prepared by chloe huber and matthew junge march 6, 2016 · prepared by chloe huber and matthew...
TRANSCRIPT
FEPPS Math Curriculum
Prepared by Chloe Huber and Matthew Junge
March 6, 2016
Contents
1 Overview 31.1 Introduction and Goals of FEPPS Math . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Course Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 A Typical Day in Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 About the Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Time Commitment and Co-Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.6 Developing Good Study Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 College Prep (i) 62.1 Course Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Course Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Calendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 College Prep (ii) 93.1 Course Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Course Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4 Quizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Math 107 124.1 Course Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Course Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.3 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.4 Quizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.5 Group Work and Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Appendix 165.1 Editing .tex files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.2 Sample Syllabi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.3 How to Survive Your College Math Class . . . . . . . . . . . . . . . . . . . . . . . . 245.4 Sample Quizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.5 College Prep (i) and Math 107 TCC Guidelines . . . . . . . . . . . . . . . . . . . . . 29
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1 Overview
1.1 Introduction and Goals of FEPPS Math
Welcome to FEPPS math! It is great that you are interested. Our math students are dynamic,motivated and a lot of fun to work with. The main purpose of FEPPS math is to make it possiblefor them to complete the math requirements for an associates degree from inside the prison. Weoffer a self-contained three-course sequence with each course about eleven weeks long. The firsttwo, College Prep (i) and (ii), are preparatory and do not count for college credit. The capstone,Math in Society, is a five credit math course that follows the guidelines set by Tacoma CommunityCollege. A future goal of FEPPS is to have more advanced math offerings, such as precalculus andcalculus.
1.2 Course Descriptions
College Prep (i) CP(i) is made to be accessible to any student. It starts with arithmetic and buildsto fractions, percents and ratios. Arithmetic, fractions, percentages. Corresponds roughly tolate middle school and early high school math. An overarching goal of the course is to teachstudents good math-specific study habits. We use the fourth edition of Elyan Martin-Gay’sBasic College Mathematics.
College Prep (ii) For students from CP(i) or with recent math experience. Real numbers, algebra,inequalities. A first course in negative numbers and basic algebra (i.e. formulas, solving for‘x’, word problems, etc...). An overarching goal of the course is to teach students good math-specific study habits. We use the ninth edition of Basic Mathematics through Applicationsby Akst and Bragg.
Math 107 A survey course of “Math in Society.” Consists of four topics chosen from: Sets andCounting, Probability, Statistics, Finance, Geometry, Graph Theory. This is an accreditedcourse at TCC. The final sections of each chapter are quite advanced. We use a mix of thefourth and seventh editions of Mathematics a Practical Odyssey by Johnson and Mowry.
1.3 A Typical Day in Class
Classes are usually 2-2.5 hours, about double a typical math class. Past teachers have found it veryhelpful to break up the period. For example, starting class with homework discussion followed bya quiz, then lecturing for thirty-sixty minutes, and using the remaining time for group work andtime for individual questions. The middle of class is usually interrupted by “movement” and is agood time for everyone to take a break.
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1.4. ABOUT THE STUDENTS CHAPTER 1. OVERVIEW
1.4 About the Students
Students are very motivated. They ask a lot of questions and are genuinely concerned about fullyunderstanding the material. Many students have yet to develop good study skills and are not goodself-directed learners. As a result, they place a lot of value on the instructor explaining thingsclearly and going through examples for the material on homework and exams.
1.4.1 Background
The students have very diverse mathematical backgrounds. Those with more recent math expe-rience can place further into the sequence. The goal is that a student who has been out of theclassroom for possibly several decades can start in College Prep (i) and ultimately be successful inMath 107. Most students are planning to receive a degree in non-science fields. Accordingly, Math107 is a terminal math course designed for students with this goal.
There are no requirements in order to take College Prep (i). For College Prep (ii) and Math 107students will have either placed into your class after taking a placement exam (see appendix) orbecause they took the previous course and received a C or above.
1.4.2 Learning Resources
Students have weekly study hall. Study hall is multi-subject, and staffed with tutors who may ormay not be math-specific. Other resources are class time and working with peers.
1.4.3 Grades
How you grade CP(i) and CP(ii) is up to you. Math 107 must be graded to the TCC grading guidelines.At the end the students with a C or higher move on to the next course. For all courses we preferyou follow the “letter grade” convention used by TCC. When writing exams it is preferable thatthe raw percentage grade corresponds directly to the letter. For example, a 91% would be an A−.This means writing exams that talented students do well on and weak students score below 60% on.Note this is different than at, say, UW Seattle where exams are often written with a goal medianof around 65%.
It is not atypical for students to fail our math courses. Students should only be passed if theyare ready for the next course, or in Math 107 if they demonstrate sufficient understanding.
1.4.4 Individual Check-Ins
Students appreciate being kept informed about their grades and progress in the class. Having one-to-one check ins before major exams is helpful. These consist of meeting with each student and:asking if the student has any questions or feedback about the course, making sure the recordedgrades are accurate, and giving a predicted grade for the term.
1.5 Time Commitment and Co-Teaching
A course must meet for 55 hours. This is typically by meeting twice a week in 2-2.5 hour classes over11-14 weeks. Most often courses are co-taught. It is very flexible how the work can be divided up.One way is by alternating days. Another option is to break the teaching up by chapter and alternateabout every 3 weeks. Regardless, co-teaching requires good communication and organization from
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1.6. DEVELOPING GOOD STUDY SKILLS CHAPTER 1. OVERVIEW
both parties. The average weekly time commitment if co-teaching once a week comes out to about8 – 10 hours per week:
Weekly Time Commitment ≈
prep, 2 hours
time in WCCW, 3 hours
transit, 2 hours
coordinating/logistics, 2 hours
.
1.6 Developing Good Study Skills
We also strive to develop good study habits. Students in CP(i) may need the most attention butattention should be given to these in all three math courses. Some math-specific study skills thatstudents may need instruction and encouragement with include:
1. Using the textbook as a resource.
2. Effective note taking.
3. Getting the most out of the homework.
4. Professionalism.
5. How much to write.
6. Working together.
7. Studying for exams.
8. Taking exams.
See the appendix for more details on each of these skills.
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2 College Prep (i)
We use the fourth edition Basic College Mathematics by Elayn Martin-Gay. The only prerequisiteis an eagerness to learn mathematics. We start from scratch.
2.1 Course Objectives
To teach arithmetic, fractions, decimals and percents in order to prepare students for real numbersand algebra. To cover some geometry. More specifically:
1. Add, subtract, multiply, divide, and simplify fractions.
2. Add, subtract, multiply, and divide decimal numbers.
3. Identify place value.
4. Round whole numbers and decimal numbers.
5. Evaluate ratios and percentages.
6. Convert between decimal, fractional, and percentage numbers.
7. Solve proportion problems.
8. Calculate areas and perimeters for rectangles and triangles.
9. Solve applications problems involving the above concepts and skills.
10. Write clear and complete solutions to mathematical problems, including correct notation andwritten explanations when appropriate.
