A Thinking Process Model
Sketching is one way to represent the models we use in our mental computations, as are the brief explanations that go with them. Use of numbers and symbols to represent our thinking is another way. Mathematicians communicate ideas as different as 'the number of sheep in the canyon" and 'how quantum particles behave', using numbers and symbols.
Here's an example of a mental computation strategy using the base ten model; see if you can describe the thinking behind the actions:
Compare your own thoughts to one possible way of describing what you saw.
Each of us might interpret the combining actions a bit differently, or have a different strategy altogether. We use our own particular inclinations and strengths to conceive of ways to think about things that are natural for us. We can make those thoughts known to others with careful communication. The best communication includes brief explanation, pictures, numbers and symbols all supporting each other.