parallelogram

 

This is a straight up student-empathy question: what was this kid’s thought process like?

Thanks to Tina for the submission!

Editor’s Note: I categorized this as Grade 7 – Geometry in the CCSS, but I’m not really sure if that’s right. Where does this belong?

  • They almost had this. 360 degrees minus the sum of the two you know, yup. And then … did they come up with 70+70=140 mentally, and then verify it below, or add it out mechanically and then move the result up? Then the student is working towards 220 by guess and check (?), not comfortable enough to add 80 once instead of 40 twice. It appears they’re distributing the 220 across all the angles, even the ones already accounted for, instead of splitting it across the two unknowns. I wonder if they (the genderless singular ‘they’) know that opposite angles are the same, or just that they look the same.

    I recommend reinforcing the “shave off 0s” trick, that 70+70=140 bears a striking resemblance to 7=7=14. Better comfort with arithmetic help clarify the main idea here that’s missing, that the 360 degrees are split up across the four angles.