11. Use a scientific calculator appropriately.
In addition arithmetic, a major goal of College Prep (i) is to develop good math study habits.We recommend starting class by going over good study skills. See the appendix “How to SurviveYour First College Math Class” for more details.
2.2 Course Content
2.2.1 Course Topics
Chapter 1 Whole Numbers
Chapter 2 Multiplying and Dividing Fractions
Chapter 3 Adding and Subtracting Fractions
Chapter 4 Decimals
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2.3. CALENDAR CHAPTER 2. COLLEGE PREP (I)
Chapter 5 Ratios and Proportions
Chapter 6 Percentages
2.2.2 Table of Contents
Chapter 1 The Whole Numbers
§1.1 – Tips for Success in Mathematics.
§1.2 – Place Value, Names for Numbers, andReading Tables.
§1.3 – Adding Whole Numbers and Perime-ter.
§1.4 – Subtracting Whole Numbers.
§1.5 – Rounding and Estimating.
§1.6 – Multiplying Whole Numbers andArea.
§1.7 – Dividing Whole Numbers.
§1.8 – An Introduction to Problem Solving.
§1.9 – Exponents, Square Roots, and Orderof Operations.
Chapter 2 Multiplying and Dividing Fractions
§2.1 – Introduction to Fractions and MixedNumbers.
§2.2 – Factors and Prime Factorization.
§2.3 – Simplest Form of a Fraction.
§2.4 – Multiplying Fractions and MIxedNumbers.
§2.5 – Dividing Fractions and Mixed Num-bers.
Chapter 3 Adding and Subtracting Fractions
§3.1 – Adding and Subtracting Like Frac-tions.
§3.2 – Least Common Multiple.
§3.3 – Adding and Subtracting Unlike Frac-tions.
§3.4 – Adding and Subtracting Mixed Num-bers.
§3.5 – Order, Exponents, and the Order ofOperations.
§3.6 – Fractions and Problem Solving
Chapter 4 Decimals
§4.1 – Introduction to Decimals.
§4.2 – Order and Rounding.
§4.3 – Adding and Subtracting Decimals.
§4.4 – Multiplying Decimals and Circumfer-ence of a Circle.
§4.5 – Dividing Decimals and Order of Op-erations.
§4.6 – Fractions and Decimals.
Chapter 5 Ratio and Proportion
§5.1 – Ratios.
§5.2 – Rates.
§5.3 – Proportions.
§5.4 – Proportions and Problem Solving.
Chapter 6 Percent
§6.1 – Introduction to Percent.
§6.2 – Percents and Fractions.
§6.3 – Solving Percent Problems UsingEquations.
§6.4 – Solving Percent Problems Using Pro-portions.
§6.5 – Applications of Percent.
§6.6 – Percent and Problem Solving: SalesTax, Commission, and Discount.
§6.7 – Percent and Problem Solving: Inter-est.
2.3 Calendar
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2.3. CALENDAR CHAPTER 2. COLLEGE PREP (I)
Week Day 1 Day 2 Comments
1 Chapter 1 Chapter 1 Syllabus and study skills2 Chapter 1 Chapter 13 Chapter 2 Chapter 24 Chapter 3 Chapter 35 Review Chapter 1, 2 Review Chapter 2,3 Review and Individual Check-ins6 Midterm: Chapters 1,2,3 Chapter 4 Midterm 1: Whole Numbers, Fractions7 Chapter 4 Chapter 58 Chapter 5 Review Chapter 49 Review Chapter 5 Midterm: Chapters 4,5 Midterm 2: Fractions, Ratios, Proportions10 Chapter 6 Chapter 611 Chapter 6 Chapter 612 Review Review Individual Check-ins and grades13 Final Comprehensive Exam
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3 College Prep (ii)
Meets twice a week for 10-14 weeks. Uses Bittinger 9th edition and covers Chapters 1,2, and partof Chapter 3 involving interpreting data and graphing lines. Involves some planning with the 107instructor as the last 2 weeks of instruction are an introduction to 107 material.
3.1 Course Objectives
All students feel comfortable with arithmetic with negative numbers and percentages. Give studentsan introduction to algebra, and learn to solve linear equations and inequalities, manipulating formu-las, and apply that knowledge to word problems. Introduction to reading graphs and graphing lines.Last two weeks may include an introduction to statistics (mean, median, mode), introduction tosets (set notation, union, intersection) and introduction to probability and counting (combinationsand permutations).
Ideally, the course would
1. Prepare students to understand and manipulate formulas in Math 107
2. Provide the basic skills to continue studying algebra
3. Prepare students to take chemistry or biology (lab sciences) where they would use basicstatistics in lab reports and to create and interpret graphs.
In addition algebra, a major goal of College Prep (ii) is to develop good math study habits.We recommend starting class by reminding students about effective study skills. See the appendix“How to Survive Your First College Math Class” for more details.
3.2 Course Content
3.2.1 Prerequisite skills
Arithmetic with whole numbers, fractions and decimals, order of operations and exponents, andpercentages.
3.2.2 Course Topics
Chapter 1 Introduction to Real Numbers and Algebraic Expressions
Chapter 2 Solving Equations and Inequalities
Chapter 3 Graphs of Linear Equations
Appendix C Sets (see attached supplementary materials)
Appendix D Mean, Median and Mode
Probability and Counting Coin flips and Dice rolls (see attached supplementary materials)
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3.2. COURSE CONTENT CHAPTER 3. COLLEGE PREP (II)
3.2.3 Table of Contents
Chapter 1 Introduction to Real Numbers andAlgebraic Expressions
§1.1 – Introduction to algebra.
§1.2 – The real numbers.
§1.3 – Addition of real numbers.
§1.4 – Subtraction of real numbers.
§1.5 – Multiplication of real numbers.
§1.6 – Division of real numbers.
§1.7 – Properties of real numbers.
§1.8 – Simplifying expressions, order of op-erations.
Chapter 2 Solving Equations and Inequalities
§2.1 – Solving equations: the addition prin-ciple.
§2.2 – Solving equations: the multiplicationprinciple.
§2.3 – Using the principles together.
§2.4 – Formulas.
§2.5 – Applications of percent.
§2.6 – Applications and problem solving.
§2.7 – Solving Inequalities.
§2.8 – Applications and problem solvingwith inequalities.
Chapter 4 Graphs of Linear Equations
§3.1 – Graphs and applications.
§3.2 – Graphing linear equations.
Appendix D Mean, Median, Mode
Appendix C SetsIn addition, §2.1 and §2.2 of the fourth ad-dition of Mathematics a Practical Odysseyare used, as well as an supplementarypacket containing definitions and exercises.
