Sometimes our boys struggle with what the mathematicians describe as "number sense," arithmetic understood by the boy in his mind, being able to see the problem as a notion, a model, conceptualizing just what is going on inside of a math equation.
For example, when we notice that a boy has difficulty transferring a diagrammed football play to his placing himself in correct position on the field, we think it is likely that he could also have difficulty seeing what is going on with an arithmetic concept. By working through the play, the boy begins to connect the concept to life on the field, repetition, correction, experience...success!
In similar fashion, these visualizations are designed to work for kids experiencing various math applications. How about some old-fashioned tech that looks a lot like a football play as a way to see what multiplying 3 x 5 looks like? These drawings are employed to teach arithmetic concepts to through arrays:
Here is another example, all this from Math With Bad Drawings:
Now, what’s the benefit of this visual model? Ah, where to begin! Without it, you’re multiplying from behind a blindfold. Tear that cloth from your eyes, and begin to see!
Take the distributive property, a seemingly opaque bit of symbolism that says a(b+c) = ab + ac. Its misuse haunts algebra teachers’ nightmares. But it’s no mystery—just a simple fact about adding two arrays together.
Well, if you're interested in this kind of visual aid, then you will want to investigate further. Here it is.