Syllabus Sections

Publish Date

08/15/2012 23:36:42

Basic Math Skills

MATD-0330

Let’s be Rational Problems 1.2 and 4.3. At the end of Let’s be Rational, following Investigation 4, you may want to revisit the overestimation and underestimation ideas from Problem 1.2 and rewrite these situations as inequalities. Here we present an example using Problem 1.2D, of how this might be accomplished. This preview shows page 1 - 2 out of 2 pages. MAC 1105 Pre-Class Assignment: Combinations of Functions Read section 2.6 ‘Combinations of Functions’ to prepare for class In this week’s pre-requisite module, we covered the topics factoring quadratic expressions and performing operations on rational expressions.

Fall 2012
09/24/2012 - 12/16/2012

Course Information

Section 082
Lecture
MWF 10:10 - 11:20
SAC1 1311
Abel Villarreal

Section 134
Lecture
TTh 15:00 - 17:25
SAC1 1320
Abel Villarreal

Office Hours

• M W F
  11:20 - 12:00 noon
  South Austin Campus (SAC)
  
• M W
  1:20 pm - 2:00 pm
  South Austin Campus (SAC)
  
• T Th
  1:20 - 2:00 pm
  South Austin Campus (SAC)
  

Course Requirements

Course Description and Rationale:

This course is designed to develop and solidify basic arithmetic and algebra skills that will be required in future math courses. The course content includes operations on whole numbers, integers, fractions, decimals, ratios and proportions, and percents. It also includes exploring and solving one-variable linear equations and applications as well as simple algebraic concepts with geometric extensions.

The Basic Math Skills course is designed to be the first of a three-course developmental course sequence that prepares students for college algebra and beyond. The sequence consists of Basic Math Skills (#0330), Elementary algebra (#0370), and Intermediate Algebra (#0390)

Required Text:

Prealgebra, 5th Edition by Blair, Tobey, Slater; ISBN #9781256748649 or 1256748641. This text is the ACC custom edition, which saves money. Used versions are NOT available as this a new edition.

The previous text, Basic Math Skills, 4th Edition contains almost the exact material but do not match on certain page numbers and homework problems. Used copies may be hard to come by.

Free Supplemental Resources:

www.interactmath.com – A web-based resource that offers unlimited online, text-specific tutorial exercises. MacIntosh computers are currently NOT supported.

www.purplemath.com – A web-based resource that offers unlimited practice and alternate explanations on many arithmetic and algebraic topics. Click on “Lesson index” at right to locate specific topics. The home page also has links to more than 15 alternate sites for free tutorials, practice, lessons, etc. as well as assorted math study skills help. This site supports both Mac and PC formats. Very easy to use.

www.austincc.edu/tutor – ACC main campus Learning Labs which offer free tutoring on a first–come first–serve basis. Access site for hours of operation.

http://patrickjmt.com/ – A vast library of short videos on hundreds of math topics. If you want a 3 to 5 minute movie tutorial on any math topic, this is the go-to site. MAC and PC friendly.

Course Grade:

The course grade is determined as follows:

Best 4 of 5 tests + final exam) divided by 5 + homwork average (up to 4 points)

All tests will be administered and monitored on a scheduled class meeting in class. The use of the testing center will be considered only under extreme and unexpected circumstances (power failure, severe weather, etc.) See course timetable.

Homework and Explorations:

There are four (4) homework sets, each based on a 4-point scale. Homework Set 1 covers Chapters 1 and 2. Homework Set 2 covers Chapters 3 and 4, and so on. The homework average (up to 4 points) is then added to the final average. The more homework turned in the more extra credit points earned. Since homework is extra

credit, no more than one (1) homework set will be accepted late.

A related real world exploration will be given between tests and due on each test day. Each exploration will be worth up to 10 bonus test points on each test. There is no penalty for not completing this extra credit. Each exploration is an opportunity to

realistically apply what you learn.

Class Participation:

Doing mathematics in front of your peers solidifys one’s mathematics foundation. I highly recommend that you DO mathematics this way as often as possible. I will keep count on the number of times you contribute to the class discussion and will use this “participation” grade in cases where your average is between an A and B, B and C, etc.

