Download How are the basic geometric figures described, named and

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Points,
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Lines and Planes
Days: 12
Grade(s):
Key Learning:
Geometry is based upon 3 concepts: point, line and plane. The
subdivisions of a line (segment and ray) are equally important with the pairs of
rays that create angles of various types and opposite rays. Students will know
how to name, sketch and measure each of these fundamental components of the
geometric world. Polygons may be classified in many ways.
Unit Essential Question(s):
How are the basic geometric
figures described, named and measured?
Concept:
Concept:
Concept:
Geometric Figures
Segments
Distance & Midpoint
Formulas
2.5.11.B
M11.C.3.1.1
Lesson Essential Question(s):
How are geometric figures named and
sketched? (A)
Lesson Essential Question(s):
What are congruent segments? (A)
Lesson Essential Question(s):
How is the distance between two
points determined?How are the
coordinates of the midpoint between
two points determined? (A)
Vocabulary:
point, line, plane, collinear, coplanar,
segment, ray, opposite rays,
intersection
Vocabulary:
coordinate, distance, length of
segment, congruent segments
Vocabulary:
midpoint, segment bisector, Midpoint
Formula, Distance Formula
Concept:
Concept:
Concept:
Angles
Polygons
M 1 1 . B . 2 . 1 . 1, 2 . 3 . 1 1 . B
Lesson Essential Question(s):
Lesson Essential Question(s):
How are angles named, measured and How are polygons classified? (A)
classified? (A)
Lesson Essential Question(s):
(A)
How are special angle pairs identified
and used? (A)
Vocabulary:
angle, sides, vertex, protractor,
congruent angles, acute, right, obtuse,
straight, angle bisector,
complementary angles,
supplementary angles, adjacent
angles, linear pair, vertical angles
Vocabulary:
polygon, sides, vertex, concave,
convex, equilateral, equiangular,
regular, triangle, quadrilateral,
pentagon, hexagon, heptagon,
octagon, nonagon, decagon,
dodecagon, n-gon
Vocabulary:
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Points,
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Lines and Planes
Days: 12
Grade(s):
Concept: Geometric Figures
point, line, plane, collinear, coplanar, segment, ray, opposite rays, intersection Concept: Segments
coordinate, distance, length of segment, congruent segments - coordinate, distance,
length of segment, congruent segments
Concept: Distance & Midpoint Formulas
midpoint, segment bisector, Midpoint Formula, Distance Formula Concept: Angles
angle, sides, vertex, protractor, congruent angles, acute, right, obtuse, straight,
angle bisector, complementary angles, supplementary angles, adjacent angles,
linear pair, vertical angles Concept: Polygons
polygon, sides, vertex, concave, convex, equilateral, equiangular, regular, triangle,
quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon,
dodecagon, n-gon -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Topic: Reasoning
Subject Area(s):
Key Learning:
Days: 13
Grade(s):
The use of reasoning skills allows conclusions to be reached.
Unit Essential Question(s):
How are inductive and
deductive reasoning used?
Concept:
Concept:
Concept:
Inductive Reasoning
Conditional Statements
M 1 1 . D . 1 . 1 . 1, 2 . 8 . 1 1 . A, 2 . 8 . 1 1 . B
2.4.11.C
Deductive Reasoning &
Proofs
2 . 4 . 1 1 . A, 2 . 4 . 1 1 . B
Lesson Essential Question(s):
What is inductive reasoning? (A)
How is it used to make and test
conjectures? (A)
Lesson Essential Question(s):
What are the various kinds of
conditional statements? (A)
How are they used to reach
conclusions? (A)
Lesson Essential Question(s):
What is deductive reasoning? (A)
How are the properties from algebra
used in geometry? (A)
How is a geometric proof developed?
