03 Jan Choose any one option from

MAT131 College Mathematics

Module 1 Discussion

Please choose one of the following problems from your textbook or one of the 6 discussion questions that accompany the videos and respond fully. Please use full sentences and use a minimum of 50 words in your responses to each question.

Section 1.1 63, 66, 68, 70

Section 1.2 61, 65, 66, 68, 76

Section 1.3 56, 58, 60

Video 5: Pascal’s Triangle – Part 1

https://mediaplayer.pearsoncmg.com/assets/y3v80ieMx2ENmsn811c4JMnaksg42_hu

This video uses a bean machine, also known as a quincunx, to demonstrate both the central limit theorem as well as Pascal’s Triangle. Students drop marbles from the top of the quincunx and see which slot they land in at the bottom. After numerous marbles have been dropped, it is observed that a bell curve forms and the presenter explains that this happens any time random processes occur. This reasoning helps explain how Pascal’s Triangle is formed, where each number represents how many paths the marble can take around that peg. All the numbers within the triangle also have different meanings, such as the rows representing the powers of 11, adding the rows giving the powers of 2, and the diagonals representing how shapes are organized in space.

Class discussion questions

1. Using what you know about Pascal’s Triangle, what is (a+b)4 ?

2. The quincunx is said to represent how random processes occur and that it will result in the bell curve. What does the presenter mean by a bell curve and when does this become more accurate?

3. At the end of the video, the presenter mentions that the diagonals represent how shapes are organized in space. What do you think he means by this?

Video 6: Pascal’s Triangle – Part 2

https://mediaplayer.pearsoncmg.com/assets/SuTiV5B1MC2VqGs9_jOXnFdioGTIQ_oR

Going along with the previous video on Pascal’s Triangle, the presenter goes into more detail on the diagonals of the triangle. He first explains that in order to create the triangle, you have to start with a triangle of ones and then add up two numbers on one row to create a new number on the row after. How shapes are organized in space is the basis for the diagonals of this triangle. It is explained that the third diagonal (1, 3, 6, 10, etc.) are the triangle numbers. The fourth diagonal numbers (1, 4, 10, 20, etc.) are the tetrahedral numbers of the third dimension. The fifth diagonal, however, can be described using the intersection points of different shapes. Fractals are then described by shading in the even numbers within Pascal’s Triangle to form the Sierpinski Triangle, a series of triangles within each other.

Class discussion questions

1. What is Pascal’s triangle? How do you find the numbers in any row of the triangle? Describe some patterns you notice within the triangle.

2. It is discussed that the entries in each diagonal represents different properties of shapes. What do you notice when you add up the numbers in each diagonal?

3. The Sierpinski Triangle is created by a series of triangles within each other. These shapes are called fractals. What other fractals can you think of?

MAT131 College Mathematics

Module 2 Discussion

Please choose one of the following problems from your textbook and respond fully. Please use full sentences and use a minimum of 50 words in your responses to each question.

Section 8.1 66, 68, 70

Section 9.1 92, 94, 96, 98

Section 9.2 84, 86, 88, 90, 92

Section 9.3 90, 92, 94, 96, 98

MAT131 College Mathematics

Module 3 Discussion

Please choose one of the following problems from your textbook or one of the class discussion questions and respond fully. Please use full sentences and use a minimum of 50 words in your responses to each question.

Section 10.1 70, 72, 74, 76

Section 10.2 54, 56, 58, 60, 62

Section 10.3 56, 58, 60, 62, 64

This video focuses on how to convert angles to distances by using trigonometric functions. The presenter begins in a park measuring the sides and angles of the cardboard skyscrapers that were built by a group of people. With discussions about corresponding sides and angles, a conclusion is drawn that larger angles have larger corresponding sides. The presenter explains the Pythagorean Theorem – that the sum of the legs squared is equal to the hypotenuse squared. One example used to explain this concept is the height of a window on a house.

https://mediaplayer.pearsoncmg.com/assets/VCSmnFqfpvNCD80bf6OEpb0QUKitgBlM

Class discussion questions

1. What kind of triangle does the Pythagorean Theorem apply to?

2. You all should remember special triangles such as 30-60-90 and 45-45-90 triangles. Use the trigonometric functions to show that the side lengths are correct.

