Title of Book:
Author:
Publisher:
ISBN:
What’s Your Angle, Pythagoras?
Julie Ellis
Charlesbridge/2004
978-1-57091-150-7
Grade Levels for Recommended Use: Seventh Grade – Tenth Grade
(8.7)
Geometry and spatial reasoning. The student uses geometry to model and describe the
physical world. The student is expected to:
(C) use pictures or models to demonstrate the Pythagorean Theorem.
Brief Summary: In ancient Greece, the young and curious Pythagoras always found himself
wondering about problems and poking his nose into everything in order to find a solution. One
day, Pythagoras overhears two workmen arguing about a ladder that one of the workmen built
that was too short to reach the 12-foot wall, even though the ladder was 12 feet long as well.
From that moment on, Pythagoras begins his adventure to discover a special number pattern, the
Pythagorean Theorem, as he stumbles upon a master builder’s right triangle rope and some
brightly colored tiles that he arranges around a right triangle. Pythagoras realizes he has figured
out the secret to right triangles and uses this new discovery and shares it with the people he
wanted to help all along! The workmen are able to build the correct size ladder using his new
discovery and his father can now travel a faster route as a merchant, all because of Pythagoras’s
curiosity! Pythagoras just needed to see things from the right angle!
Materials needed:
“Adventures with Pythagoras” game sheet, plastic bag with triangle game cards, various colors
of 1-inch math tiles (for game place holders), paper, pencil, and a calculator.
Suggested Activity: Adventures with Pythagoras
Visit this website to take a look at an additional Pythagorean Theorem game which includes a
game board master and game cards:
http://www.glencoe.com/sec/math/t_resources/gamezone/pdfs/mac3_04/class_ch03.pdf
1. Divide the students into groups of four.
2. Each group will receive their “Adventures with Pythagoras” game sheet, plastic bag with
triangle game pieces, various colors of 1-inch math tiles to be used as place holders (one unique
color per member of the group), calculator, paper, and a pencil.
3. The youngest team member will begin the game and the group will continue taking turns in a
clockwise direction.
4. The first player will shuffle the triangle game cards and choose a card randomly.
5. When the first player chooses a card, they will notice that the triangle has lengths for each leg,
but the hypotenuse, which is the side that is opposite of the right angle, does not have a
measurement for the length. The student will have to use the Pythagorean Theorem, a2 + b2 = c2 ,
to solve for the hypotenuse of the triangle.
6. The student will have a piece of paper, pencil, and a calculator to solve for the hypotenuse of
the triangle.
* HOW TO SOLVE FOR THE HYPOTENUSE:
The student will use the Pythagorean Theorem, a2 + b2 = c2 and will substitute, or plug in the
values for leg “a” and “b” with the leg lengths given on the game card. The student will square
“leg a” and square “leg b.” Next, the student will add the two products together to get a sum of
“leg a” and “leg b.” In order to solve for the hypotenuse, c2, the student must take the square
root of the sum of “leg a” and “leg b.” Your result will be equal to “c,” which is the hypotenuse.
7. The student will share their answer with the group and after verifying with the group
members, if the answer is correct, the player will be able to keep the card for their own personal
pile and place a tile place holder on the matching number on the “Adventures with Pythagoras”
game sheet.
8. Moving in a clockwise direction, the next player will complete the same process as the first
player. If the answer is incorrect, the player will put the triangle game card back under the main
deck and will not be able to place a tile on the game sheet for that particular turn.
9. The first player that has three of their tiles in a row (horizontally, vertically, or diagonally)
wins the game! If all the cards are played and no one has been able to make a row of three tiles,
the player with the most cards they answered correctly wins.
10. The game can continue for as many rounds as the teacher prefers.
11. As an extension, the teacher can create new triangle cards and can have the students solve
for “leg a” or “leg b,” given the hypotenuse and either leg.
* On the following page, the game sheet, “Adventures with Pythagoras” is provided. The
template for the triangle game card is provided as well as the right angle measurements that were
used for the cards. The hypotenuse (side c) is provided which can be used as an answer key for
the teacher. The triangle game cards (25 per group) were made with card stock and the lengths
of the legs were written on each card.
Adapted by Vanessa Garza, 2010
Adventures with Pythagoras
65
20
29
65
15
25
53
5
85
73
8.5
17
19.2
13
8.7
97
10
61
89
19.7
25
85
37
6.7
41
Template for triangle game cards
(actual game card is a 3 in. x 4 in. x 5 in. triangle made out
of cardstock)
a=3
c=?
b=4
Right Triangle Measurements
(the students are solving for side “c” in the game)
a = 3,
a = 5,
a = 7,
a = 8,
a = 9,
b = 4, c = 5
b = 12, c = 13
b = 24, c = 25
b = 15, c = 17
b = 40, c = 41
a = 12,
a = 13,
a = 16,
a = 20,
a = 28,
b = 35,
b = 84,
b = 63,
b = 21,
b = 45,
c = 37
c = 85
c = 65
c = 29
c = 53
a = 11, b = 60, c = 61
a = 9, b = 12, c = 15
a = 6, b = 8, c = 10
a = 12, b = 16, c = 20
a = 15, b = 20, c = 25
a = 33,
a = 36,
a = 39,
a = 48,
a = 65,
b = 56,
b = 77,
b = 80,
b = 55,
b = 72,
c = 65
c = 85
c = 89
c = 73
c = 97
(rounded to nearest tenth)
a = 6, b = 6, c = 8.5
a = 12, b = 15, c = 19.2
a = 6.7, b = 5.5, c = 8.7
a = 8, b = 18, c = 19.7
a = 2.4, b = 6.3, c = 6.7