Download M/J Mathematics 1 2002050

Geometry Honors (High School)
Course 1206320
Year at a Glance
Holt McDougal
Larson Geometry
Throughout the year, students will relate new vocabulary to familiar words, listen to, read, and discuss familiar and conceptually challenging text and will use new
vocabulary that is introduced and taught directly. (LA.910.1.6.1, 6.2, 6.5 and LA.1112.1.6.1, 6.2, 6.5)
Students will also use a variety of problem solving strategies and will apply these skills using axioms and theorems in writing proofs. (MA.912.G.8.1 through 8.6)
First Quarter
Chapter 1
Body of Knowledge: Geometry
Standard 1: Points, Lines, Angles, and
Planes
MA.912.G.1.1
MA.912.G.2.1, 2.7
Building Blocks of Geometry
A. Defining point, line, angle, ray, plane
B. Segments and their measures
C. Angles and their measures
D. Segment and angle bisectors
E. Introduction to perimeter,
circumference and area
Chapter 2
Body of Knowledge: Discrete
Mathematics
Standard 6: Logic
MA.912.D.6.1, 6.2, 6.4
Body of Knowledge: Geometry
Standard 4: Triangles
MA.912.G.4.5
Reasoning and Proof In Geometry
A. Inductive reasoning
B. Deductive reasoning
C. Conditional statements
D. Reasoning with properties of Algebra
E. Proving theorems
F. Planning a proof
Chapter 3
Body of Knowledge: Geometry
Standard 1: Points, Lines, Angles, and
Planes
MA.912.G.1.2, 1.3
Perpendicular and Parallel Lines
A. Lines and angles
B. Parallel and transversals
C. Proving lines and parallel
D. Lines in the coordinate plane
Second Quarter
Chapter 4
Body of Knowledge: Geometry
Standard 2: Polygons
MA.912.G.2.2, 2.6
Standard 4: Triangles
MA.912.G.4.1, 4.3
Congruent Triangles
A. Triangles and angles
B. Triangle inequality
C. Proving triangles are congruent
D. Applications in the real-world
Similarity
A. Use properties of similar triangles
B. Apply segment divided proportionally
theorems
C. Prove triangles are similar
Body of Knowledge: Geometry
Chapters 5 and 6
Body of Knowledge: Discrete
Mathematics
Standard 6: Logic
MA.912.D.6.3, 6.4
Body of Knowledge: Geometry
Standard 1: Points, Lines, Angles, and
Planes
MA.912.G.1.2
Standard 8: Mathematical Reasoning
and Problem Solving
MA.912.G.8.1 through 8.6 (on-going)
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Standard 4: Triangles
MA.912.G.2.3,4.2,4.3, 4.4, 4.6, 4.7
Properties of triangles
A. Medians, altitudes midsegment
B. Perpendiculars and bisectors
C. Inequalities in triangles
D. Construction of angles
E. Inequality theorems
NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Standard 2: Polygons
MA.912.G.2.4, 2.6
Transformations
A. Transformations
B. Reflections
C. Rotations
D. Translations
Geometry Honors (High School)
Course 1206320
Third Quarter
Chapter 7
Body of Knowledge: Geometry
Standard 5: Right Triangle
MA.912.G.5.1 through 5.4
Body of Knowledge: Trigonometry
Standard 2: Trigonometry of Triangles
MA.912.T.2.1
Right Triangles & Trigonometry
A. Pythagorean theorem and converse
B. Special right triangles
C. Similarity in right triangles
D. Right triangle trig ratios
E. Law of sines and cosines
F. Solve real-world problems using
trigonometry
Quadrilaterals
A. Polygons
B. Properties of parallelograms
C. Proving quadrilaterals are
parallelograms
D. Rhombuses, rectangles and squares
E. Trapezoids and kites
F. Proving theorems about
quadrilaterals
G. Special quadrilaterals
H. Fibonacci sequence and golden ratio
(Ch 6.3)
I. Similarity (Ch 6.3)
Chapters 10 and 11
Body of Knowledge: Geometry
Chapter 8
Body of Knowledge: Discrete
Mathematics
Standard 6: Logic
MA.912.D.6.2, 6.4
Standard 11: Sequences and Series
MA.912D.11.5
Body of Knowledge: Geometry
Standard 2: Polygons
MA.912.G.2.3, 2.5
Standard 3: Quadrilaterals
MA.912.G.3.1 through 3.4
Standard 7: Polyhedra and Other
Solids
MA.912.G.7.4
Holt McDougal
Larson Geometry
Fourth Quarter
Chapters 11 and 12
Chapter 9
Body of Knowledge: Geometry
Body of Knowledge: Geometry
Standard 2: Polygons
MA.912.G.2.5
Standard 2: Polygons
MA.912.G.2.6
Standard 7: Polyhedra and other
Solids
MA.912.G.7.1, 7.2, 7.3, 7.5, 7.6, 7.7
Area and Volume
A. Area of polygons
B. Prisms and cylinders
C. Pyramids and cones
D. Displacement and density
E. Spheres
F. Polyhedrons
G. Cross sections
H. Total surface area
I. Similar solids (Ch11.3)
Standard 4: Triangles
MA.912.G.4.8
.
