C879 task 44
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School
Western Governors University *
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Course
C879
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
2
Uploaded by GeneralElephantMaster926
A.
Write a narrative summarizing the historical development of
one
secondary algebraic topic, including how the topic originated and evolved over time. Include in your summary the contributions of significant figure(s) and diverse culture(s).
Babylonian tablets were found dating from 1700 BC showing early development of the quadratic formula. Today it is common to use the quadratic formula to solve equations with three variables but on these tablets, they were trying to solve the length and width of a rectangle. They were trying to prove x+y=b and xy=c. So if all they had was the area and the perimeter they would solve it like this: They realized that the length of the rectangle and the width of the rectangle added together equal half the perimeter. They would take half of the perimeter and divide it by two to find the average of the length and the width. The average plus the variable and the average minus the variable equal the length and the width. So they would multiply the average minus the variable by the average plus the variable equals the area. Simplifying this gives you the variable squared equals a number. The variable can be a
negative or a positive which allowed there to be two answers which can both be substituted into the original equation.
More than 2000 years after this was discovered by the Babylonians, an Arab mathematician named Muhammad bin Musa al-Khwarizmi created a formula to solve a three variable problem in which he balanced both sides of the equation. This is usually the method used today. However, his method was not used to solve equations where the first variable has an exponent. This was solved by an Italian man named Girolamo Cardano. He was able to solve variables with exponents because he recognized negative numbers. From all these methods the quadratic equation was created.
B. Explain
(suggested length of 2 paragraphs)
how you can use the historical knowledge you gained
about the topic in part A to enhance instruction and create learning opportunities in algebra for secondary students. Use specific examples to support your explanation.
Incorporating the history of the quadratic equation into the lesson would enhance the students learning experience and understanding of the quadratic equation. They would know how each part of the quadratic equation came to be and can understand why they use this specific equation to solve certain problems. This deepens their understanding of the lesson because the students know why they are learning what they are learning and it helps them to understand how the quadratic equation applies to their own lives which gives them a broader knowledge of the quadratic equation and a reason to care why it exists.
I would introduce the quadratic equation to the class and show them how it is used. For example I would give the class a three variable equation and plug it into the quadratic equation and show the students how to find x. Then I would tell the class that more than 3000
years ago nobody knew how to solve this kind of equation. The Babylonians had only discovered how to find the length and width of a rectangle when they only had the perimeter and area. I would show them step by step how to do that (See part A). Then I would tell the students 2000 years after the Babylonians discovered how to do this an Arab man named Muhammad bin Musa al-Khwarizmi discovered that they could solve three variable equations if there were no exponents using balancing. I would then show them an example of this. I would then tell them that he wasn’t able to solve exponents because he didn’t recognize negative numbers. An Italian man named Girolamo Cardano did recognize negative numbers so the quadratic equation became what it is today.
Lesson
. (n.d.). https://www.cgsd.org/site/handlers/filedownload.ashx?
moduleinstanceid=293&dataid=1512&FileName=SMP08ALG-NA-TE2-C13-L04-
13.pdf
Muhammad ibn Musa Al-Khwarizmi: The Father of Algebra | About the Hero
. (2019, July 10). Lowell Milken Center. https://www.lowellmilkencenter.org/programs/projects/view/muhammad-
ibn-musa-al-khwarizmi/hero#:~:text=Therefore%2C%20Muhammad%20used
%20completion%20and
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