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Math

Statistics and Discrete Math Curriculum Guide Grades 11-12

Objectives

Core Curr.
Content
Standards

Instructional
Activities

Assessment
(Cross-curricular)
(Multi-cultural)

Resources

 GEPA
HSPA
Terra Nova
CHAPTER 1
The student will be able to: 		  INTRODUCTION TO STATISTICS      
! Do overview. 4.3 Define statistics, population, sample, parameter, and a statistic. Quiz on definitions Statistics Textbook
Elementary Statistics 6th Ed., Mario F. Triola, NY-Addison Wesley, 1995		  
! Do the Nature of Data. 4.3
4.6		 Define the Nature of Data - primarily qualitative (categorical or attribute) data, quantitative data, discrete data, and continuous numerical data. Discuss the normal level of measurement, ordinal level of measurement, interval level of measurement, ratio level of measurement. Is statistics worth anything? p. 8
Measuring disobedience? p. 10
Is Army food good? p. 11
P. 11 Exercises 1-21		 Resource Books
Statistics-The Exploration & Analysis of Data 3rd Ed., Jay Devare, and Roxy Peck, Boston-Dunberry Press, 1997		 M. IV
! Describe the uses and abuses of statistics. 4.3
4.6
4.12		 Discuss the uses of statistics with short paragraphs, p. 12-13 P. 15-17 All exercises James T. McClare, Frank H. Dietrich XI, and Terry Sinrich, Upper Saddle River, NJ - Prentice Hall, 1997 M. III
M. IV
! Do methods of sampling. 4.2
4.13
4.16		 Define random, stratified, systematic, cluster and convenience sampling,
Fig. 1-2		 P. 22-23, 1-4 Statistics and Probability in Modern Life 6th Ed., Joseph Newmark, NY-Harcourt Brace, 1997 M. I
M. IV
! Review chapter. 4.2
4.18		 Review vocabulary list, review exercises, p. 29-30. Test Chapter 1
Interview-Lester Curtis, p. 32-33		    
CHAPTER 2   DESCRIPTIVE STATISTICS      
! Overview and to summarize data. 4.3
4.5
4.6
4.12		 Define descriptive statistics and inferential statistics. Describe a frequency table with classes. Define and describe lower class limits, upper class limits, class boundaries, class marks and class width. Relative frequency table and cumulative frequency table. P. 42-45, All exercises Teach Yourself Statistics
Alan, Graham,
Chicago, IL, NTC, Publishing Group 1994
Statistics EZ-101,
Martin Steinstein, NY, Barrin’s Educational Series, Inc., 1994
 M. III
M. IV
! Do pictures of data. 4.3
4.5
4.8
4.12		 Define histogram, pre-charts and pareto charts. Show histogram, relative frequency histogram, bell shaped curves, important distributions. Pareto charts and pre charts and explain differences. Florence Nightingale, p. 46
P. 51-54, All exercises 		Statistics - Descriptive Statistics and Probability
Elliot Tanis,
NY - Harcourt Brace, 1987		 M. II
M. III
M. IV
! Do measures of central tendency. 4.1, 4.2
4.5, 4.9
4.12		 Define a measure of central tendency, arithmetic mean, medium, and mode. Show notation necessary. Define and compute mid range. Explain the round-off rule. Describe a weighted man and one from a frequency table. Describe the best measure of central tendency and concept of skewness. Chapter Problem, p. 35
P. 66-71, All problems 		Introduction to Statistics, Susan F. Wagner,
NY Harper Perennial, 1992		 M. I
M. IV
! Do measures of variation. 4.1
4.2
4.9
4.12		 Define range, standard deviation, and variance. Procedures for computing standard deviation and variance with Form 2-4. Use proper notation calculate standard deviation from a frequency table. Use the range rule of thumb and Chebyshev’s Theorem. P. 85-90, All problems   M. I
M. II
M. IV
! Do measures of position. 4.1, 4.5
4.9, 4.12		 Define a standard or Z score. Describe quartiles, deciles, and percentiles. Show notation and flow charts. P. 98-100, All problems   M. III
M. IV
! Do exploratory data analysis. 4.1, 4.2
4.3, 4.6
4.12		 Compare and contrast EDA and Traditional statistics review stem-and leaf plots and box plots. Define upper and lower hinge, 5-number summary and box plot. P. 109-112, All problems   M. I
M. III
M. V
