Download 1 Mathematics Standard 1: Geometry Glencoe ISBN#: 0

Mathematics Standard 1: Geometry Glencoe ISBN#: 0-07865106-9
ALGEBRA, FUNCTIONS, AND GRAPHS: Students will understand algebraic concepts and applications.
Essential Question: How can we solve math using symbols and letters instead of numbers?
Benchmark
Performance Standards
A. Represent and analyze
1. Translate from verbal
mathematical situations and expression to algebraic
structures using algebraic
formulae.
symbols.
2. Given a graph, construct
a function that represents
the graph (linear only).
End Learning
Mastery
Students will write an
equation of a line given
information about its
graph.
Students will solve
problems by writing
equations.
Vocabulary/concepts:
• point-slope form
• rate of change
• slope-intercept
form
Assessment(s)
Practice Quiz 2, Student
Edition (SE), p. 150
Resources
Glencoe Key Chapters: 3
Glencoe Lesson 3.4
Open-Ended Assessment,
Teachers Wraparound
Edition (TWE), p. 150
Chapter 3 Resource Masters
pp. 145-6
Enrichment, Chapter
Resource Masters (CRM),
p.148
geometryonline.com/self_
check_quiz
TestCheck and Worksheet
Builder CD-ROM, Lesson
3-4
ACE Assessment: A certain
cellular phone company
charges a flat rate of $19.95
per month for service. All
calls are charged $0.07 per
minute of air time t. The
total charge C for a month
can be represented by the
equation C = 0.07t + 19.95.
How can the equation of
a line describe cellular
telephone service?
1
a line describe cellular
telephone service?
• Explain how the fee
for air time affects
the equation, and
• Describe how you
can use equations to
compare various
plans.
Mathematics Standard 1: Geometry
ALGEBRA, FUNCTIONS, AND GRAPHS: Students will understand algebraic concepts and applications.
Essential Question: How will pictures and concepts help me solve math problems in the real world?
Benchmark
B. Understand patterns,
relations, functions, and
graphs.
Performance Standards
End Learning
Assessment(s)
Mastery
1. Describe the concept of Students will write an
Practice Quiz 2, Student
the graph of a function.
equation of a line given
Edition (SE), p. 150
information about its graph.
Open-Ended Assessment,
2. Translate among tabular,
Students will solve
Teachers Wraparound
symbolic, and graphical
problems by writing
Edition (TWE), pp. 150,
representations of
equations.
469
functions.
Resources
Glencoe Key Chapters: 3, 9
Glencoe Lessons 3-4, 9-1
Chapter 3 Resource Masters
pp. 143-7
Chapter 9 Resource Masters
pp. 479-483
3. Describe the concept of a Students will draw reflected Enrichment, Chapter
images.
Resource Masters (CRM),
graph of an equation.
pp.148, 484
Students
will
recognize
and
4. Understand symmetry of
draw lines of symmetry
geometryonline.com/self_
graphs.
and points of symmetry.
check_quiz
Vocabulary/concepts
TestCheck and Worksheet
Builder CD-ROM, Lessons
3.4, 9.1
2
•
•
•
•
•
•
•
•
•
point-slope form
rate of change
slope-intercept form
isometry
line of reflection
line of symmetry
point of symmetry
reflection
transformation
Builder CD-ROM, Lessons
3.4, 9.1
ACE Assessment: A certain
cellular phone company
charges a flat rate of $19.95
per month for service. All
calls are charged $0.07 per
minute of air time t. The
total charge C for a month
can be represented by the
equation C = 0.07t + 19.95.
How can the equation of
a line describe cellular
telephone service?
• Explain how the fee
for air time affects
the equation, and
• Describe how you
can use equations to
compare various
plans.
Mathematics Standard 1: Geometry
ALGEBRA, FUNCTIONS, AND GRAPHS: Students will understand algebraic concepts and applications.
Essential Question: What are quantitative relationships?
Benchmark
Performance Standards
C. Use mathematical
models to represent and
understand quantitative
relationships.
1. Use a variety of
computational methods.
End Learning
Assessment(s)
Mastery
Students will write an
Practice Quiz 2, Student
equation of a line given
Edition (SE), p. 150
information about its graph.
