Download Fayette County Public Schools Geometry Curriculum Map (Long Range

Fayette County Public Schools
Geometry Curriculum Map (Long Range Plans)
SEMESTER 1
(KCAS)
Topic
***CLICK HERE FOR ALL POSTULATES & THEOREMS LISTED WITHIN DOCUMENT***
Procedures and Expectations
Solving algebraic equations, simplifying algebraic expressions
1
2
3
BIG IDEAS
(UNIT 1A)
BASICS OF
GEOMETRY




Section
(Prentice
Hall)
Know precise definitions of angles, lines, segments, parallel, and perpendicular based on undefined notions of point, line, and plane.
Prove and use theorems and definitions about angles (vertical, complementary, supplementary, etc.)
Find the lengths of line segments and the measures of angles.
Determine if segments or angles are congruent.
4
G.CO.1
5
G.CO.1
Identify and describe collinear, coplanar points, and intersecting lines, identify basic geometric symbols,
correctly name geometric figures
Describe the difference between a theorem and a postulate , use the Segment Addition Postulate to find
the measure of a segment, accurately measure a segment with a ruler, copy a segment using construction
tools
1.2
1.2/1.3
1.3/1.5
1.4/1.5
6**
G.CO.12
Find the midpoint between two points, applications of using the distance formula (find the distance
between two points, Pythagorean Theorem, perimeter, etc.), bisect a segment using construction tools
1.3/1.5
1.5/1.6
7
G.CO.9
Classify angles as right, acute, obtuse, or straight, use the Angle Addition Postulate to find the measure of
an angle, accurately measure an angle with a protractor, copy an angle using construction tools
1.4/1.5
1.4/1.5
8
G.CO.9
9
G.CO.9
10
11
Solve problems involving angle bisectors, bisect an angle using construction tools
1.5
1.5
1.6/2.6
2.5
Identify and sketch examples of vertical angles and linear pairs, solve problems involving the measures
of vertical angles and linear pairs, solve problems involving complementary and supplementary angles
Review
Exam
Unit 1A: Vocabulary
Prerequisite Skills
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


Section
(McDougalLittell)
Points, space, line, collinearity, plane, coplanar, postulate, axiom
Segment, ray, opposite rays, parallelism, skew lines
Coordinate, congruent segments, midpoint, angle, acute, right, obtuse, straight,
congruent angle
Vertical angles, adjacent, complementary, supplementary, theorem, proof


Absolute value
Solving and writing linear
equations
Solving and writing systems of
linear equations
Postulate 1.8
Theorems and Postulates (see
link at top)


Postulates 1.1, 1.2, 1.3, 1.4,
1.5, 1.6, 1.7, 1.8
Theorems 2.1, 2.2, 2.3, 2.4,
2.5
BIG IDEAS
(UNIT 1B)
TRANSFORMATIONS

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

Represent transformations in the plane using a variety of methods.
Describe rotations and reflections that carry a polygon onto it.
Use developed definitions of rotations, reflections and translations in terms of angles, circles, lines, and segments.
Draw a transformed figure (by rotating, reflecting, translating) using a variety of methods.
12
G.CO.2
Describe rigid motions in a plane, identify the three basic rigid transformations
7.1
12.1-12.3
13
G.CO.3
Describe a reflection, identify lines of reflectional symmetry, perform reflections in the
coordinate plane (include the line y = x)
7.2
12.1
14
G.CO.4
Describe a rotation, identify lines of rotational symmetry, perform rotation in the coordinate
plane about the origin and other points
7.3
12.3/12.5
15
G.CO.5
Describe a translation, perform translations in the coordinate plane
7.4
12.2
16
G.CO.2
Describe a glide reflection, describe a composition, perform compositions of transformations,
review
7.5
12.4
17
Finish review, Exam
Unit 1B: Vocabulary
Prerequisite Skills
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
Preimage, image, isometry, reflection,
transformation, rigid
Translation, composition, vector notation
Rotation
Glide reflection
Drawing reflections and
compositions
Theorems and Postulates (see
link at top)
Formative Assessment Lessons (FALs)
(click links below)