(A)
Vocabulary:
inductive reasoning, conjecture,
counterexample
Vocabulary:
If-then form, hypothesis, conclusion,
conditional, converse, inverse,
contrapositive, biconditional,
equivalent statements
Vocabulary:
deductive reasoning, Addition
Property, Subtraction Property,
Multiplication Property, Division
Property, Substitution, Reflexive,
Symmtric, Transitive, two-column
proof, theorem
Concept:
Concept:
Concept:
Special Angle Pairs
Lesson Essential Question(s):
Lesson Essential Question(s):
What can be assumed about angle pair
relationships from a diagram? (A)
Lesson Essential Question(s):
How are the properties of special
angle pairs used? (A)
Vocabulary:
Vocabulary:
Vocabulary:
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Reasoning
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Days: 13
Grade(s):
Concept: Inductive Reasoning
inductive reasoning, conjecture, counterexample Concept: Conditional Statements
If-then form, hypothesis, conclusion, conditional, converse, inverse, contrapositive,
biconditional, equivalent statements Concept: Deductive Reasoning & Proofs
deductive reasoning, Addition Property, Subtraction Property, Multiplication Property,
Division Property, Substitution, Reflexive, Symmtric, Transitive, two-column proof,
theorem -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Topic: Lines
Subject Area(s):
Key Learning:
Days: 10
Grade(s):
Special relationships apply to angles formed by parallel and
intersecting lines.
Unit Essential Question(s):
How do the position of
coplanar lines and the measurement of the
angles formed impact each other?
Concept:
Concept:
Concept:
Special angle pairs
Proving Angle
Relationships
Proving Lines Parallel
Lesson Essential Question(s):
What are the special pairs of angles
formed by a transversal and two lines?
(A)
Lesson Essential Question(s):
How are the measures of angles
formed by 2 parallel lines and a
transversal determined? (A)
Lesson Essential Question(s):
What conditions will result in parallel
lines? (A)
What is the difference between
parallel and skew lines? (A)
Given parallel lines, how are angle
relationships proven? (A)
Vocabulary:
parallel lines, skew lines, transversal,
corresponding angles, alternate
interior angles, alternate exterior
angles, consecutive interior angles,
same-side interior angles
Vocabulary:
Vocabulary:
paragraph proof
Concept:
Concept:
Concept:
Lesson Essential Question(s):
What are the slopes of parallel and
perpendicular lines? (A)
Lesson Essential Question(s):
Lesson Essential Question(s):
Vocabulary:
slope, slope-intercept form, standard
form
Vocabulary:
Vocabulary:
How are lines proven parallel? (A)
How is a paragraph proof written? (ET)
Parallel and
Perpendicular Lines
M 1 1 . C . 3 . 1 . 2, M 1 1 . D . 3 . 2 . 3, 2 . 8 . 1 1 . L
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Lines
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Days: 10
Grade(s):
Concept: Special angle pairs
parallel lines, skew lines, transversal, corresponding angles, alternate interior
angles, alternate exterior angles, consecutive interior angles, same-side interior
angles Concept: Proving Lines Parallel
paragraph proof Concept: Parallel and Perpendicular Lines
slope, slope-intercept form, standard form -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Congruent
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Triangles
Days: 10
Grade(s):
Key Learning: Congruency of triangles is determined by the distinct characteristics
of the triangles.
Unit Essential Question(s):
How are triangles proven
congruent?
Concept:
Concept:
Concept:
Triangle Characteristics
Congruent Figures
Proving Triangles
Congruent
M 1 1 . C . 1 . 3 . 1, 2 . 9 . 1 1 . G
2.9.11.B
Lesson Essential Question(s):
How are triangles classified? (A)
Lesson Essential Question(s):
What are the characteristics of
congruent figures? (A)
Lesson Essential Question(s):
How are two triangles proven
congruent? (A)
Vocabulary:
scalene, isosceles, equilateral, acute
right, obtuse, equiangular, regular,
interior angle, exterior angle
Vocabulary:
corresponding angles, corresponding
sides, congruent figures
Vocabulary:
SSS, SAS, ASA, AAS, HL
Concept:
Concept:
Concept:
Lesson Essential Question(s):
How will corresponding parts of
congruent triangles lead to other
conclusions? (A)
Lesson Essential Question(s):
Lesson Essential Question(s):
Vocabulary:
Vocabulary:
Vocabulary:
How are the measures of the angles of
a triangle determined? (A)
Corresponding Parts of
Congruent Triangles
2.9.11.D
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Congruent
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Triangles
Days: 10
Grade(s):
Concept: Triangle Characteristics
scalene, isosceles, equilateral, acute right, obtuse, equiangular, regular, interior
angle, exterior angle Concept: Congruent Figures
corresponding angles, corresponding sides, congruent figures Concept: Proving Triangles Congruent
SSS, SAS, ASA, AAS, HL -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Triangle
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Relationships
Key Learning:
Days: 9
Grade(s):
Triangle relationships can be used to find and compare angle
measures and distances.
