Download Attached course outline written by: Math 1260 Committee, Connie

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COURSE OUTLINE FORM
Course Title: Geometry
Course Prefix & No.:
Math 1260
LEC: LAB:
4.5 0
Credit Hours:
4.5
COURSE DESCRIPTION: This course covers geometric topics of logic, measurement, plane figure
relationships and figures in space are presented in this course.
COURSE PREREQUISITE (S): Within two years prior to brginning the course, either successful completion of
MATH 0930 or higher with a grade of P or C or better or MCC Placement Test
RATIONALE:
This course is design to provide the geometry skills needed by students weak in geometry. It will give an
understanding of geometric figures and properties to students in graphic arts and other programs.
REQUIRED TEXTBOOK (S) and/or MATERIALS:
Title: Essentials of Geometry for College Students
Edition: 2/e 2004
Author: Lial, Brown, Steffensen, Johnson
Publisher: Pearson
Materials: Scientific calculator, notebook, straight-edge, compass, protractor
Attached course outline written by: Math 1260 Committee, Connie Buller
Date: 5/15/04
Reviewed/Revised by: Math 1260 Committee
Date: 11/SP
Effective quarter of course outline: 13/FA
Date: 7/29/13
Academic Dean: Brad Morrison
Date: ______
Course Objectives, Topical Unit Outlines, and Unit Objectives must be attached to this form.
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COURSE OUTLINE FORM
TITLE: Geometry
PREFIX/NO: MATH 1260
COURSE OBJECTIVES:
Upon completion of this course, each student will be able to:
1.
2.
3.
4.
5.
Give examples of inductive/deductive reasoning
Give examples of direct statements, inverses, converses and contrapositives.
Define or describe points, lines and angles, postulates and theorems
Perform geometric constructions using a straight edge and compass on paper
Write basic deductive, direct and indirect proofs for selected problems with parallel lines, triangles,
polygons and circles.
6. Classify and apply geometric principles to three-dimensional and two-dimensional objects.
7. Use and apply circle relationships, including arcs, secants and tangents. Do related constructions.
8. Graph points and lines and write the equation of a line.
9. Solve right triangles using trigonometric functions, the Pythagorean Theorem, 30-60-90 and 45-45-90
relationships.
10. Use unit conversions in practical applications
TOPICAL UNIT OUTLINE/UNIT OBJECTIVES:
Unit 1: Foundations of Geometry: Inductive/Deductive Reasoning, Points, Lines and Angles,
Constructions
Upon completion of this unit of study, the student will be able to do the following:
1. Define and compare inductive/deductive reasoning, postulates and theorems
2. Write, use and compare direct statements, inverses, converses, and contrapositives.
3. Mathematically define or describe the following: points, lines, segments, rays, half-lines, angles, angle
bisectors, midpoints of segments,
4. Construct with compass and straightedge: segments, angles, angle bisectors and midpoints of segments.
Unit 2: Classify, use, and do proofs with congruent and similar triangles and quadrilaterals; Construct
medians and altitudes;
Upon completion of this unit of study, the student will be able to do the following:
1. Identify and construct scalene, isosceles, equilateral, congruent, similar, acute, obtuse and right triangles
2. Construct medians and altitudes of triangles
3. Use basic definitions, postulates and theorems to do deductive proofs with congruent triangles, and
apply their properties.
4. Construct parallel and perpendicular lines.
Unit 3: Use indirect and deductive proofs, and apply with parallel lines, quadrilaterals, similar triangles
and polygons, and use the Pythagorean Theorem
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COURSE OUTLINE FORM
Upon completion of this unit of study, the student will be able to do the following:
1. Use inductive work to make conjectures about parallel and perpendicular lines.
2. Do proofs involving congruent and similar triangles.
3. Construct parallel and perpendicular lines, congruent and similar triangles
4. Use the Pythagorean Theorem.
5. Classify a polygon by the number of sides and tell whether it is regular.
6. Identify the special types of quadrilaterals and their properties.
.
Unit 4: Use and apply circle relationships, including arcs and secants. Do related constructions.
