Download Unit descriptions

Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry (Semester Block)
Time Frame: 2 weeks (scattered through out)
Enduring Understanding: (1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (1) Does the student understand the connection between geometry and real-life applications?
(2) Can the student apply algebraic techniques to Geometric topics?
Concept/Topic
Vocabulary
Instructional
(Pre- AP covers
Indicators
Development
Assessment
Activities/
Resources
all topics/ CP
Strategies
Extension Activities
covers all topics
not designated
Pre- AP only)
See list
Tests & Quizzes
Text book or Teacher made.
First 8 indicators will be
attached
text or teacher
used throughout the
made
Internet Sites for support:
course
http://illuminations.nctm.org
http://school.discoveryeducation.com
http://www.pbs.org/teachers/
http://www.classzone.com/books/geometry/index.cfm
http://flashcardexchange.com/index.php
http://streaming.discoveryeducation.com
http://coolmath.com
http://school.discoveryeducation.com/schrockguide/assess.html
http://www.teach-nology.com
http://discoveryeducation.com
http://rubistar.4teachers.org
http://illuminations.nctm.org
http://regentsprep.org/Regents/math/geometry/mathGEOMETRY.htm,
http://www.math.com/tables/geometry/index.htm,
http://www.kutasoftware.com/freeige.html,
http://www.edhelper.com/geometry_highschool.htm
840987799
8/2/10
300 South Catawba Street, Lancaster SC 29720
-1-
Mathematics Curriculum Map
Concept/Topic
(Pre- AP covers
all topics/ CP
covers all topics
not designated
Pre- AP only)
General info
through out the
course
Indicators
(1) G-1.7 Understand the
historical development of
geometry.
General info
through out the
course
(2) G- 1.8 Connect
geometry with other
branches of mathematics.
General info
through out the
course
(3) G-1.9 Demonstrate an
understanding of how
geometry applies to realworld contexts (including
architecture, construction,
framing, and astronomy.)
840987799
Vocabulary
Development
Assessment
Strategies
Instructional
Activities/
Extension Activities
Resources
Research
Presentation of
Mathematicians and mathematicians & create a
create a
time-line
report/power
point/or photo story
to present to the
class. (create a
time-line of the
mathematicians)
8/2/10
300 South Catawba Street, Lancaster SC 29720
-2-
Mathematics Curriculum Map
Concept/Topic
(Pre- AP covers
all topics/ CP
covers all topics
not designated
Pre- AP only)
General info
through out the
course
840987799
Indicators
(4) G-1.10 Demonstrate an
understanding of geometric
relationships ( including
constructions through
investigations by using a
variety of tools such as
straightedge, compass,
patty paper, dynamic
geometric software, and
handheld computing
devices)
5) G- 2.5 Carry out
procedures to create
geometric constructions (
including the midpoint of a
line segment, the angle
bisector, the perpendicular
bisector of a segment, the
line through a given point
that is parallel to a given
line, and the line through a
given point that is
perpendicular to a given
line.)
Vocabulary
Development
Assessment
Strategies
Instructional
Activities/
Extension Activities
Resources
Extension: Pre – AP
Students should be forced
to consider the effect upon
basic geometric concepts
when applied to curved
surfaces, such as the
surface of a sphere.
Construction
Portfolio (Pre- AP)
8/2/10
300 South Catawba Street, Lancaster SC 29720
-3-
Mathematics Curriculum Map
Concept/Topic
(Pre- AP covers
all topics/ CP
covers all topics
not designated
Pre- AP only)
General info
through out the
course
General info
through out the
course
General info
through out the
course
840987799
Indicators
Vocabulary
Development
Assessment
Strategies
Instructional
Activities/
Extension Activities
Resources
(6) G-6.1 Use the distance
formula to solve problems.
(7) G-6.2 Use the midpoint
formula to solve problems.
(8) G-3.10 Use
Pythagorean theorem and
its converse to solve
problems
8/2/10
300 South Catawba Street, Lancaster SC 29720
-4-
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 2 weeks
Enduring Understanding: (1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (1) Can the student apply algebraic techniques to geometric topics?
(2) Can the student demonstrate logical thinking by creating steps in a proof?
Vocabulary
Instructional Activities/
Concept/Topic
Indicators
Development
Assessment
Extension Activities
Strategies
G-1.1 Demonstrate an
Appendix A
Inductive/deductive understanding of the axiomatic
reasoning
structure of geometry by using
undefined terms, definitions,
postulates, theorems, and
corollaries.