Resources
Glencoe Key Chapters: 3,
5, 7
3
relationships.
2. Graph a linear equation
and linear inequality in two Students will solve
variables.
problems by writing
equations.
3. Solve applications
Vocabulary/concepts
involving systems of
• point-slope form
equations.
• rate of change
• slope-intercept form
4. Create a linear equation
from a table of values
containing co-linear data.
Open-Ended Assessment,
Teachers Wraparound
Edition (TWE), pp. 150,
245, 370
5. Generate an algebraic
sentence to model real-life
situations.
Assessment, Quiz 2, CRM,
p.407
6. Write an equation of a
line that passes through two
given points.
7. Verify that a point lies on
a line, given an equation of
the line, and be able to
derive linear equations by
using the point-slope
formula.
Enrichment, Chapter
Resource Masters (CRM),
pp.148, 250, 374
Glencoe Lessons 3.4,5.1,
7.4
Chapter 3 Resource Masters
pp. 143-7
Chapter 5 Resource Masters
pp. 245-249
Chapter 7 Resource Masters
pp. 369-373
Assessment, Mid-Chapter
Test, CRM, p.409
geometryonline.com/self_
check_quiz
TestCheck and Worksheet
Builder CD-ROM, Lessons
3.4, 5.1, 7.4
ACE Assessment: The old
surveyor’s telescope shown
on p. 364 is called a
theodolite. It is an optical
instrument used to measure
angles in surveying,
navigation, and
meteorology. It consists of
a telescope fitted with a
level and mounted on a
tripod so that it is free to
rotate about its vertical and
horizontal axes. After
measuring angles,
surveyors apply
trigonometry to calculate
distance and height.
4
surveyors apply
trigonometry to calculate
distance and height.
How do surveyors
determine angle measures?
• Where are
theodolites used?
• What kind of
information can one
obtain from a
theodolite?
Mathematics Standard 1: Geometry
ALGEBRA, FUNCTIONS, AND GRAPHS: Students will understand algebraic concepts and applications.
Essential Question: What is it, and how is it changing?
Benchmark
Performance Standards
D. Analyze changes in
various contexts.
1. Analyze the effects of
parameter changes on
polynomial functions.
End Learning Mastery
Students will find the
geometric mean between
two numbers.
Students will solve
2. Solve routine two- and
three-step problems relating problems involving
relationships between parts
to ratios.
of a right triangle and the
altitude to its hypotenuse.
3. Estimate the rate of
change of a function or
Students will use the
equation by finding the
Pythagorean Theorem.
slope between 2 points on
the graph.
Students will use the
converse of the
4. Evaluate the estimated
Pythagorean Theorem.
rate of change in the
context of the problem.
Assessments
Open-Ended Assessment,
Teachers Wraparound
Edition (TWE), pp. 144,
287, 331, 348, 356
Enrichment, Chapter
Resource Masters (CRM),
pp.142, 300, 330, 356, 362
Assessment, Mid-Chapter
Test, CRM, p. 177
Resources
Glencoe Key Chapters:
3, 6, & 7
Glencoe Lessons: 3-3, 6-1,
6-6, 7-1, 7-2
Chapter 3 Resource Masters
pp. 137-141
Chapter 6 Resource Masters
pp. 295-299, 325-329
Chapter 7 Resource Masters
pp. 351-355, 357-361
Assessment, Quiz 2, CRM,
p. 175; Quiz 4, p.346; Quiz Technology:
1, p. 407
Graphing Calculator and
Computer Masters
geometryonline.com/self_
pp. 22, 27, 28, 30
5
context of the problem.
Students will write ratios.
check_quiz
5. Know Pascal’s triangle
and use it to expand
binomial expressions that
are raised to positive
integer powers.
Students will use
properties of proportions.
TestCheck and Worksheet
Builder CD-ROM, Lessons
3.3, 6.1, 6.6, 7.1, 7.2
D. Analyze changes in
various contexts. (cont’d.)
Students will find slopes of
lines.
ACE Assessment: How are
Students will use slope to right triangles used to build
identify parallel and
suspension bridges?
perpendicular lines.
Include he following in
your answer:
Students will recognize
• locations of the right
and describe characteristics
triangles.
of fractals.
• An explanation of
which parts of the
Students will identify nonright triangle are
geometric iteration.
formed by the
cables.