Theorems 12.1, 12.2, 12.3,
12.4, 12.5
Transforming 2D Figures
BIG IDEAS
(UNIT 1C)
PARALLEL AND
PERPENDICULAR
LINES
18
G.CO.1
G.CO.9
19
G.CO.9
20
G.CO.12
21 **
G.GPE.5
22
23
 Identify angles formed by two lines cut by a transversal.
 Prove that when parallel lines are cut by a transversal that alternate interior angles, corresponding angles, alternate exterior
angles are congruent; same side interior are supplementary.
 Use properties of parallel lines to determine if lines are perpendicular.
Identify parallel, perpendicular, and skew lines, identify four pairs of angles formed by
transversals (City Designer Activity)
3.1
1.3/3.1-3.2
Solve problems involving the measures of special angle pairs
3.3
3.1/3.2
Prove, by angle measurements, that two lines are parallel, construct a parallel line through a point
not on a given line using construction tools
Use the slope formula to find the slope of a line between two points, use slope to identify parallel
and perpendicular lines in the coordinate plane
Review
Exam
3.4
3.7
3.6/3.7
3.5-3.6
Unit 1C: Vocabulary
Prerequisite Skills
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
Transversal, alternate interior, exterior, same-side interior (consecutive),
corresponding
Acute triangle, right triangle, obtuse triangle, equilateral triangle, equiangular
triangle, scalene triangle, isosceles triangle, exterior angles of a polygon, remote
interior angles
Polygon, convex, concave, equilateral, equiangular, regular polygon




Solving and writing linear
equations
Theorem 2.1
Postulate 1.8
Converses
Theorem 3.7
Theorems and Postulates (see
link at top)


Postulates 3.1, 3.2
Theorems 3.1, 3.2, 3.3, 3.4,
3.5, 3.6, 3.7, 3.8, 3.9, 3.10
BIG IDEAS
(UNIT 1D)
TRIANGLE
CONGRUENCY
24
G.CO.10
25
G.CO.6
G.CO.7
G.CO.8
26
G.CO.8
27
G.CO.10
28
G.CO.10
29
G.CO.10
30
G.CO.10
31
G.CO.10
32
33
 Use rigid motion to show that triangles are congruent.
 Explain why triangles are congruent using ASA, AAS, SAS, SSS, and HL.
 Use CPCTC to show parts of triangles congruent.
 Show base angles of an isosceles triangle are congruent and use this fact to solve problems.
 Recognize congruent triangles and their parts in overlapping figures.
 Use the fact that a point on a perpendicular bisector is equidistant to the endpoints of the bisected segment to solve problems.
 Use midsegments to find angle measures and side lengths.
 Use properties of altitudes, angle bisectors and medians to solve problems.
 Find the point at which medians, altitudes, or bisectors meet and use these points to solve problems.
 Use triangle inequality to make conjectures about sides and angles in triangles.
 Use the triangle angle sum theorem and exterior angle sum theorem to solve problems.
Classify triangles based on angle measure, use the triangle sum theorem and exterior angle
4.1
3.3
theorem to solve triangles
Introduce congruence in terms of Transformations. Determine if triangles are congruent, write
4.2
4.1-4.3
congruence statements
Determine if triangles are congruent, prove that triangles are congruent using various
postulates/theorems
Use theorems to prove triangles are congruent, use the H-L theorem to prove triangles congruent,
use the base angle theorem (and converse) to prove triangles are congruent
Define a bisector, bisect a segment using construction tools, bisect an angle using construction
tools, find the missing sides of a triangle using bisectors
Define the median and altitude of a triangle, construct the median and altitude or a triangle
4.3/4.4
4.1-4.3
4.6
4.1-4.3/4.6
5.1/5.2
1.5
5.3
5.3
Find the midsegment of a triangle
5.4
5.1
Determine if three sides form a triangle, construct a triangle given three sides
5.5
5.5
Review
Exam (Intro to next unit: Classify polygons)
6.1
3.4
Unit 1D: Vocabulary
Prerequisite Skills
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Congruent polygons
Legs, base, vertex angle, base angles for
isosceles triangles, corollary
Midsegment
Distance from a point to a line
Median, centroid, altitude
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
Solving and writing linear
equations
Identifying angle pairs
Theorem 4.1
Postulates 4.1, 4.2
Listing congruent parts
(CPCTC)
Finding slope
Finding midpoint
Theorems and Postulates (see
link at top)
Formative Assessment Lessons (FALs)
(click links below)
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



