and justifying
                                        constructions

3. You can use ASA, AAS, and HL to    Key Concept 3
    prove that two triangles are       ASA, AAS, and HL Congruency
    congruent.                          Theorems
                                       Properties of isosceles and
                                        equilateral triangles



CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 4
UNIT PERFORMANCE ASSESSMENT: Students will use postulates and theorems about triangles and triangle
congruence to solve problems related to creating bridges to cross waters in Manatee County.




Geometry Honors ROADMAP                                                                                    3
UNIT 4                                                                                       BLOCK:7 periods
What are the relationships within triangles?                                         TRADITIONAL: 10 periods

KEY CONCEPT                             FOCUS CONTENT                      BENCHMARKS


1. Most triangles have more than        Key Concept 1                      MA.912.D.6.4
   one center.                           Perpendicular bisectors and
                                          circumcenters                    MA.912.G.4.2
                                         Angle bisectors and incenters
                                         Medians and centroids            MA.912.G.4.5
                                         Altitudes and orthocenters
2. You can use theorems about                                              MA.912.G.4.7
   inequalities in triangles to solve   Key Concept 2
   problems.                             Inequalities in one triangle     LA.1112.1.6.1
                                         Triangle Inequality Theorem
                                         Hinge Theorem and its converse   LA.1112.1.6.5
                                         Indirect proof




CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 5
UNIT PERFORMANCE ASSESSMENT: Students will make a mobile out of balanced triangles and then answer
questions about their mobiles using theorems about triangle inequalities.




4                                                                           MANATEE CORE CURRICULUM
UNIT 5                                                                                              BLOCK:8 periods
What does it mean to belong to the family of quadrilaterals?                                TRADITIONAL: 12 periods

KEY CONCEPT                              FOCUS CONTENT                           BENCHMARKS


1. Quadrilaterals are named,             Key Concept 1                           MA.912.G.3.1
   described, and classified based on     Defining and classifying
   the relative lengths of their sides     quadrilaterals                        MA.912.G.3.2
   and the measures of their angles.      Exploring the hierarchy of
                                           Quadrilaterals                        MA.912.G.3.3

                                                                                 MA.912.G.3.4
2. You can use ordinary proofs and       Key Concept 2
   coordinate geometry proofs to          Examining the properties of           MA.912.G.4.8
   prove properties of                     parallelograms
   parallelograms.                        Proving quadrilaterals are            LA.1112.1.6.1
                                           parallelograms
                                          Using coordinate geometry to          LA.1112.1.6.5
                                           prove properties of congruent,
                                           regular, and similar quadrilaterals


3. You can use ordinary proofs and       Key Concept 3
   coordinate geometry proofs to          Examining the properties of
   prove properties of rhombi,             rhombi, rectangles, squares,
   rectangles, squares, trapezoids,        trapezoids, and kites
   and kites.                             Comparing and contrasting
                                           special quadrilaterals on the basis
                                           of their properties
                                          Using coordinate geometry to
                                           prove properties of congruent,
                                           regular, and similar quadrilaterals

CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 6
UNIT PERFORMANCE ASSESSMENT: Students will draw from several resources in order to compile a collection of
images of quadrilaterals in the real world. Students will use these images to illustrate and prove the properties of
quadrilaterals.



Unit 5 will continue into the Third Quarter




Geometry Honors ROADMAP                                                                                                5
THIRD QUARTER
UNIT 6                                                                                         BLOCK:5 periods
How can polygons, transformations, and tessellations be used to produce works of art?   TRADITIONAL: 8 periods

KEY CONCEPT                           FOCUS CONTENT                         BENCHMARKS


1. The sum of the measures of the     Key Concept 1                         MA.912.D.9.3
   interior angles of a polygon        Convex, concave, regular, and
   depends on its number of sides,      irregular polygons                  MA.912.G.2.4
   but the sum of the measures of      Measures of the interior angles
   its exterior angles does not.        of regular and irregular polygons   MA.912.G.2.6
                                       Sums of the measures of the
                                        exterior angles of polygons         LA.1112.1.6.1
                                       Applications of properties of
                                        congruent polygons to solve         LA.1112.1.6.5
                                        mathematical or real-world
                                        problems
                                       Tessellations

2. The image of a shape created by    Key Concept 2
   a translation, reflection, or       Translations
   rotation is congruent to the        Reflections
   original shape.                     Rotations
                                       Applications of translations,
                                        reflections, and rotations to
                                        polygons to determine
                                        congruence
3. Line symmetry, rotational          Key Concept 3
   symmetry, and tessellations are
                                       Line symmetry
   used in works of art.
                                       Rotational symmetry




CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 9 (9-1, 9-2, 9-3, 9-4, 9-6, 9-7)
UNIT PERFORMANCE ASSESSMENT: Students will use regular polygons, transformations, and tessellations to
create marketing products.