Upon completion of this unit of study, the student will be able to do the following:
1. Define, draw and determine the relationships involved in chords, secants and tangents.
2. Compute the length of arcs, measures of inscribed angles and circumference of circles.
3. Define, draw and determine the relationships involved in chords, secants and tangents
4. Construct circles, and their tangents. Find the center of a circle from a given arc by construction.
Unit 5: Use and apply Solid Geometry, Analytic Geometry, Right Triangle Trigonometry
Upon completion of this unit of study, the student will be able to do the following:
1. Identify and sketch 3-dimensional geometric solids, finding their lateral areas and volumes
2. Use 30-60-90 and 45-45-90 triangle relationships and the Pythagorean Theorem to write and calculate
formulas
3. Graph point and lines.
4. Calculate slopes of lines, including parallel and perpendicular lines.
5. Write the equation of a line, and calculate distance between points.
6. Define a degree.
7. Identify the adjacent side, the opposite side and the hypotenuse of a right triangle.
8. Review the Pythagorean Theorem.
9. Define and use the sin, cos and tan of an angle as ratios of the side lengths of a right triangle
10. Use unit conversions in practical applications
opposite
(memorize these ratios): sin × = -----------------hypotenuse
adjacent
cos × = -----------------hypotenuse
opposite
tan × = -----------------adjacent
11. Find the angle when the trigonometric ratio is given.
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12. Solve right triangles using sine, cosine and tangent.
(find all sides and all angles)
a. Solve applied word problems using sin, cos and tan.
Unit 6. ENRICHMENT
These objectives are only to be taught if all of the above required objectives have been taught and
tested over following the testing guidelines.
1. Construct a Golden Rectangle
2. Construct the sum, difference, product, quotient and square root of a given line segment; divide it into
fractional parts, like thirds or fifths (these Constructible Numbers are all applications of parallel and
perpendicular lines and similar triangles)
3. Truth Tables
COURSE REQUIREMENTS/EVALUATION:
Upon completion of the objectives for this course, each of the objectives will be assessed and measured as
follows:
COURSE OBJECTIVES/ASSESSMENT MEASURES
COURSE OBJECTIVES
ASSESSMENT MEASURES
Unit 1
 Give examples of inductive/deductive
reasoning
 Give examples of direct statements, inverses,
converses and contrapositives.
 Define or describe points, lines and angles,
postulates and theorems
 Perform geometric constructions using a
straightedge and compass on paper

Unit 2
 Identify and construct scalene, isosceles,
equilateral, congruent, similar, acute, obtuse
and right triangles
 Construct medians and altitudes of triangles,
parallel and perpendicular lines using a
straightedge and compass on paper.
 Use basic definitions, postulates and theorems
to do deductive proofs with congruent
triangles, and apply their properties.



A minimum of 4 in-class, closed-book, nonotes, individual written exams covering ALL
the topical unit objectives must be completed
with a combined average score of 60% or
higher in order to achieve a course grade of C
or above.
Compass and straightedge will be required on
some exams.
A scientific calculator may be used on all
exams (no cell phone or laptop)
Other assessment measures such as homework,
papers, portfolios, may be used in addition to
the above
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Unit 3
 Write basic deductive, direct and indirect
proofs for selected problems with parallel lines
 Give examples of direct statements, inverses,
converses and contrapositives.
 Perform geometric constructions using a
straight edge and compass on paper
Unit 4
 Use and apply circle relationships, including
arcs, secants and tangents.
 Construct circles, and their tangents. Find the
center of a circle from a given arc by
construction.
 Compute the length of arcs, measures of
inscribed angles and circumference of circles.
 Define, draw and determine the relationships
involved in chords, secants and tangents
Unit 5
 Classify and apply geometric principles to
three-dimensional and two-dimensional
objects.
 Use unit conversions in practical applications
 Graph points and lines and write the equation
of a line.
 Solve right triangles using trigonometric
functions, the Pythagorean Theorem, 30-60-90
and 45-45-90 relationships.
The basic formulas for area/volume of basic shapes
and solids should be on the exam. The basic formulas
for 30-60-90 and 45-45-90 triangles should be on the
exam. The pi button should be used instead of 3.14.
Rounding should be done at the END of the problem.
Sketches done by students should be included,
particularly for solid shapes.
In the case of extenuating circumstances, you have the option of allowing students to retake at most
one (1) exam. If you choose to offer this retake, to increase the chances of improving student
learning, it is highly recommended that the student complete additional requirements before being
allowed to retake.
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COURSE OUTLINE FORM
TO THE INSTRUCTOR:
The following are recommendations for instructors teaching MATH 1260.
1. When necessary, topics from prerequisite courses should be quickly reviewed.
If time permits at the end of the quarter, enrichment topics may be included in the course as listed in
the outline.
2. Scientific calculators should be incorporated into instruction. It is the responsibility of the student to
bring a calculator to class. Cell phones are not to be used as calculators.
