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Sugar and skittle science!
This science experiment covers a fundamental part of chemistry - chemicals move from higher concentrations to lower concentrations. This is called a concentration gradient and can be found in everything from perfume vapors wafting through the room to cordial spreading out in water.
When you first add the skittle they start to dissolve in the water, sending the food colours outwards as this happens. The reason that the food colours meet in the middle of the plate as a cross and not mix is because each food colour has the same amount of sugar dissolved from each skittle. Once you add the pure sugar into the center of the food colour cross, the sugar cube beings to dissolve as well. This creates a situation where the most amount of sugar is found in the center of the plate where as the least amount of sugar is found at the edge of the plate (this area is basically pure water). As the sugar dissolved it pushed outwards into the rest of the solution, sending the coloured water outwards as well.
As a teacher, there are a number of opportunities to ask kids for their predictions and answers. They could try changing the variables to see if there is any different effect (eg, hot water vs cold water or different coloured skittles or different sugar types). They could try using M & Ms as well but the chocolate colour does get in way of the experiment.