Unit Essential Question(s):
What are the special
relationships that occur within a triangle?
Concept:
Concept:
Concept:
Isosceles Triangles
Square Roots
M 1 1 . C . 1 . 2 . 3, M 1 1 . C . 1 . 2 . 1
M 1 1 . A . 1 . 1 . 1, M 1 1 . A . 1 . 1 . 3, M 1 1 . A . 2 . 2 . 1, 2 . 1 . 1 1 . A
Pythagorean Theorem &
its converse
M 1 1 . C . 1 . 4 . 1, 2 . 1 0 . 1 1 . B
Lesson Essential Question(s):
What are the parts of an isosceles
triangle? (A)
Lesson Essential Question(s):
How are square roots of whole
numbers simplified? (A)
Lesson Essential Question(s):
How is the Pythagorean Theorem
used? (A)
How are the sides and angles of a
triangle related to each other? (A)
How are the square roots of fractions
simplified? (A)
How is the converse of the
Pythagorean Theorem applied? (A)
How are the basic operations
performed with square roots? (A)
Vocabulary:
base, vertex, base angle, vertex angle
Vocabulary:
square root, rationalize
Vocabulary:
hypotenuse, leg, Pythagorean
Theorem
Concept:
Concept:
Concept:
Special Right Triangles
Midsegments
Triangle Inequalities
Lesson Essential Question(s):
How are the lengths of the sides of a
45-45-90 triangle determined? (A)
Lesson Essential Question(s):
How are the properties of a
midsegment used to solve problems?
(A)
Lesson Essential Question(s):
When given the lengths of two sides of
a triangle, how are the possible
lengths for the third side determined?
(A)
How are the lengths of the sides of a
30-60-90 triangle determined? (A)
How are the inequalities involving the
sides and lengths of a triangle used to
make comparisons? (A)
Vocabulary:
45-45-90 triangle, 30-60-90 triangle,
short leg, long leg
Vocabulary:
midsegment
Vocabulary:
Page 1 of 2
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Triangle
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Relationships
Concept:
Days: 9
Grade(s):
Concept:
Concept:
Lesson Essential Question(s):
(A)
Lesson Essential Question(s):
Lesson Essential Question(s):
Vocabulary:
Vocabulary:
Vocabulary:
Concurrent Lines
Additional Information:
Attached Document(s):
Page 2 of 2
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Triangle
Subject Area(s):
Relationships
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Days: 9
Grade(s):
Concept: Pythagorean Theorem & its converse
hypotenuse, leg, Pythagorean Theorem Concept: Special Right Triangles
45-45-90 triangle, 30-60-90 triangle, short leg, long leg Concept: Midsegments
midsegment Concept: Isosceles Triangles
base, vertex, base angle, vertex angle Concept: Square Roots
square root, rationalize -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Similar
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Figures
Key Learning:
Days: 11
Grade(s):
Similar figures and proportions can be used to model real-life
situations.
Unit Essential Question(s):
How are ratio and proportion
used to identify relationships in similar figures?