6                                                                             MANATEE CORE CURRICULUM
UNIT 7                                                                                           BLOCK:6 periods
What does it mean for two objects or ideas to be similar?                                 TRADITIONAL: 9 periods

KEY CONCEPT                               FOCUS CONTENT                        BENCHMARKS


1. You can use AA Similarity              Key Concept 1                        MA.912.D.11.5
   Postulate to prove that two             Corresponding parts of similar
   triangles are similar.                   polygons                           MA.912.G.2.3
                                           Scale factors
                                           AA Similarity Postulate            MA.912.G.2.6
                                           Similar triangles in real-world
                                            problems                           MA.912.G.4.5

2. You can use SSS and SAS                Key Concept 2                        MA.912.G.5.2
    Similarity Theorems to prove           SSS and SAS Similarity Theorems
    that two triangles are similar.        Similar triangles in real-world    MA.912.G.8.3
                                            problems
                                           Midsegment Theorem                 LA.1112.1.6.1

3. Drawing a line through a triangle      Key Concept 3                        LA.1112.1.6.5
    parallel to one side creates           Triangle Proportionality Theorem
    segments with special                   and its converse
    properties.                            Other theorem involving
                                            segments divided proportionally


4. The image of a shape created by        Key Concept 4
    dilation is similar to the original
                                           Dilations
    shape.
                                           Perspective drawings


CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 7 and 9 (9-5).
UNIT PERFORMANCE ASSESSMENT: Students will use similarity to verify methods of creating enlargements. They
will explore pantographs and use dilations to create billboards and business cards for a client.




Geometry Honors ROADMAP                                                                                       7
UNIT 8                                                                                            BLOCK: 8 periods
How can you find the length of a side of a right triangle?                                 TRADITIONAL: 12 periods

KEY CONCEPT                             FOCUS CONTENT                            BENCHMARKS


1. In any right triangle, there is an   Key Concept 1                            MA.912.G.2.3
    important relationship, called       Applying the Pythagorean
    the Pythagorean Theorem,              Theorem and its converse               MA.912.G.5.1
                                         When c < a + b , the triangle is
                                                  2     2    2
    between the lengths of the legs
                                                          2    2    2
    and of the length of the              acute. When c > a + b , the            MA.912.G.5.3
    hypotenuse.                           triangle is obtuse.
                                         Expressing the lengths of the          MA.912.G.5.4
                                          sides of right triangles in terms of
                                          radicals in simplest form and with     MA.912.T.2.1
                                          decimal approximations
                                                                                 LA.1112.1.6.1
2. There are special relationships      Key Concept 2
   between the lengths of the sides      Relationships that exist when the      LA.1112.1.6.5
   of 30°–60°–90° and 45°–45°–90°         altitude is drawn to the
   triangles.                             hypotenuse of a right triangle
                                         Use special right triangles to
                                          solve real-world problems

3. You can use the basic                Key Concept 3
   trigonometric functions to solve      Defining “sine,” “cosine,” and
   real-world problems.                   “tangent,” and using them to
                                          solve real-world problems
                                          (including problems about finding
                                          the height of an object and
                                          problems involving an angle of
                                          elevation and an angle of
                                          depression)

4. You can use the inverse functions    Key Concept 4
   of the basic trigonometric            Defining “inverse sine,” “inverse
   functions to solve real-world          cosine,” and “inverse tangent”
   problems.                              Using the basic trigonometric
                                          functions and their inverses to
                                          solve real-world problems
                                          (including problems about finding
                                          an angle of elevation or an angle
                                          of depression)

5. Vectors need a magnitude and a       Key Concept 5
   direction.                            Vectors


CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 7 (7-4) and 8.
UNIT PERFORMANCE ASSESSMENT: Students will use special right triangles and trigonometric functions to solve
problems related to structures.




8                                                                                 MANATEE CORE CURRICULUM
FOURTH QUARTER
UNIT 9                                                                                             BLOCK:8 periods
What happens to the perimeter and area of a polygon when you enlarge it?                   TRADITIONAL: 12 periods

KEY CONCEPT                             FOCUS CONTENT                           BENCHMARKS


1. You can use formulas for the         Key Concept 1                           MA.912.G.2.5
   area of a rectangle and a             Areas of rectangles and squares
   parallelogram to develop              Areas of parallelograms and           MA.912.G.2.7
   formulas for the areas of other        triangles
   polygons, circles, and sectors of     Areas of trapezoids and               MA.912.G.6.2
   circles.                               rhombuses
                                         Areas of regular polygons             MA.912.G.6.4
                                         Using properties of congruent
                                          and similar triangles to solve        MA.912.G.6.5
                                          problems involving areas
                                         Meaning of circle, radius,            LA.1112.1.6.1
                                          diameter, circumference
                                         Finding the circumference of a        LA.1112.1.6.5
                                          circle
                                         Finding the area of a circle and
                                          sectors of a circle