G-1.2 Communicate knowledge
Appendix A
Geometric presentation:
Inductive/deductive of geometric relationships by
Present information on a
reasoning
using mathematical terminology
geometric concept
appropriately.
Inductive/deductive G-2.1 Infer missing elements of
Appendix A
reasoning
visual or numerical geometric
patterns(including triangular and
rectangular numbers and the
number of diagonals in a
polygon)
Inductive/deductive G-1.5 Use inductive reasoning to Appendix
reasoning
formulate conjectures
A/B
Inductive/deductive G-1.6 Use deductive reasoning to Appendix
Conclusion activity : Like
reasoning
validate conjectures with formal A/B
“ I have who has”…I have
and informal proofs, and give
a right angle….Who has 2
counter examples to disprove a
angles whose sum is 180
statement.
degrees?
840987799
8/2/10
Resources
300 South Catawba Street, Lancaster SC 29720
-5-
Mathematics Curriculum Map
Concept/Topic
Indicators
Inductive/deductive
reasoning
G-1.4 Formulate and test
conjectures by using a variety of
tools such as concrete models,
graphing calculators,
spreadsheets, and dynamic
geometry software.
G-1.3 Apply basic rules of logic
to determine the validity of the
converse, inverse, and
contrapositive of a conditional
statement.
G-2.4 Use direct measurement to
determine the length of a
segment, degree of an angle, and
distance from a point to a line.
G-2.3 Use the congruence of line
segments and angles to solve
problems.
G-2.2 Apply properties of
parallel lines, intersecting lines,
and parallel lines cut by a
transversal to solve problems.
Inductive/deductive
reasoning
Parallel and
Perpendicular lines
Parallel and
Perpendicular lines
840987799
Vocabulary
Development
Assessment
Strategies
Instructional Activities/
Extension Activities
Resources
Appendix A/
B
Appendix B
Logic in
Su-do-ku
Advertising
Logic Puzzle :
project/Portfolio Construction & Solution
Appendix B
Appendix C
Appendix C
8/2/10
300 South Catawba Street, Lancaster SC 29720
-6-
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 2 weeks
Enduring Understanding: 1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (1) Does the student understand relationships between different types of angles can parts of triangles?
(2) Can the student use the appropriate vocabulary and determine how to solve problems pertaining to different triangles?
Concept/Topic
Triangles
Triangles
Triangles
Triangles
Triangles
840987799
Indicators
G-3.1 & G-3.2 Carry out procedure to
compute the perimeter and area of triangles
Vocabulary
Development
Appendix D
G-3.3 Analyze how to changes in dimensions
affect perimeter and area of triangles
G-3.4 Apply properties of isosceles and
equilateral triangles to solve problems.
G-3.5 Use interior angles, exterior angles,
medians, angle bisectors, altitudes, and
perpendicular bisectors to solve problems.
Appendix D
G-3.6 Apply the triangle sum theorem to solve
problems.
Appendix D
Assessment Strategies
Putt-Putt model (Find
perimeter & area of the
project) Graded using rubric
Instructional Activities/
Extension Activities
Create a model of a putt-putt hole.(This uses scale
drawing, volume, area, perimeter, and surface
area)
Appendix D
Appendix D
Triangle mobile hanging
project
8/2/10
Feuerbach’s Nine Point circle as extension
activity on triangle centers and midpoint. (AP
only)
300 South Catawba Street, Lancaster SC 29720
-7-
Resources
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 2 weeks
Enduring Understanding: 1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (1) Can the student determine the relationship among 2 triangles or polygons to decide if they are congruent or similar?
(2) Can the student analyze whether 2 triangles or 2 polygons are similar using different methods?
Concept/Topic
Trianlges
Indicators
G-3.7 Apply the triangle inequality theorem
to solve problems
Congruence of
figures Triangles /
polygons
Similar figures
G-3.8 Apply congruence and similarity
relationships among triangles to solve
problems (note: congruence is done, then
similarity is done in separate
sections/chapters)
G-2.6 Use scale factors to solve problems
involving scale drawings and models. (use
when teaching similarity)
G-2.7 Use Geometric probability to solve
problems.
G-3.9 Apply theorems to prove that triangles
are either congruent or similar.
Similar figures
Similar figures
Congruent Triangles
/Similar triangles
840987799
Vocabulary
Development
Appendix D
Assessment Strategies
Appendix D
Appendix H
Proof Puzzle Quiz
Appendix H
Putt – Putt model shown on
graph paper.