Late Work:

Late work is defined as assigned work that is no more than two (2) class days late. There is a one (1) point penalty for late work. Thus, the highest score a homework set may receive is a 3 out of 4 points. NO MORE than 1 homework set will be accepted and counted late.

In-Progress Grade:

An in-progress (IP) grade is a neutral, non-passing grade. It is not counted in the gpa, but may count as a “withdrawal (W)” for financial aid purposes. It is usually awarded to students who attend class regularly, do all the assigned work and cannot maintain a passing average. The math department chairperson must approved an IP. The student will have to retake the course the next semester AND pay for the course AGAIN. Students may not receive more than two (2) IP’s in this or ANY developmental course.

Makeup Tests:

A student can miss one (1) of the first four tests. NO MORE. Test 5 is optional and may replace a missed test or the lowest of your first 4 test scores. Test 5 cannot be used to replace the final exam.

Attendance Policy:

According to the Texas Success Initiative (TSI), attendance is required in this course. Students with four (4) or more absences MAY BE withdrawn. See an ACC advisor for further clarification.

Readings

Fall 2012 Timetable (16 weeks)

WEEK MONDAY WEDNESDAY FRIDAY

1 Aug. 27 1.1, 1.2 Aug. 29 1.3, 1.4 Aug. 31 1.5, 1.6

2 Sept. 3 Labor Day Sept. 5 1.7, 1.8 Sept. 7 1.9, 2.1

3 Sept. 10 2.2, 2.3 Sept. 12 2.4, 2.5 Sept. 14 2.6

4 Sept. 17 Test #1 Sept. 19 3.1, 3.2 Sept 21 3.3, 3.4

5 Sept. 24 4.1, 4.2 Sept. 26 4.3, 4.4 Sept. 28 4.5, 4.6

6 Oct. 1 Test #2 Oct. 3 5.1, 5.2 Oct. 5 5.3

7 Oct. 8 5.4 Oct. 10 5.5 Oct. 12 5.6

8 Oct. 15 5.7 Oct. 17 Test #3 Oct. 19 6.1, 6.2

9 Oct. 22 6.3 Oct. 24 7.1 Oct. 26 7.2

10 Oct. 29 7.3 Oct. 31 7.4 Nov. 2 7.5

11 Nov. 5 8.1 Nov. 7 8.2 Nov. 9 8.3

12 Nov. 12 8.4 Nov. 14 Test #4 Nov. 16 8.5

13 Nov. 19 8.6 Nov. 21 8.7 Nov. 23 Gobble-Gobble

14 Nov. 26 8.9 Nov. 28 9.1, 9.2 Nov. 30 10.1

15 Dec. 3 10.3,10.5 Dec. 5 10.6 Dec. 7 10.7

16 Dec. 10 Test #5* Dec. 12 Final Review Dec. 14 Final Exam

*(optional)

12 week Timetable

WEEK TUESDAY THURSDAY

1 Sept. 25 1.1 – 1.4 Sept. 27 1.5 – 1.7

2 Oct. 2 1.8, 1.9, 2.1, 2.2 Oct. 4 2.3 – 2.6

3 Oct. 9 Test #1 Oct. 11 3.1 – 3.4

4 Oct. 16 4.1-4.3 Oct. 18 4.4 – 4.6

5 Oct. 23 Test #2 Oct. 25 5.1 – 5.3

6 Oct. 30 5.4 , 5.5 Nov. 1 5.6 , 5.7

7 Nov. 6 Test #3 Nov. 8 6.1 – 6.3, 7.1

8 Nov. 13 7.2 – 7.5 Nov. 15 8.1, 8.2, 8.3

9 Nov. 20 8.4 – 8.7 Nov. 22 Gobble-Gobble

10 Nov. 27 8.9, 9.1, 9.2 Nov. 29 Test #4

11 Dec. 4 10.1, 10.3, 10.5 Dec. 6 10.6, 10.7

12 Dec. 11 Final Review Dec. 13 Final Exam

Dec. 11 Test #5 (optional)

Course Subjects

Chapter 1: This chapter covers all the whole number operations and related applications and algebraic topics. You should concentrate on the vocabulary, translating, and property concepts. In sections 1.8 and 1.9 concentrate on the algebraic concepts. The applications in chapter one are fairly straightforward and students will be tempted to just write down the answer. Don't. Instead create a systematic process of problem solving.