Theorems 4.1, 4.2, 4.3, 4.4,
4.5
Postulates 4.1, 4.2, 4.3
Corollaries to 4.3, 4.4
Theorems 5.1, 5.2, 5.3, 5.4,
5.5, 5.8
Analyzing Congruence Proofs
BIG IDEAS
(UNIT 1E)
QUADRILATERALS
34
G.CO.11
35
G.CO.11
36
G.CO.11
37
G.CO.11
38
G.GPE.7
39
40
 Recognize and sort quadrilaterals by their properties.
 Use properties of parallelograms to solve problems (opposite sides congruent, opposite angles congruent, diagonals bisect each
other, rectangles have congruent diagonals)
 Prove a quadrilateral is a parallelogram.
 Determine if a parallelogram is a square or rectangle.
 Use properties of squares, rectangles, trapezoids, and kites to solve problems.
 Find the measures of interior and exterior angles of polygons.
Intro to Quadrilaterals—properties and find the sum of interior angles (polygon formulas)
6.1
3.4/6.1
Use the properties of parallelograms to solve for x and y
6.2
6.2-6.4
Use the properties of rectangles, rhombi, and squares to solve for x and y
6.4
6.4
Prove a quadrilateral is a parallelogram based on angle measures
Area and perimeter of quadrilaterals
Review
Exam
Unit 1E: Vocabulary
Prerequisite Skills
Theorems and Postulates
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Parallelogram, rhombus,
rectangle, square,
trapezoid, isosceles
trapezoid, kite
Consecutive angles
41
42
Solving and writing linear equations
Solving and writing linear equations
Theorem 3.9
Finding midpoint
Theorem 2.1
Theorem 3.1
Theorem 2.1
Theorem 3.1
Theorem 3.7
Final Exam Review
Final Exam
** indicates a day that can be moved to second semester if needed
Theorems 6.1, 6.2, 6.3, 6.4, 6.5,
6.6, 6.7, 6.8, 6.9, 6.10, 6.11, 6.12,
6.13, 6.14
Formative Assessment Lessons (FALs)
(click links below)

Evaluating Statements About
Length and Area
SEMESTER 2
(KCAS)
BIG IDEAS
(UNIT 2A)
SIMILARITY
1
G.SRT.2
2
G.SRT.1
3
G.SRT.3
4
G.SRT.3
5
G.SRT.4
6
G.SRT.5
7
8
G.SRT.8
Topic
Section (ML)
 Use dilations to define and explain similarity. (angles congruent, sides proportional)
 Determine if two triangles are similar and if so write similarity statements.
 Prove triangles similar by AA, SAS, and SSS and use proportions to find the length of a missing side.
 Use the geometric mean to find the length of a missing side in a right triangle with altitude drawn to hypotenuse.
 Use the side-splitter theorem and triangle angle bisector theorem to solve problems.
Introduction to Similarity—Solve word problems involving ratio & proportion, state properties of
8.1/8.2
similar figures
Describe a dilation, dilate a figure in the coordinate plane
8.7
Find missing values (sides/angles) in similar figures
Section (PH)
8.1-8.2
12.7
8.3/8.4
8.1-8.2
Prove that triangles are similar & Quiz
8.5
8.3
Use the proportionality theorems to find missing values in similar triangles
8.6
8.5
Solve problems involving similar right triangles (geometric mean/altitude to the hypotenuse)
9.1
8.4
Review
Exam & Introduction to solving right triangles using Pythagorean Theorem
9.2
7.2
Unit 2A: Vocabulary
Prerequisite Skills
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Cross-product property
Extended proportion
Geometric mean
Golden Ratio and Rectangle
Indirect Measurement
Proportion
Ratio
Scale, scale drawing, scale factor
Similar
Similarity Ratio
Simplifying expressions
Midsegments
Congruency
Congruency Postulates
Medians
Altitudes
Perimeter and area
Theorems and Postulates (see link
at top)
Formative Assessment Lessons (FALs)
(click links below)