Probability and CountingBasic definitions and exercises taken froma supplementary packet and §3.1 and §3.2from the fourth addition of Mathematics aPractical Odyssey.
3.2.4 Calendar
Week Day 1 Day 2 Comments
1 1.1 1.2, 1.3 1.1, 1.2, 1.32 1.4, 1.5 1.6, 1.7 1.4, 1.5, 1.6, 1.73 1.7, Factoring/Distributing Worksheet 1.8, 2.1 1.7, 1.8, 2.14 2.2 2.3 2.2, 2.35 Review Chapter 1 Review Chapter 2 Review and Individual Check-ins6 Midterm 2.4, 2.5 Midterm, 2.4, 2.57 2.6, 2.7 2.8 2.6, 2.7, 2.88 3.1 3.1, 3.29 Appendix D Appendix C Appendix C, D10 Probability Review Probability11 Review Final Final
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3.3. HOMEWORK CHAPTER 3. COLLEGE PREP (II)
3.3 Homework
It has worked well to assign all of the odd problems from each section and collect two-to-threesections per week. This has proven to be about the right amount of work. At the end of eachsection are more challenging questions and mixed reviews, and it is up to the instructor to assignthem or not. Homework is usually just graded for completeness and makes up a small percent ofthe total grade.
3.4 Quizzes
Quizzes are an optional component of the course. We have found it to be a good way to measurewhere the class is on each topic. Quizzes are 8-10 questions and about twenty minutes in length.See the appendix for a sample quiz.
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4 Math 107
This is a TCC accredited math course and a standard course across community colleges in Washing-ton state (under the name Math& 107). When planning your class please see the appendix forthe TCC course guidelines. This contains more information about course outcomes as well ascomments on the appropriateness of each section in obtaining these outcomes. A difference is that,instead of the seventh, we use the fourth edition of Mathematics a Practical Odyssey by Johnsonand Mowry. There is a lot of emphasis on group work and on real-world applications. Class mustmeet for 55 hours. For example, meeting twice a week in 2.5 hour classes for 11 weeks. Or, say,meeting twice a week in 2 hour classes for 14 weeks.
4.1 Course Objectives
Math 107 is offered as a quantitative skills course for students whose majors have no specific math-ematical requirements. The purpose of the course is to introduce students to practical applicationsof mathematics in areas which they might not have guessed involve mathematics. Although sometopics taught in the course will require algebra and graphing skills, the emphasis of the courseshould be applications that are not highly algebraic in nature. The course should expose studentsto and give them appreciation for various uses of mathematics of their everyday lives.
4.2 Course Content
4.2.1 Prequisites
Students are expected to be comfortable with negative numbers, working with formulas, basicalgebra, inequalities and understanding/interpreting graphs. This is all on the level of CollegePrep (ii).
4.2.2 Course Topics
The instructor has a lot of liberty with the course content. A course consists of 3-4 topics chosenfrom the following chapters:
Chapter 2: Sets and Counting
Chapter 3: Probability
Chapter 4: Statistics
Chapter 5: Finance
Chapter 6: Voting and Apportionment
Chapter 7: Number Systems and Number Theory
Chapter 8: Geometry
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4.2. COURSE CONTENT CHAPTER 4. MATH 107
Chapter 9: Graph Theory
A goal of Math 107 is to demonstrate that math is more than formulas and calculations. For thisreason, it is required that the course balance algebraic sections (i.e. Chapters 3,4,5,6) with thoseemploying different types of reasoning (Chapters 2,7,8,9). The final sections of each chapter getfairly difficult, so do not think you need to cover everything in a chapter.
4.2.3 Table of Contents
Chapter 2 Sets and Counting
§2.1 – Sets and set operations.
§2.2 – Applications of venn diagrams.
§2.3 – Introduction to combinatorics.
§2.4 – Permutations and combinations.
Chapter 3 Probability
§3.2 – Basic terms of probability.
§3.3 – Basic rules of probability.
§3.4 – Combinatorics and probability
§3.5 – Expected value.
Chapter 4 Statistics
§4.1 – Populations, sample and data.
§4.2 – Measures of central tendency.
§4.3 – Measures of dispersion.
§4.4 – The normal distribution.
Chapter 5 Finance
§5.1 – Simple interest.
§5.2 – Compound interest.
§5.3 – Annuities.
§5.4 – Amortized loans.
Chapter 6 Voting and Apportionment
§6.1 – Voting Systems.
§6.2 – Methods of Apportionment.
§6.3 – Flaws of Apportionment.
Chapter 7 Number Systems and Number The-ory
§7.4 – Prime Numbers and Perfect Num-bers.
§7.5 – Fibonacci Numbers and the GoldenRatio.
Chapter 8 Geometry
§8.1 – Perimeter and area.
§8.2 – Volume and surface area.
§8.3 – Egyptian geometry.
§8.4 – The Greeks.
§8.5 – Right triangle trigonometry.
§8.6 – Linear perspective.
§8.7 – Conic sections and analytic geometry.
§8.8 – Non-Euclidean geometry.
§8.9 – Fractal geometery.
Chapter 9 Graph Theory (Not in 4th edition,but can use photocopies of the 7th edition.)
§9.1 – A walk through Konigsburg.
§9.2 – Graphs and Euler trails.
§9.3 – Hamilton Circuits.
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4.3. HOMEWORK CHAPTER 4. MATH 107
4.2.4 Sample Calendar
Week Day 1 Day 2 Comments and Extra Worksheets
1 2.1 2.2 heavy on notation2 2.3 2.43 3.1 3.2 DIY playing cards experiment.4 3.3 3.4 lottery regressive tax mini-project5 3.5 3.5 Powerball worksheet, students struggle with 3.56 Review Midterm 1-1 conferences day before the midterm7 4.1 4.2 self-learn 4.1 due as hw8 4.3 4.4 predicting oil-supply9 9.1,9.2 9.2 handshakes & Konigsburg Worksheet for 9.110 9.3 9.3, Random Graphs Galton-Watson worksheet11 Review Final two days of review and conferences are helpful
4.3 Homework
It has worked well to assign all of the odd problems from each section and collect two sections perweek. This has proven to be about the right amount of work. Do give some care with the lastproblems of each section since they sometimes involve internet research or lines of inquiry tangentto the core material. Students don’t have access to many resources outside of class, so giving themproblems with an answer in the back of the book is helpful. Homework is usually just graded forcompleteness and makes up a small percent of the total grade.
4.4 Quizzes
Using quizzes is at the instructor’s discretion. We have found it to be a good way to measure wherethe class is on each topic. Student’s appreciate them since it keeps them focused and gives an ideaof what exams will be like. Quizzes are 8-10 questions and about twenty minutes in length. Seethe appendix for a sample quiz.
4.5 Group Work and Projects
Communicating math well is a focus of the course. For this reason, written assignments (projects)and group work should make up a significant part of class time and assignments.