! Review. 4.2, 4.5
4.17, 4.18		 Go over vocabulary list and formulas. Do review exercises, pp. 114-116 Test Chapter 2
Group Project - from Data to Decision, p. 116		   M. I
M. V
CHAPTER 3   PROBABILITY      
! Do overview and fundamentals of problem. 4.1
4.3
4.9		 Define experiment, event, sample event, and sample space. Show notation for finding probability. Rules for relative frequency and classical approach. Extend discussion to Law of Large Numbers, random sample of one element or simple random sample. Define complementary events. Discuss paragraph on "how probable?", p. 130
P. 130-133, All exercises 		  M. I
M. III
M. IV
! Do addition rule. 4.3
4.5
4.15		 Define compound event. Show notation for addition rule. Do addition rule. Explain mutually exclusive events through use of flow chart or Venn diagrams and flow chart. Define complimentary events and notation needed. PP. 139-141, All exercises   M. III
M. IV
! Do multiplication rule. 4.1
4.3
4.9
4.12		 Explain tree diagrams and show notation. Explain difference between independent and dependent events through the multiplication rule. Define conditional probability and the probability of "at least one" Review two important aspects of the multiplication rule® acceptance sampling and redundancy. PP. 152-157, All exercises
Have students get additional information on Boyes’ Theorem 		  M. III
M. IV
! Do probability through simulations. 4.3
4.5
4.12		 Define simulation - discuss computer simulations. Do a menu-tab display (if computer available) Show a random number generation on graphing calculator. Have students research the "Monty Hall Problem", p. 162, 1-5   M. I
M. III
M. IV
! Do counting. 4.1, 4.3
4.6, 4.12		 Explain the fundamental counting rule, factorial rule, permutations rule, and combinations rule. PP. 170-173, All problems   M. I
M. IV
! Review for test. 4.2
4.18		 Vocabulary List, p. 174
Important Formula, p. 175
Review Exercise, pp. 176-178 		Test Chapter 4
P. 179, from Data to Decision
Drug testing of job applicants
Interview, pp. 180-181		   M. I
M. IV
R. II
CHAPTER 4   PROBABILITY DISTRIBUTION      
! Do overview and random variable. 4.1
4.3
4.14		 Define random variable, discrete random variable, continuous random variable and a probability distribution. Discuss requirements for a probability distribution. Review mean, median variance and standard deviation. Review expected values (and definition). PP. 194-197, 1-27   M. I
M. IV
R. II
! Do binomial experiments. 4.2
4.8
4.9
4.12		 Define binomial experiment and indicate notation for a binomial distribution. Use 2 methods to show possible solutions. Define the poison distribution. PP. 208-212, All problems   M. I
M. IV
! Complete the mean, variance and standard deviation for the binomial distribution. 4.1
4.3
4.12
4.16		 Go over Formula 4-1 / 4-4 and Formula 4-7 / 4-9. Show two methods. Discuss querying theory, p. 213
Go over examples and solutions. 		PP. 217-219   M. IV
! Review Chapter 4. 4.2
4.5
4.18		 Review - Vocabulary List and Important Formulas. Review exercises, pp. 221-222 Test Chapter 4
From Data to Decision, p. 223 		  M. I
M. V
CHAPTER 5   NORMAL PROBABILITY DISTRIBUTION      
! Do Overview and the Standard Normal Distribution. 4.3
4.5
4.8
4.12		 Review uniform distribution, density curve. Define the standard normal distribution. Find probabilities when given Z score. Use symmetry to fine area to left of mean. Show notations. Find the Z scores when given probabilities. PP. 236-238, All exercises   M. III
M. IV
! Find Nonstandard Normal Distributions. 4.3
4.5
4.11
4.12		 Find the probabilities when given scores. Normal Distribution. Do example and solutions. Find the scores when given probabilities. Explain example and solution. PP. 248-252, All exercises
Reliability and Validating, p. 247 		  M. I
M. IV
! Do the Central Limit Theorem. 4.1
4.10
4.12		 Define sampling distribution of sample means. Go over illustrations shown by dice. Do Central Limit Theorem - with given, conclusions & uses. Do notation. Do examples and solution. PP. 261-265, All exercises