Postulate 8.1
Theorems 8.1, 8.2, 8.3, 8.4,
8.5, 8.6
Corollaries to 8.3, 8.4
Solving Geometry Problems:
Floodlights
BIG IDEAS
(UNIT 2B)
RIGHT TRIANGLE
TRIGONOMETRY
9
10
G.SRT.6
11
G.SRT.6
12
G.SRT.6
13
G.SRT.6
14
G.SRT.7
15
G.SRT.8
16
17
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Use the Pythagorean Theorem to solve problems.
Use special triangles (3-4-5, 7-24-25, 5-12-13, 8-15-17, 30⁰-60⁰-90⁰, 45⁰-45⁰-90⁰) to solve for missing sides in right triangles.
Use trigonometric ratios to solve problems.
Use simple properties of trig ratios (ex. sine ratio to find cosine of complementary angles, trig ratios are equal in similar
triangles.
 Solve indirect measurement problems using trigonometry.
Simplify radicals and radical expressions (include all operations)
9.2
7.1
(addendum to
7.1 on p 355
(alg 1 review)
Use the Pythagorean Theorem to solve for missing sides in a right triangle, use the converse of the
9.2/9.3
7.2
Pythagorean Theorem to determine if a triangle is acute, right, or obtuse
Solve special right triangles (45-45-90 and 30-60-90)
9.4
7.3
Quiz and find trigonometric ratios in a right triangle
9.5
9.1-9.2
Solve for missing sides in right triangles using trig ratios (include applications)
9.5
9.1-9.3
Solve word problems using trigonometry, use the inverse to solve right triangles (include
applications)
Review
Exam
9.6
9.1-9.3
Unit 2B: Vocabulary
Prerequisite Skills
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Angles of Depression and Elevation
SohCahToa
Initial and terminal point
Writing and solving equations
Solving proportions
Simplifying radicals
Writing ratios
Finding measures of angles
Triangle angle sum theorem
Theorems and Postulates
(see link at top)
Formative Assessment Lessons (FALs)
(click links below)


Theorems 7.4, 7.5, 7.6,
7.7, 7.8, 7.9

Geometry Problems: Circles and
Triangles
Proofs of the Pythagorean
Theorem
BIG IDEAS
(UNIT 3)
VOLUME
18
G.GMD.4
19
G.GMD.4
20
G.GMD.1, G.GMD.3
21
G.GMD.1, G.GMD.3
22
G.GMD.1, G.GMD.3
23




Master finding the area of a two dimensional figure.
Find the surface area of a 3 dimensional figure.
Find the volume of a cylinder, pyramid, cone or sphere.
Find the 2 dimensional cross section of a three dimensional object and find the 3 dimensional object based on the rotation of a two
dimensional figure.
 Know the relationship between perimeter, area, and volume involving the ratio of sides
Introduction to 3-dimensional figures—naming solids, identifying edges, faces, and vertices
10.1/supplement
(Euler’s Theorem), rotating a 2D figure about an axis to create 3D figures, review of perimeter and
12.1
plane area
10.1/supplement
Find the volume of a prism and cylinder
12.4
10.5
Find the volume of a pyramid and cone
12.5
10.6
Find the volume of a sphere, and review
12.6
10.7
Exam
Unit 3: Vocabulary
Prerequisite Skills
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Solid
Altitude and Slant height
Base
Cone
Cross-section
Cylinder
Prism
Pyramid
Sphere
Volume
Edge, face, vertices
Rotation about axis


Area
Perimeter and
circumference
Pythagorean Theorem
Solving and writing
equations
Theorems and Postulates (see link at
top)
Formative Assessment Lessons (FALs)
(click links below)



