https://docs.google.com/document/d/1hZviigiQwa6W2WqWgd-QMK7UFant9hpmP3YZ4sXtKdw/edit
Geogebra Lesson: Finding Pythagorean triples
Grades: 7-10
A Pythagorean triple is a set of three integers a, b, and c which form the sides of a right angled triangle.
It also needs to fit the rule a2 + b2 = c2
There are an infinite amount of Pythagorean triples and there is a very simple way to find them
Below is a formula used to create Pythagorean triples.
With m and n being positive integers
a = m² + n²
b = 2mn
c = m² - n²
m > n
We can use this formula and the help of Geogebra to create as many Pythagorean triples as we would like
Click on the input line and type in the first part of the Pythagorean triple formula (a = m² + n²)
Click on create sliders when the prompt appears
Organize the sliders
Right click on each slider and change object properties
Change the min to 0 and the max to 100
Change the increment to 1
Make sure you do both sliders
Click on the input line and type in the last parts of the formula (b = 2mn, c = m² - n², m > n )
Now we can move the sliders to find numerous Pythagorean triples!
Make sure the M slider is always greater than the N slider
Let’s try some questions using the sliders
If m=12 and n=5 what is the Pythagorean triple? _________
m=26, n=17? _________
m=58, n=35? _________
m=72, n=88? _________
*Notice it says false in the upper left corner telling you there is no Pythagorean triple for these values.
Find 3 Pythagorean triples whose values are multiples of each other
Find the m and n values of the triple with values a=40 b=24 c=32
Find some Pythagorean triples that include prime numbers
A “Primitive” Pythagorean triple is one in which there is no common factor among the three terms.
Can you find a primitive Pythagorean triple?
Given the three numbers of any Pythagorean triple, can you find three numbers that will always divide into one or more of the sides?
Above is my Geogebra lesson. I did my lesson on Pythagorean triples.This technology helped provide an easy way to find numerous Pythagorean triples. I believe that this could be a good lesson to teach students about Pythagorean triples. it is fairly easy to do and it teaches you a lot.
Grades: 7-10
A Pythagorean triple is a set of three integers a, b, and c which form the sides of a right angled triangle.
It also needs to fit the rule a2 + b2 = c2
There are an infinite amount of Pythagorean triples and there is a very simple way to find them
Below is a formula used to create Pythagorean triples.
With m and n being positive integers
a = m² + n²
b = 2mn
c = m² - n²
m > n
We can use this formula and the help of Geogebra to create as many Pythagorean triples as we would like
Click on the input line and type in the first part of the Pythagorean triple formula (a = m² + n²)
Click on create sliders when the prompt appears
Organize the sliders
Right click on each slider and change object properties
Change the min to 0 and the max to 100
Change the increment to 1
Make sure you do both sliders
Click on the input line and type in the last parts of the formula (b = 2mn, c = m² - n², m > n )
Now we can move the sliders to find numerous Pythagorean triples!
Make sure the M slider is always greater than the N slider
Let’s try some questions using the sliders
If m=12 and n=5 what is the Pythagorean triple? _________
m=26, n=17? _________
m=58, n=35? _________
m=72, n=88? _________
*Notice it says false in the upper left corner telling you there is no Pythagorean triple for these values.
Find 3 Pythagorean triples whose values are multiples of each other
Find the m and n values of the triple with values a=40 b=24 c=32
Find some Pythagorean triples that include prime numbers
A “Primitive” Pythagorean triple is one in which there is no common factor among the three terms.
Can you find a primitive Pythagorean triple?
Given the three numbers of any Pythagorean triple, can you find three numbers that will always divide into one or more of the sides?
Above is my Geogebra lesson. I did my lesson on Pythagorean triples.This technology helped provide an easy way to find numerous Pythagorean triples. I believe that this could be a good lesson to teach students about Pythagorean triples. it is fairly easy to do and it teaches you a lot.