3. Compass and straightedge constructions should be incorporated into instruction. It is the
responsibility of the student to bring a compass and straightedge to class.
4. Assistance is available in the Academic Resource Centers /Math Centers. Solids and rulers are
available for you as an instructor, and also available for student use. Check with Academic Resource
Centers/Math Center personnel at your site.
5. The Academic Resource Centers/Math Center staff are available to refer students to the tutorial
material and to answer some specific questions. However, their presence does not replace the
instructor’s responsibility for helping his/her students outside of class.
COURSE REQUIREMENTS/EVALUATION:
Upon completion of the objectives for this course, the following objectives will be assessed and measured as
follows:
1. A minimum of four in-class, no notes, closed book exams must be taken individually covering all the
required (not enrichment) topical unit objectives. The combined average of these tests must be 60%
or above to achieve a grade of C or above.
2. Other assessment tools such as journals, group work, quizzes, and homework can be used as part of
the assessment.
TEXTBOOK-SPECIFIC INFORMATION:
The following is a listing of specific sections from the Lial/Brown/Steffenson/JohnsonTable of
Contents required to be taught during one quarter. The following schedule of lectures can be used by
the instructor as a guide when planning the course syllabus. You should follow the timeline listed for
each of the sections. This gives you thirty-two 55 minutes periods to teach the material (with one
additional day for your discretion), five periods to test review, and five periods to administer tests in a
typical 44 day quarter meeting four days a week for 55 minutes.
Section 1.1 (1-31 odd)
Objective 1: Define Inductive Reasoning
Objective 2: Define an Axiomatic System
Objective 3: Define Deductive Reasoning
Section 1.2 (1-29 odd)
Objective 1:. State undefined terms
Objective 2: State postulates about points, lines, planes, and real numbers
Section 1.1 should be
covered in one 55 minute
class along with the
syllabus.
Section 1.2 should be
covered in one 55 minute
class.
Section 1.3 (1-67 odd)
Objective 1: Define line segment and ray
Objective 2: Define angles, including degrees, minutes, seconds, and
borrowing to find complements/supplements
Objective 3: Identify special angles (adjacent,complementary,
supplementary, acute, obtuse, right)
Sections 1.3 should be
covered in one 55 minute
class.
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Section 1.4 (1-28 odd)
Objective 1: Define conditional, converse, inverse and contrapositive
statements
Objective 2: Introduce deductive proofs
Note: these terms will be used later in the course, particularly with
isosceles triangles and also parallel lines
Section 1.5 (1-31 odd)
Objective 1: Define the format of a formal geometric proof
Objective 2: Describe the thinking process in a formal proof
Objective 3: Use the format of the thinking process
Objective 4: Define vertical angles; use them with proofs
Note: it is very nice to bring wax paper, and have students fold 2
intersecting lines to make vertical angles, and see that they seem to be
equal.
Section 1.4 should be
covered in one 55 minute
classes.
Section 1.6 (1-29 odd) + 6 Constructions Involving Lines and Angles
Objective 1: Define perpendicular lines
Objective 2: Define angle bisector
Objective 3: Use compass and straightedge to do 6 basic constructions:
copy segment; copy angle; bisect segment, bisect angle, drop a
perpendicular to a line from a point off the line; construct a perpendicular to
a line from a point on the line)
Note: The sheet at the end of this course outline is the last sheet of my first
Unit exam, and lists the last 5 of the 6 basic constructions (copy segment;
copy angle; bisect segment, bisect angle, drop a perpendicular to a line
from a point off the line; construct a perpendicular to a line from a point on
the line)
Note: it is nice to bring wax paper, have students fold a line, mark 2
points on it (can pierce the paper with their compass point), and fold one
point over the other, creasing the new line—it is a perpendicular bisector of
the segment determined by the two points.
Section 2.1 (1-45 odd) ; Review
Objective 1: Identify parts of a triangle
Objective 2: Classify triangles by their sides; by their angles
Objective 3: Define interior and exterior angles of a triangle
Objective 4: Find the perimeter of a triangle
Section 1.6 should be
covered in one 55 minute
class; students will
need compass and
straightedge
Unit Exam 1 (Chapter 1 only; constructions required—compass
needed)
Note: a straightedge may be simply a folded sheet of paper; you may
choose to loan students a piece of string to tie around their pencil if they
have forgotten their compass)
Section 2.2 (1-29 odd)
Objective 1: Define congruent segments, angles, and triangles
Objective 2: State the SAS, ASA, SSS postulates
Objective 3: Use the postulates to show congruence of triangles.
