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Bees Lab Report

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The unit we just concluded is called Bees. Bees was all about finding the area of shapes, using trigonometric functions and/or the Pythagorean theorem to find the side length(s) of a triangle, using trigonometric inverses to find the angles of a triangle, using triangles to see what polygon has the largest area when the perimeter of the polygons was 300 feet, and finding the volume, surface area, and lateral surface area of three dimensional prisms. A polygon is a two dimensional figure with at least three straight sides. Perimeter is the distance around a polygon.To find the perimeter of a shape, you need to add the lengths of all the sides of the shape. Look at Visual 1 to see an example of the perimeter of a polygon. Visual 1 Area is the number of unit squares that can be contained within a polygon. There are different area formulas for different polygons. The simplest area formula is the area formula for rectangles …show more content…

As I said in my cover letter, the Pythagorean theorem equation is a^2+b^2=c^2 and c^2 will always represent the hypotenuse which is the longest side of the right triangle while a^2 and b^2 can any of the other two sides. Look at Visual 6 to see an example of how to use Pythagorean theorem to solve for the side length of a triangle. Visual 6 Start with: a2 + b2 = c2 Put in what we know: 52 + 122 = c2 Calculate squares: 25 + 144 = c2 25+144=169: 169 = c2 Swap sides: c2 = 169 Square root of both sides: c = √169 Calculate: c = 13 The last thing that we learned about concerning right triangles were trigonometric inverses. As I mentioned in my cover letter, trigonometric inverses are used to find the angles of a right triangle. The trigonometric inverses we used were sin^-1, cos^-1, and tan^-1. Look at Visual 7 of an example of how to use a trigonometric inverse to solve for the angle of a right triangle. Visual

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Lesson 1, finding the area of different shapes, differed greatly in classifications assigned to the task outlined in the study. Consistent with all other lesson plans in the classifications A and E located in the lower-level demands, the students’ were assigned a task that required memorization of the formula used for calculating the area of a rectangle (p. 49). Unlike the previous nine lessons, the students task of “finding different ways to find the area of different rectangular-based shapes” (p. 50) involved problem-solving skills.

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He had drawn the interiors of rooms and labeled them and specified their dimensions, down to inches, in his precise, blocky

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He found the first “reliable figure” for π(pi) (Source A). In ancient Greece, the crude number system was very inefficient, and Archimedes made it easier to understand and count to higher numbers (Source B). Finally, he used the first known form of calculus while studying curved surfaces under Euclid, not to be later worked on for 2,000 years by Isaac Newton (Source A).

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Activity 21 emphasizes the different classifications of triangles. Triangles are three-sided polygons classified by the length of each side and the measurement of each angle. An Equilateral triangle has sides that are all the same length. Isosceles triangles have at least two congruent sides. The length of the sides of a Scalene triangle are incongruent.

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Last but certainly not least, the principle of proportion can be identified when you look into the distance you can clearly see the size difference between objects that are farther away such as the mountains and ones that are closer such as the common

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The learning objective for lesson one is, “students will be able to identify and draw points, lines, line segments, rays, and angles.” The learning objective for lesson two is, “students will be able to classify triangles by the size of their angles.” The learning objective for lesson three is, “students will be able to identify and draw parallel lines and perpendicular lines.” The learning objective for lesson four is, “students will be able to sort and classify quadrilaterals.”

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As I finished my breakfast, I had the opportunity to join the campus tour or attend a mock math class, named, “Calculus at Cornell by Professor Strogatz.” Since I have a strong affinity for math, I decided to attend the mock math class. As we settled down, Professor Strogratz, a tall, middle-aged man strode in front of the room. He announced, “Good morning. Although your travel agenda says you are in a calculus class, we will focus on a simple trigonometric equation: the Pythagorean equation, particularly its ‘odd number’ triplets, and see where it guides us to.”

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Regardless of his important contributions to pure mathematics, he is best remembered for his discovery of a method used to determine the volume of an object with an irregular shape. The formulas produced by Archimedes helped calculate the area of regular shapes. He produced these formulas using a method in which he captured new shapes using

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Many people wondered throughout history how Pythagoreans saw the world as just simple values or equations. The contribution of Pythagoras makes him so

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The missing angle would be 90.The reason the missing side would be 90 is because a right triangle has a right angle in it and a right angle always adds up to 90°. My team and I are going to do an experiment on making a triangle in a ramp form. We are trying to see how many math and science books it will take to make a good enough triangle for a cup to roll down. The ramp can’t be

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Plato’s, Meno, is quite significant to the history of mathematics. During the fifth century BCE Greek mathematics was more theoretical and self-conscious; it would be paired together with philosophy in their education. Although most of Plato’s piece is largely focused on Socrates and Meno struggling to define what “virtue” is, mathematics is still an extremely important role. This is quite evident when the boy is asked to find a square equivalent to double the size of the current square. The boy confidentially answers that the lines are double the size because the square is double the size, even though this is wrong since it gives four times the size.

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There are many different ways of how trigonometry applies to the real world. For example, some occupations that use trigonometry on an everyday basis are astronauts, physicists, architects, surveyors, crime scene investigators, and engineers. In history, trigonometry can be traced all the way back to about 4,000 years ago. Another example of how we apply trigonometry on an everyday basis is technology and music. Sound navigates through waves and this style is still not as formal as a sine or cosine capacity, but it is effective in advancing computer music.

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Geometry- Faces, Edges, and Vertices, (Newport News Public Schools, 2015) follows the 4E lesson plan model. The four components of this model include; engage and hook, explain and model, explore and apply, and evaluate. The lesson is designed to meet the Virginia Standards of Learning “2.16 the student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism)” (Virginia Department of Education, 2010).

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Around 469 to 399 BC, two of Socrates pupils tried to square the circle by theorizing that if you double the number of sides in a polygon enough, it will become a circle. It failed to a degree (it must be because Archimedes has taken the credit for this discovery), until Archimedes came in 287-212 BC. Archimedes is considered one of the most brilliant mathematicians in the known ancient world. He worked out that 223/71<22/7, which was the first theoretical calculation of pi. His results were measured by approximating the area of a circle based upon the area of a regular polygon inscribed within the circle and the area of a regular

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Pythagoras and his followers believed that everything in the “world could be expressed by an arrangement involving just the whole numbers” [3]. However, they were truly perplexed to discover that the diagonal of a square was incommensurable with its side. For example, a square with a side length of 1 would produce a diagonal with a length of √(2 ). This ratio could not be expressed by the whole numbers, and in fact, the ratio was a nonrepeating, nonterminating, decimal series [3]. In modern day mathematics, these numbers are known as irrational.

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