Chapter 2: Chapter two introduces signed numbers. Signed numbers will be with you throughout your study of mathematics.

Chapter 3: Chapter three introduces some basic algebraic concepts and geometry formulas. This early introduction to basic algebraic concepts allows students to continue to integrate algebra with arithmetic throughout the text.

Chapter 4: The understanding of fractions, ratios, and proportions are concepts covered in the fourth chapter. Sections 4.3 and 4.4 (simplifying fractional expressions) are the most important.

Chapter 5: Chapter 5 covers the arithmetic of fractions. Concentrate on understanding the algorithms of fraction operations. This will help you in later courses when you work with rational expressions.

Chapter 6: Chapter six covers the basic operations of polynomials. Omit 6.4.

Chapter 7: Chapter seven covers solving equations and solving word problems using equations. It is very important for students to learn to solve equations of the form ax + b = c.

Chapter 8: Decimals and percents are covered in chapter eight. You should move quickly through the first half of chapter eight and save some time for the last five sections on percents. We cover all of the material in chapter eight; however, section 8.7 and 8.8 cover the same concept using different methods.

Chapter 9: The syllabus covers only the first two sections of chapter nine on reading different types of graphs and calculating the mean, median, and mode.

Chapter 10: The syllabus covers all of chapter ten, except sections 10.2 and 10.4. This is the only geometry that students will learn, so it is important for them to know how to use the formulas.

Student Learning Outcomes/Learning Objectives

Overall objectives:

1. Students will feel a sense of accomplishment in their increasing ability to use mathematics to solve problems of interest to them or useful in their chosen fields. Students will attain more positive attitudes based on increasing confidence in their abilities to learn mathematics.

2. Students will learn to understand material using standard mathematical terminology and notation when presented either verbally or in writing.

3. Students will improve their skills in describing what they are doing as they solve problems using standard mathematical terminology and notation.

Student Learning Outcomes: Upon successful completion of this course, a student will be able to do:

I.Concepts and skills associated with whole numbers

1.write the standard form of a whole number

2.round whole numbers and use rounding to estimate values involving whole number arithmetic

3.perform the four basic arithmetic operations (+, -, x and ÷) on whole numbers

4.solve application problems involving the four basic operations on whole numbers

5.identify the order relation between two whole numbers

6.simplify exponential expressions with whole number exponents

7.use the order of operations to simplify expressions.

8.prime factor whole numbers

9.find the least common multiple of two or more whole numbers

II.Concepts and skills associated with fractions

1.perform the four basic arithmetic operations on fractions

2.solve application problems involving the four basic operations on fractions

3.simplify fractions to lowest terms

4.convert between mixed numbers and improper fractions

5.use the order of operations to simplify expressions with fractions, exponents, grouping symbols,

6.identify the order relation between two fractions

III.Concepts and skills associated with decimals

1.write the standard form of a decimal

2.round decimals and use rounding to estimate values involving decimal arithmetic

3.perform the four basic arithmetic operations on decimals

4.solve application problems involving the four basic operations on decimals

5.convert between fractions and decimals

6.use the order of operations with decimals, exponents, grouping symbols, arithmetic operations.

7.identify the order relation between two decimals or between a decimal and a fraction

IV.Concepts and skills associated with integers and rational numbers

1.perform the four basic arithmetic operations on rational numbers

2.use the order of operations with rational numbers, exponents, arithmetic operations

3.solve application problems involving the four basic operations on rational numbers

4.identify the order relation between two rational numbers

V.Concepts and skills associated with ratios, proportions and percents

1.convert between fractions and percents and between decimals and percents

2.solve percent equations

3.find the missing number in a proportion

4.solve ratio and proportion application problems

5.solve application problems involving percents

VI.Concepts and skills involving linear equations in one variable

1.solve linear equations in one variable involving integers, decimals and fractions