Note: it can be helpful to write SAS  SAS as the end of a proof instead of
simply SAS
Note: it is helpful to bring a scissors and two sheets of paper, cutting out
One 55 minute class;
students will need
compass and
straightedge
Section 1.5 should be
covered in one 55 minute
class.
Section 2.1 and Review
should be covered in one
55 minute class.
Section 2.2 should be
taught in one 55 minute
classes.
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a shape on both sheets at the same time, and using that to demonstrate
the idea of congruence—and then moving the two shapes to let students
see the shapes are still congruent even if they have a different orientation.
Section 2.3 (1-25 odd + 18,20) construct angle bisectors and segment
bisectors
Objective 1: Define and use Corresponding Parts of  Triangles are 
Objective 2: Prove the Angle Bisector and Segment Bisector Constructions
Note: Although the book uses CPCTE, this is pretty meaningless to students—it is
safer to abbreviate word “Corresponding”, and use the triangle and congruence
symbols)
Note: Problems 17-20 are very nice practical applications of congruence, and one
reason we selected this text; the problems in this text are not paired, and so we
include the evens on these practical applications.
Section 2.4 (1-29 odd + 28) construct medians, altitudes, angle
bisectors
Objective 1: Prove some properties of isosceles trianges
Objective 2: Identify the converse of a statement, and concurrent lines
Objective 3: Define and construct medians, altitudes and angle bisectors of
triangles
Objective 4: Investigate some properties of concurrent lines in triangles
Note: Very nice to mention the application of medians to constructing
mobiles in art projects; do not make students memorize words like
centroid, orthocenter, or incenter, but they should be able to construct
these, and understand some of the properties.
Section 2.3 should be
taught in one 55 minute
classes; students will
need compass and
straightedge
Section 2.4 should be
taught in one 55 minute
classes; students will
need compass and
straightedge
Section 2.5 (1-19 odd)
Objective 1: Define the LA theorem for right triangles and prove congruent
Objective 2: Define the LL theorem for right triangles and prove congruent
Section 2.5 should be
taught in one 55 minute
class.
Section 2.6 (1-29 odd) construct congruent triangles given parts
Objective 1: Construct triangles with various given parts
Objective 2: Construct altitudes and medians of triangles
Review
Section 2.6 should be
taught in one 55 minute
class. Students will need
compass and
straightedge
One 55 minute class
Test 2 (chapter 2) Compass and Straightedge required.
One 55 minute class
Sections 3.1 (1-29 odd) Section 3.2 (1-41 odd)
Objective 1: Indirect Proof
Objective 2: The Parallel Postulate
Objective 3: Define angles formed by parallel lines and a transversal
(corresponding, alternate interior, alternate exterior; compare to
vertical)
Objective 4: Describe ways to prove lines parallel, and prove theorems
Note: it is very nice to bring wax paper, and fold parallel lines, crossed by
a transversal, and have students mark and note the various angles formed.
Dry erase markers are handy to mark on the wax paper.
Sections 3.3 (1-31 odd) Section 3.4 (1-41 odd)
Objective 1: Define and classify polygons, with perimeter, diagonals,
interior and exterior angles
Sections 3.1 and
3.2should be taught in
one 55 minute class.
Sections 3.3 and 3.4
could be taught in One
55 minute class, but also
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Objective 2: Construct parallel lines with compass and straightedge
Objective 3: Calculate degrees of angles in polygons, both interior and
exterior
Note: there are formulas, but it is easier to cut polygons into triangles,
using the idea that there are 1800 in a triangle; use the idea of zooming out
to help students recognize that there will be 360o circling around the dot
that the polygon finally shrinks down to, counting only one exterior angle at
each vertex (this is a limiting idea from calculus, but you need not mention
that).
Objective 4: prove AAS, HA and HL theorems (using congruent triangles
and corresponding parts of  Triangles are 
Section 4.1 (1-20 odd) and Section 4.2 (1-11 odd)
Objective 1: Define and classify parallelograms
Objective 2: Use properties of parallelograms, rhombi and kites and do
related proofs
could be taught in two,
depending on your
class—watch the time at
the end.
Students will need
compass and
straightedge
Section 4.3 (1-35 odd, also #24)
Objective 1: Define rectangles and squares, with their properties
Objective 2: Prove and use the theorem about segments joining the
midpoints of two sides of a triangle.
