## Reflection: Problem-based Approaches Use It - Section 1: Set the Stage

I had an interesting experience with this part of the lesson.  I've used the idea of the Pyramids and a knotted rope for other classes, but this was the first time I had a student who was adamant that the 3-4-5 would not always make a right triangle.  He insisted that there had to be a way to hold the corners and get either an obtuse or an acute triangle.  I tried to explain that the squares of the sides would always equal the hypotenuse, but he didn't really care about Pythagoras.  This could have been very distracting but instead I took time for all the students to work with their own sets of knotted string.  They spent a several minutes trying to pull the knots into a non-right triangle, following the constraint that they needed 3, 4, and 5 for the lengths of the sides.  This eventually persuaded the disputing student and even helped him (and others) build their understanding of and confidence in the Pythagorean Theorem.

Student challenge to Pythagoras
Problem-based Approaches: Student challenge to Pythagoras

# Use It

Unit 2: Algebraic Arithmetic
Lesson 7 of 11

## Big Idea: First you create it, then you use it...this lesson allows students to use the polynomial identities they just proved.

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Standards:
Subject(s):
Math, algebraic expression, Algebra, Expressions (Algebra), algebraic methods, Algebra II, master teacher project, 11th Grade, Pythagorean Triples
55 minutes

### Merrie Rampy

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