Vocabulary/Concepts
• geometric mean
• Pythagorean triple
• cross-product
• extremes
• means
• proportion
• ratio
• rate of change
• slope
• slope-intercept form
• fractal
• iteration
• self-similar
Mathematics Standard 2: Geometry
6
GEOMETRY and TRIGONOMETRY: Students will understand geometric concepts and applications.
Essential Question: How can I use math to describe two-dimensional shapes and three-dimensional solid shapes?
A. Analyze characteristics 1. Interpret and draw twoStudents will find
Practice Quizzes, Student
Glencoe Key Chapters:
and properties of two- and dimensional objects and
perimeters and areas of
Edition (SE): Quiz 2, p. 80; 2-9, 11-13
three-dimensional
find the area and perimeter parallelograms.
Quiz 1, p. 138; Quiz 1, p.
Glencoe Lessons: 2.1, 2.3,
geometric shapes and
of basic figures (triangles,
198; Quiz 1, p. 306; Quiz
2.4, 2.8, 3.1, 3.2, 3.5, 4.1,
develop mathematical
rectangles, circles, rhombi, Students will determine
1, p. 423; Quiz 2, p. 497;
4.3-4.5, 5.1, 6.2, 6.3, 7.2,
arguments about geometric parallelograms, trapezoids) whether points on a
Quiz 1, p. 609; Quiz 2, p.
8.1, 8.3, 8.4, 9.1, 9.5, 11.1relationships.
coordinate plane define a
621; Quiz 1, p. 659; Quiz
11.4, 12.2-12.6, 13.1
parallelogram.
2,
p.
670
2. Find the area and
Glencoe Chapter Resource
perimeter of a geometric
Students will find areas of Open-Ended Assessment,
Masters:
figure composed of a
triangles, trapezoids, and
Teachers Wraparound
pp. 57-61, 69-73, 75-79,
combination of two or
Edition (TWE), pp. 66, 80, 99-103, 125-129, 131-135,
more rectangles, triangles, rhombi.
87, 114, 131, 138, 157,
149-153, 183-187, 195and/or semicircles with
Students will find areas of 183, 198, 206, 213, 245,
199, 201-205, 207-211,
just edges in common.
regular polygons and
297, 306, 356, 409, 423,
245-249, 301-305, 307circles.
430, 469, 497, 600, 609,
311, 357-361, 417-421,
3. Find and use measures
616, 621, 648, 654, 659,
429-433, 435-439, 479of sides and interior and
483, 503-507, 611-615,
exterior angles of triangles Students will find areas of 665, 670, 694
irregular
figures,
and
of
617-621, 623-627, 629and polygons to classify
Enrichment, Chapter
633, 667-671, 673-677,
figures (scalene, isosceles, irregular figures on the
Resource Masters (CRM), 679-683, 685-689, 691and equilateral, rectangles, coordinate plane.
pp. 62, 74, 80, 104, 130,
695, 723-727
and other convex
Students will identify and 136, 154, 188, 200, 206,
polygons.)
classify triangles by
212, 250, 306, 312, 362,
Technology:
422, 434, 440, 484, 508,
Graphing Calculator and
4. Interpret and draw three- angles, and by sides.
616, 622, 628, 634, 672,
Computer Masters
dimensional objects and
Students will find the sum 678, 684, 690, 696, 728
pp. 19, 30-32, 37-38
find the surface area and
of
the
measures
of
the
volume of basic figures
interior angles of a
Assessment, Mid-Chapter
(spheres, rectangular
polygon,
and
the
sum
of
Test, CRM, p. 121, 241,
solids, prisms, polygonal
the exterior angles of a
347, 475, 657, 719
cones), and calculate the
surface areas and volumes polygon.
of these figures as well as
figures constructed from
unions of rectangular
solids and prisms with
faces in common, given
7
A. Analyze characteristics
and properties of two- and
three-dimensional
geometric shapes and
develop mathematical
arguments about geometric
relationships. (Cont’d)
figures constructed from
unions of rectangular
solids and prisms with
faces in common, given
the formulas for these
figure.
5. Demonstrate an
understanding of simple
aspects of a logical
argument:
•
•
identify the
hypothesis and
conclusion in
logical deduction
use counterexamples to show
that an assertion is
false and recognize
that a single
counterexample is
sufficient to refute
an assertion.
