Introduction to the DaMath Board Game Part 1

DaMath is a math board game coined from the word dama, a Filipino checker game, and mathematics. It was invented by Jesus Huenda, a high school teacher from Sorsogon, Philippines. It became very popular in the 1980s and until now played in many schools in the Philippines.

DaMath can be used to practice the four fundamental operations and also the order of operations. It has numerous variations, but in the tutorial below, we will discuss the Integers DaMath. Note that explaining this game is quite complicated, so I have divided the tutorial into three posts.

The DaMath Board

The board is composed of 64 squares in alternating black and white just like the chessboard. The four basic mathematical operations are written on white squares as shown in Figure 1. Each square is identified by a (column, row) notation. The top-left square, for example, is in column 0 and row 7, so it is denoted by (0,7).  Continue reading

Guest Post: Calculating Trignometric Values

Many students who start to learn Trigonometry often ask themselves how do we come to know that

\sin 30^\circ = \frac{1}{2} or \cos 45 ^\circ = \frac{\sqrt{2}}{2}

or for that matter any other trigonometric value?

Most of us would say use a trigonometric table or use a scientific calculator and you get the value. That’s okay, but the question still remains unanswered. How does a calculator come to know that \tan 15^\circ = 0.26794919... or how did the mathematicians create the entire trig tables when calculators were not invented? There should be some formula that tells us as to how the values are calculated. More importantly, can I, using a standard calculator, find the approximate value of let’s say \sin 50.5^\circ? Yes, there is a simple formula to find the value of sine of any acute angle. Though the formula does not give accurate results, it comes handy to know the value of \sin \theta  where 0^\circ \leq \theta \leq 90^\circ.

 \sin x ^\circ = \frac{4x(180 - x)}{40500 - x(180 - x)}.

This rational approximate formula was discovered by Bhaskara I of India in the seventh century. This simple formula enables us to calculate the sine of any given acute angle (any even obtuse angle) with a maximum absolute error of 0.00163.  Continue reading

Book of Proof: A Very Good Introductory Book to Mathematical Proofs

Two weeks ago, I finished reading Book of Proof  (link goes to Amazon) by Professor Richard Hammack, and so far, it was the best book that I have read about introduction to mathematical proofs. I recommend this book to high school students who are interested in pursuing a mathematics degree, to college students who are math majors, and to teachers who will teach or who are teaching an introductory course on mathematical proofs. Here are some of the reasons why I really like this book.

Clear Explanations

The explanations of concepts in this book are very clear and the concepts are well-connected. Maybe this is because the author’s long experience in teaching this course (or maybe he is just a very good teacher). This book is a product of the author’s lecture notes on teaching mathematical proofs for the past 14 years.  Continue reading

Free Peer-Reviewed Math Ebooks from OpenStax

If you are looking for free math resources, I found a website that offers peer-reviewed math ebooks for college and AP Courses. This website is OpenStax which is based in Rice University and supported by several foundations. Below are the links to the math ebooks.

Aside from the math ebooks on Science, Social Science, Humanities, and AP Courses are available on the website.

For more free resources, you can visit Math and Multimedia’s All for Free page.

Understanding Domain and Range Part 4

In this post, we summarize the previous three articles about domain and range. In the first part of the series, we focused on the graphical meaning of domain and range. We have learned that the domain of a function can be interpreted as the projection of its graph to the x-axis. Similarly, the range of the function is the projection of its graph to the y-axis.

domain and range

Graphical meaning of domain (red) and range (green)

In the second part of the series, we learned to analyze equations of functions to determine their domain and range. We learned the restrictions in the domain and range of functions are affected by the following: squares in the expressions, square root signs, absolute value signs, and being in the denominator. In exploring these we concluded the following:

  • Expressions under the square root sign result to a positive real number or 0.  This means that we have to set the inequality such that the expression is greater than or equal to 0, and then find the permissible values of x.
  • Expressions containing squares result to a positive real number or 0. This affects the range of the function.
  • Expressions inside the absolute value sign result to a positive number of 0. This also affects the range of the function.
  • Expressions in the denominator of fractions cannot be 0 because it will make the function undefined. So, we need to find the value of x that makes the denominator by 0. To do this, we equate the expression in the denominator to 0 and find the value of x. The values of x are the restrictions in the domain.

In the third part of the series, we examined functions that have more complicated equations than those in the second part of the series.

Before I end this series, there is one more concept about domain that I want you to remember. That is, the domain of all polynomial functions is the set of real numbers. That’s why the domain of linear functions and quadratic functions in Part 1 and Part 2 is the set of real numbers.

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