Introduction to Coordinate Geometry

The Cartesian plane is one of the greatest inventions in mathematics.  Had Rene Descartes not invented the rectangular coordinate system, calculus would not have progressed immensely as we are using it in our time.

The Number Line

The coordinate system was derived from the correspondence between the real numbers and the points on number line.  Each point on the number  line corresponds to a real number and each real number corresponds to a point on the number line. The number line represents the ‘entirety’ of the real numbers.  By convention, the number line is a horizontal line where the negative numbers are placed on the left of 0, and  the positive numbers on the right. » Read more

Matchsticks, Linear Relations, and Multiple Representations


We have mentioned the different types of functions in the Introductions to Functions post.  In this post, we are going to learn about linear function and its  characteristics.

To start, let us examine the problem below taken from the TIMSS 2003 released items given to Grade 10 students in more than 40 countries all over the world.

Matchsticks are arranged as shown in the figures.

If the pattern is continued, how many matchsticks would be used to make figure 10.

A. 30                      B. 33                      C. 36                      D. 39                      E. 42

The problem is too easy that even a first grade pupil would be able to answer it given enough time. Smart students would be able to easily see patterns. For example, they can relate the number of squares to the number of matchsticks.  If they cannot find a pattern, the last resort would be by brute force; that is, by manually drawing the tenth figure. » Read more