Ethics in Experiments, p. 259 		  M. IV
M. V
! Do the normal distribution as approximation to a binomial distribution. 4.3, 4.5
4.12, 4.16		 Go over the normal distribution. Define a continuity correction. Use a flow chart to show solving a binomial probability problems. Do examples and solutions. Discuss computer applications. PP. 272-276, All examples   M. III
M. IV
! Review Chapter. 4.2
4.17
4.18		 Do vocabulary list, p. 276
Review important formulas.
Review exercises, pp. 278-179, 1-10		 Test Chapter 5
From Data to Decision - How can we out smart users of counterfeit coins in vending machines?
Interview, pp. 282-283 		  M. I
M. V
CHAPTER 6   ESTIMATES AND SAMPLE SIZE      
! Overview and to do estimating a population mean. 4.3
4.6
4.12		 Define an estimation, point estimate, confidence interval (or interval estimation), degree of confidence (confidence coefficient), a critical value and margin of error. Formula 6-1. Calculating E when O (standard deviation) is unknown. Do round off rule for confidence intervals. Discuss small sample cases and the student t distribution. Show formula for student t distribution and definition of degrees of fraction. Do formula 6-2 for margin of error. Find the sample size for estimating the mean and the round off rule. PP. 302-307, 1-32, All computer applications
Large sample sizes isn’t good enough, p. 298		 M. I
M. III
M. IV
M. V
R. II
! Estimate a population proportion. 4.1
4.3
4.5
4.12		 Show notation for sample proportion, Formula 6-4 margin of error of the estimate of P. Show confidence interval and round off rule. Determine sample size - with formula 6-5 and 6-6 and round off rule for determining sample size. PP. 313-317, All exercises
TV Sample Size, p. 309
How one telephone survey was conducted, p. 313		 M. IV
! Do estimating a population variance. 4.3
4.6
4.10
4.12		 Explain a chi-square distribution and formula 6-7. Explain the properties of the distribution of chi-square statistic. Discuss confidence interval for the population variance, notation, and round off rule. Wisdom of Hindsight, p. 323
How valid are crime statistics?,
p. 324
PP. 326-329, All Exercises		 M. III
M. IV
! Review chapter. 4.2
4.17
4.18		 Go over vocabulary list and important formulas. Review exercises, pp. 331-333, all exercises. Test Chapter 6
From Data to Decision: He’s angry but is he right?, p. 335		 M. I - M. V
CHAPTER 7 HYPOTHESIS TESTING
! Do overview and fundamentals of hypothesis testing. 4.3
4.12		 Discuss the components of a final hypothesis test - including null and alternative hypothesis. Read very important notes 1-3, pp. 341-342 and Type I and Type II Errors. Go over key components in hypothesis testing and flow charts. Two-tailed, left and right tailed tests. Drug Screening: False Positives,
p. 343
PP. 348-349, 1-15
Chapter Problem, p. 337 		M. I
M. III
M. IV
! Do testing a claim about a mean: Large Samples. 4.2
4.5
4.8
4.12		 Test statistics for claims about y when n> 30 including flow chart. Show distributions of means. Define a P-value and show flow chart of event. Flow chart for P-value method of testing hypothesis. Test claims with confidence intervals. P-Value Misuse, p. 356
PP. 363-367, All exercises 		M. I
M. IV
! Test a claim about a mean: Small Samples. 4.3
4.5
4.12		 How chart for choosing between the normal and student t distributions. Test statistics for claims about it. Important properties of the student t distribution. Examples and solutions - P-Value. PP. 374-377, All exercises
Small Sample, p. 370 		M. II
M. IV
! Test a claim about a proportions. 4.3
4.5
4.8
4.12		 Use assumptions when testing a claim about a population proportion, probability, or percentage. Test statistics for testing a claim about a proportion and notation. Examples and solutions, The P-Value Method. Muzak Commercials, p. 379
PP. 383-386, All exercises 		M. IV
M. V
