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Course Syllabus for Fundamentals of Mathematics II

ASSESSMENTS:

Prior to enrolling in this course, the student must demonstrate eligibility to enroll in the following: MATH
1314, MATH 1350, or MATH 1414.

PREREQUISITE : Math 1314, Math 1414, or Math 1350

COREQUISITE: None

TEXTBOOK:

A Problem Solving Approach To Mathematics For Elementary School Teachers, 9th ed., by Rick
Billstein, Shlomo Libeskind, and Johnny W. Lott 2007, Pearson Education.

SUPPLIES: Calculator with yx, ln x, ex, and log x keys, or graphing calculator (optional).

COURSE DESCRIPTION:

Concepts of geometry, probability, and statistics, as well as applications of the algebraic properties of real
numbers to concepts of measurement with an emphasis on problem solving and critical thinking. This
course is designed specifically for students who seek middle grade (4-8) teacher certification and includes
the foundational math concepts taught at the middle grade level.

COURSE MEASURABLE LEARNING OBJECTIVES:

Upon completion of this course, the student should be able to do the following:

1. Recognize, name, and compare two - and three-dimensional shapes
2. Explore congruent and similar objects through geometric constructions
3. Graph and solve linear equations and systems of linear equations
4. Measure attributes of two- and three-dimensional objects in the English and the metric
systems
5. Use transformations of the plane to illustrate symmetries, size transformations,
and tessellations
6. Use probabilities, simulations, and counting techniques to solve problems and analyze
games
7. Select and use appropriate statistical methods to analyze data and reason statistically

COURSE REQUIREMENTS:

Attending lectures, completing assignments, and exams.

ACADEMIC ETHICS:

The college may initiate disciplinary proceedings against a student accused of scholastic dishonesty.
Scholastic dishonesty includes, but is not limited to, statements, acts, or omissions related to
applications for enrollment or the award of a degree, and/or the submission of material as one’s own
work that is not one’s own. Scholastic dishonesty may involve one or more of the following acts:
cheating, plagiarism, collusion, and/or falsifying academic records.

Cheating is willful giving or receiving of information in an unauthorized manner during an
examination, illicitly obtaining examination questions in advance, using someone else’s work for
assignments as if it were one’s own, copying computer disks or files, and any other dishonest means of
attempting to fulfill the requirements of a course.

Plagiarism is the use of an author’s words or ideas as if they were one’s own without giving credit to
the source, including, but not limited to, failure to acknowledge a direct quotation.
Contact Dean of Students at 972.881.5771 for the student disciplinary process and procedures or
consult the CCCCD Student Handbook.

Collusion is intentionally or unintentionally aiding or attempting to aid another in an act of scholastic
dishonesty, including but not limited to, providing a paper or project to another student, providing an
inappropriate level of assistance, communicating answers to a classmate during an examination, removing
tests or answer sheets from a test site, and allowing a classmate to copy answers.

SPECIFIC REQUIREMENTS/COURSE CONTENT:

The student will be responsible for knowing all definition and statements of theorems for each section
outlined in the following modules.

Module 1: Introductory Geometry

The student will be able to:

1. Define and illustrate: collinear points, line segment, ray, coplanar points, coplanar lines, skew
lines, intersecting lines, concurrent lines, parallel lines, perpendicular lines, half-planes, line
perpendicular to a plane, transversal.
2. Classify angles as acute, right, obtuse, or straight.
3. Use a protractor to measure an angle.
4. Define and illustrate a curve as: simple, nonsimple, closed, nonclosed, convex, concave.
5. Define and illustrate polygons, polygonal region, interior angle of a polygon, exterior angle of
a convex polygon, diagonal of a polygon, regular polygon.
6. Define, illustrate, and know the notation for congruent segments and congruent angles.
7. Classify triangles a right, acute, obtuse, scalene, isosceles, equilateral.
8. Classify quadrilaterals as trapezoid, kite, isosceles trapezoid, parallelogram, rectangle,
rhombus, square .
9. Illustrate the hierarchy among polygons.
10. Define and illustrate comparisons of 2 angles such as adjacent, complementary,
supplementary, vertical, interior, exterior, alternate interior, alternate exterior, and
corresponding.
11. Determine the sum of the measures of the exterior angles of a convex polygon.
12. Determine the sum of the measures of the interior angles of a convex polygon.
13. Determine the measure of a single interior angle of a regular polygon.
14. Define and illustrate simple closed surfaces in three-dimensions.
15. Define and illustrate convex and concave polyhedra and their faces, vertices, and edges.
16. Define and illustrate the different types of prisms and pyramids.
17. Define and illustrate the five regular polyhedra.
18. Define the relationship between the number of faces, the number of edges, and the number of
vertices of any polyhedron.
19. Determine polyhedra formed from a net.
20. Define and illustrate the different types of cylinders and cones.
21. Define and illustrate a sphere.

