# problems solving

Mathematics is evident in nearly every facet of life. From cell phones to robots or digital cameras to tablets, many of the technologies today that we consider commonplace, even essential, would not exist without the understanding of numbers. Having an awareness of the evolution of math and numbers throughout history reveals the rich presence of math in everyday life.

In Part I of this project, you will complete four problems (two from each chapter) similar to ones that you have done for homework. You will need to show the solution to the problem and explain your solution using the concepts and terminology that you have learned.

Begin with an Introductory paragraph about what you have been studying in this class. Do not just provide a list of topics, think about how to explain the “general ideas” of the class to your reader

This should be followed by **four problems** (two from each Chapter) selected from the Word document provided below. Your assignment should explain to the reader what the problem asks you to do, provide a complete solution to the problem, followed by a paragraph that explains __not only how to solve__ the problem but the **relevance or importance** of this topic. You may label the four problems “Problem #1”, “Problem #2” and so on

Here’s an example using the following problem:

**Solution:** In this problem we are asked to find the set A’, which is the complement of the set A. Using roster notation, A = {9, triangle, circle, square}. To find the complement of A, we need to find all the other elements of the universal set, U, that do not appear in A. That would include the values 3, 7, and ? inside set B, as well as the 8 and #, which are not in either sets A or B. The final solution is: **A’ = {8, #, 3, 7, ?}**

This problem illustrates the importance of mathematical notation and interpretation of a graphical representation. To solve this problem, we must not only know what the __complement__of a set is, but also how to parse a Venn diagram and represent various sub-sets.

· Finally, write a conclusion paragraph that summarizes how your view of mathematics has improved or matured over the last two weeks. How can you apply this __new skill or knowledge__ to your educational degree or personal goals?

**Week 2 Final Project: Part I: Chapter Problems**

**Chapter 1 (Problem Solving and Critical Thinking):** __Select TWO problems__ from the following list:

1a. Write two statements similar to the following, then explain which one of them is inductive reasoning and which one is deductive reasoning. Show that you understand the difference between these two types of reasoning.

Person A states “The course policy states that if you turn in at least 80% of the homework, your lowest exam grade will be dropped. I turned in 90% of the homework, so I conclude that lowest grade will be dropped”.

Person B states “We examine the fingerprints of 1000 people. No two individuals in this group of people have identical fingerprints. We conclude that for all people, no two people have identical fingerprints”.

1b. Make up a new problem using patterns similar to this problem from Example 4 in Section 1.1.

Your pattern may use shapes, colors, or textures. Be sure to explain in detail how to solve your problem.

1c. Explain how to ROUND a number to any place. Give at least three examples. Why is this important?

1d. Make up a new problem similar to this one: “The cost of renting a boat from Estes Rental is $9 per 15 minutes. The cost from Ship and Shore Rental is 20 per half-hour. If you plan to rent the boat for three hours, which business offers the better deal and by how much.”

Your problem should involve at least two options that need to be evaluated. Be sure to explain in detail how to solve your problem.

**Chapter 4 (Number Representation):** __Select TWO problems__ from the following list:

4a. Explain why a symbol for *zero* is needed in a positional system, but NOT in other systems. Given an example of each type of system.

4b. Convert each of the following base ten numerals to a numeral in the given base:

Convert 67 to base three

Convert 1544 to base five

Convert 59 to base two

Explain why it is important to understand the base for a number as well as the value.

4c. Use the symbols in the Egyptian Numeration system, as shown, to write 3,524,634 as an Egyptian numeral. [**Hint:** Write it on paper, then take a picture with your phone and upload to your document.]

4d. Assume there is a system that represents numbers exactly like the Greek Ionic system, but with different symbols. The symbols are as shown here.

Express each of the following as a Hundu-Arabic numeral: SPF, nfVRH, and pUF.

Explain whether this system is a positional system or not.

Chapter 4, “Number Representation and Calculation” (p. 211)

· Section 4.1, “Our Hindu-Arabic System and Early Positional Systems”(pp. 212–217)

· Section 4.2, “Number Bases in Positional Systems” (pp. 220–225)

· Section 4.3, “Computation in Positional Systems” (pp. 227–233)

· Section 4.4, “Looking Back at Early Numeration Systems” (pp. 236–240)

· Blitzer, R. (2014). *Thinking mathematically *(6th ed.). Boston, MA: Pearson.

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Mathematics is evident in nearly every facet of life. From cell phones to robots or digital cameras to tablets, many of the technologies today that we consider commonplace, even …