! Test a claim about a standard deviation or variance. 4.3
4.6
4.8
4.12		 Assumption for testing claims about O (standard deviation) or O2 (variance)
Show formula and notation - Properties of the chi-square distribution, P-value examples and solutions. 		Product Testing, p. 393
PP. 393-397, 1-24, all 		M. IV
! Review Chapter 7. 4.2
4.17
4.18		 Review vocabulary lists and important formula. Review exercises, pp. 399-400 Test Chapter 7
From Data to Decision: Developing a plan for scheduling movies Interview, p. 404 		M. I - M. V
CHAPTER 8 INFERENCES FROM TWO SAMPLES
! Do overview and inferences about two means: Dependent Samples. 4.1
4.5
4.6		 Define independent and dependent. Show notation for two dependent samples. For hypothesis tests for two dependent samples. Show examples and solutions. Do confidence intervals. Crest and dependent sample, p. 412
Statistical significance versus practical significance, pp. 416-418, 1-18 all 		M. I
M. III
M. IV
! Do inferences about two means: Independence and large samples. 4.8
4.9
4.12		 Test statistics for two means: independent and large samples, confidence intervals examples and solutions. Gender Gap in Drug Testing,
p. 423
PP. 425-427, Ex. 1-20 all 		M. III
M. IV
! Compare two variance. 4.4
4.6
4.8		 Show assumption, show notations for hypothesis test with two variance, test statue for hypothesis test with two variances - example and solution. Drug Approval, p. 436
PP. 432-437, All exercises 		M. IV
! Do inferences about two means: Independent and small samples. 4.1
4.6
4.8
4.12		 Go over assumptions. Case 1: Both population variances are known;
Case 2: Equal variances (fuel to reject O12 = O22) and Case 3: Unequal variances (reject O12 = O22 ) Review all examples and solutions. Go over flow charts, pp. 446-447.		 PP. 448-451, All exercises M. III
M. IV
M. V
! Do inferences about two proportions. 4.3
4.7
4.12		 Go over assumptions and notations for hypothesis testing. Do pooled estimate of p1 & p2 and for two proportions. Examples and solutions. Review confidence intervals. Polio Experiment, p. 454
Examples 1-20, pp. 461-464		 M. I
M. IV
! Do review of chapter. 4.2
4.17
4.18		 Go over vocabulary test, p. 464
Review exercises, pp. 465, 468-470
Important formulas, pp. 466-467 		Test Chapter 8
From Data to Decision, p. 471		 M. I - M. IV
CHAPTER 9 CORRELATION AND REGRESSION
! Do overview and correlation. 4.1
4.3
4.7
4.12		 Define a correlation, linear correlation, coefficient and gutter diagram. Show notation for the correlation coefficient. Rounding the linear correlation coefficient. Shorter version of hypothesis testing using flow charts. Do test statistic t or r for linear correlation common errors involving correlation. Define central. Do exercises and solutions Power Lines Correlate with Cancer
P. 483
PP. 487-492, 1-32 		M. I
M. III
M. IV
! Do regression. 4.3
4.5
4.8
4.12		 Define regression equation and line and notation. Formulas 9-2, 9-3, and 9-4.
Rounding y Intercept B. and the Slope B, Define marginal change and predictions (including flow chart). Define least square property and confidence intervals.		 Los Angeles Ozone, p. 499
PP. 504-507, 1-30 		N. I
M. III
M. IV
! Do variation and prediction intervals. 4.3, 4.8
4.12, 4.16		 Define total deviation, explained and unexplained deviation. Define the coefficient of determination, standard error or estimate. Do prediction interval for y. Do examples and solutions. Unusual Economic Indicators,
p. 510
PP. 514-516, 1-20 		M. I
M. III
M. IV
! Do multiple regression. 4.3
4.12
4.16		 Define multiple regression equation and notation: Define the adjusted coefficient of determination - adjusted R2. Find the best multiple regression equation - steps. Predicting wine before its time, p. 522
PP. 523-525, 1-10 		M. I
M. IV
M. V
! Review chapter. 4.2
4.17
4.18		 Review vocabulary list, p. 526 and formulas p. 527
Review exercises, pp. 528-530 		Test Chapter 9
From Data to Decision, p. 531
Chapter Problems, p. 473 		M. I - M. V
UNIT I