6. Demonstrate an
understanding of inductive
and deductive reasoning,
explain the difference
between inductive and
deductive reasoning, and
identify and provide
examples of each:
• for inductive
reasoning,
demonstrate
Students will recognize
the conditions that ensure a
quadrilateral is a
parallelogram.
Students will prove that a
set of points forms a
parallelogram in the
coordinate plane.
Students will draw 2dimensional models for 3dimensional figures.
Students will find surface
area.
Students will find lateral
areas and surface areas of
prisms.
Students will find lateral
areas and surface areas of
cylinders.
Students will find lateral
areas and surface areas of
regular pyramids.
Students will find lateral
areas and surface areas of
cones.
Assessment, CRM, p.119,
Quiz 2; p. 120, Quiz 4; p.
175, Quiz 1; p. 176, Quiz
3; p. 239, Quiz 2; p. 345,
Quiz 1; p. 345, Quiz 2; p.
407, Quiz 1; p. 473, Quiz
2; p. 655, Quiz 1 & Quiz 2;
p. 656, Quiz 3; p. 717,
Quiz 1 & Quiz 2; p. 718,
Quiz 3
geometryonline.com/self_
check_quiz
TestCheck and Worksheet
Builder CD-ROM, Lessons
2.1, 2.3, 2.4, 2.8, 3.1, 3.2,
3.5, 4.1, 4.3-4.5, 5.1, 6.2,
6.3, 7.2, 8.1, 8.3, 8.4, 9.1,
9.5, 11.1-11.4, 12.2-12.6,
13.1
ACE Assessment: Explain
the similarities and
differences between
finding the lateral area and
surface area of a cone
versus the lateral area and
surface area of a regular
pyramid.
Students will find volumes
of prisms and cylinders.
8
A. Analyze characteristics
and properties of two- and
three-dimensional
geometric shapes and
develop mathematical
arguments about geometric
relationships. (Cont’d)
demonstrate
• understanding that
showing a
statement is true
for a finite number
of examples does
not show it is true
for all cases unless
the cases verified
are all cases.
• For deductive
reasoning, prove
simple theorems.
Students will analyze
statement in if-then form.
Students will write the
converse, inverse, and
contrapositive of if-then
statements.
7. Write geometric proofs
(including proofs by
contradiction), including:
Students will name and
label corresponding parts
of congruent triangles.
a. Theorems involving the
properties of parallel lines
cut by a transversal line
and the properties of
quadrilaterals.
Students will identify
congruence
transformations.
b. Theorems involving
complementary,
supplementary, and
congruent angles.
c. Theorems involving
congruence and similarity.
d. The Pythagorean
Theorem.
Students will make
conjectures based on
inductive reasoning.
Students will find
counterexamples.
Students will identify and
use perpendicular bisectors
and angle bisectors for
triangles.
Students will identify and
use medians and altitudes
in triangles.
Students will recognize
and apply properties of
rectangles.
Students will determine
whether parallelograms are
rectangles.
9
whether parallelograms are
rectangles.
A. Analyze characteristics
and properties of two- and
three-dimensional
geometric shapes and
develop mathematical
arguments about geometric
relationships. (Cont’d)
Students will draw
reflected images.
Students will recognize
and draw lines of
symmetry and points of
symmetry.
Students will determine
whether a dilation is an
enlargement, a reduction,
or a congruence
transformation.
Students will determine
the scale factor for a given
dilation.
Students will use the Law
of Detachment, and the
Law of Syllogism.
Students will identify the
relationships between two
lines and two points.
Students will name angles
formed by a pair of lines
and a transversal.
Students will use the
properties of parallel lines
to determine congruent
angles.
10
to determine congruent
angles.
Students will use algebra
to find angle measures.
A. Analyze characteristics
and properties of two- and
three-dimensional
geometric shapes and
develop mathematical
arguments about geometric
relationships. (Cont’d)
Students will recognize
angle conditions that occur
with parallel lines.
Students will prove that
two lines are parallel based
on given angle
relationships.
Students will write proofs
involving supplementary
and complementary angles.
Students will write proofs
involving congruent and
right angles.
