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    Basic High School Math Review
    Basic High School Math Review
    Basic High School Math Review
    Ebook175 pages2 hours

    Basic High School Math Review

    By Jim Elander

    ()

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    About this ebook

    Basic High School Math Review
    with
    Decision Making Skills


    A basic Math review for students who will be taking entrance
    exams for college, community college, trade school,
    professions, GED Test, and making future life decisions. This
    is a review to refresh the mathematics with decision making
    skills to make it more meaningful and useful.

    Don't tell me what to think, but teach me how to think!

    YOUNG PEOPLE WHO HAVE ACQUIRED THE ABILITY TO ANALYZE
    PROBLEMS, GATHER INFORMATION, PUT THE PIECES TOGETHER TO
    FORM TENTATIVE SOLUTIONS WILL ALWAYS BE IN DEMAND.
    J. G. Maisonrouge
    Former Board Chairman
    IBM World Trade Corp.




    By James Elander
    (Forever a student,teacher, author)
    LanguageEnglish
    PublisherXlibris US
    Release dateAug 31, 2013
    ISBN9781483605555
    Basic High School Math Review
    Author

    Jim Elander

    Jim Elander, after using the WW 2 GI Bill to attend college, began his teaching career in a small school where he taught all the math and also physics and chemistry. He learned a lot! Then earned his masters in Mathematics and taught one year in a larger school before going to Purdue as a General Electric Fellow for more Math. His next school, 2500 – 4300 students, which was really a college prep public school. (Oak Park and River Forest High School, Oak Park, IL) A school that expected much from the students and faculty. During the 26 years at Oak Park, he was president of two professional organizations, served on many North Central Evaluation teams, and three National Science Foundation programs. Besides being a Department Chair, he also served on the MAA- IL section Geometry committee. In 1990 his first geometry book was published. This is his second innovated geometry program that correlates decision-making skills with geometry. His final teaching position was at North Central College in the 80s before retiring. The objective for these activities is give teachers some ideas and ways to make the hectic days before holidays or other special days better learning experiences.

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      Book preview

      Basic High School Math Review - Jim Elander

      Contents

      Session 1

      Some Old and Some New

      Session 2

      Review 1

      Session 3

      Implications and Applications

      Session 4

      The use and misuse of Basic Statistics

      Session 5

      Applications with Problem Solving

      Session 6

      Implications and Polls

      Session 7

      3-D Applications

      Session 8: Applications: Some old, some new

      Session 9

      Algebra and Number Activities (Some different types of thinking!)

      Session 10

      Epilogue or The Final Word

      Session 11

      Additional Selected Activities for Math Review

      Index 1

      Basic Definitions

      Index 2

      Postulates

      Index 3

      Essential Geometry Theorems

      Index 4

      Conversion Information

      Index 5

      Suggestions for further reading

      Index 6

      Quotes

      Session 1

      Some Old and Some New

      You either make your own decisions or you become a slave to other decision makers.

      Unknown

      A Democracy’s success depends on an educated voting public.

      Unknown

      Parents (Teachers) should not teach their children (students) what to think, but teach them How to think and make decisions.

      Elander

      Session 1. Introduction

      Most of the students who will use this Review and apply to an institution which usually requires some type of admission information and regardless of your plans for the future, you will always be making decisions.

      All entrance assessments contain questions related to Geometry, but many students have forgotten most of their Geometry and Algebra. So this review will contain a basic review and applications of these subjects plus provide the basis for Decision Making or Critical Thinking as related to everyday situations.

      In the following set of questions you will be given a few examples of the mathematical questions and a reminder that all conclusions are based on undefined terms, defined terms, basic assumptions and previous conclusions (deductive reasoning), plus making conclusions from a few previous cases (inductive reasoning). (If you don’t understand Deductive or Inductive Reasoning and how they are used in decision making, this review will aid you.)

      Examples:

      U.S. Constitutional Amendment XIX.

      The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex.

      (The answers are the author’s. Your answers may differ due to rounding.)

      What does abridged mean? (This may be an undefined term to you.)

      What is the Total number of words? # _____                28

      How many would you classify as Undefined? # _____                17

      How many would you classify as Defined? # ____                11

      What is the percent of the total number of words that you classified as undefined?

