## Matchsticks, Linear Relations, and Multiple Representations

**Introduction**

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