Technology and History of math task 1
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School
Western Governors University *
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Course
OOT2
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
4
Uploaded by MegaWrenMaster928
Katie Groves ID #: 010507667
September 24, 2023 Mathematics Technology and History Task 1 A. 1.
51133.087
2.
a. b. 349215.767
3.
4.
The benefit to using an exact solution for a real-world mathematical scenario is it gives an accurate answer. It is precise and certain so there is not margin for error in the data. The benefits to using an approximate solution in real-world math scenarios is that it can give an idea of the data so that it can be tested in models to find solutions that work. Sometimes we use approximate values because it is impossible to make a perfect exact answer for the scenario, so we use the approximation of the answer. For example, problems with irrational solutions we use
the approximations because the exact solution will continue forever and can never fully be expressed without approximating it. 5.
The advantage to using graphing calculators or other specific technologies in the classroom are if students are graphing situations where the numbers are very large then they can use a calculator to get more accurate graphs than if they were doing it by hand. The calculator will be able to zoom in and show specific areas of the graph whereas the hand drawn graph would be much more difficult to change the viewing area of the graph without regraphing the whole problem. Another advantage of using a graphing calculator in class is that the calculator can compute and graph and create a table much faster than a student can do by hand. Using a calculator is much more time effective in the classroom than doing everything by hand. When creating a table of values, the students can use the table feature instead of having to calculate the information by and each time. B. 1. I used GeoGebra to create a right triangle I used the polygon creator and inputted 3 points. I then used the angle measure button on each of the angles and it measured my 3 angles for me. I also found the side length of the triangle as 5, 5, and 7.1 by clicking the distance or length button under measurement. C. 1. I used GeoGebra to explore Pythagorean theorem. Pythagorean theorem states that with a right triangle a
2
+
b
2
=
c
2
. For this triangle it has a right angle which means that it is a right triangle.
S0 5
2
+
5
2
=
7.1
2
which equals 25+25=50.41 which is 50=50.41 the reason it isn’t an exact match is because the square root of 50 is an approximation. √
50
=
7.071067812
…
and GeoGebra approximated it to 7.1. SO this proved that the Pythagorean theorem is accurate for this triangle and
it is a right triangle which I also proved by measuring this angle in GeoGebra. When I use the dynamic features and move point B I still have a right triangle and can still use Pythagorean theorem
to prove that a
2
+
b
2
=
c
2
Because 5
2
+
3.3
2
=
6
2
again it is an approximation, so the number are rounded. 35.89
=
36
when 35.8 is rounded to the nearest whole number you get 36=36. Moving any point if I still have my right angle will work for the Pythagorean theorem.
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D. I used GeoGebra for my part B. I found it very easy to use and to find the different ways to create shapes measure angles and lines. I then tried to do the same thing on the desmos geometry software. I found it more difficult to use because of the interface. It took me longer to find the button to make a polygon because it wasn’t labeled the way GeoGebra had their labeled. I did like that when I measured the angles of my triangle in desmos it measured all 3 of them at the same time where in GeoGebra I have to measure them all separately. I was not able to find how to measure my line lengths in desmos which was much easier to find in GeoGebra. Even after rewatching the video in the course I couldn’t figure out how to find the distance of my triangle length. I could find the lengths of other lines but not the one created as a polygon. The cost of both programs is free so that is a benefit to both of them. I love using desmos as a graphing calculator and the activities that you can do in class however for geometry tasks I prefer GeoGebra.