# BesouriZ – a game about the equivalence between sum and multiplication

BesouriZ is an interdisciplinary digital game between Mathematics and Biology, whose name refers to the words Besouros (Beetles) and Matriz (Matrix). In it the player needs to help Entomologist (specialist in insects) Estefani, in filling out pictures with collections of deer beetles. Taking the pots with beetles to the specialist so that together they can fill the picture without any beetles left (https://scratch.mit.edu/projects/360458545/).

This game, despite being quite simple, deals with an essential aspect for understanding mathematics. The fact that understanding the concepts is more important than memorizing procedures. In this case, Estefani is forming rectangular frames with beetles, so the spaces to be filled are determined by the vertical x horizontal dimensions. For example, in the prominent figure of this post the picture is 3×10, so it fits 30 beetles. But looking at the available beetles, we need to determine a way to get to 30 beetles. In this case, there are two pots with 9 beetles and two pots with 6 beetles, but there are also 3 pots with 7 beetles and pot with 9 beetles. With this, we arrive that there is an equivalence between the multiplication operation and the sum operation, because:

3×10 =2×9 + 2×6 = 3×7 + 1×9

They are all equivalent expressions with the same value. The way we operate depends on the occasion and the convenience. In this game, the formation of the staff occurs mainly from unequal sums. That is, in a 7×4 frame, we may want to complete it by joining:

A) 4 pots of 7 beetles

B) 7 pots of 4 beetles

But these are situations that may not correspond with the reality of the pots we have, so there are other, less conventional ways:

C) 2 pots of one beetles + 2 pots of 9 beetles + 1 pot of 8 beetles

D) 1 pot of 8 beetles + 2 pots of 3 beetles + 3 pots of 4 beetles

…

The combination options are huge, and in all of them we can see that the game allows an analysis of the solution under development. Because we can accidentally miss any of the quantities and notice in the number of empty spaces that something went wrong, and thus seek among our resources a way to correct.

These are simple problems, but applicable to different situations in real life, such as the arrangement of bank notes and coins to pay bills without needing to receive change.

But why keep talking about the game if you can get to know it better by playing it below? Don't forget to comment (criticism is always welcome, whether positive or not).