4.5.1 Group Work
At times the culture inside WCCW poses logistical and social obstacles to group work. A logisticalproblem is that it is often impossible for certain students to study together outside of class. Asocial challenge may be that a student strongly prefers to work alone, or that certain students maynot get along well. This requires some flexibility on the part of the instructor. Still making timefor in-class group work is important.
4.5.2 Project(s)
It is also recommended to have a project in the course. Big projects are great, but it is also fine tohave two or three mini-projects that go into more depth on a topic. Just be sure that these have
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4.5. GROUP WORK AND PROJECTS CHAPTER 4. MATH 107
either a writing or presentation component.Since student access to information is limited, designing projects requires creativity and flexibility
from the instructor. There is a small collection of suggested projects in the dropbox Math 107directory. Past projects have been on topics such as, “Lottery as a regressive tax”, “CalculatingPowerball Odds”, and “Predicting Oil Supply with the Normal Distribution”.
4.5.3 Technology
Using a calculator when appropriate is a course outcome. Whenever possible place emphasis onthe “advanced features” students can use on their scientific calculators. For example, doing com-binations and permutations or computing sample means and variance.
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5 Appendix
5.1 Editing .tex files
Much of the course material is written in LaTex (as .tex files). This is a powerful program fortypesetting mathematics. To edit these files you need to download the library (see http://latex-project.org/ftp.html) and also an editor. For Mac we recommend TexShop and for WindowsTexMaker. The learning curve is a bit steep on using the software, but it is rather quick andpowerful once you get the hang of it. Editing the problems in existing documents will likely requiregoogling a tutorial, but should be fairly straightforward.
5.2 Sample Syllabi
See the next seven pages. Presented in order: CP(i), CP(ii) and Math 107.
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Page 1 of 3
Fall 2014 MATH 075, Arithmetic Review Friday 01:20PM – 03:45PM Instructor: Matthew Mburu
Course Description:
This course is designed to help students master the concepts of basic mathematics and prepare them for college algebra. Topics include review of basic mathematics including arithmetic of whole numbers, fractions, decimals, percentages, ratios, proportions, and geometry.
Course Learning Objectives: i. Add, subtract, multiply, and divide whole numbers. ii. Add, subtract, multiply, divide, and simplify fractions. iii. Add, subtract, multiply, and divide decimal numbers. iv. Identify place value. v. Round whole numbers and decimal numbers. vi. Evaluate ratios and percentages. vii. Convert between decimal, fractional, and percentage numbers. viii. Solve proportion problems. ix. Calculate areas and perimeters for rectangles and triangles. x. Solve applications problems involving the above concepts and skills. xi. Write clear and complete solutions to mathematical problems, including correct notation and written
explanations when appropriate. xii. Use a basic calculator appropriately.
Textbooks and Supplemental Materials: Basic College Mathematics textbook by Elayn Martin-Gay
Instructional methods: Instructional methods include but are not limited to lectures, group discussions, quizzes, assignments, and examinations. Handouts, classroom aids, and additional reading materials will be provided in the course of the semester.
Assignments: Homework problems are assigned to assist you in understanding the important concepts discussed in the text. Since it is very important that you come prepared to learn in class, I will expect that you have read and understood the text and supplemental readings assigned for each class as well as attempted the assigned class assignments. In addition, you may wish to attempt as many of the remaining (or additional) exercises and problems as you need to confirm your understanding of the pertinent concepts. Students are encouraged to discuss assignments with other students, but work turned in should be their own.
Page 2 of 3
Practice Problems: Answers to practice problems can be found at the back of your textbook; these problems are reviewed in class to emphasize course content, they are not collected nor graded by your instructor. However, the completion of these exercises is directly correlated to your success in this course.
Evaluation criteria for tests, exams, projects and other assignments: Quizzes must be taken on the scheduled day and at the scheduled time. THERE ARE NO MAKEUP QUIZZES. Quizzes normally take between fifteen and thirty minutes to complete. Credit cannot be made up nor will credit be given for missed or late quizzes. Quizzes cannot be taken early. See daily outline for the date quizzes and examinations are tentatively scheduled. Quizzes and or exams may be objective, subjective, or a combination of both.
Grading standards: Your final grade will be determined by (1) Attendance, (2) Participation, (3) Quizzes, (4) Assignments, and (5) Examinations. Students are responsible for all assigned reading and should be prepared to answer questions on the subject matter contained in the chapter assigned. It is expected students will read each chapter. Exams can only be rescheduled if the student consults with the instructor prior to the scheduled examination. Late assignments will receive zero points. Students can drop one of the lowest quiz scores.
Final grades will be determined as follows:
GRADE PERCENTAGE A 93 - 100
A- 90 - 92 B+ 86 - 89
B 81 - 85 B- 76 - 80 C+ 71 - 75
C 66 - 70 C- 61 - 65 D+ 55 - 60
D 50 - 54 E 0 - 49
Academic Dishonesty: Students are expected to be honest and forthright in their academic endeavors. Cheating, plagiarism, fabrication or other forms of academic dishonesty corrupt the learning process and threaten the educational environment for all students. In this course, sanctions for academic dishonesty will be as follows: In the event a student is found to have received or given help during a quiz or examination, or used outside materials, that student will receive a failing grade in the course.
Homework 15% Quizzes 20% Midterm Exams 25% Final Exam 40% Total 100%
Page 3 of 3
Course Requirements: 1. Attendance and Participation: Students are expected to attend each class, and be prepared to
participate in class discussions. You are required to do your homework and complete the practice exercises; these will help you understand the key concepts and procedures we cover in class.
2. Homework: All assigned homework is to be submitted at the beginning of class on the due date. Credit will be given for effort (showing your steps and workings) regardless of whether the answer is correct or not. Therefore, it is very important that you show all your steps while working on problems.
3. Questions: You are encouraged to ask questions in class – if you do not understand something, would like something explained in a different way, or a clarification, please ask me. I request that you raise your hand to ask questions and/or to respond to questions so that we can have one person speaking at any given time. Remember, you have the right to ask questions related to this class and you have the right to have your questions answered.
4. Answers to practice questions and some homework are posted at the back of your book – please feel free to check your answers against the textbook’s answers.
5. Study Hall Sessions: Instructor led study halls will be held each week on Tuesday from 6:20PM to 8:45PM. Please take advantage of this invaluable resource.
Tentative Course calendar: This is the tentative schedule for this class and is subject to change. Any changes will be communicated to you in advance.
