September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
Course Code 1206320
Course
Category 6-12
Subject Area Mathematics
Course Type Level 3
Course Title Geometry Honors
Course Level 3
Course Length Full year
Credit
Description 1
Abbreviated
Title Geometry Honors
RELATED BENCHMARKS (40) :
These Benchmarks should be infused throughout the course.
LA.910.1.6.1 The student will use new vocabulary that is introduced and taught directly;
LA.910.1.6.2 The student will listen to, read, and discuss familiar and conceptually challenging text;
LA.910.1.6.5 The student will relate new vocabulary to familiar words;
Paraphrases vocabulary words to give definitions back in their own
LA.1112.1.6.1 words
LA.1112.1.6.2 Uses vocabulary to solve sample problems
These topics are to be taught during the first semester; supplemented as Bell Work or FCAT Practice.
Probability and Statistics
A. Specify sample spaces and events.
B. Find the probability that an event will occur and odds of event
C. Recognize and analyze frequency distributions.
D. Work with histograms.
E. Find mean, median, mode, and range.
F. Construct stem and leaf plots, box and whisker plots
G. Identify misuse of statistics.
Algebra
A. Equivalent forms of numbers
B. Effects of operations on numbers
Draft Overview / FCAT
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
C. Relative size of numbers
D. Algebraic expressions, equations and inequalities
E. Systems of linear equations and inequalities
F. Quadratic Formula
G. Interpret data in charts, tables, and plots
H. Desribes realtionships, patterns and functions
Ratio, Proportion & Percent Problems
Scientific Notation
Direct Variation
Venn Diagrams and Unions and Intersections
Draft Overview / FCAT
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
Completed During Quarter 1
Focus: Points, Lines, Planes, and Angles
Benchmarks:
Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a
MA.912.G.1.2
straight edge and compass or a drawing program, explaining and justifying the process
Identify and give examples of: indefined terms, axioms, theorems, inductive and proofs and inductive and
MA.912.D.6.5
deductive reasoning
Content Sections
A. Understand the terms equidistant, points and line.Sketch points and lines. 1-1
B. Understand the undefined terms point, line, plane, and defined terms collinear, coplanar and
1-2
intersection. Sketch points, lines and planes.
C. Use segment and ruler postulates. Use the distance formula to measure distances 1-3
Approximately D. Use angle postulates. Classify angles as acute, right, obtuse, or straight. And find their measures 1-4
8days E. Use postulates and theorems relating points, lines and planes. 1-5
Focus: Deductive Reasoning
Benchmarks:
MA.912.A.3.2 Identify and apply distributive, associative, and commutative properties of real numbers and the properties of equality
MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional coordinate systems
MA.912.G.1.2 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
MA.912.G.1.3
Identify and use the relationships between special pairs of angles formed by parallel lines and transversals
Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a
MA.912.G.8.5
variety of ways to present deductive proofs, such a flow charts, paragraphs, two-column, and indirect proofs.
Content Sections
A. Recognize and analyze a conditional statement. State converse of conditional statements and use
2-1
counterexamples. Recognize and use definitions and biconditional statements
2-2
B. Use algebraic properties of Equality and congruence properties in proofs..
Draft Quarter 1
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
C. Use and understand the Midpoint Theorem and the Angle Bisector Theorem 2-3
D. Apply the definitions of complementary and supplementary angles. State and use the theorem about
vertical angles 2-4
Approximately
13 days E. Apply the definition and theorem about perpendicular lines 2-5
F. State and apply the theorems about angles supplementary to, or complementary to, congruent
angles. Plan proofs and then write them in two-column form 2-6
Focus: Parallel Lines and Planes
Benchmarks:
MA.912.D.6.4
Use methods of direct and indirect proof and determine whether a short proof is logically valid
MA.912.G.1.3
Identify and use the relationships between special pairs of angles formed by parallel lines and transversals
MA.912.G.2.1
Identify the measures of interior and exterior angles of polygons, justifying the method used.
MA.912.G.2.2
Determine the measures of interior and exteriof angles of polygons, justifying the method used
Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral,
MA.912.G.4.1
and equinangular
Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a
MA.912.G.8.5
variety of ways to present deductive proofs, such a flow charts, paragraphs, two-column, and indirect proofs.