2.solve application problems that yield linear equations

VII.Concepts and skills associated with polynomials

1.identify terms of a polynomial, and classify polynomials by number of terms

2.use the exponent laws to simplify algebraic expressions involving whole number exponents

3.use the order of operations to evaluate variable expressions and formulas

4.combine like terms

5.add and subtract polynomials

6.multiply monomials by polynomials

VIII.Use statistics to collect and interpret data

1.determine the mean, median, and mode

2.interpret graphs (pictographs, circle graphs, bar graphs and line graphs) and analyze data

IX.Concepts and skills associated with geometry

1. know the appropriate vocabulary/facts about angles, triangles, rectangles, squares, and circles

2. find perimeters of rectilinear figures

3. use standard formulas to find perimeters and areas of triangles, rectangles, squares and circles

4. find complementary and supplementary angles

5. find angles associated with parallel lines cut by a transversal

Prime Time

Main Ideas | Worked Homework Examples

In Prime Time students will explore certain important properties of whole numbers, especially those related to multiplication and division. The investigations in this unit will help students to:

• Understand relationships among factors, multiples, divisors, and products;
• Recognize and use properties of prime and composite numbers, even and odd numbers, and square numbers;
• Use rectangles to represent the factor pairs of numbers;
• Develop strategies for finding factors and multiples, least common multiples, and greatest common factors;
• Recognize and use the fact that every whole number can be written in exactly one way as a product of prime numbers;
• Use factors and multiples to solve problems and to explain some numerical facts of everyday life;
• Develop a variety of strategies for solving problems building models, making lists and tables, drawing diagrams, and solving simpler problems.

Bits and Pieces I

Main Ideas | Worked Homework Examples

In Bits and Pieces I students will investigate and make sense of rational numbers and operations with rational numbers. The investigations in this unit will help students to:

• Build an understanding of fractions, decimals, and percents and the relationships between and among these concepts and their representations;
• Develop ways to model situations involving fractions, decimals, and percents;
• Understand and use equivalent fractions to reason about situations;
• Compare and order fractions;
• Move flexibly between fraction, decimal, and percent representations;
• Use benchmarks such as 0, 1/2 , 1, and 1/4 to help estimate the size of a number or sum;
• Develop and use benchmarks that relate different forms of representations of rational numbers (for example, 50% is the same as 1/2 and 0.5);
• Use physical models and drawings to help reason about a situation;
• Look for patterns and describe how to continue the pattern;
• Use context to help reason about a situation;
• Use estimation to understand a situation.

Shapes and Designs

Main Ideas | Worked Homework Examples

Shapes and Designs was created to help students to:

• Understand some important properties of polygons and recognize polygonal shapes both in and out of the classroom;
• Investigate the symmetries of a shape-rotational or reflectional;
• Estimate the size of any angle using reference to a right angle and other benchmark angles;
• Use an angle ruler for making more accurate angle measurements;
• Explore parallel lines and angles created by lines intersecting parallel lines;
• Find patterns that help determine angle sums of polygons;
• Determine which polygons fit together to cover a flat surface and why;
• Explain the property of triangles that makes them useful as a stable structure for building;
• Reason about and solve problems involving shapes.

Bits and Pieces II

Main Ideas | Worked Homework Examples

Bits and Pieces II was created to help students make sense of one aspect of rational number: fraction operations. The investigations in this unit will help students to:

• Use benchmarks and other strategies to estimate the reasonableness of results of operations with fractions;
• Develop ways to model sums, differences, products, and quotients with areas, strips, and number lines;
• Use estimates and exact solutions to make decisions;
• Look for and generalize patterns in numbers;
• Use knowledge of fractions and equivalence of fractions to develop algorithms for adding, subtracting, multiplying and dividing fractions;
• Recognize when addition, subtraction, multiplication, and division is the appropriate operation to solve a problem;
• Write fact families to show the inverse relationship between addition and subtraction, and between multiplication and division;
• Solve problems using arithmetic operations on fractions;
• Look for and generalize patterns.