SECTION 1 - FAIR VOTING

Chapter 1

! Voting in democratic institutions.

 

 4.3, 4.6
4.14, 4.17		 Introduce topic and give outline of information to follow including class project. Class Projects, p. 6, 1, 3, 4 Voting and Apportionment
Sandi Bennett, et al, The Apportionment Problem, The Search for the Perfect Democracy, HiMap Module 8, Lexington, MA Comap, Inc. 1986 		M. I
M. III

Chapter 2

! Do at-large election, multimember districts, and redistricting.

 4.3, 4.8
4.14		 Explain concept of multimember district, concept of redistricting and why it is done. Class Projects, p. 12, 1-3
(Group assignment)		 Fair Voting-Weighted Votes for Unequal Constituencies, William F. Lucas, Histo Map-Module 19, Lexington, MA, Comap, Inc., 1992 M. I
M. III

Chapter 3

! Explain proportional weighted voting.

 

 4.3, 4.5
4.6, 4.14		 Explain different types of voting including corporations and county boards. Show weights versus power is a false assumption. See tables 1-7. Students are to find newspaper and/ or magazine articles and relate to this topic. Is Democracy Fair? The Mathematics of Voting and Apportionment,
Leslie Johnson Nielsen & Michael deVilliers, Berkeley, CA, Key Curriculum Press, Inc. 1997 		M. I
M. III
R. III

Chapter 4

! To measure
power.

 

 4.1, 4.5
4.6, 4.14		 Define power and a weighted voting system. Use examples, pp. 25-26. Show the Bazhaf Power Index and show how to compute it using tables 8-9. Show an example using four votes Exercises, pp. 32-34, 1-11 all M. I
M. III

Chapter 5

! Do adjusted weighted voting.