Students will use the SSS
and SAS postulates to test
for triangle congruence.
Students will use the ASA
Postulate and AAS
Theorem to test for triangle
congruence.
Students will identify
similar figures.
Students will solve
2problems involving scale
factors.
11
2problems involving scale
factors.
Students will identify
similar triangles.
A. Analyze characteristics
and properties of two- and
three-dimensional
geometric shapes and
develop mathematical
arguments about geometric
relationships. (Cont’d)
Students will use similar
triangles to solve problems
Students will use the
Pythagorean Theorem.
Students will use the
converse of the
Pythagorean Theorem.
Vocabulary/Concepts
• apothem
• irregular figure
• irregular polygon
• acute triangle
• equiangular
triangle
• equilateral triangle
• isosceles triangle
• obtuse triangle
• right triangle
• scalene triangle
• diagonal
• axis
• circular cone
• lateral area
• lateral edges
• lateral faces
• net
• oblique cone
• oblique cylinder
12
A. Analyze characteristics
and properties of two- and
three-dimensional
geometric shapes and
develop mathematical
arguments about geometric
relationships. (Cont’d)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
oblique prism
regular pyramid
right cone
right cylinder
right prism
slant height
surface area
volume
conclusion
conditional
statement
contrapositive
converse
hypothesis
if-then statement
inverse
logically equivalent
related conditionals
conjecture
counterexample
inductive reasoning
congruence
transformations
altitude
centroid
circumcenter
concurrent lines
incenter
median
orthocenter
perpendicular
bisector
point of
concurrency
rectangle
isometry
13
•
•
•
•
•
•
•
•
A. Analyze characteristics
and properties of two- and
three-dimensional
geometric shapes and
develop mathematical
arguments about geometric
relationships. (Cont’d)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
line of reflection
line of symmetry
point of symmetry
reflection
transformation
dilation
similarity
transformation
deductive
reasoning
Law of Detachment
Law of Syllogism
alternate exterior
angles
alternate interior
angles
consecutive interior
angles
corresponding
angles
parallel lines
parallel planes
skew lines
transversal
included angle
included side
scale factor
similar polygons
Pythagorean triple
14
Mathematics Standard 2: Geometry
GEOMETRY and TRIGONOMETRY: Students will understand geometric concepts and applications.
Essential Question: How can a point be located on a plane (flat) surface?
Benchmark
B. Specify locations and
describe spatial
relationships using
coordinate geometry and
other representational
systems.
Performance Standards
1. Demonstrate
understanding of the
construction of the
coordinate plane, know the
names of the origin,
coordinate axes and four
quadrants, draw and label
them correctly, find the
coordinates of an indicated
point, and plot a point with
given coordinates.
2. Determine the midpoint
and distance between two
points within a coordinate
system and relate these
ideas to geometric figures
in the plane (e.g., find the
center of a circle given two
endpoints of a diameter of
the circle).
3. Given two linear
equations, determine
whether the lines are
parallel, perpendicular, or
coincide.
End Learning
Mastery
Students will find the
distance between two
points.
Students will find the
midpoint of a segment.
Students will identify and
name polygons.
Students will find the
perimeters of polygons.
Students will write an
equation of a line given
information.
Assessment(s)
Practice Quiz 2, Student
Glencoe Key Chapters: 1,
Edition (SE), p. 150, p. 306, 3-6, & 11
p.609
Glencoe Lessons 1.3, 1.6,
Open-Ended Assessment,
3.4, 4.1, 4.4, 5.1, 6.1-6.3,
Teachers Wraparound
11.2
Edition (TWE), pp. 27, 50,
150, 183, 206, 245, 287,
Glencoe Chapter Resource
297, 306, 609
Masters
pp. 13-17, 31-35, 145-6,
Enrichment, Chapter
183-187, 201-205, 245-249,
Resource Masters (CRM), 295-299, 301-305, 307-311,
pp. 18, 36, 148, 188, 206,
617-621
250, 300, 306, 312, 622
Assessment, Mid-Chapter
Test, CRM, p. 53, 241, 347
Students will solve
problems by writing
equations.
Assessment, CRM, p. 51,
Quiz 2; p. 52, Quiz 4; p.