Covering and Surrounding

Main Ideas | Worked Homework Examples

In Covering and Surrounding student work with investigations leads them to:

• Understand area and relate area to covering a figure;
• Understand perimeter and relate perimeter to surrounding a figure;
• Develop strategies for finding areas and perimeters of rectangular shapes and non-rectangular shapes;
• Discover relationships between perimeter and area. including that each can vary while the other stays fixed;
• Understand how the areas of simple geometric figures relate to each other (e.g. the area of a parallelogram is twice the area of a triangle with the same base and height);
• Develop formulas and procedures-stated in words and/or symbols-for finding areas and perimeters of rectangles, parallelograms, triangles, and circles;
• Develop techniques for estimating the area and perimeter of an irregular figure;
• Recognize situations in which measuring perimeter or area will help answer practical questions.

Bits and Pieces III

Main Ideas |Worked Homework Examples

Bits and Pieces III, along with Bits and Pieces I and Bits and Pieces II, completes the development of meaning of, and operations on, fractions, decimals, and percents. This unit will help students to:

• Connect to what students already know about operations on fractions and whole numbers;
• Develop and use benchmarks and other strategies to estimate the answers to computations with decimals;
• Develop meaning of and algorithms for operations with decimals;
• Use the relationship between decimals and fractions to develop and understand why decimal algorithms work;
• Use the place value interpretation of decimals to make sense of short-cut algorithms for operations;
• Generalize number patterns to help make sense of decimal operations;
• Understand when addition, subtraction, multiplication or division is an appropriate operation to use to solve a problem;
• Understand that decimals are often associated with measurements in real world situations;
• Solve problems using operations on decimals;
• Use understanding of operations and the meaning of percents to solve percent problems of the form a% of b equals c for any one of the variables a, b, or c;
• Create and interpret circle graphs

How Likely Is It?

Main Ideas | Worked Homework Examples

The unit How Likely Is It? was created to help students:

• Understand that probabilities are useful for predicting what will happen over the long run
• Understand the concepts of equally likely and not equally likely;
• Understand that a game of chance is fair only if each player has the same chance of winning, not just a possible chance of winning;
• Understand that there are two ways to build probability models: by gathering data from experiments (experimental probability) and by analyzing the possible equally likely outcomes (theoretical probability);
• Understand that experimental probabilities are better estimates of theoretical probabilities when they are based on larger numbers of trials;
• Develop strategies for finding both experimental and theoretical probabilities;
• Critically interpret statements of probability to make decisions or answer questions.

Data About Us

1.2 Operations With Rational Numbersmr. Mac's Page Key

Main Ideas | Worked Homework Examples

The unit Data About Us was created to help students:

• Understand and use the process of data investigation by posing questions, collecting and analyzing data distributions, and making interpretations to answer questions;
• Represent data distributions using line plots, bar graphs, stem-and-leaf plots, and coordinate graphs;
• Compute the mean, median, or mode and the range of the data;
• Distinguish between categorical data and numerical data and identify which graphs and statistics may be used to represent each kind of data;
• Make informed decisions about which graph or graphs and which of the measures of center (mean, median, or mode) and range may be used to describe a data distribution;
• Develop strategies for comparing data distributions

Ruins of Montarek (CMP1)

1.2 Operations With Rational Numbersmr. Mac's Page Shortcut

Main Ideas | Worked Homework Examples

1.2 Operations With Rational Numbersmr. Mac's Page Number

The unit Ruins of Montarek was developed to help students:

• Read and create two-dimensional representations of three dimensional buildings
• Communicate spatial information
• Observe that the back view of a cube building is the mirror image of the front view and that the left view is the mirror image of the right view
• Understand and recognize line symmetry
• Explain how drawings of the base outline, front view and right view describe a building
• Construct cube buildings that fit two-dimensional building plans
• Develop a way to describe all buildings that can be made from a set of plans
• Understand that a set of plans can have more than one minimal building, but only one maximal building
• Explain how a cube can be represented on isometric dot paper, how the angles on the cube are represented by angles on the dot paper, and how the representations fit what the eye sees when viewing the corner of a cube building
• Make isometric drawings of cube buildings
• Visualize transformations of cube buildings, and make isometric drawings of the transformed buildings
• Reason about spatial relationships
• Use models and representations of models to solve problems