 4.3
4.5
4.14		 Define adjusted weighted voting. Give examples with three and four values. Determining the appropriate weights. Exercises, pp. 45-46, 1-7 all M. I
M. III
! Review Chapter. 4.2
4.17
4.18		 Go over all sections, definitions, and problems. Test Section I
Group Project 		M. I
M. II
R. III
W. I
UNIT I
Part 1 - The Hamilton Method of Apportionment 		SECTION 2 - THE APPORTIONMENT PROBLEM
! Apportion the student council and goal of apportionment. 4.3
4.5
4.10
4.14		 Introduce concept of apportionment. Discuss difference between majority, plurality, "winner take all" or proportional representative. Students are to do problems, pp. 2-4. Discussion, p. 5 about method. Plurality Election Decision, pp. 1-2
IS DEMOCRACY FAIR 		Voting and Apportionment
Sandi Bennett, et al, The Apportionment Problem, The Search for the Perfect Democracy, HiMap Module 8, Lexington, MA Comap, Inc. 1986 		M. I
M. III
R. III
! Do quotas and use Hamilton’s method. 4.2
4.3
4.8
4.14		 Define quotas and discuss aspects of Hamilton’s method of apportionment. Do problems and examples, pp. 8-13. Apportionment, p. 61
Alexander Hamilton’s Method of Apportionment, p. 67
Quota method of Apportionment,
p. 129
IS DEMOCRACY FAIR 		Fair Voting-Weighted Votes for Unequal Constituencies, William F. Lucas, Histo Map-Module 19, Lexington, MA, Comap, Inc., 1992 M. I
M. III
M. IV
R. III
! Do the Alabama paradox and other problems. 4.1
4.3
4.5
4.8		 To explain how a state can lose a seat when the house size increases but there are no population changes. Show other problems effecting the quotas which cause unfairness. Show another flaw in Hamilton’s method "The Population Paradox". Paradoxes of Apportionment - Activity 14, p. 109
Is It Fair? Activity 13, p. 97
IS DEMOCRACY FAIR
Exercises pp. 23-27, all problems
HiMap-Module 8 		Is Democracy Fair? The Mathematics of Voting and Apportionment,
Leslie Johnson Nielsen & Michael deVilliers, Berkeley, CA, Key Curriculum Press, Inc. 1997		 M. I
M. III
R. II
! Do the Quota Method of Apportionment. 4.1, 4.3
4.8, 4.10		 Go over rounding off fractional parts of a quarter. What type of problems might occur. Adjusted quotion. The Quota Method of Apportionment, Activity 17
IS DEMOCRACY FAIR 		Voting and Apportionment
Sandi Bennett, et al, The Apportionment Problem, The Search for the Perfect Democracy, HiMap Module 8, Lexington, MA Comap, Inc. 1986 		M. I
M. V
! Look at other methods of apportionment. 4.3, 4.6
4.10, 4.14		 Look at Jefferson’s Apportionment, Hill Method and the Webster method and any other methods. Thomas Jefferson’s Method of Apportionment, Activity 11
Daniel Webster’s Method of Apportionment (Activity 12)
Joseph A Hill’s Method of Apportionment (Activity 15)
IS DEMOCRACY FAIR 		Fair Voting-Weighted Votes for Unequal Constituencies, William F. Lucas, Histo Map-Module 19, Lexington, MA, Comap, Inc., 1992 M. I
R. I
! Review apportionment. 4.2
4.17
4.18		 Go over all forms of apportionment. Review ordinal ballots, compare and contrast Jefferson and Hamilton. Test on Apportionment.
Group repeat on what shaped the Government Structure. 		Is Democracy Fair? The Mathematics of Voting and Apportionment,
Leslie Johnson Nielsen & Michael deVilliers, Berkeley, CA, Key Curriculum Press, Inc. 1997 		M. I
M. III
R. II
UNIT II
 MATHEMATICAL MODELS
Section 1 - Fair Divisions Fair Divisions - Module 9
! Divide a cake. 4.1
4.6
4.8		 Introduction discussing activity of shaving. Show several types of fair divisions and discuss problems of each type. Rank different methods of division, pp. 2-4 Fair Divisions: Getting Your Fair Share, HiMap Module 9, Sandy Bennett, ET AL, Lexington, MA, Comap, Inc. 1987 M. I
M. III
M. IV
M. V
4.2, 4.3
4.14
4.17		 Discuss Basic Assumption for division methods of dividing cake among three people. Group activity to develop a method to divide a cake among three people.
4.11 Discuss the Moving Knife Solution and another fair division algorithm. Problem 10, p. 18 and problem 5, p. 14; Exercises pp. 12-25 all
! Do the problem of dividing estates. 4.1
4.8
4.10		 Go over the problem of indivisible objects. Consider several ways of dividing up an Estate. Go over how to test if the method is fair. Exercises, pp. 31-35, all problems M. I
M. III
! Go over a history of fair division problems. 4.3
4.5
4.14
4.18		 Discuss the various activities on pages 37-38. Have students give a problem and a fair solution. Handed in for grade. M. III
Section 2 - Drawing Pictures with One Line
! Do Euler and one-line games. 4.2
4.3
4.11
4.14		 Go over information concerning these games: The drawing game and who plays it. The mathematical history of one-line picture. Explain what a graph is. Show examples of applications. Finding an Eulerion circuit and the onion skin and connectedness algorithm. Discuss Euler’s solution and why it is true. Have students look up Leonhand Euler and do a short biography.
Exercises, p. 1-20, Relevant to each section

Drawing Pictures with One Line, Histo Map Module 21, Darrah Chavey, Lexington, MA, Comap, Inc. 1992

 

 M. II
M. III
! Do real-world problems. 4.3
4.6
4.11
4.14		 Explain and review "Real-World" problems such as: Plotters and computer controlling machining tools, metal cutting problems, Chinese postman problem, the longest stroll, routing, several crows, one-way streets and directed graphs, laying out a galley, and the garbage collection problem. Exercises on all pages 21-49
Go over all solutions
Quiz on each type of solution 		M. I
M. III
M. IV
M. V
Section 3 - Problem Solving Using Graphs
! Do graphs, paths, circuits, and an algorithm. 4.3
4.7
4.14		 Review Euleran Paths. Discuss the Konagsberg bridge problem and translate it into a graph. Trace without lifting pencil. Exercises 1-2, p. 8 Problem Solving Using Graphs, HiMap Module 6, Margaret B. Cozzens and Richard Porter, Lexington, MA, Comap, Inc. 1987 M. II
M. III
! Do minimum spanning tree. 4.1
4.4
4.8
4.16		 Consider various network problem similar to one in book. Discuss notation of the greedy algorithm. Show technique of minimum spanning tree. Worksheet 2 M. II
M. III
M. IV
! Do shortest route problem. 4.2
4.11
4.11		 Discuss the problem of determining a big-sell strategy and indicate that this can be considered the shortest (least cost). Use Dyhstre’s algorithm to solve the buy-sell problems. Worksheet 3 and exercises 4 and 5, pp. 20, 22 M. II
M. III
! Do traveling circus problems. 4.2
4.6
4.14
4.16
4.17		 Look at examples of traveling salesman problem. Work out solutions and watch how long it take. Review how long it takes to develop the solution algorithm. Exercise 6
Project on Spanning Trees
Contest - quiz everyone		 M. III
M. V
Section 4 - Decision on Decision Methods
! Do the assignment problem. 4.1
4.4
4.11
4.16		 Discuss the nature of an assignment problem to be represented to explain each type. Tables on p. 12 Exercises 1-7, pp. 11-12 Decision Making and Math Models - HiMap Module 14, G. Surya Kumar, Lexington, MA, Comap, Inc., 1989 M. I
M. III
M. V
! Do project management. 4.3
4.4
4.11
4.18		 Discuss types of projects from setting a table to building a ship. Questions that need to be answered. Do the critical path method - look at tables 20-22

