I have watched average mixes of 2nd and 3rd graders using these strategies successfully in our local schools. It is not just for the top students.
Our teachers use “Number Talks,” with the goal of getting students comfortable with using multiple ways to solve the same problem using mental math. This is new in the past 2-3 years. The kids sit on the floor in a group at the front without paper. The teacher puts an equation on the board that’s appropriate for the grade level. For example, two digit addition for some grades and two digit multiplication for other grades.
Kids hold up fingers to indicate how many ways they’ve thought of for solving the problem mentally. For example, subtracting from one number and adding to the other to make numbers easier to add is essentially “bridge to 10”. Or, using distributive property for multiplication.
The teacher calls on students to have them explain their solutions. The teacher writes the solution method on the board and says something like “I see, Susie is using doubling with bridge to 10.” That way, the kids see multiple solutions, and the advanced students typically come up with more complex ways to solve problems. We have trained the teachers in the names for these strategies, including strategies that kids might discover early but that are normally introduced in higher grades.