Module 2: Constructions, Congruence, and Similarity

The student will be able to:

1. Define and illustrate similar objects.
2. Define and illustrate congruent objects.
3. Define and illustrate a circle, its center, its radius, an arc of a circle, the center of an arc, a
minor arc, a major arc, and a semicircle.
4. Construct congruent segments and congruent angles.
5. Determine if two triangles are congruent by SSS, SAS, ASA.
6. Construct a triangle given three sides.
7. Construct a triangle congruent to a given triangle by using two sides and the included angle.
8. Define and illustrate the perpendicular bisector of a segment.
9. Define and illustrate the altitude of a triangle.
10. Define and illustrate an isosceles triangle and its properties.
11. Construct the perpendicular bisector of a segment.
12. Construct a circle circumscribed about a triangle.
13. Define, illustrate, and know the properties of the six quadrilaterals.
14. Construct parallel lines, angle bisectors, and perpendicular lines.
15. Define and illustrate a tangent to a circle, a circle inscribed in a triangle, the incircle and the
incenter.
16. Define and illustrate similar figures and their scale factor .
17. Determine if two triangles are similar by AA.
18. Construct congruent parts of a segment.
19. Define and illustrate a midsegment.
20. Find indirect measurements using similar triangles.
21. Define and illustrate terms relating to the Cartesian coordinate system: origin, x-axis, y-axis, x-
coordinate, y-coordinate, graph.
22. Graph linear equations .
23. Find the equation of a line .
24. Find the x- intercept , y-intercept, and slope of a line.
25. Solve a system of linear equations by the substitution method, the elimination method, and
geometrically.

Module 3: Concepts of Measurement

The student will be able to:

1. Use dimensional analysis to convert from one unit of measure to another in the English system.
2. Define units of length in the metric system, and convert from one unit to another.
3. Determine the greatest possible error of a measurement.
4. Define and use the distance properties and the Triangle Inequality .
5. Find the perimeter of a polygon.
6. Find the circumference of a circle.
7. Given the radius of a circle, find the length of a semicircle or an arc whose central angle is
known.
8. Find areas of polygons on a geoboard or dot paper.
9. Convert units of area in the English and in the metric systems.
10. Find the area of a parallelogram, a triangle, a trapezoid, a regular polygon, a circle, and a sector of a circle.
11. Use the Pythagorean Theorem to determine the sides of a right triangle.
12. Define formulas for the 45-45-90 right triangle and the 30-60-90 right triangle.
13. Determine if a triangle is a right triangle by using the converse of the Pythagorean Theorem.
14. Use the Distance Formula to find the distance between two points.
15. Derive and use formulas for the surface area of a right prism, a right circular cylinder, a right
regular pyramid, a right circular cone, and a sphere.
16. Convert English and metric measures of volume.
17. Derive and use formulas for the volume of a right prism, right circular cylinder, right pyramid,
right circular cone, and sphere.
18. Determine the relationships among metric units of volume, capacity, and mass.
19. Convert units of temperature between the Celsius and Fahrenheit scales.

Module 4: Motion Geometry and Tessellations

The student will be able to:

1. Construct the image of a geometric figure under a translation.
2. Construct the image of a geometric figure under a rotation.
3. Construct the image of a geometric figure under a reflection.
4. Construct the image of a geometric figure under a glide reflection.
5. Construct an image that is similar to a geometric figure under a size transformation.
6. Determine whether a geometric figure has line symmetry, rotational symmetry, or point
symmetry.
7. Describe figures according to their symmetries.
8. Define and illustrate tessellations of the plane.
9. Determine which geometric figures tessellate the plane.

Module 5: Probability

The student will be able to:

1. Decide whether a probability is determined experimentally or theoretically.
2. Compute experimental and theoretical probabilities.
3. Determine the probability of mutually exclusive events, non-mutually exclusive events, and
complementary events.
4. Use a tree diagram to determine outcomes and probabilities of multistage experiments.
5. Define independent events and find the probability of two independent events occurring.
6. Model games that involve probability.
7. Use area models to determine probabilities geometrically.
8. Use simulations to compute probability.
9. Compute odds in favor and odds against.
10. Compute conditional probabilities.
11. Compute expected value and determine if a game is fair.
12. Compute the number of permutations or combinations of objects.
13. Use permutations and combinations in probability.

Module 6: Data Analysis/Statistics

The student will be able to:

1. Represent and interpret categorical and numerical data using statistical graphs: pictographs, dot
plots, stem-and-leaf plots, histograms, bar graphs, line graphs, scatterplots, circle graphs.
2. Compute and interpret measures of central tendency: mean median.
3. Find the mode of given data.
4. Compute and interpret measures of the spread of data: range, interquartile range, variance,
mean absolute deviation, standard deviation.
5. Determine if any outliers exist for given data.
6. Construct box plots.
7. Interpret and apply the graphs of normal distributions and the percentages that represent
approximations of the total percent of area under the curve.
8. Explore abuses and misleading uses of statistics.

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