I had someone ask a really great question on my Subtraction Snake Game and I wanted to share it with everyone:

Question:
"Please why can't you subtract from a colored bead and black and white bead, wouldnt exchanging it be a little confusing for the child?"

My Answer:
This experience of positive and negative numbers, as well as the experience of exchanging, needs to have different sensorial impressions for young students. My students have never had a problem getting confused by this. In fact, I have had many students obsess over each part of this game, but students will pick up on what their guide does and feels about the lesson, so if you give the impression you don't like it or you try to skip over it, they will follow your example. I would encourage you to love each step of the process and that will spill over to the child's experience. As Montessori would say, "Have faith in the child." When you have faith in the child, you will discover that they will adapt to the material much easier than adults - and part of the reason why is that as adults, our minds are already thinking two steps ahead because we already understand the concepts like subtraction so well. But in order to value each part of this lesson, you need to approach this lesson from the mindset of a young child who is still learning this concept and still has a need for concrete sensorial impressions of math.

Each function for subtraction and addition need to be represented with a different impression, and the concept of exchanging also requires a different experience. It is important that each function has a different sensorial impression so that the mind sees, feels and experiences what is happening differently with each function. Also keep in mind that one of the purposes of the snake game is to understand different combinations of ten, so we want to show all the different ways to make ten, including the exchanging. The black and white beads demonstrate a different way to create ten and they signal that something different is happening and we need to demonstrate that function to the child very concretely and not take that step forgranted by skipping over it just because it is easier for the adult.

As an adult with a fully developed abstract mind for simple math operations, yes, skipping the exchange would be easier for us, but the young child is still developing that abstract mind. During the ages of 0-6 years old, they have a concrete mind and need to see each representation of function clearly. In addition to that, there are more snake game lessons in elementary, such as negative numbers, so each part of the snake game builds into the next variation, which is more complicated.

Don't forget, "The hands are the instrument of the mind." So the more we use our hands to manipulate materials and get that concrete experience of an abstract idea, the better those ideas will solidify inside the mind. It's creating neural pathways in the brain. What we learn with our hands always gets communicated to the mind and sets the foundation for more abstract learning later in life!