It doesn’t count if it doesn’t stick

I saw this comment today when we had snow predicted (and school got out two hours early), but when I first read it, I thought about how appropriate it is for teaching.  In teaching to the students, it doesn’t count as valid teaching if the concepts don’t stick with our students.  We are working on how to make similar figures in 7th grade math, and I’m stressing that similar figures need to have the same scale factor for each dimension.  I keep asking “what number do you need to multiply by to go from the old figure to the new figure?” and defining this as the scale factor.  We did multiple examples with both rectangles and triangles, and demonstrated the scale factor is bigger than 1 when we are going from a small shape to a large shape, and the reciprocal going from the big shape to the smaller.  At the end of the class, I gave the students an exit ticket with two sets of triangles: one set was similar shapes because each side was multiplied by 2 to get the other side, and the other set had triangles whose dimensions were changed by an addition of 1 to each side.  Five students out of 24 got it wrong, so at least the majority were following along.  But for those five, why did they think those triangles were similar?  The right idea didn’t stick.