Mathematical hitsory and technology task 4
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Jan 9, 2024
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Katie Groves ID #: 010507667
October 8, 2023 Mathematics Technology and History Task 4
A. Area and circumference of circles 1. Standard: 7.G.4 State the formula for the area and circumference of a circle and use them to solve problems 2. The first history of area was in ancient Babylon for tax purposes. Ask students why was it important for the ancient Babylonians to find area? How would they figure out how much people owe for taxes without area? The Babylonians were also the first to calculate area of circles by using 3 for pi. IN one of their Babylonian tablets, they indicate a value of 3.125 for pi. The Egyptians also calculated are
that approximated value of 3.605 for pi. Later Archimedes in Greece discovered area and perimeter of circles. He was the first to prove it formally. Archimedes used the Pythagorean theorem to find the area of 2 regular polygons that were inscribed in a circle. 3. Students are going to find area and circumference of circles by finding pi themselves as well as using technology. Students will get a compass and create a circle on their page. They will then use a ruler to to find the diameter of the circle. They will then use yard an cut out their diameter in the yard. They will have to fill up the circle with the diameter sized yarn piece until they have full wrapped their circle. This should take
about 3.14 pieces of their yarn. They will approximate the perimeter of the circle using they yarn they cut. Then using geogebra they will create a circle with the same diameter that they just created on their paper and compare the 2 circles circumferences. Once students have derived their own formulas and use of pi they will then test out Archimedes method of deriving pi but inscribing a polygon inside of a circle and finding the perimeter of that and comparing it to the perimeter of the circle. As a closing to the lesson students will discuss how Archimedes found pi and how they dived their own pi with the yarn and the circle. a. Student will engage in with the historical component of the activity by trying out how Archimedes discovered pi and seeing how it compares to their method of finding pi with the yarn. They will compare the 2 methods and discuss with each other and the class how Archimedes helped form the modern approaches to geometry. B. Incorporating history into math improves student learning about the history of things helps students feel motivated and might give them a better attitude about completing their work. It allows students to understand the background of what they are learning and the why. When students understand the why behind things and where it comes from they are more engaged and more interested in the topic. In the article by Butuner it talks about how using the history of math in classroom students are able to learn
that mathematics isn’t static and that it is a developing science. They can see how topics have changed and developed over time. (Butuner, 2020). Using history can excite and challenge students to know that math isn’t just a static boring subject but a ever changing world of numbers that has been created since the beginning of civilizations. C. In WWII, allies were trying to figure out how many tanks or piece of weaponry the Germans had total.
They used the serial numbers from captured tanks and used estimators to calculate the total number of tanks in the German arsenal. Statisticians used the formula N
=
m
+
m
n
−
1
. Where N is the population max, m=the sample max, and n is the sample size. Using this formula they were able to use the serial numbers of the captured tanks to find the total number of tanks that the Germans had. They were able to figure out that there were estimated to be 246 tanks being made per month. This differed drastically from what the intelligence estimates had thought. After the war the Germans supplies were inspected, and it was found out that the estimations made by the statisticians were extremely accurate. They produced about 245 tanks per month. This problem was an example of minimum variance unbiased estimator. 2. This had an impact on the field of statistics because the intelligence estimates were so inaccurate, and the use of the minimum variance unbiased estimator (MVUE) was much more accurate. You could double the sample mean, multiply the sample standard deviation and it would still be the formula with the lowest variance. 3. I can incorporate the history of the impact from the German tank problem into my classroom and promote student engagement by simulating the German tank problem. My students learn about WWII in 7
th
grade and work on a history fair project. I can work with my social studies teacher, and we can simulate what happened during the war. We can have a sample size of tanks (from army men) and write serial numbers on the bottom. Then teach the kids how to use the sample size with the MVUE to calculate how many tanks there are total. They can then create their project on how to do this and how many tanks there are total. The kids can present it at the history fair and explain how the allies calculated how many tanks were there total and how they were able to calculate how many tanks were in their simulated project in the same way.
Sources: (n.d.). A Brief History Of Pi
. Exploratorium. Retrieved October 8, 2023, from https://www.exploratorium.edu/brief-history-pi-p
Butuner, S.O. & Baki, A. (2020). The use of history of mathematics in the mathematics classroom: An action study. International Journal of Education in Mathematics, Science and Technology (IJEMST), 8(2), 92-117.
Stephanie Glen
. "German Tank Problem" From
StatisticsHowTo.com
: Elementary Statistics for the rest of us!
https://www.statisticshowto.com/german-tank-problem/
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