Concept:
Concept:
Concept:
Ratio & Proportion
Similar Polygons
Proving Triangles Similar
M 1 1 . D . 2 . 2 . 3, M 1 1 . A . 2 . 1 . 2, M 1 1 . A . 2 . 1 . 3
M11.C.1.3.1
2.9.11.B
Lesson Essential Question(s):
How are ratios simplified? (A)
Lesson Essential Question(s):
What are similar polygons? (A)
Lesson Essential Question(s):
How are tirangles proven similar? (A)
How are proportions solved? (A)
How is the length of a missing side
found? (A)
How are ratios and proportions used to
solve problems? (A)
What is the relationship between the
scale factor and the perimeter and
What is geometric mean? (A)
area of similar figures? (ET)
What are the properties of
proportions? How are they used? (A)
How are proportions used with scale
drawings? (A)
Vocabulary:
Vocabulary:
Vocabulary:
ratio, proportion, geometric mean,
similar polygon, scale factor, similarity AA Similarity, SSS Similarity, SAS
means, extremes, Cross Multiplication, ratio
Similarity
Reciprocal Property, Diagonal Switch,
Add Denominator
Concept:
Concept:
Concept:
Lesson Essential Question(s):
How are proportional relationships
applied in triangles? (A)
Lesson Essential Question(s):
Lesson Essential Question(s):
Vocabulary:
Triangle Proportionality Theorem
Vocabulary:
Vocabulary:
Proportional
Relationships Within
Triangles
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Similar
Subject Area(s):
Figures
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Days: 11
Grade(s):
Concept: Ratio & Proportion
ratio, proportion, geometric mean, means, extremes, Cross Multiplication, Reciprocal
Property, Diagonal Switch, Add Denominator Concept: Similar Polygons
similar polygon, scale factor, similarity ratio Concept: Proving Triangles Similar
AA Similarity, SSS Similarity, SAS Similarity Concept: Proportional Relationships Within Triangles
Triangle Proportionality Theorem -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Topic: Quadrilaterals
Subject Area(s):
Key Learning:
Days: 10
Grade(s):
The properties of quadrilaterals and other polygons can be used to
find side lengths and angle measures.
Unit Essential Question(s):
How are the properties of
quadrilaterals and other polygons used to find
side lengths and angle measures?
Concept:
Concept:
Concept:
Convex Polygons
Parallelograms
Special Parallelograms
M 1 1 . C . 1 . 2 . 2, 2 . 9 . 1 1 . C
Lesson Essential Question(s):
How area angle measures in convex
polygons found? (A)
Lesson Essential Question(s):
What are the characteristics of a
parallelogram? (A)
Lesson Essential Question(s):
What is the definition of each type of
parallelogram? (A)
When given angle measurement, how How can a quadrilateral be proven to
is the number of sides determined? (A) be a parallelogram? (ET)
What are the properties of the special
parallelograms? (A)
Vocabulary:
diagonal, regular polygon, interior
angle, exterior angle
Vocabulary:
parallelogram
Vocabulary:
rectangle, square, rhombus
Concept:
Concept:
Concept:
Lesson Essential Question(s):
Lesson Essential Question(s):
Vocabulary:
Vocabulary:
Trapezoids & Kites
Lesson Essential Question(s):
What is the definition of a trapezoid
and a kite? (A)
What are the properties of trapezoids
and kites? (A)
Vocabulary:
trapezoid, isosceles trapezoid, kite,
base, leg, base angle, midsegment
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Topic: Quadrilaterals
Subject Area(s):
Days: 10
Grade(s):
Concept: Convex Polygons
diagonal, regular polygon, interior angle, exterior angle Concept: Parallelograms
parallelogram Concept: Special Parallelograms
rectangle, square, rhombus Concept: Trapezoids & Kites
trapezoid, isosceles trapezoid, kite, base, leg, base angle, midsegment -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Topic: Circles
Subject Area(s):
Key Learning:
Days: 10
Grade(s):
The properties of angles, arcs, chords, tangents and secants can be
used to solve problems involving circles.
Unit Essential Question(s):
How can the relationships
between a circle and its arcs, lines, segments
and angles be used to solve problems?
Concept:
Concept:
Concept:
Circle Basics
Tangents
Arcs
M11.C.1.1.2
M 1 1 . C . 1 . 1 . 1, 2 . 9 . 1 1 . F
Lesson Essential Question(s):
What are the basic parts of a circle?
(A)
Lesson Essential Question(s):
What are the properties of a tangent?
(A)
Lesson Essential Question(s):
How are arcs named and classified?
