# Maths

### Exploring factors and Factoring Trinomials

Discussion: Exploring factors and Factoring Trinomials

**Required Resources**

Read/review the following resources for this activity:

- OpenStax Textbook Readings
- Lesson in Canvas
- Assignments in Knewton
- Adding and Subtracting Polynomials
- Product Properties of Exponents
- Multiplying Polynomials
- Special Products of Binomials
- Quotient Properties of Exponents and Dividing Monomials
- Dividing Polynomials
- The Greatest Common Factor and Factoring by Grouping

**Initial Post Instructions**

We start the week by introducing polynomials. We will learn how to identify and simplify polynomials. We will also learn how to find the greatest common factor (GCF) among them. As our knowledge of polynomials grows, we will then move on to factoring trinomials. For your first post, search online for an article or video that describes how polynomials can be used in the real world. Provide a one paragraph summary of the article or video in your own words.

**Follow-Up Post Instructions**

Respond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.

### Categories of descriptive statistics:

Visit one of the following newspapers’ websites: __USA Today__, __New York Times__, __Wall Street Journal__, or __Washington Post__. Select an article that uses statistical data related to a current event, your major, your current field, or your future career goal. The chosen article must have a publication date during this quarter.

The article should use one of the following categories of descriptive statistics:

- Measures of Frequency – Counting Rules, Percent, Frequency, Frequency Distributions
- Measures of Central Tendency – Mean, Median, Mode
- Measures of Dispersion or Variation – Range, Variance, Standard Deviation
- Measures of Position – Percentile, Quartiles

Write a two to three (2-3) page paper in which you:

- Write a summary of the article.
- Explain how the article uses descriptive statistics.
- Explain how the article applies to the real world, your major, your current job, or your future career goal.
- Analyze the reasons why the article chose to use the various types of data shared in the article.
- Format your paper according to the
__Strayer Writing Standards__. Please take a moment to review the SWS documentation for details.

### Observing Mathematics

**Part 1: Observation**

Observing a classroom environment can provide much needed detail and understanding of students’ learning needs and continued progress.

For this field experience, observe a K-8 classroom during a math lesson. During your observation of the lesson, complete the “Math Observation” template.

Speak with your mentor teacher and, provided permission, use any remaining time to seek out opportunities to observe and/or assist your mentor teacher or another teacher and work with a small group of students on instruction in the classroom. Your mentor teacher must approve any hours spent observing another classroom environment.

With the help of your mentor teacher, identify 3-5 students above, at, or below standard achievement in the classroom environment that would benefit from additional learning support. Ask your mentor teacher for the unit and standards and unit the class is currently learning, in order to develop the pre-assessment for Clinical Field Experience B.

**Part 2: Reflection**

Following your observation, discuss the math lesson with your mentor teacher. In 250-500 words summarize and reflect on your observation and, and describe how you will apply what you have learned to your future professional practice.

Your discussion should include the following:

- How do you engage students in learning opportunities specific to mathematics?
- What strategies do you use to apply real-world relevancy to math lessons?
- How do you modify or adjust instruction based on responses from students?
- How do you prepare to teach instruction in mathematics (vocabulary, knowledge of material, content standards, and resources)?

### Mathematical history

Write a reflection paper of at least 1 page addressing the following topics and questions. In your paper, include your name, the course name and section, and the date in the header. Use Times New Roman, size 12 font and double space.

· Your mathematical history: In high school i have taken algebra I and II, Geometry.

o What math classes have you taken in the past?algebra I and II, geometry

o Share a memory that stands out from your previous math courses, either good or bad.I remember in the 10th grade I was taking geometry and the teacher called on me to do a problem and I could not get the correct answer and he screamed at me with a high pitch voice. I was terrified being in his class.

o Share an example of how you have had to use math outside of the classroom. As an certified medical assistant, I use math daily especially drawing up botox.

· Your feelings about math Basic math do not bother me because I am very good with that but algebra I am not so good.

· Your future as related to math. I think as long as I can do basic math I am okay in society.

o Are there math courses required for your degree? If so, what are they? What will you be taking next? Yes math is required with my degree as business administration. I do not know the next math I will be taking.

o Do you see this course as useful for you in your career or personal life? No I do not see this course useful in my career. As long as a person know basic math I think he or she will be okay.

### Arclength and Reparametrization

(1) Write a short essay on this topic, using examples: Why is it that we need to consider reparametrizations of a curve? Why have we chosen arclength as the “correct” parametrization? What is arclength, and how do we go about using it? How practical is reparametrization by arclength?

(2) Reparametrize the curve below by arclength: α(t) = (e ^t cos(t), e^t sin(t), e^t )

### Regular parametrized curves.

(1) There are several geometric reasons why we choose to work with only regular parametrized curves. Write a short essay to describe a few of those reasons, using examples to illustrate your points.

(2) Show that the curve β(t) = (sin(3t) cos(t),sin(3t) sin(t), 0) is a regular curve. Then find the equation of its tangent line at the time t = π/3.

### Frenet-Serret

Write a short essay that describes two different interpretations of the curvature κ of a space curve. Be sure to include as one of your descriptions a discussion of what κ means in terms of the motion of the Frenet-Serret framing of the curve.