Objective 3: Construct a rectangle with compass and straightedge
Objective 4: Discuss and use practical applications of the above
Section 4.4 (1-31 odd + divide a segment into parts by construction
and parallel lines)
Objective 1: Define and use properties of trapezoids
Objective 2: Divide a segment into n equal parts by construction, using
parallel lines. Note: do both by compass and straightedge, but also show
students how it can be done with lined paper (see example in book)
Section 4.3 should be
taught in one 55 minute
class.
Students will need
compass and
straightedge
Section 4.4 should be
taught in one 55 minute
class.
Students will need
compass and
straightedge
Section 5.1 (1-37 odd)
Objective 1: Review ratio and proportion
Objective 2: Define means and extremes, and mean proportional
(geometric mean)
Objective 3: Do multiple proportions, such as the proportions of blending
paint is 3:5:2 for red, white and blue
Note: Students will be unfamiliar with this practical application—an easy
way is 3x + 5x + 2x = the number of ounces needed in the final mixture.
Note: an old-fashioned way of writing proportions is 2:3::4:6. The inner two
are the means; the outer two are the extremes, and the means-extremes
property is what some call “cross-multiplying” for proportions.
Section 5.1 should be
taught in one 55 minute
class.
Section 5.2 (1-45 odd)
Objective 1: Define similar polygons
Objective 2: Prove triangles similar with AA = AA
Objective 3: Calculate proportions formed by a line intersecting a triangle
that is parallel to one side
Objective 4: Calculate proportions formed by a line bisecting one angle of
a triangle.
Sections 5.2 should be
taught in one 55 minute
class.
Sections 4.1 and 4.2
should be taught in one
55 minute class
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Section 5.3 (1-45 odd) and Section 5.4 (1-45 odd)
Objective 1: Calculate proportions formed by an altitude to the hypotenuse
of a right triangle (it is a mean proportional; construct a mean proportional)
Objective 2: Use and apply the Pythagorean Theorem
Note: Although the Pythagorean Theorem is presented in its traditional
a2+b2 = c2 format, it removes one layer of abstraction if it is presented as
leg2 + leg2 = hypotenuse2. This is particularly practical as most triangles in
ordinary use do not come pre-labelled a,b,c and in this course there will be
much use of 30-60-90 and 45-45-90 triangles, which depend on the
Pythagorean Theorem
Review; Section 6.1 (1-33 odds)+ Handout Using Circles Practically
Objective 1: Define circles, arcs, inscribed and central angles
Objective 2: Prove and use the facts that inscribed angles are ½ the
measure of their intercepted arcs; central angles are equal to their inscribed
arcs
Objective 3: Using Circles practically
Note: Encourage students to draw circles to illustrate their homework
problems in this and following circle sections—an easy way to sketch a
circle is to use a small coin, like a penny
Note: The handout has the formula for area of a circle, and also has unit
conversions. The answers are on the handout.
Sections 5.3 and 5.4
should be taught in one
55 minute class.
Students will need
compass and
straightedge
Unit Test 3 (Chapters 3,4,5 only)
Section 6.2A (1-15 odd)
Objective 1: Define and use chords of circles
Objective 2: Find angles and segment lengths created by intersecting
chords
One 55 minute class.
Section 6.1A should be
taught in one 55 minute
class.
Section 6.2B (17-33 odd) + worksheet using circles practically
Objective 1: Define and use secants of circles
Objective 2: Find angles and segment lengths created by intersecting
secants
Note: do #31, 33 with students in class—the main aim should be that they
can find the angles and segment lengths, though understanding where
these theorems come from reinforces similar triangle relationships and
inscribed and central angle relationships
Section 6.3 (1-39 odd)
Objective 1: Define and Use Tangents to a Circle
Objective 2: Construct a Tangent to a Circle from a point on the circle
Objective 3: Construct a Tangent to a Circle from a point off the circle
Objective 4: Construct the center of a circle, given an arc from the circle
Objective 5: Find lengths of tangents and segments formed by tangents;
Objective 6: Find angles formed by tangents
Objective 7: Find the distance to the horizon, using tangent properties
Note: These applications have much to do with the concepts of 6.1 and 6.2
Section 6.2B should be
taught in one 55 minute
classes.
Review
Unit Exam 4 (Chapter 6) scientific calculators; compass/straightedge
used
Section 8.1 (1-31 odd) + Euler, Hamilton
Objective 1: Determine the behavior of lines and planes in space
One 55 minute class
One 55 minute class
Section 6.1 and Review
should be taught in one
55 minute class. The
test will only cover
Chapters 3,4,5
Section 6.3 should be
taught in one 55 minute
class.