Theorems 10.1, 10.2, 10.5, 10.6,
10.7, 10.8, 10.9, 10.11, 10.12

2D Representations of 3D Objects
Calculating Volumes of Compound
Objects
Evaluating Statements About
Enlargements (2D and 3D)
BIG IDEAS
(UNIT 4)
COORDINATE
GEOMETRY
24
G.GPE.7
25
G.GPE.5
26
G.GPE.4
27
G.GPE.4
28
G.GPE.4, G.GPE.1
29
G.GPE.2, G.GPE.1
30
31
 Use distance and midpoint formulas to find length and midpoint of a segment in the coordinate plane
 Use coordinate geometry to determine the type of quadrilateral
 Use coordinate geometry to prove theorems about 2 dimensional figures
 Determine and write equations of circles and parabolas
Find the slope between two points, find the distance between two points, and find the midpoint of
two points
Write the equation of a line (include parallel and perpendicular lines)
Quiz and use formulas (from day 23) to solve triangle problems in the coordinate plane (prove a
triangle is equilateral, right, etc.)
Use formulas (from day 23) to solve quadrilateral problems in the coordinate plane (prove a
quadrilateral is a rectangle, square, etc.)
Write equations of circles given the center and radius, graph a circle, prove a point is on a circle in
the coordinate plane
**can be moved to beginning of circles unit
Write the standard form equation of a parabola given the vertex, directrix, and/or focus.
3.5
3.6
Supplement
6.3
10.6
11.5
Supplement
Review
Exam
Unit 4: Vocabulary
Prerequisite Skills
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Slope, distance, midpoint
Slope-intercept form
Point-slope form
Parallel and perpendicular
Center, radius, diameter
Circle
Parabola
Vertex, focus, directrix
Solving and writing equations
Reciprocals
Graphing a point
Graphing horizontal and vertical
lines
Theorems and Postulates (see link
at top)
Formative Assessment Lessons (FALs)
(click links below)




Theorems 6.6, 6.7, 6.8, 11.13
Equations of Circles 1
Equations of Circles 2
Finding Equations of Parallel and
Perpendicular Lines
BIG IDEAS
(UNIT 5)
CIRCLES
32
G.C.1, G.C.2, G.C.4
33
G.C.4
34
G.C.5
35
G.C.2, G.C.3
36
G.C.5
37
38
 Prove that all circles are similar
 Identify and use relationships among inscribed angles, radii, and chords
 Construct circumscribed and inscribed circles on a triangle and use them to describe properties of angles of a quadrilateral
 Construct tangent lines to a circle
 Show that the arc intercepted by an angle is proportional to the radius
Identify, sketch, and/or define segments related to a circle (radius, diameter, tangent, secant, etc.),
10.1/10.2
7.6
identify and name arcs of a circle (major, minor, semicircle), construct a line tangent to a circle
from a point not on the circle, prove all circles are similar
Determine whether or not a line is tangent to a circle, solve problems involving tangent segments
drawn to an external point, find the measures of tangent-tangent angles and their intercepted arcs
Find the measure of central angles, find the measure of intercepted arcs
11.1
Solve problems involving inscribed angles (including angles inscribed in a semicircle are right
angles), construct the inscribed and circumscribed circles of a triangle
Find arc length and sector area of a circle
11.3
11.4
7.6/7.7
Review
Exam & Intro to Probability (Use the Fundamental Counting Principle to count the number of ways
an event can happen)
Unit 5: Vocabulary
Prerequisite Skills
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Circumscribe
Inscribe
Arc
Point of tangency
Secant
Equation of circle
Tangent to circle
Sector
11.2
Naming, finding angles
Angle addition
Circumference
Area
Theorems and Postulates (see
link at top)
Formative Assessment Lessons (FALs)
(click links below)



Postulate 7.1
Theorem 7.14, 7.16, 11.1,
11.2, 11.3, 11.4, 11.5, 11.6,
11.7, 11.8, 11.9, 11.10

Inscribing and Circumscribing
Right Triangles
BIG IDEAS
(UNIT 6)
PROBABILITY
39
S.CP.9
40
S.CP.2
41
S.CP.2
42
S.CP.2
43
S.CP.3, S.CP.4, S.CP.5,
S.CP.6
44
 Describe the sample space of an event using unions, intersection, complements
 Determine probability of independent events
 Understand the concepts of conditional probability and find conditional probabilities
 Use two way frequency tables to approximate probabilities
 Use probability to make decisions on fairness of a situation
Use counting techniques to solve problems (include combinations and permutations)
MILC
Calculate simple probability (include complements)
MILC
Probability of Multiple Events –include dependent/independent events, mutually/non-mutually
exclusive events, and unions/intersections
MILC
Conditional Probability
PH Algebra 2
(11.2)
Quiz
Unit 6: Vocabulary
Prerequisite Skills
Theorems and Postulates
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Sample space
Union
Intersection
Complement
Probability
Independent event
Conditional probability
Two-way frequency table
Permutations and combinations
Mutually exclusive
45
46
Final Exam Review
Final Exam
Ratios
Percent
MILC
Formative Assessment Lessons (FALs)
(click links below)


Modeling Conditional
Probabilities 1: Lucky Dip
Modeling Conditional
Probabilities 2