Chabot College Fall 2014
•
MTH 41 - Number Systems
•
Development of quantitative reasoning skills through exploration of mathematical topics. Topics include structure of numeration systems including the real number system and its subsystems, number theory, and computational algorithms.
•
Prerequisite: MTH 53 (completed with a grade of "C" or higher) or , MTH 53B (completed with a grade of
"C" or higher) or , MTH 54 (completed with a grade of "C" or higher) or , MTH 54L (completed with a grade of "C" or higher) or , MTH 55 (completed with a grade of "C" or higher) or , MTH 55L (completed with a grade of "C" or higher) or an appropriate skill level demonstrated through the Early Assessment Program or an appropriate skill level demonstrated through the Mathematics assessment process.
3.00 units
Lecture
Laboratory
Clinical
Total
Units
3.00
3.00
Contact Hours
Week Term
3.00
0
0.00
3.00
52.50
0
0.00
52.50
•
1. use formulas and the metric system to find areas and volumes;
2. use dimensional analysis to perform multi-step unit conversions;
3. use scientific notation to perform calculations and make comparisons;
4. create and solve linear equations involving fractions, decimals, and percents;
5. interpret absolute value;
6. interpret and apply formulas involving several variables and parameters;
7. create, apply, and interpret graphs and equations of linear and piecewise linear functions;
8. create, apply, and interpret graphs and equations of exponential functions;
9. create, apply, and interpret graphs and equations of variation functions, including square root functions;
10. apply and interpret logarithmic models;
11. apply proportional reasoning appropriately in real-life situations;
12. calculate and interpret linear and exponential rates of growth;
13. create appropriate graphical displays of univariate quantitative and categorical data;
14. create and interpret scatterplots of bivariate quantitative data
15. calculate and interpret the mean and median for a set of data;
16. create and interpret frequency and relative frequency tables;
17. interpret two-way tables for bivariate categorical data;
18. apply and interpret the relative frequency definition of probability;
19. use two-way tables to calculate and interpret conditional probabilities;
20. calculate and interpret weighted averages;
21. recognize the Normal distribution as an example of a probability distribution;
22. use a graphing calculator and statistical software as tools in problem solving.
23. describe data using concepts of frequency and measures of central tendency;
24. identify functions, find domain and range, and use function notation in the context of real data;
25. identify the slope of a line using that it is parallel to another line;

26. find average rates of change;
27. graph and find the equations of linear functions in the context of real data;
28. solve problems involving direct and inverse proportionality;
29. find linear models for data;
30. find linear system models for data and interpret solutions to these linear systems;
31. perform operations using the properties of rational exponents;
32. graph exponential functions and interpret real growth and decay situations and data with exponential functions;
33. solve exponential equations using logarithms;
34. analyze real situations and data by using exponential functions with base e and natural logarithmic functions;
35. find inverse functions and compose functions in the context of real data;
36. graph quadratic, power, and logarithmic functions;
37. analyze real situations and data using quadratic functions;
38. choose an appropriate model for a realistic situation given a choice of mathematical models.
39. perform basic operations on complex numbers;
40. solve quadratic equations by factoring, completing the square, and quadratic formula;
41. find complex roots of a quadratic equation;
42. sketch the graphs of functions and relations: a. algebraic, including polynomial and rational b. logarithmic c. exponential d. circles;
43. find and sketch inverse functions;
44. perform function composition;
45. solve exponential and logarithmic equations;
46. apply the concepts of logarithmic and exponential functions;
47. solve systems of linear equations in three unknowns using elimination and substitution;
48. apply the properties of and perform operations with radicals;
49. apply the properties of and perform operations with rational exponents;
50. solve equations and inequalities involving absolute values;
51. solve equations involving radicals;
52. find the distance between two points;
53. find the midpoint of a line segment.
•
1. evaluate the equivalence of numeric algorithims;
2. explain the advantages and disadvantages of equivalent algorithms;
3. perform calculations with place value systems;
4. apply algorithms from number theory to determine divisibility;
5. compare and contrast least common multiple and greatest common divisor;
6. analyze the roles least common multiple and greatest common divisor have in standard algorithms;
7. explain the concept or rational numbers using ratio and decimal representations;
8. analyze and determine the equivalency of arithmetic algorithms of the ratio and decimal representations of rational numbers;
9. analyze the structure and properties of different number systems including real numbers and its subsystems;
10. illustrate the use of a number line representation; and
11. develop activities implementing curriculum standards.
•
1. Numeration systems
A. Historical
B. Hindu-Arabic
C. Place-value
2. Basic number theory
A. Divisibility
B. Prime and composite numbers
C. Prime factorization

•
D. Fundamental Theorem of Arithmetic
E. Least Common Multiple
F. Greatest Common Divisor
3. Integers
A. Structure
B. Properties
4. Rational numbers
A. Structure
B. Properties
C. Ratio
D. Proportions
5. Real numbers
A. Structure
B. Operations
C. Properties
D. Rational and irrational numbers
E. Decimal representations
F. Number line representation
6. Computational algorithms
A. Equivalency
7. National and state standards for elementary school mathematics
1. Demonstration/Exercise
2. Group Activities
3. Lecture/Discussion
4. Textbook reading assignments
5. Problem Solving
6. Presentation of audio-visual materials
7. Computer-based interactive curriculum
8. Hands-on Activities
9. Diagnostic Quizzes
10. Verbal explanation and demonstration.
11. Handouts and rule interpretations.
•
•
A. The NCTM Standards state "All students should solve simple problems involving rates and derived measurements for such attributes as velocity and density." Provide two examples that satisfy this statement and justify your choices.
B. What is the largest three-digit prime all of whose digits are prime?
C. An iPod is on sale for $159.20 and its normal price is $199. A student says that the percent discount is 39.8%. Is the student correct? If not, where did the student go wrong?
A. Class Work
B. Homework
C. Quizzes
D. Final Examination
E. Group Projects
F. Online Assignments
G. Class Participation
H. Exams/Tests
1. Musser, G. L. Burger, W. F. Peterson, B. E (2011). Mathematics For Elementary Teachers A
Contemorary Approach (ninth/e). John Wiley & Sons, INc..
2. Billstein, R. Libeskind, S. Lott, J. W (2013). A Problem Solving Approch to Mathematics for
Elementary School Teachers (eleventh/e). Pearson.
3. Long, C, T. De Temple, D. W. Millman, R. S (2012). Mathematical Reasoninig for Elementary
Teachers (sixth/e). Addison Wesley.
4. MyMathLab. Pearson, (Latest/e).

•
1. Scientific calculator