239, Quiz 2; p. 345, Quiz 1
Students will identify and & Quiz 2; p.655, Quiz 1
classify triangles by angles, geometryonline.com/self_
and by sides.
check_quiz
Students will use the SSS
and SAS Postulates to test
for triangle congruence.
Resources
Technology:
Glencoe Graphing
Calculator and Computer
Masters
Pp. 18, 27
TestCheck and Worksheet
Builder CD-ROM, Lessons
1.3, 1.6, 3.4, 4.1, 4.4, 5.1,
6.1-6.3, 11.2
15
4. Use basic geometric
ideas (e.g., the Pythagorean
theorem, area, and
perimeter of objects) in the
context of the Euclidean
Plane, calculate the
perimeter of a rectangle
with integer coordinates
and sides parallel to the
coordinate axes and with
sides not parallel.
6.1-6.3, 11.2
Students will identify and
use perpendicular bisectors,
medians, altitudes, and
ACE Assessment: How do
angle bisectors.
engineers use geometry?
• Why do engineers
Students will identify and
use triangles in
use medians and altitudes in
construction?
triangles.
• Why do you think
Students will write ratios.
the pressure applied
Students will use
to the ground from
properties of proportions.
the Eiffel Tower is
so small?
Vocabulary:
Division Property of
Equality
Multiplication Property of
Equality
inequality
variable
unknown
numerical expression
algebraic expression
evaluate
Students will model and
solve contextualized
problems using various
representations, such as
graphs, tables, formulas,
and equations.
16
and equations.
Vocabulary:
Venn diagram
sets
models
graphs
charts
Mathematics Standard 2: Geometry
GEOMETRY and TRIGONOMETRY: Students will understand geometric concepts and applications.
Benchmark
B. Specify locations and
describe spatial
relationships using
coordinate geometry and
other representational
systems. (cont’d.)
Performance Standards
End Learning
Mastery
Students will identify
similar figures.
Assessment(s)
Resources
Students will solve
problems involving scale
factors.
Students will identify
similar triangles.
Students will use similar
triangles to solve problems.
Students will find areas of
triangles, trapezoids, and
rhombi.
17
B. Specify locations and
describe spatial
relationships using
coordinate geometry and
other representational
systems. (cont’d.)
Vocabulary/Concepts
• midpoint
• segment bisector
• concave
• convex
• n-gon
• perimeter
• polygon
• regular polygon
• point-slope form
• slope-intercept form
• acute triangle
• equiangular triangle
• equilateral triangle
• isosceles triangle
• obtuse triangle
• right triangle
• scalene triangle
• included angle
• altitude
• centroid
• circumcenter
• concurrent lines
• incenter
• median
• orthocenter
• perpendicular
bisector
• point of
concurrency
• cross-product
• extremes
• means
• proportion
• ratio
• scale factor
18
•
similar polygons
Mathematics Standard 2: Geometry
GEOMETRY: Students will understand geometric concepts and applications.
Essential Question: How does it move?
Benchmark
C. Apply transformations
and use symmetry to
analyze mathematical
situations.
Performance Standards
End Learning
Mastery
Students will draw
reflected images.
Assessment(s)
1. Describe the effect of
rigid motions on figures in
the coordinate plane and
space that include rotations, Students will recognize
translations, and reflections: and draw lines of symmetry
and points of symmetry
a. determine whether a
Students will draw
given pair of figures on a
coordinate plane represents translated images using
coordinates.
the effect of a translation,
reflection, rotation,and/or
Students will draw
dilation.
translated images by using
b. sketch the planar figure repeated reflections.
that is the result of a given
transformation of this type. Students will draw rotated
images using the angle of
rotation.