Standard 6: Circles
MA.912.G.6.1 through 6. 7
Geometry of Circles
A. Arc lengths and area of sectors
B. Ratio of areas
C. Chord properties
D. Tangent properties
E. Arc and angle properties
F. Circumference / diameter ratio
G. Inscribed angles
H. Area and circumference
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Year at a Glance
NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Body of Knowledge: Discrete
Mathematics
Standard 6: Logic
MA.912.D.6.4
Standard 9: Vectors
MA.912.D.9.3
Coordinate Geometry
A. Vectors
B. Midpoint formula(Ch 8)
Geometry Honors (High School)
Course 1206320
Qtr 1
Qtr 2
Qtr 3
YEAR LONG
Qtr 4
MA.912.G.8.1
High
Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms,
definitions, postulates, and theorems.
MA.912.G.8.2
Moderate
Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check,
solving a simpler problem, writing an equation, and working backwards.
MA.912.G.8.3
Moderate
Determine whether a solution is reasonable in the context of the original situation.
MA.912.G.8.4
High
Make conjectures with justifications about geometric ideas. Distinguish between information that supports a
conjecture and the proof of a conjecture.
MA.912.G.8.5
High
Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and
compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and
indirect proofs.
MA.912.G.8.6
High
Perform basic constructions using straightedge and compass, and/or drawing programs describing and
justifying the procedures used. Distinguish between sketching, constructing, and drawing geometric figures.
Week of Explicit
Instruction
Quarter 1
MA.912.G.1.1
Moderate
Find the lengths and midpoints of line segments in two-dimensional coordinate systems.
MA.912.G.1.2
Moderate
Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge
and compass or a drawing program, explaining and justifying the process used.
MA.912.G.1.3
Moderate
Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.
MA.912.G.2.1
High
Identify and describe convex, concave, regular, and irregular polygons.
MA.912.G.2.7
Moderate
Determine how changes in dimensions affect the perimeter and area of common geometric figures.
MA.912.D.6.1
Moderate
Use truth tables to determine truth values of propositional statements.
MA.912.D.6.2
Moderate
Find the converse, inverse, and contrapositive of a statement
MA.912.D.6.4
Moderate
Use methods of direct and indirect proof and determine whether a short proof is logically valid.
MA.912.G.4.5
Moderate
Apply theorems involving segments divided proportionally.
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REV 11/08/12
NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Year at a Glance
Holt McDougal
Larson Geometry
Text Alignment
Text Alignment
Geometry Honors (High School)
Course 1206320
Week of Explicit
Instruction
Quarter 2
MA.912.G.2.2
Moderate
Determine the measures of interior and exterior angles of polygons, justifying the method used.
MA.912.G.2.6
High
Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform
transformations in the plane.
MA.912.G.4.1
Moderate
Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and
equiangular.
MA.912.G.4.3
High
Construct triangles congruent to given triangles.
MA.912.D.6.3
Moderate
Determine whether two propositions are logically equivalent.
MA.912.D.6.4
Moderate
Use methods of direct and indirect proof and determine whether a short proof is logically valid.