Content Sections
A. Distinguish between intersecting lines, parallel lines, and skew lines. State and apply the theorem
about the intersection of two parallel planes by a third plane. Identify and define relationships between
any two lines and the relationships of the angles formed when they are cut by a transversal. 3-1
B. Use postulates and thereoms of parallel lines to solve problems and to complete two-column proofs. 3-2
C. Use postulates and thereoms of parallel and perpendicular lines to solve problems and to complete
two-column proofs. 3-3
Draft Quarter 1
Approximately
13 days
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
D. Classify triangles according to sides and to angles. State and apply the theorem and the corrollaries
about 1) the sum of the measures of the angles of a triangle 2) the measure of an exterior angle of a
triangle 3-4
Approximately E. Understand convex and regular polygons. Find the measures of interior and exterior angles of
13 days convex polygons 3-5
F. Understand and use inductive reasoning 3-6
Focus: Congruent Triangles
Benchmarks:
MA.912.D.6.4 Use methods of direct and indirect proof and determine whether a short proof is logically valid
Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral,
MA.912.G.4.1
and equinangular
MA.912.G.4.2 Define, identify and construct altitudes, medians, angle bisectors, perpendicular bisectors
MA.912.G.4.3 Construct triangles congruent to given triangles
MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles
MA.912.G.8.5 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a
Content Sections
A. Identify corresponding parts of congruent figures 4-1
4-2
B. Apply SSS, SAS, and ASA to determine if triangles are congruent and write the proofs in two-column form
C. Deduce information about segments and angles after proving that two triangles are congruent 4-3
D. Apply the theorems and corrollaries about isosceles triangles 4-4
E. Apply AAS Theorem and HL Theorem to determine if triangles are congruent and write the proofs in two-
Approximately 4-5
column form. Prove that two overlapping triangles are congruen
15 days F. Prove two triangles are congruent by first proving two other triangles congruent 4-6
G. Apply the definitions of the median and altitude of a triangle and the perpendicular bisector of a triangle or a
4-7
segment.
2 days for intro, syllabus,
and pre-test
Draft Quarter 1
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
Completed During Quarter 2 (Finish chapter 4)
Focus: Quadrilaterals
Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram,
MA.912.G.3.1
trapezoid, and kite
MA.912.G.3.2
Compare and contrast special quadrilaterals on the basis of their properties
MA.912.G.3.4 Provegeometric involving quadrilaterals by contradiction and proofs involving coordinate geometry. Use and compare a
Write theorems proofs, including proofs
MA.912.G.8.5 variety of ways to present deductive proofs, such a flow charts, paragraphs, two-column, and indirect proofs.
Benchmarks: Content Sections
A. Define and identify parallelogram and apply theorems and parallelograms to numeric and
algebraic problems 5-1
B. Apply the theorems about parallelograms to prove a quadrilateral is a parallelogram and to
solve for missing sides and angles 5-2
C. Apply theorems about parallel lines and apply midpoint theorems for triangles 5-3
Approximately D. Define and apply corollaries of rectangle, fhombus, and square and apply related theorems to
11 days categorize given quadrilaterals 5-4
E. Define and identify trapezoids, and apply related theorems to solve for measures of angles,
sides, and angles of given figures 5-5
Focus: Inequalities in Geometry
MA.912.D.6.2 Find the converse, inverse, and contrapositive of a statement
MA.912.D.6.4 Use methods of direct and indirect proof and determine whether a short proof is logically valid
MA.912.G.4.7 Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem
Benchmarks: Content Sections
Apply inequality properties to lengths of segments and measures of angles. Use the Exterior Angle Inequality
6-1
Theorem
B. State the contrapositive and inverse of an if-then statement 6-2
6-3
C. Write indirect proofs in paragraph form
Approximately Draft Quarter 2
11 days
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
6-4
D. State and apply the inequality theorems and corollaries for one triangle
Approximately
6-5
11 days E. State and apply the inequality theorems for two triangles
Focus: Ratio, Proportion and Similarity
MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical or real-world problems
MA.912.G.2.4 Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons, to determine congruence,
Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors, orthocenter,
MA.912.G.4.2
centroid, incenter, and circumcenter
MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas
MA.912.G.4.5 Apply theorems involving segments divided proportionally
MA.912.G.8.2 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler
Benchmarks: Content Sections
A. Express a ratio in simplest form. Solve proportions and express in equivalent forms 7-1/7-2
7-3
B. Apply the properties of similar polygons.
C. Use the AA Similarity Postulate to prove triangles are similar. Use the similar triangles to deduce information
Approximately about segments and angles
7-4
12 days D. Use the SAS Similarity Theorem and the SSS Similarity Theorem to prove triangles similar 7-5
E. Apply the Triangle Proportionality Theorem and the Triangle Angle-Bisector Theorem. 7-6
5 days review and exam
Draft Quarter 2
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
Completed During Quarter 3
Focus: Pythagorean Theorem , Special Triangles, Tangents to Circles, Arcs and Angles
Benchmarks:
MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse
MA.912.G.5.2 State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle
MA.912.G.5.3 Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems
Determine the center of a given circle. Given 3 points not on a line, construct the circle that passes
MA.912.G.6.1
through them. Construct tangents to circles.
Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and
MA.912.G.6.2
concentric circles
MA.912.G.6.3
Prove theorems related to circles, including related angles, chords, tangents and secants
Determine and use measures of arcs and related angles (central, inscribed, and intersections
MA.912.G.6.4
of secants and tangents)
Content Sections
A. Determine the geometric mean and apply this relationship to the altitude drawn to the
hypotenuse of a right triangle 8-1
Approximately
14 days B. Apply the Pythagorean Theorem 8-2
C.Apply the converse of the Pythagorean Theorem and related theorems about obtuse and
acute angles 8-3
D. Use special triangles to find the lengths of a triangle 8-4
A. Define a circle, a sphere, and terms related to them. Recognize inscribed polygons and
circumscribed circles 9-1
B. Apply theorems that relate tangents and radii, Recognize circumscribed polygons and
inscribed circles. 9-2
C. Define and apply properties of arcs and central angles. 9-3
Focus: Areas of Polygons
Draft Quarter 3
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals,
pentagons, etc.)
Use properties of congruent and similar triangles to solve problems involving lengths and
MA.912.G.4.4
areas
Solve real-world problems using measures of circumference, arc length, and areas of circles and
MA.912.G.6.5
sectors
Benchmarks: Content Sections
A. Apply the area postulates to polygons 11-1
B. Apply formulas for area of parallelograms, triangles, and rhombuses and trapezoids 11-2/11-3
D. Apply formulas for area of regular polygons. Define and identify central angle and
apothem of a polygon 11-4
E. Apply the formulas for circumference and areas of circles 11-5
F. Apply the formulas for arc length and the areas of sectors of a circle 11-6
Approximately G. Find the ratio of the areas of two triangles. Apply the relationships between scale factors,
14 days perimeters, and areas of similar figures. 11-7
Focus: Areas and Volumes of Solids
MA.912.G.7.2 Describe the relationships between the faces, edges, and vertices of polyhedra
MA.912.G.7.3 Identify, sketch, find area and/or perimeters of cross sections of solid objects
MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of solids
MA.912.G.7.6 Identify and use properties of congruent and similar solids
Determine how changes in dimensions affect the surface area and volume of common
MA.912.G.7.7 geometric solids
Draft Quarter 3
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
Benchmarks: Content Sections
A. Solve problems using surface area formulas and volume formulas of prisms 12-1
B. Solve problems using surface area formulas and volume formulas of pyramids 12-2
C. Solve problems using surface area formulas and volume formulas of right cylinders and
cones 12-3
Approximately D. Solve problems using area and volume of a sphere 12-4
10 days E. Apply the properties of similar solids 12-5
7 days have been allotted for FCAT Testing and Make-up Testing
Draft Quarter 3
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
Completed During Quarter 4
Focus: Right Triangles and Trigonometry and Circles
Benchmarks:
MA.912.G.6.3 Prove theorems related to circles, including related angles, chords, tangents and secants
Determine and use measures of arcs and related angles (central, inscribed, and intersections of
MA.912.G.6.4
secants and tangents)
MA.912.G.6.5
Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors
MA.912.T.2.1 Define and use the trig ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles
MA.912.T.2.2 Solve real-world problems involving right triangles using technology when appropriate
\ Sections
A. Solve right triangle problems using tangent ratio for an acute angle 8-5
B. Solve right triangle problems using sine and cosine ratios for an acute angle 8-6
Approximately C. Use trig ratios and their inverses to solve real-life problems 8-7
15 days D. Apply theorems about the chords of a circle 9-4
E. Solve problems involving inscribed angles and angles formed by chords, secants, and tangents with vertices on a circle
9-5
F.. Solve problems involving inscribed angles and angles formed by chords, secants, and tangents with vertices not on a circle
9-6
G. Solve problems involving lengths of chords, secant segments, and tangent segments 9-7
Focus: Coordinate Geometry
Benchmarks:
MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional coordinate systems
MA.912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines and transversals
MA.912.D.9.3 Use vectors to model and solve application problems
Content Sections
Approximately A. Use the distance and midpoijnt formula. Apply the general equation of a circle 13-1/13-5
10 days
B. Use the slope formula. Determine if lines are parallel, perpendicular, or neither by slope 13-2/13-3
C. Understand the properties of vectors 13-4
D. Identify slope and y-intercept of lines. Graph a line and find the intersection of two lines. 13-6
E. Write an equation of a line when points or slope of a line is given. 13-7
Draft Quarter 4
September, 2008 The School District of Osceola County
Algebra I
Curriculum Calendar
Focus: Transformations
Benchmarks:
MA.912.G.2.4 Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons, to determine congruence,
Content Sections
A. Recognize basic terms of mapping and transformations. 14-1
Approximately B. Identify and use reflections in a plane and sketch lines of symmetry. 14-2
12 days D. Identify and use translations and glide reflections in the plane. 14-3
C. Identify rotations in a plane and use rotational symmetry in real-life situations 14-4
E. Identify dilations in a plane. 14-5
F. Describe composition transformations. 14-6
8 days Review and Semester Exam
Draft Quarter 4