(A)
How is the measure of an arc
determined? (A)
Vocabulary:
circle, center, radius, diamter, chord,
secant, tangent, concentric circles
Vocabulary:
Vocabulary:
arc, central angle, intercepted arc,
minor arc, semicircle, major arc
Concept:
Concept:
Concept:
Segments in a Circle
Angles in a Circle
2.9.11.E
Lesson Essential Question(s):
How are the properties of chords
applied? (A)
Lesson Essential Question(s):
How is the measure of an inscribed
angle determined? (A)
How are the measures of segments
formed by chords, secants and
tangents determined? (A)
How are the measures of angles
formed by chords, secants and
tangents determined? (A)
Vocabulary:
Vocabulary:
inscribed angle, inscribed polygon,
circumscribed polygon
Lesson Essential Question(s):
Vocabulary:
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Topic: Circles
Subject Area(s):
Days: 10
Grade(s):
Concept: Circle Basics
circle, center, radius, diamter, chord, secant, tangent, concentric circles Concept: Arcs
arc, central angle, intercepted arc, minor arc, semicircle, major arc Concept: Angles in a Circle
inscribed angle, inscribed polygon, circumscribed polygon Concept: Tangents
-
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Area &
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Perimeter
Key Learning:
Days: 12
Grade(s):
The formulas for perimeter, cirumference and area can be used to
find and compare measures in the real world.
Unit Essential Question(s):
How are the dimensions and
area of plane figures determined?
Concept:
Concept:
Concept:
Parallelograms &
Triangles
Trapezoid, Kite and
Rhombus
Circumference & Arc
Length
Lesson Essential Question(s):
How do you find the area and
dimensions of parallelograms and
triangles? (A)
Lesson Essential Question(s):
How do you find the area of a
trapezoid, kite and rhombus? (A)
Lesson Essential Question(s):
How do you find the circumference of
a circle? (A)
Vocabulary:
Vocabulary:
Vocabulary:
Concept:
Concept:
Concept:
Lesson Essential Question(s):
Lesson Essential Question(s):
Vocabulary:
Vocabulary:
M 1 1 . D . 3 . 1 . 2, M 1 1 . B . 2 . 2 . 3, M 1 1 . B . 2 . 2 . 4, M 1 1 . B .
2 . 3 . 1, 2 . 2 . 1 1 . B
Area of a Circle and a
Sector
Lesson Essential Question(s):
How do you find the area of a circle?
(A)
How do you find the area of a sector of
a circle (ET)
Vocabulary:
sector of a circle
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Area &
Subject Area(s):
Perimeter
PEQUEA VALLEY SD
Date: November 9, 2009 ET
Days: 12
Grade(s):
Concept: Parallelograms & Triangles
- base, height, composite shape, area, perimeter
Concept: Area of a Circle and a Sector
sector of a circle -
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Volume
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
& Surface Area
Key Learning:
Days: 6
Grade(s):
Surface area and volume formulas can help you solve problems in
three dimensions.
Unit Essential Question(s):
How are the surface area and
volume of three dimensional shapes
determined?
Concept:
Concept:
Concept:
Prisms and Cylinders
Pyramids and Cones
Spheres
Lesson Essential Question(s):
How are the volumes of right prisms
and cylinders determined? (A)
Lesson Essential Question(s):
How are the volumes of pyramids and
cones determined? (A)
Lesson Essential Question(s):
How is the volume of a sphere
determined? (A)
How are the surface areas of prisms
and cylinders determined? (A)
How are the surface areas of pyramids How is the surface area of a sphere
and cones determined? (A)
determined? (A)
Vocabulary:
right prism, right cylinder, surface
area, lateral surface area, volume
Vocabulary:
pryamid, regular pyramid, slant
height, cone
M 1 1 . B . 2 . 2 . 1, M 1 1 . B . 2 . 2 . 2, M 1 1 . B . 2 . 2 . 4, M 1 1 . B .
2.3.1
Vocabulary:
sphere, hemisphere
Additional Information:
Attached Document(s):
Page 1 of 1
2009 Pequea Valley SD Curriculum
Enriched Geometry
Curriculum:
Course:
Topic: Volume
Subject Area(s):
PEQUEA VALLEY SD
Date: November 9, 2009 ET
& Surface Area
Days: 6
Grade(s):
Concept: Prisms and Cylinders
right prism, right cylinder, surface area, lateral surface area, volume Concept: Pyramids and Cones
pryamid, regular pyramid, slant height, cone Concept: S p h e r e s
sphere, hemisphere -
Page 1 of 1
Related documents