Students will need
compass and
straightedge
Section 8.1 should be
taught in one 55 minute
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Objective 2: Define vertices, edges, faces and polyhedrons; sketch 3-d
shapes;
Objective 3: Use toothpicks and raisins to model polyhedrons; use them
to work with Euler’s formula
Note: divide students into small groups of 2 or 3. Give each group some
toothpicks and raisins (explain that the raisins have been dropped on the
floor, so they won’t eat them) and have them build polyhedra. Toothpicks
are edges; raisins are vertices; the polyhedra are hollow (don’t count any
toothpicks used just for internal struts).
Euler’s circuit: can cover all the edges without retracing any edge (like
snow-plowing streets—don’t want to re-trace any streets) and return to
start.
Euler path: the same, tracing all edges, but not making a complete
circuit—end somewhere other than start
Hamiltonian circuit: the same, but going to all vertices without visiting a
vertex twice, and returning to start
Hamiltonion path: the same, but going to all vertices without being able to
return to start.
Note: this activity does two things: it gives students a glimpse of how
geometry is being used today in graduate school projects, and more
importantly it REALLY lets them know what is a vertex (raisin) an edge
(toothpick) and a face. It also REALLY helps them distinguish between
lateral surface area and volume. Then do Euler’s formula for each structure
the students have made.
Section 8.2 (1-31 odd)
Objective 1: Defining prisms, lateral surface area and volume
Objective 2: Sketching prisms
Objective 3: Finding surface area and volume
Objective 4: Using 30-60-90 triangles to find the area of a hexagon
Objective 5: Use unit conversions in practical applications
Note; Keep memorization to a minimum by having students break
complex shapes into familiar triangles and rectangles.
Note: Help students understand that volume of a prism is simply how many
layers there are of the base. V = Area of base x height. This is true no
matter what the shape of the base.
Note: in sketching a solid, give a bit of a pinch to the congruent bases (a
rectangle looks like a non-rectangular parallelogram; a circle looks like a
non-circular ellipse). Let the sides of the rectangles be parallel to each
other, and then connect the corresponding vertices, letting the “hidden”
sides appear with dashed lines.
Section 8.3 (1-19 odd)
Objective 1: Defining pyramids, slant height and altitudes
Objective 2: Find lateral area and volume
Objective 3: Use unit conversions in practical applications
Note: Again, break complex shapes into familiar triangles and rectangles
rather than using formulas like LA = ½ pl. There is enough for them to
memorize without that.
Note: A good activity is to take a pointed solid (cone or pyramid) and its
related cylinder or cone. Show the bases are congruent, and the heights
are the same. Ask the students how many pyramids (cones) it takes to fill
class.
Teacher: bring
toothpicks and raisins
Section 8.2 should be
taught in one 55 minute
class.
Teacher: bring
geometric solids (may
be found in mailroom or
also in Math Centers)
Section 8.3 should be
taught in one 55 minute
class.
Teacher: bring
geometric solids (may
be found in mailroom or
also in Math Centers;
bring a larger container
of small beans or rice
for volume experiment
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the related prism (cylinder). Go around the room, recording guesses. Then
fill the pointed one with small beans or rice, and pour it into the larger
shape. The conclusion is that it takes 3 of the pointed to equal one of the
other. This helps in understanding the formulas for volume.
Note: In sketching a pyramid, give a pinch to the base as described
earlier. Let a dot stand for the point that is the apex of the pyramid, and
connect the dot to each vertex of the base. In this class, all pyramids will
be right pyramids, though the set of geometric solids may have some slant
pyramids.
Section 8.4 (1-39 odd)
Objective 1: Define cylinders and calculate volume and surface area
Objective 2: Define cones and calculate volume and surface area
Objective 3: Use unit conversions in practical applications
Note: Be certain to use the pi button on their calculators instead of 3.14
Note: Roll a sheet of paper. The students already know the area of a
rectangle to be base x height. Now the base is the circumference of a
circle, so the lateral area must be 2  rh.
Note: if you didn’t do the volume with cylinders/cones and beans
earlier, this would be a good place. I like it earlier so that students can see
the overall ideas of Volume upright solid = Area of Base x height; Volume
upright cone/pyramid = 1/3 Area of Base x height.
