PLEASE HELP US OUT WITH THIS: When you go to the open lab next door in 403, please make sure you sig

1
PLEASE HELP US OUT WITH THISWhen you go to the
open lab next door in 403, please make sure you
sign in on the log sheet and enter your
instructors name and your section number. We
need to collect this information to document lab
usage and ensure future funding for tutors.
This is section number 00 ??? My instructors
last name is ??? (Your instructor will write
this information on the whiteboard please copy
it into your notebook.)
Removable stickers with tutoring schedules still
available grab one now and stick it on your
laptop.
2
Please CLOSE YOUR LAPTOPS and turn off and put
away your cell phones.
Sample Problems Page Link (Dr. Bruce Johnston)
3
Gateway Quiz Information

• You will be taking an 8-question Gateway Quiz at
  the beginning of the next class session, without
  a calculator.
• The Gateway Quiz will consist of 8 questions
  similar to the ones on fractions and the order of
  operations that were due at the beginning of
  todays class.
• This Gateway Quiz will count just 5 points
  towards your 1000 course points, and (unlike in
  Math 010) you wont have to get 100 on it to
  pass the class.
• HOWEVER, if you arent able to do most of these
  problems without a calculator, you will very
  likely have a difficult time doing the polynomial
  factoring and rational expression problems in the
  last half of this course, and you might want to
  consider taking Math 010 before taking this class
  to increase your chances of success (and lower
  your stress) in Math 110.

4
More Gateway Quiz Information

• We will spend some time today on how to do these
  kinds of problems, and you will have another set
  of eight practice Gateway problems to do at the
  end of the homework assignment due at the next
  class session (along with another worksheet to
  show your work on these problems, which are the
  last 8 problems in the assignment on sections
  1.2/1.3.)
• You can also view a set of slides (or print a
  handout) with either step-by-step solutions or
  just an overview of sample problems completely
  worked out just click the PowerPoint Lecture
  Slides link in todays assignment folder and then
  click on the Gateway link.
• The TAs and teachers in the open help lab next
  door in 403 can also give you one-on-one help
  with the practice Gateway problems after class
  today (up until 730 p.m.) or tomorrow in the 403
  open lab starting at 800 a.m.

5
Section 1.2 (OK, time to take notes now...)

• Sets of numbers
• Natural (counting) numbers
• N 1, 2, 3, 4, 5, 6 . . .
• Whole numbers
• W 0, 1, 2, 3, 4 . . .
• Integers
• Z . . . -3, -2, -1, 0, 1, 2, 3 . . .

6

• More Sets of numbers
• Rational numbers the set (Q) of all numbers
  that can be expressed as a quotient of integers,
  with denominator ? 0
• Irrational numbers the set (I) of all numbers
  that can NOT be expressed as a quotient of
  integers
• Real numbers the set (R) of all rational and
  irrational numbers combined
• The information on sets is easy to forget come
  quiz or test time, so make sure you have it
  written down in your notes!

7
Page 11 in your textbook (online or hardcopy
version) provides a helpful diagram of all these
number sets and their relationships to each
other. (Access the online version in each
Assignments folder.) Underneath this diagram on
page 11 are some example problems (EXAMPLE 5)
that will be useful in preparing to do the
homework problems.
8
Sample problem from todays homework
9

• Absolute Value
• The absolute value of a number is the distance of
  that number away from 0 on a number line.
• ?a?? 0 always, since distances are non-negative.
• (We say non-negative to include positive numbers
  and zero.)

?a? a, if a is 0 or a positive number.
Example ?10? 10 ?a? -a, if a is a negative
number Example ?-10? -(-10) 10
10
Examples

• ?5? 5
• ?-5? 5
• -?5? -5
• ?0? 0
• -?-5? -5

Note the difference the placement of the
negative sign makes!!!
11

• Translating Words into Algebraic Symbols
• Addition (the symbol ) is denoted by the phrases
• sum, plus, added to, more than, increased by
• Subtraction (the symbol -) is denoted by the
  phrases
• difference of, minus, subtracted from, less
  than decreased
• Multiplication (the symbol or ) is denoted
  by
• product, times, multiply, twice
• Division (the symbol / or ) is denoted by
  the phrases
• quotient, divide, ratio, divided by

12

• Examples
• Translate each phrase to an algebraic expression.
  Use the variable x to represent each unknown
  number.
• Eight times a number.
• Three more than 8 times a number.
• The quotient of a number and -7.
• One and six-tenths subtracted from twice a number.

13
Sample problem from todays homework
14
Section 1.3 Properties of Real Numbers

• If b is a real number, 0 b 0 and b 0 0.
• If b is a real number,
• If b is a nonzero real number,
• Reciprocals are two numbers whose product is 1.
• Example

15
Sample problem from todays homework
16
Important Note

• In homework and on tests and quizzes, the
  computer will mark an answer wrong if it has a
  negative sign in the denominator.
• EXAMPLE
• Right way _ 14
• 3
• Wrong way 14
• -3

17

• Exponential notation for 35
• Base is 3
• Exponent is 5
• The notation means 3 3 3 3 3

Evaluate 43. 43 4 4 4 64


18
NOTE Many of todays homework problems as well
as Gateway problems 7 8 all require using the
order of operations.

• Order of operations
• First, calculate expressions within grouping
  symbols
• (parentheses, brackets, braces,absolute values,
  fraction bars).
• If there are nested sets of grouping symbols,
  start with the innermost ones first and work your
  way out.
• Exponential expressions left to right
• Multiplication and division left to right
• Addition and subtraction left to right