Practice, Student Edition
(SE), Quiz 2, p. 482; Quiz
2, p. 497
Students will identify
2. Deduce properties of
figures with rotational
figures using
transformations that include symmetry.
translations, rotations,
reflections, and dilations in
a coordinate system:
Geometryonline.com/self_
check_quiz
Open-Ended Assessment,
Teachers Wraparound
Edition (TWE), pp. 469,
475, 482, 497
Enrichment, Chapter
Resource Masters (CRM),
pp. 484, 490, 496, 508
Assessment, Mid-Chapter
Test, CRM, p.409
Resources
Glencoe Key Chapters 9
Glencoe Lessons 9.1-9.3,
9.5
Glencoe Chapter Resource
Masters
pp. 479-483, 485-489, 491495, 503-507
Technology:
Glencoe Graphing
Calculator and Computer
Masters
pp. 33-34
Assessment, CRM, Quiz 1,
p. 535
19
translations, rotations,
reflections, and dilations in
a coordinate system:
TestCheck and Worksheet
Students will determine
Builder CD-ROM, Lessons
whether a dilation is an
9.1-9.3, 9.5
enlargement, a reduction, or
a. identify congruency and a congruent transformation.
similarity in terms of
Students will determine the ACE Assessment:
transformations.
scale factor for a given
Explain how amusement
rides exemplify rotations.
b. determine the effects of dilation.
Include the following in
the above transformations
Vocabulary/Concepts:
your answer:
on linear and area
• angle of rotation
• a description of how
measurements of the
•
center
of
rotation
the Tilt-A-Whirl
original planar figure.
• composition
actually rotates two
• dilation
ways, and
• direct isometry
• other amusement
• glide reflection
rides that use
• indirect isometry
rotation.
• invariant points
• isometry
• line of reflection
• line of symmetry
• point of symmetry
• reflection
• rotation
• rotational symmetry
• similarity
transformation
• translation
Mathematics Standard 2: Geometry
GEOMETRY and TRIGONOMETRY: Students will understand geometric concepts and applications.
Essential Question: Can problems be solved without using numbers?
20
Benchmark
End Learning
Assessment(s)
Mastery
D. Use visualization, spatial 1. Solve real-world
Students will name and
Practice Quiz, Student
reasoning, and geometric
problems using congruence label corresponding parts of Edition (SE), Quiz 1, p.
modeling to solve
and similarity relationships congruent triangles.
198; Quiz 1, p. 306; Quiz 2,
problems.
of triangles.
p. 323; Quiz 1, p. 363; Quiz
Students will identify con- 2, p. 393; Quiz 1, p. 609
2. Solve problems
gruence transformations.
Open-Ended Assessment,
involving complementary,
supplementary, and conStudents will identify
Teachers Wraparound
similar triangles.
Edition (TWE), pp. 114,
gruent angles.
198, 306, 315, 323, 356,
363, 370, 376, 383, 390,
3.Solve problems involving Students will use similar
triangles to solve problems. 600, 609, 616
the perimeter, circumference, area, volume, and
Students will use proporEnrichment, Chapter
surface area of common
tional parts of triangles.
Resource Masters (CRM),
geometric figures.
pp. 104, 200, 312, 318, 324,
362, 368, 374, 380, 386,
4. Solve problems using the Students will divide a
segment into parts.
392, 616, 622, 628
Pythagorean Theorem.
D. Use visualization, spatial
reasoning, and geometric
modeling to solve
problems. (Cont’d)
Performance Standards
5. Understand and use
elementary relationships of
basic trigonometric
functions defined by the
angles of a right triangle.
Students will recognize
and use proportional relationships of corresponding
angle bisectors, altitudes,
and medians of similar
triangles.
6. Use trigonometric
functions to solve for the
length of the second leg of
a right triangle given the
angles and the length of the
first leg.
Students will recognize
and use proportional relationships of corresponding
angle bisectors, altitudes,
and medians of similar
triangles.
Assessment, Mid-Chapter
Test, CRM, pp. 347, 409,
657
Resources
Glencoe Key Chapters: 2,
4, 6, 7, 11
Glencoe Lessons: 2.8, 4.3,
6.3-6.5, 7.2-7.7, 11.1-11.3
Glencoe Chapter Resource
Masters
pp. 99-103, 195-199, 307311, 313-317, 319-323,
357-361, 363-367, 369-373,
375-379, 381-385, 387-391,
611-615, 617-621, 623-627
Technology:
Glencoe Graphing
Calculator and Computer
Masters
pp. 28-30, 37-38
Assessment, CRM, Quiz 4,
p. 120; Quiz 2, p. 345; Quiz
3, p. 346; Quiz 1, p. 407;
Quiz 2, p.407; Quiz 3, p.