WEEK DATE CHAPTER
WEE
K 1 SEP 5 NO CLASS
WEE
K 2 12 Introduction
Chapter 1: WHOLE NUMBERS
WEE
K 3 19
Chapter 1: WHOLE NUMBERS Quiz
WEE
K 4 22 Chapter 2: MULTIPLYING AND
DIVIDING FRACTIONS
WEE
K
4 26 Quiz Chapter 3: ADDING AND SUBTRACTING FRACTIONS Review: Word Problems
WEE
K 5 OCT 3 Review Chapters 1, 2, 3
Handout / Group Work
WEE
K 6 10
Mid-Term Exam: Whole Numbers & Fractions Chapter 4: DECIMALS
WEE
K 7 17 Quiz
Chapter 4: DECIMALS
WEEK DATE CHAPTER
WEE
K 8 24 Chapter 5: RATIOS & PROPORTIONS
WEE
K 9 31 Quiz
Chapter 5: RATIOS & PROPORTIONS
WEE
K 10
NOV 7 Mid-Term Exam: Decimals, Ratios, and Proportions
WEE
K 11
14 Chapter 6: PERCENTAGES
WEE
K 12
21 Chapter 6: PERCENTAGES Quiz
WEE
K 13
28 NO CLASS
WEE
K 14
DEC 5 REVIEW
WEE
K 15
12 FINAL COMPREHENSIVE EXAM
N.B: Do not miss study Hall Sessions J
College Prep II SYLLABUS Winter 2015
General Course Information
Overview: The goal of this course is to prepare students for Math 107. We will focus on develop-ing comfort with: decimals, fractions, percentages, exponents, order of operations, basic algebra,applying formulas, sets, and inequalities.
Some noteworthy topics which will not be covered are: graphing, linear equations, polynomials,and functions. These skills (though important) are not necessary to succeed in Math 107.Text: Elementary and Intermediate Algebra; Bittinger, Ellenbogen, Johnson. Ninth Edition.Calculator: Permitted on exams and homework.Homework: Weekly. Graded for completion. (10%)Quizzes: There will be approximately one quiz a week (not on weeks of exams). The lowest scorewill be dropped. (25%)Exams: One midterm on Chapter 1 (25%) and a cumulative final exam (40)%).
Prerequisite Skills Needed
The prerequisites are the material covered in College Prep I. To be successful a student must becomfortable with:
• Types of numbers (decimals, fractions, mixed numbers, integers).• Adding, subtracting, multiplying, dividing integers.• Arithmetic with fractions (there will be some review of this).• Percents and ratios.• Order of operations.• Word problems.
Overview of Material
Chapter 1: Introduction to Algebraic Expressions§1.1 – Introduction to algebra.§1.2 – Commutative, associative and distributive laws.§1.3 – Fractions.§1.4 – Positive and negative real numbers.§1.5 – Addition of real numbers.§1.6 – Subtraction of real numbers.§1.7 – Multiplication and division of real numbers.§1.8 – Exponents and order of operations.
Chapter 2: Equations, Inequalities, and Problem Solving§2.1 – Solving equations.§2.2 – Using the principles together.§2.3 – Formulas.§2.4 – Applications with percent.§2.5 – Problem solving.§2.6 – Solving inequalities.§2.7 – Solving applications with inequalities.
Chapter 3: Introduction to Graphing§3.1 – Reading Graphs, Plotting Points, and Scaling.
Appendix: Sets and statisticsC – SetsD – Mean, median, and mode.
Schedule
Week Date Sections1 1/5-1/7 1.1, 1.2, 1.32 1/12-1/14 1.4, 1.5, 1.63 1/21-1/23 1.7, 1.84 1/26-1/28 2.1, 2.25 2/2-2/4 2.36 2/9-2/11 Review, Midterm7 2/18-2/20 2.4, 2.58 2/23-2/25 2.6, 2.79 3/2-3/4 A : D,C10 3/9-3/11 3.111 3/16-3/18 Review, Final
Math& 107 Math in Society Winter 2015 Matthew Junge PhD(c) Mondays and Wednesdays from 1:20 – 3:45. January 5th – March 18th No class will be held on 1/19 or 2/16. These classes will be made up on 1/23 and 2/20 from 1:20 – 3:45 Course Description: A general education course investigating quantitative reasoning and its applications and role in society. Topics may include graph theory, statistics, coding, game theory, symmetry, and geometric and numerical patterns. Mathematical theory combined with quantitative skills will be used in applications to a variety of problems encountered in mathematics and the world. A thematic approach may be taken in this course. Our aim is to introduce practical applications of mathematics in the real world. A large portion of class time centers around group work with emphasis on problem solving and clearly communicating mathematical ideas. Attention will be given to analyzing real world data in groups. We will start with combinatorics, probability and statistics. Then we will switch gears and explore graph theory. At the end we will study a link between all four topics – random graphs. There will be several mini-projects along the way. The course objectives listed below make reference to the following Math Department Program Learning Outcomes:
1. Create, interpret, and analyze graphs and charts that communicate quantitative or relational information.
2. Determine, create, and use appropriate and reasonable mathematical constructs to model, understand, and explain phenomena encountered in the world.
3. Determine and carry out an appropriate algorithm to solve problems that are amenable to mathematical solutions.
4. Communicate mathematical information formally, using appropriate math notation and terminology, and informally by using everyday language to express ideas.
5. Use technology to analyze and solve mathematical problems and to effectively communicate solutions to problems, particularly those that cannot be solved efficiently by other means.
Course Objectives: Upon successful completion of the course, the student will be able to:
1. Discern and explain the use of mathematics in many facets of society. PLO: 1, 2 2. State concrete examples of how quantitative reasoning and mathematical techniques can and
have been used to model and solve real world problems. PLO: 2, 3, 4 3. Demonstrate the use of quantitative reasoning skills and problem solving in areas they can be
expected to encounter in their own lives and cultures. PLO: 2, 3
4. Solve problems, organize and write clear descriptions of how these problems are solved and how mathematics is used in solving problems including correct mathematical notation. PLO: 3, 4, 5
5. Use logic and critical thinking skills to read, organize, and analyze quantitative information. PLO: 4, 5
6. Identify appropriate algorithms and correctly perform them in order to solve elementary problems that emulate some of society’s problems. PLO: 3
7. Demonstrate knowledge of some topics of current interest in mathematics. PLO: 2 8. Create and interpret mathematical graphs and charts. PLO: 1 9. Use technology as an analytic tool to model and solve problems. PLO: 4, 5 10. Work in small groups on group problems or projects. PLO: 4
Prerequisites: Math 095 with a minimum grade of C or equivalent; and English/ 095 with a minimum grade of C or assessment above ENGL/ 095 or equivalent. Text: Mathematics: A Practical Odyssey, Johnson and Mowry Calculators: A TI-30X IIS will be given to all students on the first day of the semester. Course Calendar: Week 1 (1/5 1/7) -‐ Sections 2.1, 2.2 Week 2 (1/12 1/14) – Sections 2.3, 2.4 Week 3 (1/19 1/21) – Sections 3.2, 3.3 Week 4 (1/26 1/28) – Sections 3.4, 3.5 Week 5 (2/2 2/4) -‐-‐ Section 3.6, Lotteries as Regressive Tax (mp)and Midterm Review Week 6 (2/9 2/11) -‐-‐ Midterm, 4.1 Week 7 (2/16 2/18) – Sections 4.2, 4.3 Week 8 (2/23 2/25) – Sections 4.4, 9.1 Predicting Oil Supply (mp) Week 9 (3/2 3/4) -‐-‐ Sections 9.2 and 9.3 Week 10 (3/9 3/11) – Section 9.4 and Random Graphs (mp) Week 11 (3/16 3/18) -‐-‐ Review and Final Exam Exams: Midterm Exam: 25% of final Grade Final Exam: 45% of final Grade Quizzes: There will be weekly quizzes. The lowest score of all the quizzes will be dropped. The quizzes will be worth 15% of the final grade. Mini-Projects: There will be three written mini-projects. These can be done in groups of 1-3 people and are work 5% of your grade. Exam/Quiz Make-up Policy: If students miss the mid-term or final exam, they will not be allowed to make it up. Other Required Work: You will have to complete weekly homework, which will be worth 10% of your grade and will be graded for completion only. All homework will be written.