19

• Order of Operations Memory Device
• Please excuse my dear Aunt Sally
• 1. Please (Parentheses)
• 2. Excuse (Exponents)
• 3. My Dear (Multiply and Divide)
• 4. Aunt Sally (Add and Subtract)
• or just remember PEMDAS

20
Sample Gateway Problem 7
Strategy Calculate out the entire top expression
and then the entire bottom expression, using the
order of operations on each part. Then simplify
the resulting fraction, if necessary.
TOP EXPRESSION 24 4(7 2) Step 1
Parentheses 24 4(7 2) 24 4(9)
Step 2 Exponents 24 4(9) 2222
4(9) 16 4(9)
(because 2222 422 82
16) Step 3 Multiply/Divide 16 4(9) 16
49 16 36 Step 4 Add/Subtract 16
36 -20
21
Now calculate the bottom expression 2(62) 4

• Step 1 Parentheses 2(62) 4 2(8) 4
• Step 2 Exponents There arent any in this part.
• Step 3 Multiply/Divide 2(8) 4 28 4
  16 4
• Step 4 Add/Subtract 16 4 20
• Now put the top over the bottom and simplify the
  resulting fraction
• TOP 24 4(7 2) -20 -1
  -1
• BOTTOM 2(62) 4 20 1

22
Full Solution to Sample Problem 7
Here is the work we expect to see on your
worksheet 24 4(7 2) 24 4(9) 16 4(9)
16 36 -20 -1 -1 2(62) 4 2(8)
4 16 4 20 20
1
23
Sample Gateway Problem 8

• Strategy Deal with the expressions inside the
  grouping symbols (parentheses, brackets) first,
  starting with the innermost set (-3 6).
• STEP 1 (inside the parentheses)
• 317 5(-3 6) - 10 317
  5(3) - 10
• STEP 2 (inside the brackets multiply first,
  then add and subtract)
• 317 5(3) -10 317 53
  -10 317 15 - 10
• 317 15 - 10 332 - 10
  322
• STEP 3 Do the final multiplication 322 322
  66

24
Full Solution to Sample Problem 8
Here is the work we expect to see on your
worksheet
317 5(-3 6) - 10 317 5(3) - 10
317 15 - 10 332 - 10 322 66
25
If you want more tips on Gateway Problems 1-6
(and todays homework problems 43-50)click on
the PowerPoint Slides item in todays Assignment
folder for Sections 1.2 1.3, then click on
Gateway Quiz Solutions, then click on the top
item in the list (Gateway Problem Solution
Detail Slides)
26
IMPORTANT

• Todays assignment has a paper worksheet (handed
  out in class today) that must be completed and
  turned at the start of the next class session.
• On this worksheet, you must show complete,
  detailed, step-by-step work for the last 8
  problems of the assignment (43-50), just as is
  shown on the Gateway solution slides.
• Each of these eight problems has a weight of 2
  points, and your teacher will decrease your
  online score for this assignment by one point for
  each of those 8 problems for which you do not
  show complete, correct, step-by-step work.

27
Now open your laptops

• Open your browser of choice (e.g. Internet
  Explorer, Firefox, Safari, etc.)
• Log on to Course Compass (www.coursecompass.com )
  using the user id and password you created
  when you registered.
• Click on the name of this course (Fall 2009
  Math110)

28
Heres what you should now be seeing

• Now click the green Assignments button at the
  left side of the screen.
• Then click on todays lesson (Sections 1.2
  1.3).

29
Heres what you should now be seeing

• The top link will always take you to the
  PowerPoint lecture slides that are available for
  you to print before class to take notes on or to
  look at after class to review any points that
  went by too fast during the lecture.
• At the bottom of the Assignments screen for each
  day youll find a link to the homework assignment
  thats due before the next class. (Click where it
  says Click here to do the assigned homework)
  DO THIS NOW.
• From the list that appears, select the homework
  for todays section (1.2/1.3)

30

• Now click on Question 1

31
Heres what you should now be seeing

• After you enter the answer to a problem, click
  Check Answer to see if its correct. For most
  problems, youll get three tries to get it right.
• Even if you get a problem wrong three times, you
  can do it over up to nine more times until you
  get it right. (The computer will generate a new
  version for you to try when you click similar
  exercise.)

32

• If you are having trouble with a problem, check
  the on-line help available for each problem
• Help Me Solve This
• Textbook Pages
• Animation(for some problems)

33

• IMPORTANT Even if you get a problem wrong on
  each of your three tries, you can still go back
  and do it again by clicking similar exercise at
  the bottom of the exercise box. You can do this
  nine times, for a total of 30 tries (3 tries at
  each of 10 different problems. You should always
  work to get 100 on each assignment!

34
Another Thing to Remember

• Take notes as you do each homework problem. Write
  down all steps (show your work!). Again, this
  helps tremendously when youre studying for
  tests.
• (Some days we might do a random notebook
  check after lecture, and will give attendance
  points only to those whove taken legible notes.)

35
If theres still time left in the class session
after lecture, you should stay in the classroom
to work on your homework until the end of the
session. If you have finished the homework
already, or if you get it finished before the end
of the class period, show your on-screen 100
score to the teacher or TA and you may then leave
class early.
36
Reminders

• Todays homework assignment on sections 1.2-1.3
  is due at the start of our next class session,
  along with the completed paper worksheet showing
  your work for problems 43-50.
• The Syllabus Quiz is due next session at the
  start of class. You can review/redo this quiz as
  many times as you want to get 100. Only your
  best score counts towards your grade.

37

• REMEMBER Come to the open lab if you need help.
  There are more than 40 open lab hours each week.