Lesson #2 - Augsburg College

Lesson #5: Pythagorean Triples
Approximate lesson length: 1 day
Precedes lesson #6
Fits well with lesson #3 and #4
Lesson Objectives:
• Discover the Pythagorean Theorem: a 2 + b 2 = c 2
• Learn about and be able to describe Pythagorean Triples
Materials:
• Paper and pencil
• Rulers
• Calculators
• Sticks/straws
• Scissors
Geometry: A Shapely Approach to Math
Have students pick their own two numbers to represent a and b. These numbers should be somewhere
between 5 and 15. You should also pick two numbers. Then show them this equation:
a 2 + b 2 = c 2
Next (and this is the hardest part), show the students how to compute c. This may require a discussion
about squares, square roots, and the “Golden Rule of Algebra” (whatever you do to one side of an equation
you must do to the other). If this seems beyond the scope of understanding, it would be reasonable to sim-
ply state as a given that . However you get there, you want to eventually show the group how
to compute using your values of a and b as an example. Depending on the type of calculator,
you may have to do this calculation in parts. In other words, you may have to compute a 2 , then clear the
screen and compute b 2 , then clear the screen again and add those two numbers, and finally take the square
root of that sum. Refer to the end of the lesson for some examples of this computation.
Once everybody has computed their c, have students write down their values for a, b, and c so they
don’t forget them. (You may want to emphasize that it is important not to mix up the numbers.) Then have
the students measure and cut straws or sticks to the lengths of these values (in centimeters). It might be
good to have them somehow mark which straws are a, b, and c (remember, we don’t want to mix up which
numbers are which). Finally, have them put the sticks/straws together to form a triangle. (If you’ve done
the Lesson #3: Congruent Triangles, you might recall that there is only one way to make a triangle if you
know the lengths of all three sides.)
Lay out all of the triangles where everybody can see them. Pose the question: What do you notice
about all of the triangles? (They all have right angles!) Is there any pattern as to where a, b, and c are with
respect to the right angle? (a and b are the sides that form the right angle, and c is always the longest side.)
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