Course Outline: MAT 003, 095

Updated Sun Jan 22 10:09:00 PST 2006

Text

  1. Introductory and Intermediate Algebra Custom Edition for CSUDH, by Lial, Hornsby, McGinnis. Addison Wesley. ISBN # 0536 86183. (Includes Algebra Review Cards and MathXL). MathXL is an online homework, tutorial, and assessment system that is available to students on the web at http://www.mathxl.com
  2. Supplementary Material on Units excerpted from Chapter 2. of the textbook Using and Understanding Mathematics (3rd ed.) by Bennett and Briggs, published by Addison-Wesley, used with the publisher's permission. Your instructor will provide you with a user name and password so that you may download this copyrighted material.

Grading

MAT 003 (3 unit class, CR/NC grading)

MAT 095 (1 unit class, CR/NC grading)

Tests and final exams are common for all sections. All decisions regarding quizzes, homework, attendance, class participation, etc. are made by the individual instructor.

Rubric for correcting show work problems:

Discussion

This remedial math sequence focuses on preparing students to succeed in MAT 105, MAT 131 and general education science classes. Word problems are the most important focus of the course. It consists of four components, MAT 003 part 1, 2, and 3, and MAT 095. Each component lasts five weeks and ends with a common exam. Instructors may add additional tests, homework, etc. as they see fit.

Below are the sections that will be covered in the tests, and some comments on them. Exam problems will be similar to exercises that are listed, plus there will be some problems on the supplementary material on units and conversions. (The exercise lists are just for information. Instructors will choose for themselves what to assign. They won't assign all these exercises, there are too many.) I have tried to list here only what seems essential for MAT 105, MAT 131, and required general ed. science courses. Instructors may wish to supplement the material listed here with material from other sections or sources if they feel this will help the students. But I think we should assume students have already seen all this stuff so we don't need to cover it all, instead concentrate on concepts and things students are likely to misunderstand or avoid, like word problems. Instructors will decide for themselves how much time to spend on each topic but please leave some time at the end for review for the exams.

In the course outlines below, a listing like "1.5 #33-68. (signed numbers, difference, sum)" means that problems similar to exercises 33-68 in section 1.5 may appear on the exams. The comments at the end of the line describe the contents: signed numbers, differences, and sums.

MAT 003 (part 1)

MAT 003 (part 2)

MAT 003 (part 3)

MAT 095

Supplementary Material on Units

This material is discussed in Chapter 2 of Bennett and Briggs' book Using and Understanding Mathematics. Copies have been provided by our publisher, Addison Wesley. See the "Text" section above .

Supplementary material on the use of units and dimensional analysis should be integrated into the review material in chapter 1 while you're reviewing basic stuff like arithmetic with fractions and mixed numbers, percents, etc. Tell students they should always use units (feet, pounds, square inches, etc.) whenever they work problems involving real objects, and this will be enforced by the instructor. It will help them think and write clearly. Seven horses is "7 horse" not "7" and the area of a rectangle 7 ft. wide by 3 ft. tall is 21 square ft., not 21. When you're counting it's important to remember what you're counting!

Review the distributive law as in 3 horses + 4 horses = 7 horses i.e. 3(horses)+4(horses)=(3+4)(horses); in this context it's obvious, it's just counting. But 3 inches + 4 feet is not 7 (something???). Adding (and subtracting) "like terms" makes sense but adding and subtracting "unlike terms" usually doesn't, unless you first convert them into like terms. Example: adding feet and inches, addition and subtraction of fractions with different denominators. It's strange but true that multiplying or dividing unlike quantities is easy (example: (3)(horse)=(3 horses), fractions without common denominators (2/3)(4/5)=(2x4)/(3x5), (men)(hours)=man-hours, (miles)/(hours)=miles per hour = speed, but adding or subtracting them isn't easy unless you can convert them to the same kind of thing (examples: to add 2/3 to 4/5 you have to convert them to fifteenths, to add inches to feet you first convert both to inches or feet), and often isn't possible and leads to nonsense as in e.g. miles + hours. If they understand this they should find the rules for fractions pretty natural.

Arithmetic with Mixed numbers. Adding things like 1'6"+3'8", or combinations of hours and minutes: the key of course is to make you convert to common units. (There are extra twists with clocks because of mod 12). Make them pay attention to the order of operations and parentheses. They should see that sums and products can be reordered but differences or quotients can't (commutative and associative law but this terminology isn't essential).

Teach them how to use dimensional analysis when they're converting or combining units, and make sure they use it. Writing down units explicitly will help them solve problems involving ratios and conversions of one unit to another. They should be able to solve problems like these:

  1. How many inches are there in 3 miles?
  2. If a man walks 3 miles per hour how many furlongs can he walk in a fortnight (if he never stops)? (1 mile = 8 furlongs and 1 fortnight = 14 days). What is his speed in yards per day?
  3. How many gallons are there in a rectangular box that measures 3 ft. x 4 ft. x 5 ft. ? 1 US liquid gallon = 231 cubic inches.
  4. If your car gets 20 miles per gallon and gas costs 6.71 Mexican pesos per liter then how much would it cost to buy enough gasoline to drive from Tijuana to Guadalajara, a distance of 2344 kilometers? 1 US dollar = 11.331 Mexican pesos, 1 mile = 1609.344 meters, 1 gallon = 1.3785 liters (approximately).

You can find good sources on the web. Some are listed below. [Please help me find some more!]

Make sure they understand what "=" means and you won't accept incorrect usage. (Common error: students often write "=" when they want to say "this is the next step" instead of "these things are the same". Don't let them do that!). Make sure they understand the meaning of "of" (multiply, as in 3 of those or half of that) and "per" (divide, as in miles per hour). When multiplying and dividing the units need not agree e.g. man-hours, miles per hour.

When students work word problems, always insist that they write down the units and handle them correctly!! Also insist that they show their work, use "=" correctly, write clearly and neatly, and present their solutions in an organized way. This will help them (and whoever reads their work) when things get complicated. We will insist on correct usage when we grade the "show your work" problems on exams.

Resources on the Web

Math XL

Math XL is an online homework, tutorial, and assessment system that is bundled with our text. http://www.mathxl.com

Units:

I found those with google.

  1. This one has interesting historical notes: A Dictionary of Units of Measurement http://www.unc.edu/~rowlett/units/
  2. the universal currency converter http://www.xe.com/ucc/
  3. google "unit measurement": http://www.ex.ac.uk/cimt/dictunit/dictunit.htm
  4. google "dimensional analysis": http://www.chemistrycoach.com/use.htm
  5. google "calculator tutorial" provides links. It may be better to go to manufacturer's website.
  6. scientific calculator exercises: http://www.math.uncc.edu/~droyster/courses/spring96/maed3103/Lesson3_2.html

Graphs and Charts:

  1. bar graph: http://cstl.syr.edu/fipse/TabBar/RevBar/REVBAR.HTM

Good word problems

These problems are at the middle school level, which is about right for this class:

  1. NCTM middle school word problems http://www.nctm.org/middle/archive.asp
  2. http://www-spof.gsfc.nasa.gov/stargaze/Smap.htm "From Stargazers to Starships" see http://www-spof.gsfc.nasa.gov/stargaze/Smath.htm "math refresher". Has a nice short on history of algebra, more.
  3. 9th grade algebra proficiency test http://www.grc.nasa.gov/WWW/K-12/p_test/math_pro1.html