Working in groups of 2 or 3, you will propose a research project motivated by a hypothesis or question. Data will be gathered from some source (media, observation, questionnaires) and analyzed using the techniques in class (mean and variance). You will be asked to reflect on the quality of the data and whether any conclusions can be drawn. Your hypothesis, data, analysis and findings will be written up in a short paper and presented in a 5 minute presentation. This project will be worth 10% of your grade. Late Work: Late work is not accepted without a valid excuse. Grading: Homework (10%) + Quizzes (20%) + Midterm (25%) + Final (45%) Attendance: You are allowed two unexcused absences. Withdrawal: Withdrawal must be done officially through the registrar's office by the 55th calendar day of the quarter. I do not give the WI grade in lieu of a grade the student finds unacceptable. If you just stop coming to class and taking exams, you will receive a grade of E. Incompletes: The ‘I’ grade is given at the discretion of the instructor when the student has completed more than 60% of the quarter and has a plan to finish the remaining work. The student and instructor must fill out a contract form which contains the specific requirements to be completed, the time allowed for completion, and the grade to be assigned if the contract is not completed. Other Classroom Policies: Please come ready to learn, ask questions and to be respectful. Academic Dishonesty: As stated in the TCC catalog, “Students are expected to be honest and forthright in their academic endeavors. Cheating, plagiarism, fabrication or other forms of academic dishonesty corrupt the learning process and threaten the educational environment for all students.” The complete Administrative Process for Academic Dishonesty is available on the TCC website at www.tacomacommunitycollege.com/stuonline/policies/start.htm. In this course, sanctions for academic dishonesty will be as follows: Maximal loss of points from dishonesty. Possibly further punitive actions. Where to get Help: Study hall and your peers. Course Concerns: If you have questions or concerns about this class or me, please contact Mary Weir. Policy Changes: I reserve the right to change the policies outlined in this syllabus in the event of extenuating circumstances. Changes will be announced in class. If you are absent from class, it is your responsibility to check for announcements made while you were absent.
5.3. HOW TO SURVIVE YOUR COLLEGE MATH CLASS CHAPTER 5. APPENDIX
5.3 How to Survive Your College Math Class
Mathew Saltzman and Marie Coffin; Clemson University
Introduction:
No one is born knowing how to play the piano, fix the plumbing, or fly an airplane. Manyof us never acquire these skills. But most of us realize that we could acquire these skills if wewere willing to put in the work required to learn them. Not everyone can be a concert pianist,but nearly everyone could learn to play a few songs, with lessons and practice. So too withmathematics. Not everyone can discover a new mathematical theory, but nearly everyone can learnto use mathematical tools with facility and confidence.
When someone tries to learn volleyball or ballroom dancing for the first time, they often feelconfused and clumsy. There is too much going on at once, and it’s hard to know which mistake tofix first. A good coach can help by teaching one skill at a time, and then showing the student howall those skills fit together. If you sometimes feel that too much is going on at once in your mathclass, these notes can help. We have tried to break the process of learning mathematics down intosmall skills, and then show how they all fit together to make you a successful user of mathematics.
Study Skills:
Read your textbook twice (at least) Don’t expect to fully grasp the material in your math texton the first pass. Even the very best professional mathematicians don’t just read a text once.It may take you two, three, or more passes through the material to really understand it all.When you encounter a multi-line derivation, figure out what steps were performed to go fromline to line.
Taking Notes In note-taking, it is often the case that less is more. It is not possible to transcribeevery word the instructor says, nor every word he writes on the board, nor should you attemptto do so. Class time should be devoted to an exchange of ideas among the students and theinstructor. If you are actually paying attention (this is sometimes called “active listening”) inclass, you will not need a transcription of everything that occurred. You can facilitate goodnote-taking by spending a few minutes before class reading through the material that willbe covered. Do not try to absorb every detail; try to assimilate the main ideas and glancethrough the examples. When you do not follow the lecture, it is much better to ask a questionthan to become a scribe. In fact, if you have a question, it is likely that someone else in theclass has the same question. You’ll be doing them and yourself a favor by speaking up. Classtime should be a balanced mixture of listening, thinking, questioning, and note taking. If youfind that you are devoting most of your class time to one activity and neglecting others, wesuggest you attempt to restore a balance.
Homework Generally, homework assignments provide the instructor with a spot-check on yourperformance and provide you with some feedback on how you measure up to class standards.Ultimately, it is your responsibility to practice on enough problems so that you feel in com-mand of the material and ready to perform on an exam. Most instructors are more than happyto answer questions that you might have about problems that you try beyond the assignedones. In fact, you earn your instructors’ respect and attention if you let them know you aretrying problems on your own. Many textbooks have worked examples that are similar to thehomework problems. If you do not know where to start a problem, try to find an example that
24
5.3. HOW TO SURVIVE YOUR COLLEGE MATH CLASS CHAPTER 5. APPENDIX
looks similar and use it as a guide. Be aware that you are using a crutch when you do this.You have not really mastered your homework until you can work the problems alone, withouthints from the book. If you don’t understand, ask your instructor for help. It’s best to ask forhelp as soon as possible- since math courses typically build one concept on another, anythingyou don’t understand today will probably lead to further problems tomorrow. Students oftenwait to ask questions, hoping the difficulty will “clear up” on its own. This strategy rarelyworks.
Professionalism In most courses outside of mathematics, and in most jobs outside of college, itwould be considered unacceptable to turn in handwritten first drafts on paper torn fromspiral notebooks, with cross-outs, illegible scribbles, arrows pointing from one paragraph tothe next, on several sheets attached by folding over the top corners. The same standards ofprofessionalism apply to your homework. Take some pride in your product: Make a cleancopy of your solutions on paper with clean edges, in order, written legibly, and stapled orclipped. Your instructor will be impressed.