Note: to illustrate the effect of the round-off error occurring with use of
3.14 for  consider a LARGE cylindrical tank holding corn syrup (like
at Cargill). Let the tank be about 40 feet high, and with a diameter of 20
feet. Find how many gallons of corn syrup are in there, and multiply by the
cost per quart. See how many gallons are given for free, and the cost, if
the seller uses 3.14. This is a nice exercise in unit conversions as well,
which employers of our Metro students say that they need to have in
employees. Ask the students whether they are rounding down or up in
using 3.14, and why they think Cargill might value use of the  button
Note: To illustrate the area of a circle  r2, sketch a circle, and divide it
up into sections, with vertex at center, and as narrow a sections as you
can. Now take those sections and sketch them lined up wide end, point
end, wide, point, so that they now seem to form a rectangle. Students
know the area of a rectangle is base times height: if the sections were cut
VERY narrow, the height corresponds to the radius, and the base
corresponds to ½ a circumference. So it makes the Area of a circle:  r
(r)=  r2 more believable.
Note: Linear measure is in 1 dimension, so plain feet/inches/cm; area,
involving 2 dimensions and multiplication, is measured in square units;
volume, involving 3 dimensions, is measured in solid units, or cubic
units.
Note: In unit conversion, it is sometimes difficult for students to realize
that while 3 feet = a yard, 9 square feet = 1 square yard, and 27 cubic feet
= 1 cubic yard. When ordering cement for a project, this matters….
Section 8.5 (1-29 odd)
Objective 1: Define a sphere and calculate surface area and volume
Objective 2: Break composite shapes into simpler forms like hemispheres
and cylinders to find area and volume
Objective 3: Use unit conversions in practical applications
Section 8.4 should be
taught in one 55 minute
class.
Teacher: bring
geometric solids (may
be found in Math
Centers)
Section 8.5 should be
taught in one 55 minute
class.
Teacher: bring
geometric solids (may
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Note: pronounce sphere as ss-FEER
Note: do the even numbered problems in class, particularly #24, 26, 28.
Problems 25,27,29 depend on these, and address the general objective of
unit conversion
Section 9.1 (1-55 odd) and Section 9.2 (1-51 odd)+ worksheet using
lines in business
Objective 1: Use the Cartesian coordinate system
Objective 2: Apply the Pythagorean Theorem to find the distance between
two points; use averaging to find the midpoint between two points
Objective 3: Define and use slope of a line, including parallel and
perpendicular lines
Objective 4: Write and graph the equation of a line
Objective 5: Use practical applications of using equations to describe lines
be found in Math
Centers)
At the close of this
chapter, return the set
of solids to where you
found them, so another
class can use the; the
set in the Math Centers
is for the students’ use
outside of class.
Sections 9.1 and 9.2
should be taught in one
55 minute class.
Note: Although it is possible to clear fractions and use the traditional slope
formula (assuming all points on a line have the same slope, so you can use
(x,y) instead of (x2,y2) and get y – y1 = m(x – x2), it is easier for students to
derive the equation of a line by substituting the slope and a single known
point into y = mx + b and then solving for b. It is also much easier to
remember y = mx + b than the other form.
Note: Because students are by now VERY familiar with the Pythagorean
Theorem, and with parallel and perpendicular lines, and with bisecting
segments, this is not as hard as if it were done in an Algebra class.
Section 10.1 (1-25 odd) and Section 10.2 (1-35 odd)
Objective 1: Define and use Sine, Cosine, and Tangent ratios, including
30-60-90.
Objective 2: Find an angle, given its trig ratio
Note: These sections will serve as a review of much learned earlier, such
as “opposite side” and right triangles, as well as 30-60-90 and 45-45-90
(which come from base angles of isosceles triangles, and diagonals of
squares). A way to introduce the trig ratios is to sketch a right triangle,
choosing one of the acute angles, and labeling the adjacent, opposite sides
as well as the hypotenuse. Let students help ‘discover’ the 6 possible
ratios—and then define them as Sine Cosine and Tangent. They do need
to know SohCahToa (Sine = opp/hyp; Cosine = adj/hyp; Tan = opp/adj)
but not to memorize the reciprocal functions of
Cosecant/Secant/Cotangent). They have already used the mnemonic
(P)EMDAS for order of operations—this is My Dear Aunt Sally’s mother’s
maiden name…)
Note: Do not make students rationalize denominators, but show them
how to check their answers against the book answers, using their
calculators.
Sections 10.1 and 10.2
should be taught in one
55 minute class.
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Note; Using the inverse function to find the underlying angle is an
extension of what they have always done to solve linear equations (do the
same to both sides). Students will need help in finding the Sine-1 key on
their calculators. Make sure students have their calculators in degree
mode, and do several in class.