Exercises 8-12, pp. 21-25
22 & 24 are considered to be test on chapter

 N. I
M. III
! Do dynamic programming. 4.2
4.14
4.17
4.18		 Discuss that this has less structure.
Show various stages. Look at tables 25-28 showing steps. 		Problems in section - done as group project for grade M. I
M. III
UNIT III CODES
! Do coding.

Section 1

! Do secret codes.

 4.2
4.3
4.6
4.14
4.17		 Discuss what constitutes a secret code. Show how to encode a message.

Group project on use of codes in World War II.

 

 Codes Galore, Joseph Malkevitd, Gary Froelich, and Daniel Froelid, Histo Map-Module 18, Lexington, MA, Comap, Inc., 1993 M. I
M. III
M. IV

Section 2

! Do zip codes.

 

 Show how a zip code is important for mail. Do binary operations. Show how to read the code on a post card. Group work on "breaking" a code on a post card. Discrete Mathematics Through Applications, Nancy Crisler, Patiena Fishay, Gary Froelich,
NY, W.H. Freeman & Co., 1994

Section 3

! Do ISBN codes.

 

 Explain what an ISBN code is. Discuss error detecting with the system. Activities pp. 57-65 Discrete Mathematics, John A. Dossey, Albert D. Otts, Lawrence E. Spence, Charles Vanden Eynden, NY Addison-Wesley, 1997

Section 4

! Do bank identification codes.

 Explain how bank identification codes are used. Quiz Exclusions in Modern Mathematics 2nd Ed., Peter Tannenbaum, Robert Arnold, Englewood Cliffs, NJ, Prentice Hall, 1995

Section 5

! Do channels.

 

 4.1
4.3
4.4
4.11
4.14
4.17
4.18		 Explain what a channel is. [Example 3, p. 25] Show how a channel can misbehave. PP. 66-69, all activities relating to sections 5-9 Codes Galore, Joseph Malkevitd, Gary Froelich, and Daniel Froelid, Histo Map-Module 18, Lexington, MA, Comap, Inc., 1993 M. I
M. V

Section 6

! Explain error-correcting codes.

 

 How to set up error-correcting codes. Using space technology, example 5. Discuss contributors to the field. Group project on one problem handed in for evaluation Discrete Mathematics Through Applications, Nancy Crisler, Patiena Fishay, Gary Froelich,
NY, W.H. Freeman & Co., 1994

Section 7

! Do linear codes.

 

 What is a linear code. Discuss minimum hamming distance. Example 6-11, 36-37. Figures in section Quiz on technology Discrete Mathematics, John A. Dossey, Albert D. Otts, Lawrence E. Spence, Charles Vanden Eynden, NY Addison-Wesley, 1997

Section 8

! Do check digits.

 

 Another type of error correcting digits parity check digits. Exclusions in Modern Mathematics 2nd Ed., Peter Tannenbaum, Robert Arnold, Englewood Cliffs, NJ, Prentice Hall, 1995

Section 9

! Do applications.

 How to detect errors. Digital technology and UPC codes. Figures 10 & 11, p. 44

NOTE SPECIAL EDUCATION MODIFICATIONS SUGGESTIONS. SEE IEP FOR SPECIFIC ACCOMMODATIONS.
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