MA.912.G.1.2
Moderate
Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge
and compass or a drawing program, explaining and justifying the process used.
MA.912.G.2.3
High
Use properties of congruent and similar polygons to solve mathematical or real-world problems.
MA.912.G.4.2
Moderate
Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors,orthocenter, centroid,
incenter, and circumcenter.
MA.912.G.4.3
High
Construct triangles congruent to given triangles.
MA.912.G.4.4
Moderate
Use properties of congruent and similar triangles to solve problems involving lengths and areas.
MA.912.G.4.6
High
Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.
MA.912.G.4.7
Moderate
Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge theorem.
MA.912.G.2.4
High
Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine
congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are
congruent to the original shape. Create and verify tessellations of the plane using polygons.
MA.912.G.2.6
High
Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform
transformations in the plane.
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REV 11/08/12
NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Year at a Glance
Holt McDougal
Larson Geometry
Text Alignment
Geometry Honors (High School)
Course 1206320
Week of Explicit
Instruction
Quarter 3
MA.912.G.5.1
High
Prove and apply the Pythagorean theorem and its converse.
MA.912.G.5.2
Moderate
State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.
MA.912.G.5.3
Moderate
Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems.
MA.912.G.5.4
High
Solve real-world problems involving right triangles.
MA.912.T.2.1
Moderate
Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right
triangles.
MA.912.D.6.3
Moderate
Determine whether two propositions are logically equivalent.
MA.912.D.6.4
Moderate
Use methods of direct and indirect proof and determine whether a short proof is logically valid.
MA.912.D.11.5
High
Explore and use other sequences found in nature such as the fibonacci sequence and the golden ratio.
MA.912.G.2.3
High
Use properties of congruent and similar polygons to solve mathematical or real-world problems.
MA.912.G.2.5
Moderate
Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons,
etc.).
MA.912.G.3.1
Moderate
Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus,
parallelogram, trapezoid, and kite.
MA.912.G.3.2
Moderate
Compare and contrast special quadrilaterals on the basis of their properties.
MA.912.G.3.3
High
Use coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals.
MA.912.G.3.4
High
Prove theorems involving quadrilaterals.
MA.912.G.7.4
Low
Identify chords, tangents, radii, and great circles of spheres
MA.912.G.6.1
High
Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them.
Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons.
MA.912.G.6.2
Low
Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.
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NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Year at a Glance
Holt McDougal
Larson Geometry
Text Alignment
Geometry Honors (High School)
Course 1206320
MA.912.G.6.4
Moderate
Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and
tangents).
MA.912.G.6.5
High
Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.
MA.912.G.6.6
Moderate
Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in
center-radius form, state the center and the radius of the circle.
MA.912.G.6.7
Moderate
Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of
the circle.
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NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Year at a Glance
Holt McDougal
Larson Geometry
Geometry Honors (High School)
Course 1206320
Week of Explicit
Instruction
Quarter 4
MA.912.G.2.5
Moderate
Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons,
etc.).
MA.912.G.7.1
Moderate
Describe and make regular, non-regular, and oblique polyhedra, and sketch the net for a given polyhedron and vice
versa.
MA.912.G.7.2
Moderate
Describe the relationships between the faces, edges, and vertices of polyhedra.
MA.912.G.7.3
Moderate
Identify, sketch, find areas and/or perimeters of cross sections of solid objects.
MA.912.G.7.5
Moderate
Explain and use formulas for lateral area, surface area, and volume of solids.
MA.912.G.7.6
Moderate
Identify and use properties of congruent and similar solids.
MA.912.G.7.7
Moderate
Determine how changes in dimensions affect the surface area and volume of common geometric solids.
MA.912.G.2.6
High
Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform
transformations in the plane.
MA.912.G.4.8
High
Use coordinate geometry to prove properties of congruent, regular, and similar triangles.
MA.912.D.6.4
Moderate
MA.912.D.9.3
High
Use methods of direct and indirect proof and determine whether a short proof is logically valid.
Use vectors to model and solve application problems.
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REV 11/08/12
NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Year at a Glance
Holt McDougal
Larson Geometry
Text Alignment