© 2016 by One on Epsilon PTY LTD

# Designing Square Root Marbles for iOS

October 23, 2016

A few months ago we set out to develop a fun and educational game. This was to be the first One on Epsilon product. We were seeking to rapidly develop a product that is not too complex, yet serves a specific purpose in alignment with our overarching mission: Creating positive and fun content that supports learning and drives curiosity.

In planning out Square Root Marbles, we surveyed the hundreds of fun and educational Apps that are out there. We downloaded quite a few, and let our kids play. We observed what appears to work, and what doesn't. Many games deal with addition, subtraction, multiplication and division. The core concepts of elementary math. But we, on the other hand, wanted to expose audiences to additional elementary concepts that can be learned through a fun game. One such concept that we considered are the prime numbers: A whole number, greater than one, is prime if it is only divisible by 1 and itself. The primes are thus, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,.... Get the pattern? No? Don't worry, no-body fully does yet - hence the field of research called number theory. In fact, many mathematicians believe that there isn't a predictable simple pattern.

But there was already quite a nifty game dealing with primes: Factor Samurai. In purchasing and playing with that game (both us and kids), we saw that it was pretty nice. It is a quick action game, where the player needs to "slash" (as a Samurai) the composite (non-prime) numbers, and leave the primes alone. The composites then break up into factors (e.g. 15 would break up into 5 and 3). Simple, fun, educational, positive. A nice game.

OK, so primes were taken care of. Good! What more? We considered Perfect Squares (Square Numbers)  and Square Roots. The perfect squares are 0, 1, 4, 9, 16, 25, 36, 49,.... That is, these numbers constitute areas of squares whose sides are of length 0, 1, 2, 3, 4, 5, 6, 7,.... Given a square with a given area, the square root of it is simply the length of the side of that square. The square root of 2 is not immediately obvious to calculate (in fact it is an irrational number). But if one considers square roots of the first few perfect squares: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, then calculating the square root is as easy as thinking about the multiplication table. For example, the square root of 36 is 6, because 6 times 6 is 36. We thus decided to make a game, where the player would mostly have to think about perfect squares while playing. The result, is our Square Root Marbles.

It may be that your kids think that they have mastered the multiplication table and are bored with it. But in fact, if you test them on 7x8 or 6x9, you may perhaps observe that they may still need a brush up. Playing square root marbles and thinking about perfect squares does just that. The diagonal elements of the multiplication table are the perfect squares. Thus for example 7x8 = 56 can be obtained by thinking about the perfect square 7x7=49 and adding one more 7. Similarly for other numbers.

During the development process and since the launch, we have been looking at both children and adults playing Square Root Marbles. It is always fun to watch because it is interesting to think about the mental processes happening in the players' heads as they play. They are doing math, and they are enjoying. They are reshuffling what they know about elementary arithmetic and they are learning more as they do that. All this without being directly quizzed. In fact, we designed the 30 levels of Square Root Marbles so that they cause the players to implicitly think about basic algebra by having to plan their moves ahead of time. Try it and you will see.

Our audiences claim that the game is extremely fun. It is operated by tilting the device and requires some dexterity as well as quickness (fighting the clock). These are matched with neat graphics and music together with funny voices saying "Square Root Marbles" every time a perfect square is matched, yielding an extra life and more time. It is quite an addictive game. If you download and play the game, don't hesitate to send us any feedback that you have. You may even wish to have your voice included in future versions. Let us know.

As for the implementation and testing, that was a fun journey in its own right. We started our journey with Square Root Marbles on iOS implemented in Swift using SpriteKit. Development using Swift was rewarding and we are thankful to the great community of developers sharing ideas and tips over the web. An Android version will be available soon too. We will write a separate blog entry detailing some of our experiences with the implementation process.

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