2. The ratio of the perimeters of       Key Concept 2
   similar polygons is equal to the      Perimeters of rectangles,
   scale factor (similarity ratio) of     squares, and other polygons
   the polygons and the ratio of
                                         Using properties of congruent
   their areas is a2:b2, where a:b is
                                          and similar triangles to solve
   the scale factor.
                                          problems involving lengths and
                                          areas
                                         Relationship of the perimeters of
                                          similar figures
                                         Relationship of the areas of
                                          similar figures
                                         Determining how changes in
                                          dimensions affect the perimeter
                                          and area of rectangles when one
                                          dimension is scaled up but the
                                          other one is not

CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 10.
UNIT PERFORMANCE ASSESSMENT: Students will find the amount of baseboard and the amount of carpeting
needed for rooms of various shapes and find the cost for those materials. Students will use a scale factor to find
the perimeter and area of a room that is an enlargement of one of the original rooms.




Geometry Honors ROADMAP                                                                                              9
UNIT 10                                                                                          BLOCK:8 periods
What are the relationships between two-dimensional and three dimensional figures?        TRADITIONAL: 12 periods

KEY CONCEPT                             FOCUS CONTENT                          BENCHMARKS


1. You can describe polyhedra in        Key Concept 1                          MA.912.G.7.2
   terms of their faces, vertices and    Cutting out the net for various
   edges.                                 polyhedra, cones, and cylinders;     MA.912.G.7.3
                                          then folding, and taping to model
                                          the polyhedron                       MA.912.G.7.5
                                         Sketching the net for a given
                                          polyhedron and vice versa            MA.912.G.7.6
                                         Describing and making regular,
                                          non-regular, and oblique             MA.912.G.7.7
                                          polyhedra
                                         The relationship between the         LA.1112.1.6.1
                                          number of faces, edges, and
                                          vertices of polyhedra (Euler’s       LA.1112.1.6.5
                                          formula)

2. Most formulas for the volume of      Key Concept 2
   a three-dimensional solid are         Spheres; chords, tangents, radii,
   based on the formula V = Bh,           and great circles of spheres
   where B is the base of the solid      Volume of prisms, cylinders,
   and h is its height.                   pyramids, cones, and spheres
                                         Identifying and using properties
                                          of congruent three-dimensional
                                          solids

3. The formulas for the surface         Key Concept 3
   areas and lateral areas of prisms,    Surface area of prisms, cylinders,
   cylinders, pyramids, and cones         pyramids, cones, and spheres
   are based on the formulas for         Lateral area of prisms, pyramids,
   the area of polygons and circles.      cylinders, and cones.

                                        Key Concept 4
4. The ratio of the surface areas of
                                         Determining how changes in
   similar solids is a2:b2, and the
                                          dimensions affect the surface
   ratio of their volumes is a3:b3,
                                          area and volume of common
   where a:b is the scale factor
                                          three-dimensional geometric
   (similarity ratio) of the solids.
                                          solids
                                         Relationship of the surface areas
                                          of similar three-dimensional
                                          solids
                                         Relationship of the volumes of
                                          similar three-dimensional solids

CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 11.
UNIT PERFORMANCE ASSESSMENT: Students will make and describe several polyhedra representing real-world
objects and make and check predictions about the surface area and volume of the polyhedra.




10                                                                               MANATEE CORE CURRICULUM
UNIT 11                                                                                         BLOCK:5 periods
How can you describe circles and the angles created by chords, secants, and tangents?    TRADITIONAL: 8 periods

KEY CONCEPT                           FOCUS CONTENT                           BENCHMARKS


1. Angles drawn through or            Key Concept 1                           MA.912.G.6.1
   alongside circles divide them in    Meaning of arc, arc length, chord,
   different ways.                      secant, tangent, concentric           MA.912.G.6.3
                                        circles
                                       Finding arc length                    MA.912.G.6.6
                                       Using the definition of the
                                        measure of an arc in terms of the     MA.912.G.6.7
                                        measure of its central angle
                                       Using the relationship between        LA.1112.1.6.1
                                        the measure of an inscribed
                                        angle and the arc it intercepts       LA.1112.1.6.5
                                       Using the relationships between
                                        the measures of angles created
                                        by intersections of tangents and
                                        secants and the arcs they
                                        intercept

                                      Key Concept 2
2. You can use the Pythagorean         Given the center and the radius
   Theorem to find the equation of      of a circle, sketch the graph of
   any circle.                          the circle
                                       Given the equation of a circle in
                                        center-radius form, sketch the
                                        graph of the circle
                                       Given the center and the radius,
                                        find the equation of a circle in
                                        the coordinate plane
                                       Given the equation of a circle in
                                        center-radius form, state the
                                        center and the radius of the circle
                                       Finding the locus
CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 12.
UNIT PERFORMANCE ASSESSMENT: Students will complete a project about the geometry in the world around
them by drawing on what they have learned throughout the course.




Geometry Honors ROADMAP                                                                                     11

				
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