408; Quiz 4, p. 408; Quiz 1,
p. 655; Quiz 2, p. 655
geometryonline.com/self_
check_quiz
TestCheck and Worksheet
Builder CD-ROM, Lessons
2.8, 4.3, 6.3-6.5, 7.2-7.7,
11.1-11.3
21
first leg.
triangles.
Builder CD-ROM, Lessons
2.8, 4.3, 6.3-6.5, 7.2-7.7,
11.1-11.3
7. Know and use angle and
side relationships in
problems with special right
triangles.
Students will write proofs
involving supplementary
and complementary angles. ACE Assessment: The
Chicago Metropolitan
Students will write proofs Correctional Center is a 27involving congruent and
story federal detention
right angles.
center. The cells are
arranged around a loungeStudents will find
like common area. The
perimeters and areas of
architect found that a
parallelograms.
triangular floor plan
allowed for the maximum
Students will determine
number of cells to be most
whether points on a
efficiently centered around
coordinate plane define a
the lounge.
parallelogram.
How are triangles used in
building design?
Students will find areas of
• Why was the
triangles, trapezoids, and
building triangular
rhombi.
instead of
rectangular?
Students will find areas of Why couldn’t the Law of
regular polygons and
Sines be used to solve the
circles.
triangle?
Students will use the
Pythagorean Theorem.
D. Use visualization, spatial
reasoning, and geometric
modeling to solve
problems. (Cont’d)
Students will use the
converse of the
Pythagorean Theorem.
Students will use
properties of 45-45-90
triangles.
22
problems. (Cont’d)
Students will use
properties of 30-60-90
triangles.
Students will find
trigonometric ratios using
right triangles.
Students will solve
problems using
trigonometric ratios.
Students will solve
problems involving angles
of elevation, and angles of
depression.
Students will use the Law
of Sines to solve triangles.
Students will solve
problems by using the Law
of Sines.
Students will use the Law
of Cosines to solve
triangles.
Students will solve
problems by using the Law
of Cosines.
D. Use visualization, spatial
reasoning, and geometric
modeling to solve
problems. (Cont’d)
Vocabulary/Concepts:
23
reasoning, and geometric
modeling to solve
problems. (Cont’d)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
congruence
transformations
congruent triangles
midsegment
apothem
ambiguous case
angle of depression
angle of elevation
cosine
Law of Cosines
Law of Sines
Pythagorean identity
Pythagorean triple
Reciprocal identities
sine
solving a triangle
tangent
trigonometric
identity
trigonometric ratio
trigonometry
Mathematics Standard 3: Geometry
DATA ANALYSIS AND PROBABILITY: Students will understand how to formulate questions, analyze data, and determine probabilities.
Essential Question: What is a statistical method?
reasoning, and geometric
modeling to solve
A.
Select and
use
1. For univariate data, be
problems.
(Cont’d)
appropriate statistical
able to display the
methods to analyze data.
distribution and describe its
shape using appropriate
summary statistics, and
understand the distinction
between a statistic and a
parameter:
congruence
transformations
Students
will identify
and
• congruent
triangles
use •perpendicular
bisectors,
midsegment
medians,
altitudes, and
• apothem
angle
bisectors.
• ambiguous case
• angle of depression
Students
willofidentify
and
• angle
elevation
use •medians
cosineand altitudes in
triangles.
• Law of Cosines
• Law of Sines
• Pythagorean identity
• Pythagorean triple
•
Open-Ended Assessment,
Teachers Wraparound
Edition (TWE), p. 245
Glencoe Key Chapter: 5
Enrichment, Chapter
Resource Masters (CRM),
pp. 250
Glencoe Chapter 5
Resource Masters
pp. 245-249
Glencoe Lessons 5.1
24
parameter:
Vocabulary/Concepts:
• altitude
Calculate and apply
• centroid
measures of central
• circumcenter
tendency (mean, median,
• concurrent lines
mode) and measures of
• incenter
variability (range, quartiles,
• median
standard deviation)
• orthocenter
• perpendicular
bisector
• point of
concurrency
geometryonline.com/self_
check_quiz
TestCheck and Worksheet
Builder CD-ROM, Lesson
5.1
ACE Assessment:
Explain how you can
balance a paper triangle on
a pencil point. Include the
following in your answer:
• which special point
is the center of
gravity, and
• a construction
showing how to find
this point.
25