Appendix H
Instructional Activities/
Extension Activities
Straw activity to show possible side values or
not.(Use straws of different lengths and paper
clips to try to connect the straws together to make
a triangle)
Proof Puzzles done in Groups. (6-8 proofs cut
apart)
Putt-Putt model
Putt-Putt model
Appendix D
8/2/10
300 South Catawba Street, Lancaster SC 29720
-8-
Resources
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 2 weeks
Enduring Understanding: (1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (a) Can the students find or identify the different ways that you can find the sides of right triangles and angle measures?
(b) Can the students use different methods to find side and angle measures of right triangles?
Concept/Topic
Right triangles
Right triangles
Right Triangles
Right triangles
840987799
Vocabulary
Indicators
Development
G-3.10 Use the Pythagorean theorem and its
Appendix I
converse to solve problems.
G-3.11 Use the properties of 45-45-90 and
Appendix I
30-60-90 triangles to solve problems
G-3.12 Use trigonometric ratios (sine, cosine, Appendix I
and tangent) to solve problems involving right
triangles.
G-4.5 Apply the properties and attributes of
quadrilaterals and regular polygons and their
component parts to solve problems.
Instructional Activities/
Extension Activities
Assessment Strategies
Trig Ratio Class activity/
project to be graded.
Measuring the height of tall
objects.
Appendix I
Indirect measurement project: Extension: Unit
circle derivation. (Pre-AP only)
Kite project
8/2/10
300 South Catawba Street, Lancaster SC 29720
-9-
Resources
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 3 to 4 weeks (can be 2 different topics)
Enduring Understanding: (1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (a) Can the student identify how the parts (angles and sides) of quadrilaterals related?
(b) Can the students identify how the perimeters and areas related for different figures?
(c) Can the students find interior and exterior angle measures and side values of quadrilaterals and polygons.
Vocabulary
Instructional Activities/
Concept/Topic
Indicators
Development
Assessment Strategies
Extension Activities
Congruent/Similar
G-4.6 Apply congruence and similarity
Appendix D / H
shapes
relationships among shapes. (Include
quadrilaterals and polygons) to solve
problems.
For 2 separate units
G-4.1 Carry out the procedure to compute the Appendix F / K
Quadrilaterals
perimeter of quadrilaterals, regular polygons,
/ polygons
and composite figures.
Quadrilaterals
G-4.2 Carry out a procedure to find the area
Appendix F/K
/ polygons
of quadrilaterals, regular polygons, and
composite figures.
Quadrilaterals
G- 4.3 Apply procedures to compute
Appendix F/K
Quadrilateral KWL chart for the properties of the
/ polygons
measures of interior and exterior angles of
different quadrilaterals
polygons
Quadrilaterals
G-4.4 Analyze how changes in dimensions
Appendix F/K
Dance Floor Design Project
/ polygons
affect the perimeter and area of quadrilaterals
(Pre-AP)
and regular polygons.
840987799
8/2/10
300 South Catawba Street, Lancaster SC 29720
- 10 -
Resources
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 1 week /self study Pre-AP
Enduring Understanding: (1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (1) Can the student analyze what type transformation has occurred?
(2) Can the student apply basic vector operations?
Concept/Topic
Translations
Translations
(Pre - AP only)
Translations/vectors
(Pre-AP only)
Translations/vectors
(Pre-AP only)
Translations/vectors
(Pre-AP only)
Translations/vectors
(Pre-AP only)
840987799
Indicators
G-6.3 Apply transformations—translation,
reflection, rotation, and dilation—to figures in
the coordinate plane by using sketches and
coordinates.
G-6.4 Apply Transformations (including
translation and dilation) to figures in the
coordinate plane by using matrices.
Vocabulary
Development
Assessment Strategies
Appendix G
G-6.5 Carry out a procedure to represent the
sum of vectors geometrically by using the
parallelogram method.
G-6.6 Carry out a procedure to determine the
magnitude and direction of the resultant of two
vectors by using the Pythagorean theorem.
Appendix G
G- 6.7 Carry out a procedure to compute the
magnitude of the resultant of two perpendicular
vectors by using the Pythagorean theorem.
G- 6.8 Carry out a procedure to determine the
direction of the resultant of two perpendicular
vectors by using a scale drawing and direct
measurement.
Appendix G
Instructional Activities/
Extension Activities
Animation by matrix project
Activity: Matrix Multiplication and vector
cross-multiplication.