How much to write The question often arises: How much detail should be included in a homeworksolution? The answer: enough but not too much. Enough: Include enough detail to give yourinstructor a clear indication that you know how to solve the problem. Not too much: Onthe other hand, you don’t need to show every simple arithmetic operation. So who is youraudience for homework problems? Hint: It’s not your instructor - he or she already knowshow to solve the problem. A good guideline is to write for the person who sits next to you inclass.
Working together Studying in groups of two or three can be an enormous aid to learning, if doneright.
• Do discuss how to solve problems with your partners.
• Do compare answers. If you disagree, talk about why, and keep at it until you come toa consensus. Everyone should feel confident in the solution.
• Do write up your solutions on your own. This is the step where you solidify yourknowledge.
• Don’t be a free rider. If you find yourself copying solutions without understanding, youare not making effective use of your study group.
• Don’t let your partners ride for free. It does them a grave disservice.
Exams:
Studying for Exams Mathematics exams typically emphasize skills and concepts, neither of whichcan be memorized the night before the exam.
• The single most important way to study for exams is to master the homework assign-ments as they are given. Prior to the exam, review all the relevant homework and payparticular attention to areas where you had trouble the first time. Work at least oneproblem of each type, to make sure you still remember how to do it. If you have trouble,review the concepts and work more problems of that type, until they are easily solved.Imagine yourself explaining a concept to someone else. Could you make the ideas clear?If not, you probably don’t really understand it.
25
• Review your notes. Most instructors emphasize the same material on exams that theyemphasized in class.
• If the idea of taking tests makes you nervous and you fear that you’ll “freeze up”, thebest defense is practice in conditions that are as much like an actual test as possible.Choose a set of problems from the text or elsewhere, set a timer, close your book, andgo to it. Most exams are timed. You can give yourself an advantage in this area byworking enough problems that the solutions come quickly and easily. Time that youspend trying to remember how to work a problem is time that you don’t spend writingthe exam. In addition, the knowledge that you can work a great many problems withease provides a sense of confidence.
Taking Exams There is no question that the most important factor in doing well on timed examsis knowing the material well enough to work problems quickly and with confidence. Buteffective time management can help you do the best you can, whatever you actually know.
• Read the entire exam over quickly, as soon as you get it, and plan your attack.
• Divide your allotted time into chunks for each problem.
• You don’t need to do the problems in order. You should feel free to skip around. Doproblems that you know you can do well first. You’ll gain confidence, and you’ll guaranteeyourself the points.
• Don’t let yourself get stuck on a problem. If you use up the time you allotted or you arenot making progress, move on! If you have time, you can come back to a problem later.
• If you need help understanding a question, ask! (If you need help answering a question,that’s another matter.)
• Try to save some time at the end to go back and check your work.
• Many instructors will give partial credit for partial answers. But you need to demonstratethat you know what steps you would carry out to find the correct answer. Write downwhat you know about the problem.
5.4 Sample Quizzes
First page is for College Prep (ii) and the second is for Math in Society.
Name: Quiz 3 Retake
1. Distribute: 3(1 + 2x)
2. Distribute: 7(a− b+ 7)
3. Factor: 19− 19x
4. Factor:1
5x+
4
5
5. Collect like terms: 3.6a− 1.9a
6. Collect like terms: 7b− b− 7− 3b− 10
7. Simplify: −(3 + z)
8. Simplify: (33÷ 3− 9)− (16 + 8)
Name: Quiz 8
1. Draw a graph with 5 vertices that has an Euler trail but no Euler circuit.
2. Find an Euler circuit in the following graph:
3. Use the nearest neighbor algorithm to find a Hamilton circuit in the following graph:
4. Use the cheapest edge algorithm and the repetetive nearest neighbor algorithm to find two Hamiltoncircuits in the graph below:
1
2
3
4
0.61.3
0.4 .3
0.10.8
1.2
2
2.2
1.1
0.7
5. Describe a situation in the present or future that you think would benefit from understanding graphtheory. Or explain why nothing in your life would benefit :)
5.5. COLLEGE PREP (I) AND MATH 107 TCC GUIDELINES CHAPTER 5. APPENDIX
5.5 College Prep (i) and Math 107 TCC Guidelines
See the next 15 pages for these documents.
29
COURSE GUIDELINES
MATH 75: Review Arithmetic March 2012
Revised by Jackie Gorman
Course Overview: TCC supports many of the current trends in math education that call for an increased emphasis on graphing and application problems with a possible slight de-emphasis on symbolic manipulation. For Math 75, this means that the most important topics to cover are the concepts behind the algorithms and when to use the algorithms rather than putting all the emphasis on the “how to do.” Course Description: Review of basic mathematics including arithmetic of whole numbers, fractions, decimals, percentages, ratios, proportions and plane geometry.
The course objectives listed below make reference to the following Math Department Program Learning Outcomes:
1. Create, interpret, and analyze graphs and charts that communicate quantitative or relational information.
2. Determine, create, and use appropriate and reasonable mathematical constructs to model, understand, and explain phenomena encountered in the world.
3. Determine and carry out an appropriate algorithm to solve problems that are amenable to mathematical solutions.
4. Communicate mathematical information formally, using appropriate math notation and terminology, and informally by using everyday language to express ideas.
5. Use technology to analyze and solve mathematical problems and to effectively communicate solutions to problems, particularly those that cannot be solved efficiently by other means.
Course Objectives: Upon successful completion of this course, students should be able to:
1. Add, subtract, multiply, and divide whole numbers. (3, 4) 2. Add, subtract, multiply, divide, and simplify fractions. (3, 4) 3. Add, subtract, multiply, and divide decimal numbers. (3, 4) 4. Identify place value. (3, 4) 5. Round whole numbers and decimal numbers. (3) 6. Evaluate ratios and percents. (2, 3, 4) 7. Convert between decimal, fractional, and percentage numbers. (3, 4) 8. Solve proportion problems. (2, 3, 4) 9. Calculate areas and perimeters for rectangles and triangles. (2, 3, 4) 10. Solve applications problems involving the above concepts and skills. (2, 3, 4) 11. Write clear and complete solutions to mathematical problems, including correct
notation and written explanations when appropriate. (4) 12. Use a basic calculator appropriately. (5)
Math 75 alternative Course Guidelines: Page 2
Required Text: A New Beginning: Introductory College Mathematics, by Nancy Crisler and Gary Simundza. Calculator: Four-function basic calculator is required. Students should be allowed to use calculators on most exams. Graphing calculators are NOT appropriate at this level and their use should NOT be allowed on exams. Final Exam: It is the Math Department policy that a comprehensive final exam will be given in all sections of Math 75. This exam is to be given during Finals Week during the time period published in the college Final Exam Schedule. Each instructor is responsible for preparing his or her own exam. However, a portion (approximately 5 or 6 questions) of the exam will be common to all sections of Math 75. The course lead for Math 75 is responsible for preparing and distributing the common final exam questions. Homework: Homework is an important tool to help students reinforce their skills. Instructors should either collect some homework, or give quizzes, in order to provide feedback on the quality of the students’ knowledge. A New Beginning contains a wide assortment of problems. It is worthwhile to carefully look through all problems and assign a mixture of each type. Exploring Concepts, at the beginning of each exercise section, contains new ideas that probably were not covered in class. Picking one of these problems occasionally will help students to learn on their own, as well as containing some interesting and often important ideas. Developing Skills are practice problems, the heart of homework practice. These problems cover a nice assortment of levels. Applying the Knowledge contains application problems. These are often the most important problems to assign. Algebraic Thinking help students to get a head start on Math 85. Write about It problems are rich problems that will help students synthesize concepts. These often work nicely as small group problems, test questions as well as projects or turn-in written problems. Resources There is no official teacher’s edition of our text. However, two resources can be picked up from the MARC. The first is an answer key to the text and the second is an instructor’s resource book. I hope they are helpful. Copies of group activities, a glossery for the textbook, sample exams, and other resources can be found on the R:/drive at R:/Course Resources/math 75/. Fraction bars, base-10 pieces and other manipulatives can be found in Building 10 classrooms (either room 10 or 12), which are designated for Math 75 classes.
