Currently in this game there is a piece that takes two fractional lasers and adds them together in to one laser. In order for the piece to add the fractions the fractions must have a common denominator.
Using this approach forces students to add fractions by creating a common denominator and can effectively teach the idea that a common denominator is necessary through the rule, but because the piece simply requires this to happen, students likely aren’t going to understand why finding a common denominator is necessary, just that it is necessary.
This isn’t the end of the world. Once the pattern is firmly established then it makes it much easier to explore the explanation of why a common denominator is necessary. Still I would much rather find a way for the students to figure out that a common denominator is necessary rather than simply forcing such a rule.
You could imagine having students try to add fractions without a common denominator. They might just add the numerators and the denominators. You could create a situation where there would be a natural feedback loop showing that this doesn’t reflect reality and help them explore how to do the calculation more accurately. I just haven’t yet figured out a good practical metaphor and feedback loop to accomplish this.
I’ll continue to think about it. If anyone has any ideas I would love to hear them.