Steps for Solving Equations

In CCSS, the description of Standard 8 for Mathematical Practice says, "Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts."

This week, I was tutoring an 8th grade student who was very bogged down when solving equations. Her teacher, like many others, was requiring students to "show all of the work." Here is an example of work that the student was showing to solve the equation 7x – 17 = 11. Notice that her first step was to write +17 under each side and draw lines to add. My concern is that this step detracts from key idea of equation solving, which is to write equivalent equations that become simpler and simpler until the solution is clear.

In most textbooks, the second line above would be shown as an equation:
7x – 17 + 17 = 11 + 17
This is OK since it is an equivalent equation, but the goal should be for students to do more steps mentally, as follows (in black text):

When I encourage students to use shortcuts and show only key steps, they usually respond positively. They are glad to try to do more of the work mentally, and it is easier for them to see the progression to simpler and simpler equivalent equations. As a result, students become more confident and their homework papers look neater!