(Pre - AP only)
Appendix G
Appendix G
8/2/10
300 South Catawba Street, Lancaster SC 29720
- 11 -
Resources
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 2 weeks
Enduring Understanding: (1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (1) Can the student determine how arc measures, angle measures, chords, tangent lengths, and secants are related?
(2) Can the students use properties of circles to solve for arc length, chord values, and other segment and angle measures in circles?
Vocabulary
Instructional Activities/
Concept/Topic
Indicators
Development
Assessment Strategies
Extension Activities
Resources
Circles
G-5.1 Carry out a procedure to compute the
Appendix J
circumference of circles.
Circles
G-5.2 Carry out a procedure to compute the
Appendix J
area of circles.
Circles
Circles
Circles
Circles
Circles
840987799
G-5.3 Analyze how a change in the radius
affects the circumference or area of a circle.
G-5.4 Carry out a procedure to compute the
length of an arc or the area of a sector of a
circle.
G- 5.5 Apply the properties of the component
parts of a circle (including radii, diameters,
chords, sectors, arcs, and segments)
Appendix J
G-5.6 Apply the properties of lines that
intersect circles (including two secants, two
tangents, and a secant and a tangent) to solve
problems.
G-5.7 Apply the properties of central angles,
inscribed angles, and arcs of circles to solve
problems.
Appendix J
Appendix J
Appendix J
Indirect Measurement of cylindrical object radius
Extension: Derivation of “Power of a Point”
(Pre-AP only)
Appendix J
8/2/10
300 South Catawba Street, Lancaster SC 29720
- 12 -
Mathematics Curriculum Map
Grade Level: 10th
Title: Geometry
Time Frame: 2 weeks
Enduring Understanding: (1) Explore definitions, properties, and attributes of 2 and 3 dimensional objects.
(2) To study conceptual issues of length, area, and volume and their complex interrelationships
Essential Questions: (1) Can the student find the surface area and volume of 3- dimensional shapes?
(2) Can the students identify parts needed to find the surface area and volume of different 3-dimensional shapes.
(Prism, Pyramid, Cylinder, Cone, and Sphere)
(3) Can the student determine which formula to use for different shapes?
Vocabulary
Instructional Activities/
Concept/Topic
Indicators
Development
Assessment Strategies
Extension Activities
Surface Area and
G- 7.1, 7.2 & 7.3 Carry out a procedure to
Appendix L
Putt Putt model / project
Project: Packaging items
Volume
compute the surface area and volume of three(Pre- AP will use
dimensional objects (including cones,
bases of all types of
cylinders, pyramids, prisms, spheres, and
polygons.)
hemispheres.)
(CP will use basic
polygons, triangle &
quadrilateral)
Surface Area and
G- 7.4 Apply congruence and similarity
Appendix L
Geometric Hanging Project
Volume
relationships among geometric objects to
(CP or Pre –AP)
solve problems with 3-dimensional shapes.
Surface Area and
G-7.5 Apply a procedure to draw a top view,
Appendix L
Volume
front view, and side view of a threedimensional object.
Surface Area and
G-7.6 Apply a procedure to draw an isometric Appendix L
Volume
view of a three-dimensional object.
