## Overlearning for Automaticity

June 2, 2009

This is going to be my motto for next year! I’m especially going to drill into their heads (i.e. venting from this year):

• Pythagorean triples — on the last day of school, students should not still have to think through $3^2+4^2=5^2$!
• If $x^2=a$, then $x=\sqrt{a}$
• Understanding why it makes sense to solve the equation $25=\frac{1}{2}(75-x)$ by multiplying both sides by 2 first. (Not to mention, how to multiply both sides by 2.)
• Learning to see right triangles in problems.
• Identifying the hypotenuse of a right triangle.
• Understanding the difference between angle measure and lengths on triangles.
• Linear pairs and vertical angles — without my having to say, “Notice the straight line …”
• Area, circumference, and volume formulas
• The arcs of a circle add up to 360°
• The difference between perimeter and area — especially on a rectangle

I may come up with more later, but these are the ones that are especially frustrating for me right now. I know it’s not all the kids’ fault — I haven’t (apparently) taught it enough or in such a way that it has sunk into their heads, but it’s still annoying to have more than one student stare at a right triangle with legs of 3, x, and 5, and not realize that the missing leg is 4.