3. What are some other instances in which a person may need to use Trigonometric functions? Include anything that you may use in your life and you can also include that they can be used to find distances between celestial bodies or the distance from shore to a point at sea

4. The mnemonic of SOHCAHTOA is expanded to “Stephen, Oh Heck, Crocodiles And Hedgehogs Took Our Apples.” What other words can you think of to help remember this?

MAT131 College Mathematics

Module 4 Discussion

Please choose one of the following problems taken from Chapter 4 of Thinking Critically to Solve Problems: Combining Values and College Mathematics and respond fully. Please use full sentences and use a minimum of 50 words in your responses to each exercise chosen.

1. Write a report illustrating how geometry is used in industry. Be sure to include how the values of community, responsible stewardship, and excellent affect the industry you researched.

2.. Compare and contrast how a designer architect might use geometry. How does Geometry effect the community from the designer and architect perspective?

3. Bigger is often cheaper per item or amount. For example, buying food in bulk. We see this with the growth in the number of warehouse clubs that sell items in larger quantities for a lower per item cost. What are some situations when bigger is not better, even when it is cheaper?

MAT131 College Mathematics

Module 5 Discussion

Please choose one of the following problems from your textbook or one of the class discussion questions and respond fully. Please use full sentences and use a minimum of 50 words in your responses to each question.

Section 11.1 25, 26, 28, 30

Section 11.2 64, 66, 68, 70, 72

Section 11.3 72, 74, 76, 78, 80

Section 11.4 74, 76, 80, 82, 84

Section 11.5 24, 26, 28, 30

This video utilizes a soccer team and a band to help understand how combinations and permutations work. Coaches sometimes assign very specific roles, such as left midfield, right midfield, and center midfield, while others just say you three go play midfield. The presenter is able to explain how this mathematically creates a large difference. Allowing the players to choose their specific positions on an 11 player team changes the possibilities from 11 x 10 x 9 x 8 to (11 x 10 x 9 x 8)/(4 x 3 x 2 x 1). The presenter then explains that Pascal’s Triangle can also be used to calculate combinations. For example, to find out what choosing 2 from 4 is, count down 4 rows then over 2 numbers. The same simple processes of adding numbers together produce all sorts of things that we can see around us in the world.

https://mediaplayer.pearsoncmg.com/assets/0pVSwpUf3CZoJ3fluGnTq7kQ7UQRo99A

Class discussion questions

1. The presenter gives the formula for combinations as nCr = (n!)/((n-r)!r!). Using this formula, what is 5 choose 2?

2. Explain what the difference is between a combination and a permutation is. Explain this in your own words, without a definition or formula.

3. It’s often said that one of the most difficult hands to get in poker is a royal flush consisting of a 10, Jack, Queen, King, and Ace of the same suit. Using the information about combinations, what is the probability that you will get dealt a royal flush?

MAT131 College Mathematics

Module 6 Discussion

Please choose one of the following problems from your textbook and respond fully. Please use full sentences and use a minimum of 50 words in your responses to each question.

Section 11.6 94, 96, 98, 100, 102, 104, 106

Section 11.7 74, 76, 82, 84, 86, 88

Section 11.8 20, 22, 24, 26, 28, 30

MAT131 College Mathematics

Module 7 Discussion

Choose any one option from “Social Justice across the Curriculum” found in Chapter 7 of Thinking Critically to Solve Problems: Combining Values and College Mathematics” and respond fully with a minimum of 50 words.

MAT131 College Mathematics

Module 8 Discussion

Choose any one option from “Social Justice across the Curriculum” found in Chapter 8 of Thinking Critically to Solve Problems: Combining Values and College Mathematics” and respond fully with a minimum of 50 words.