Proofs of the Pythagorean Theorem

A little background

  • In case you are trying the MARS MAP Classroom Challenges for the first time, it is recommended that you read the Brief Guide for teachers and administrators before you get started.
  • Before the lesson, students attempt the assessment task individually. You then review students' work and formulate questions that will help them to improve.
  • The lesson begins with a whole-class discussion of the geometric diagram from the assessment task. Students then work collaboratively on the task, in pairs or threes, to produce a better collective solution than those they produced individually. Throughout their work they justify and explain their decisions to peers.
  • In the same small groups, students critique examples of other students' work.
  • In a whole-class discussion, students explain and evaluate the arguments they have seen and used.
  • Finally, students work alone on a new task similar to the original assessment task.
  • Additional resources for this lesson include: proofs_of_pythagorean_theorem_slides.ppt

Objectives

  • To help you assess how well students are able to produce and evaluate geometrical proofs.
  • To help you identify and assist students who have difficulties in interpreting diagrams.
  • To help you identify and assist students who have difficulties in identifying mathematical knowledge relevant to an argument.
  • To help you identify and assist students who have difficulties in linking visual and algebraic representations.
  • To help you identify and assist students who have difficulties in producing and evaluating mathematical arguments.
60 mins K-12.MP.3 K-12.MP.7 HSG.CO.C.9 HSG.CO.C.10 HSG.CO.C.11 HSG.SRT.B.4 HSG.SRT.B.5
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