840987799
8/2/10
300 South Catawba Street, Lancaster SC 29720
- 13 -
Resources
Mathematics Curriculum Map
Appendix A
 Conjecture
 Inductive reasoning
 Counterexample
 Definition, undefined
 Point, line, plane
 Collinear, coplanar
 Line segment
 Endpoints
 Ray
 Initial point
 Opposite rays
 Intersect, intersection
 Postulation, or axioms
 Coordinate
 Distance, length
 Between
 Distance Formula
 Congruent segments
 Angle
 Sides, vertex of an angle
 Congruent angles
 Measure of an angle
 Interior of an angle
 Exterior of an angle
 Acute, obtuse angles
 Right, straight angles
 Adjacent angles
 Midpoint
 Bisect
840987799
 Segment bisector
 Compass, straightedge
 Construct, construction
 Midpoint Formula
 Angle bisector
 Vertical angles
 Linear pair
 Complementary angles
 Complement of an angle
 Supplementary angles
 Supplement of an angle
Appendix B
 Conditional statement
 If-then form
 Hypothesis
 Conclusion
 Converse
 Negation
 Inverse
 Contrapositive
 Equivalent Statement
 Perpendicular lines
 Line perpendicular to a plane
 Biconditional statement
 Logical argument
 Law of Detachment
 Law of Syllogism
 Theorem
 Two-column proof
 Paragraph proof
8/2/10
Appendix C
 Parallel lines
 Skew lines
 Parallel planes
 Transversal
 Corresponding angles
 Alternate interior angles
 Alternate exterior angles
 Consecutive interior angles
 Same side interior angles
 Flow proof
Appendix D
 Equilateral triangles
 Isosceles triangle
 Scalene triangle
 Acute triangle
 Equiangular triangle
 Right triangle
 Obtuse triangle
 Vertex of a triangle
 Adjacent sides of a triangle
 Legs of a right triangle
 Hypotenuse
 Legs of an isosceles triangle
 Base of an isosceles triangle
 Interior angle
 Exterior angle
 Corollary
 Congruent
 Corresponding angles
300 South Catawba Street, Lancaster SC 29720
- 14 -
Mathematics Curriculum Map
 Corresponding sides
 Base angles
 Vertex angles
 Coordinate proof
Appendix E
 Perpendicular bisector
 Equidistant from two points
 Distance from a point to a point
 Equidistant from two lines
 Perpendicular bisector of a triangle
 Concurrent lines
 Point of concurrency
 Circumcenter of a triangle
 Angle bisector of a triangle
 Incenter of a triangle
 Median of a triangle
 Centroid of a triangle
 Altitude of a triangle
 Orthocenter of a triangle
 Midsegment of a triangle
 Indirect proof
Appendix F
 Polygon
 Sides of a polygon
 Vertex, vertices
 Convex
 Non-convex, concave
 Equilateral polygon
 Equiangular polygon
 Regular polygon
840987799
 Diagonal of a polygon
 Parallelogram
 Rhombus
 Rectangle
 Square
 Trapezoid
 Bases of a trapezoid
 Base angles of a trapezoid
 Legs of a trapezoid
 Isosceles trapezoid
 Midsegment of a trapezoid
 Kite
Appendix G
 Image
 Pre-image
 Transformation
 Isometry
 Reflection
 Line of reflection
 Line of symmetry
 Rotation
 Center of rotation
 Angle of rotation
 Rotational symmetry
 Translation
 Vector
 Initial point
 Terminal point
 Component form
 Glide reflection
8/2/10
 Composition
 Frieze pattern, or border pattern
Appendix H
 Ratio
 Proportion
 Extremes
 Means
 Geometric mean
 Similar polygons
 Scale factor
 Dilation
 Reduction
 Enlargement
Appendix I
 Pythagorean triple
 Special right triangles
 Trigonometric ratio
 Sine
 Cosine
 Tangent
 Angle of elevation
 Solve a right triangle
 Magnitude of a vector
 Direction of a vector
 Equal vectors
 Parallel vectors
 Sum of two vectors
Appendix J
 Circle
 Center of circle
300 South Catawba Street, Lancaster SC 29720
- 15 -
Mathematics Curriculum Map
 Radius of circle
 Congruent circles
 Diameter of circle
 Chord, secant, tangent
 Tangent circles
 Concentric circles
 Common tangent
 Interior of a circle
 Exterior of a circle
 Point of tangency
 Central angle
 Minor arc and its measure
 Major arc and its measure
 Semicircle
 Congruent arcs
 Inscribed angle
 Intercepted arc
 Inscribed polygon
 Circumscribed circle
 Tangent segment
 Secant segment
 External segment
 Standard equation of a circle
 Locus
Appendix K
 Center of a polygon
 Radius of a polygon
 Apothem of a polygon
 Ventral angle of a regular polygon
 Circumference
840987799
 Arc length
 Sector of a circle
 Probability
 Geometric probability
Appendix L
 Polyhedron
 Face
 Edge
 Vertex
 Regular polyhedron
 Convex
 Cross section
 Platonic solids
 Tetrahedron
 Octahedron
 Dodecahedron
 Icosahedron
 Prism
 Bases
 Lateral faces
 Right prism
 Oblique prism
 Surface area of a polyhedron
 Lateral area of a polyhedron
 Net
 Cylinder
 Right cylinder
 Lateral area of a cylinder
 Surface area of a cylinder
 Pyramid
8/2/10













Regular pyramid
Circular cone
Lateral surface of a cone
Right cone
Volume of a solid
Sphere
Center of a sphere
Radius of a sphere
Chord of a sphere
Diameter of a sphere
Great circle
Hemisphere
Similar solids
300 South Catawba Street, Lancaster SC 29720
- 16 -