Section 10.3 (1-23 odd) and Section 10.4 (1-19 odd)
Objective 1: Solving Right Triangles
Objective 2: Practical Applications using trigonometry
Note: This again will provide a review of earlier material. The angles of
elevation/depression are the alternate interior angles. To avoid making
round-off errors worse, use given measurements when possible.
Review
Test 5 (chapters 8,9,10)
Note: on the exam, you may wish to have the following formulas:
Use the

Sections 10.3 and 10.4
should be taught in one
55 minute class.
One 55 minute class.
One 55 minute class
period.
button on your calculator; label units on final answer
 r 2 Circumference circle: 2  r Vol cylinder:  r 2 h
2
Vol prism: lwh Lateral Area cylinder: 2  rh Surface area sphere: 4  r
Area circle:
1
1
4
 r 2 h Vol sphere:  r 3 Vol pyramid lwh
3
3
3
1
bh SohCahToa
Area triangle:
2
Vol cone:
MATH 1260
Using Circles Practically
C. Buller
accompanying Section 6.1
Show work
Round answers to the nearest tenth, if necessary. Use the π button
Note: Area of a circle = πr2; Circumference of a circle = πd
1. A circular garden at the Elkhorn Valley Campus has radius 9 m. If a 1 meter-wide circular walk surrounds it, what is the area of
the walk?
a).Draw a picture representing the situation.
b) What is the area of the walk?
1b) ________
2. A 12-inch diameter pizza costs $8.50. A 16-inch diameter pizza costs $11.50. Which pizza costs less per square inch?
Hint: “per” means to divide by the square inch
a) What is the cost per square inch of the smaller pizza?
2a) ________
b) Which one costs less per square inch?
2b)________
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c) What might be a good reason to buy the pizza that costs more per square inch?
3. Mrs. Buller has a patio in the shape of a trapezoid with bases 8.1 yd and 6.7 yd and height 5.8 yd. A circular dining area in the
center of the patio has diameter 3.2 yd and is covered with Aztec tile. Assuming no waste, how much will it cost to the nearest dollar
to cover the remainder of the patio with outdoor carpeting that costs 80¢ per square foot?
Hint: be careful about conversions here
a)
Draw a picture representing the situation.
b) What is the dollar cost of the outdoor carpeting?
3b)_______
Answers: 1a) 59.7 m2
2a) 7.5¢
2b) The larger, by nearly 2¢ a square inch 3b ) $251
MATH1260
Lines in Business
C. Buller
accompanying Section 9.2
Show work
Round answers to the nearest penny, if necessary
1. Mr. Toline owns a small business that manufactures picture frames. He has determined that the weekly cost in dollars y of
making a number of picture frames x is described by the equation
y = 6x + 200.
a).Find the cost of making 80 picture frames in one week.
1a)_________
b) How many frames were made during a week when the costs were $1100?
1b) ________
2.
Mrs. Buller makes wood-burning kilns. She discovers that 10 kilns can be constructed for $2800, and 24 kilns can be made
for $6125.
Let y be the cost of making x kilns.
a) Find a linear equation describing this relationship. Hint: (x,y) = (kilns, cost)
2a) y = ___________
b) Use your equation to calculate the cost of making 31 kilns 2b) ______________
c) What do you think the $425 in the answer to 2a stands for?
3.
In 2004 (call this year 0), the Metropolitan Manufacturing Company had sales of $40,000. In 2009 (call this year 5), the total
sales were $170,000.
Let y be the total sales in year x.
a) Find a linear equation describing this relationship. Hint: (x,y) = (year, sales)
3a) y = ___________
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b) Use your equation to estimate the sales in year 2014
3b) ______________
c) Why might this estimate be wrong, even if you got the answer to 3a right?
Answers: 1a) $680
Revised 05-25-12
1b) 150
2a) y = 237.5x + 425
2b) $7787.50 3a ) y = 26000x + 40000 3b) $300,000
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(Page 17 of 17)
Five Basic Constructions
To be used in Unit 1; on Test 1 I allow 16 of the 100 points for doing any 4 of the 5—my 5 point bonus is to do the fifth one.
For the following five constructions. Show compass marks.
a)
Bisect
AB
A
b) Bisect Angle A
B
A
c) Copy Angle C at P
d) Construct a line perpendicular to l from D
D
C
P
e) Construct a perpendicular to m at E
E
ESO Revised 3-13-01