      Hint: The number of undefined words (The, of, to, etc.) is what percent of the total number of words?

                Write the question in equation form and solve.

                          Undefined # = x% of total # 17=x%(28)

                                                                  17=x(1/100)(28)

                                                        Where did the 1/100 come from?

                                                        Solving: x = 60.7%

      Questions:         1. What number (numeral?) does the symbol % represent?

                (What is the difference between number and numeral?

                We usually don’t differentiate between the to terms.)

                2. What number (numeral?) does XIX represent? 19

                3. What year was the XIX Amendment adopted? 1919-20

      From the above, we could jump to a general conclusion that about 60% of the Constitution consists of undefined terms. You should question that general conclusion since it is based on only one small case. (This is an example of Inductive Reasoning. What does inductive reasoning mean to you from this one example?)

      An example of Deductive Reasoning is: Some States in the South passed laws that required a tax in order to vote, therefore town X required a tax in order to vote. (This is an example of Deductive Reasoning, which is drawing a conclusion from a general statement to a specific case.)

      This was ruled unconstitutional since it violated the XIX Amendment.

      (Decisions (good or bad) are base on the following:

                Inductive Reasoning

                Deductive Reasoning

                          Direct and Indirect

      What you see?

      What you read and the quality of the material.

      What you listen to or don’t listen to on the radio, or

      lectures, conversations, or even gossip, and don’t question

      the qualifications of the persons providing the information.

      What you watch on TV and its validity.

      Advertisements

      Polls and their results

      (You need to know how the poll information was

      collected, when, where, and how it was collected,

      who was asked, the wording of the questions, plus

      the number interviewed.)

      Implications and their forms with interpretations

      (Converses, Inverses, and Contrapositives)

      (The above will all be explained, reviewed and

      applied later.)

      An interesting example of a conclusion related to What we see. is illustrated in the following. The following picture will illustrate this. Look at it from the right and then from the left. Which do you see, the face of an old woman, or a young woman? What if you were a witness to an accident? What would you report?

      (I have no idea where following clever picture came from.)

      40767.png

      What is seen may be reported differently by two witnesses!

      A logical system is based on undefined terms, defined terms, assumptions or postulates, and theorems or laws which are justified by the first four, and of course decisions resulting from them. (A great example of a logical non-mathematical system is the Declaration of Independence by Jefferson.) (Have you read it? If not I suggest you take 15 minutes and read the first few pages.)

      You will understand the full meaning of the above statement by the end of this review.

      Following are two postulates for a logical Geometry system.

      Postulate. 4:         The shortest distance between two points is the

      measure of the straight line segment. (This is not

      always true as every taxicab driver knows.)

      Example: A taxicab driver has two options to travel from A to B.)

      40746.png

      Postulate 5:         The shortest distance from a point to a line is the

      perpendicular distance. (This also may not true in the

      taxi world and in earth navigation.)

      Activity 1:

      1. Use your ruler to draw the following triangles, with sides x, y, and z as given in centimeters.

      In each case compare x + y related to z, x + z related to y, and y + z related to x.

      From the comparisons, complete the following:

      The sum of the measures of any two sides (segments) of a triangle is…

      Which postulate is this based on?

      Try to draw the triangle with sides of 2 in, 1 in, and 3 in.

      Try to draw the triangle with sides of 2 in, 4 in, and 1 in.

      If x + y > z, then is x > z - y valid?

      Using the results from number 1 and given a triangle with sides 10, 18 and x, then what do you know about the length of side x?

      Complete the two following inequalities where x, y and z are the sides of a plane triangle.

      1. x+ y ? z         2. z ? x ? y

      Hint: In a triangle, the sum of the measures of two sides is greater… . third side, and the third side is greater than… . the… . two other… sides.

      Hint: From the postulate, we know that x + y > z. Can you use algebra to arrive at z > |x-y| Why the absolute value symbol?

      2. In the two figures below, how many ways can a taxi driver select to travel from A to B? (Condition: The cab must be always moving in the direction of B.)

      40724.png

      3. Complete the following and then write a conclusion.

      a. 9 times 1917 = ? Add the digits in the product to a one-digit number.

      Answer: The product in ‘a’ is 17253. Adding results is 9.

      b. 9

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