There are many problems throughout the text labeled IN YOUR OWN WORDS. Just relax; do not be afraid to give your opinion. For the most part, these questions do not have “right” or “wrong” answers. You should spend about five minutes in answering each of these questions.
Even though these are IN YOUR OWN WORDS problems, they also point to two essential ideas of this course, so it would be a good idea to be able to recite each of these ideas from memory: Problem 3 is the order of operations and Problem 4 is the scientific method.
There are many problems throughout the text labeled IN YOUR OWN WORDS. Just relax; do not be afraid to give your opinion. For the most part, these questions do not have “right” or “wrong” answers. You should spend about five minutes in answering each of these questions. Note that the order of operations shows a stop sign. This sign is used to denote something that is important for your successful completion of the material in this book.
Copy down the problem as you see it in the book, and then carry out the order of operations as described by the first stop sign in this section. You will find it easier if your organize your work as shown here (for Problem 16a ):
8 + 2(3 + 12) – 5 * 3 = 8 + 2(15) – 15 * 3
= 8 + 30 – 45
= -7
If a conclusion is reached by looking for a pattern, and then forming a conclusion, it is inductive reasoning. This is type of reasoning is also known as the scientific method where you look for patterns, formulate a conjecture, and then test that conjecture. On the other hand, if a conclusion is reached using laws of logic, then it is deductive reasoning.
See Example 1. Problem 22 asks for the four pattern. Consider (in order):
1*4 = 4
2*4=8
3*4 = 12, and 1 + 2 = 3
4*4 = 16, and 1 + 6 = 7
5*4 = 20, and 2 + 0 = 2
6*4 = 24, and 2 + 4 = 6
7*4 = 28 and 2 + 8 = 10, and 1 + 0 = 1
8*4 = 32, and 3 + 2 = 5
9*4 = 36, and 3 + 6 = 9
10*4 = 40, and 4 + 0 = 4
11*4 = 44, and 4 + 4 = 8
It seems that we have found a pattern. What is that pattern?
Problems 21, 23, and 24 work the same way.
See Example 2; look for a pattern. If you see the sum of the first 25 consecutive odd numbers, start with one odd number:
1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
Do you see a pattern? If not, continue with the pattern.
Review magic squares at the beginning of this section.
Problems 31 and 32
If you have never seen a Suduko puzzle, check them out online. Many people spend countless hours on these puzzles, which remind us of magic squares. Try these problems…. perhaps you, too, will become “hooked.”
Review magic squares at the beginning of this section.
See Example 3.
Begin by drawing Euler circles for the first premise. Then, complete the circles for the second premise to see if the argument is valid or not.
Note: Homework Hints are given only for the Level 1 and Level 2 problems.
However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section). As a last resort, you can call the author at (707) 829-0606.
On the other hand, the problems designated “Problem Solving” generally require techniques that do not have textbook examples.
There are many sources for homework help on the internet.
Algebra.help
Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.
http://www.algebrahelp.com/
Quick Math
This site provides online graphing calculators. This is especially useful if you do not have your own calculator.
http://www.quickmath.com/
The Math Forum @ Drexel
This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.
http://mathforum.org/