Reflection on Pythagorean Thoerem Lesson & Comprehensible Input

 Last week (week of Feb 24) we wrapped up our unit on the Pythagorean Theorem. We spent a good deal of time reviewing key vocabulary, predominantly "leg," "hypotenuse" and "square root." I found myself intentionally adjusting my speech when making sure to use the proper vocabulary word, while sometimes I find myself rapidly thinking out loud during more basic explanations. For example, I don't worry too much about slowing my speech when I say, "I'm going to add 2 and 3." I say it as fast as I can write it on my screen. But by the end of the unit, I had found a cadence with saying at a specific tempo, "A squared plus b squared...calculate...take your square root...round correctly," and students were building fluency by those repeated instructions. 

I digress. So I presented them with this question: 

"On the coordinate plane, what is the length of the line segment that connects points at (-1, 0), and (6, 2)?" 

I displayed the question, read it aloud, then asked the students, "What is this problem asking you to do, that I promise you already know how to do?" Answers were slow to come in. A few brave souls posited that we should plot the points. A couple students said "find the length" but since those words were from the question I asked them give me more detail about what that meant. Overall I can't recall that anyone confidently replied that we need to use the Pythagorean Theorem to find the length of that line, c, on a right triangle on the Coordinate Plane. 

Then I zoomed out and revealed a Coordinate Plane. The enthusiasm to get to work and solve was palpable. They knew to plot the points. From there many could imagine the right triangle and we were home free from there. 

My point to them was this: you already know how to solve this problem, so why is this question so complex? Because there are no clues to get you started. On the state test they will not give you a coordinate plane for you to work out your answers, nor will there be "How To" box of instructions that I provide with our practice problems. 

In the end it was a great discussion on how to not get stuck because of the wording of a question. We are continuously talking about what tools they will have available to them if they get stuck. We look at these state test practice questions and we look for the action words and the describing words to decode what task the question is asking them to complete.