Math 75 alternative Course Guidelines: Page 3
Course Content:
Chapter 1
Use Chapter 1 to set the tone of the class. Starting out with decoding provides both motivation and is an excellent time to start students working in small groups. 1.1 Integers and the Number Line
The decoding activity is an excellent course opener and a good introduction to signed numbers.
1.2 Collecting and Displaying Data
The investigation in this section is a nice continuation of the first day’s activity,
1.3 Place Value and Rounding Large number prefixes in the exercises is important. Bases other than base ten are interesting but not essential. There are interesting Write About It problems.
1.4 Geometry: Perimeter and Polygons Cover the section, emphasizing perimeter. Introduce names of polygons and properties of polygons but treat lightly.
1.5 Mathematical Patterns Nice section, but can be skipped or covered lightly if time is a problem
Math 75 alternative Course Guidelines: Page 4
Chapter 2 Comments Rather than worrying about students having the algorithms down perfectly, it is important to have students know the algorithm, be able to explain their work, find mistakes and know when to use which algorithm. Group work can be very helpful in this chapter.
2.1 Adding and subtracting Whole Numbers.
Investigation helps capture interest as well as show the connections between operations. Estimation is important. Work lightly with properties.
2.2 & 2.3 Multiplying / Dividing Whole Numbers. Help students to learn their multiplication facts in non-stressful ways (problem #1 is beneficial). Emphasis on meaning of multiplication and division. The number theory ideas in the 2.3 assignments are important.
2.4 Exponents and Order of Operations Exponents and order of operations will probably be new to most students. Exponents are important. Treat order of operations lightly.
2.5 Geometry: Area and Volume The concepts of area and volume are important. Allow time for investigations and problem solving if you have it.
2.6 Displaying Data: Line and Bar Graphs Optional. Do only if you have time.
Math 75 alternative Course Guidelines: Page 5
Chapter 3
It is important to take the time to help students understand the concepts of fractions in section 1 and of decimals in sections 2 through 4. 3.1 Making Sense of Fractions.
Cover Completely. There are pre-made fraction bars and fractions strips.
3.2 Relating Fractions and Decimals. Again, the concepts here are important. Emphasizing estimation and number sense are helpful in understanding the concepts.
3.3 Multiplying Decimals Placing the decimal point is more important than working problems with many digits.
3.4 Dividing Decimals The estimation problem in Exploring Concepts is interesting.
3.5 Summarizing Data: Mean, Median, Mode, and Range Optional: If there is time, this is a nice section. Otherwise, be sure they understand the concept of mean.
Math 75 alternative Course Guidelines: Page 6
Chapter 4
4.1 Multiplying Fractions
Teaching students to “cancel out” ones will help with algebra skills.
4.2 Dividing Fractions Word problems are important here since students typically confuse when to divide and when to multiple when working with fractions.
4.3 & 4.4 Adding and Subtracting: Part 1 and Part 2 Knowing what to do and developing number sense is much more important than spending a lot of time adding or subtracting with “ugly fraction.”
4.5 Displaying data: Stem plots and Box plots Again, this is optional.
Chapter 5
5.1 Ratios and Rates The unit conversion concept will be very important for many sciences classes.
5.2 through 5.5
Proportions, Percents and Percent calculations It is helpful to teach these using both proportions and translating into equations.
Math 75: Comments on Pedagogy Homework: Homework is an important tool to help students reinforce their skills. Instructors should either collect some homework, or give quizzes, in order to provide feedback on the quality of the students’ knowledge. Collaborative Learning: You are strongly encouraged to have students work together in groups in your class. The text has many good group activities you can use. Projects/Writing Assignments
Math 75 alternative Course Guidelines: Page 7
The Math Department has agreed that students need some experience working with a topic in more detail and depth than is normally provided by homework assignments and exams. Therefore, it is highly recommended that there be some type of graded assignment that gives the student an opportunity to investigate a topic in more detail or to see the application of a topic in their world. These assignments can take many forms. They can be one of the investigations from the book or something external that you assign.
Sample Calendar for Math 75 The calendar below lays out the curriculum according to the sequence of the book
• An instructor may change the order of the topics but should allow, at minimum, the number of class periods indicated on the calendar.
• The test dates are simply suggestions as to how to break-up the material. You may choose to test on a schedule that is different from this suggested schedule.
• This calendar does not take into account holidays, professional development days, or Educational Planning Day, all of which vary from quarter to quarter. Therefore, only 9 weeks of classes are scheduled.
• You may find that you have to spend more time than scheduled on a topic. It is important that you find the balance between depth and breathe of material. Generally finding the balance is the hardest part of teaching. If you find yourself behind, feel free to contact the course lead for ideas of where to cut material rather than just leaving off topics at the end.
Day 1 Day 2 Day 3 Day 4 Day 5 WK 1 Activity:
Coding (1.1) 1.1 Debrief 1.3 1.3/1.4 1.4/GSI
Wk 2 2.1
2.2 2.2/2.3 2.3/2.4 2.4/2.5
Wk 3 review Test 1 #3.1 Activity: Quality Control
3.1 Activity: Equivalent Fraction Bars
3.2
Wk 4 3.2
3.3 3.4 3.4 Review
Wk 5 Test 2 4.1 Activity Packaging
4.1 4.2 4.2
Wk 6 4.3 Activity 4.3 4.4 4.4
Review
Wk 7 Test 3
5.1 Activity 5.1 Activity Animal population
5,2
Wk 8 5.3 5.3 5.4
5.4 5.5
Wk 9 5.5
Catch-up/Review
Catch-up/Review
Review Test 4
Wk 10 Review
review
