Type Texttype Texttype Textlevel Eled Mg Hsdate Of Observ ✓ Solved

Level: Eled, MG, HS Date of observation:_______________________ Variable Behaviors Observation Notes Lesson Planning Pressures -Lack of effort in putting together a lesson. -Clear instruction -Pacing -Modeling of Procedures Learning Environment -Student rapport -Student comfort level -Lecturing teacher -Hands on content -Positive narration Technology Implementation -Use or lack of use in teacher led technology -Use or lack of use in student led technology -How is the present technology being used or not used?

A Review of Averaging Formulas Math 1010 Intermediate Algebra Group Project The Story: Alyssa works for an online company that helps thousands of small business owners across the country to advertise themselves and find customers in need of their services. After the job is completed, Alyssa’s company encourages the customers to review the business on a scale of 1 to 5 stars. This review is saved within Alyssa’s database so that future customers can see the average number of stars a business has received on the online service. That way the customers can find the best rated person for the job. Alyssa found that many business owners had questions about how they could improve their rating. One common question was: “How many 5-star reviews in a row do I need to improve my rating from where I’m at to a 4.5?†Or a 4.2? Or whatever threshold they were interested in? Rather than having to work this out from scratch in every scenario, it is more efficient to create a formula so the answer can be found quickly and efficiently. We will start out with some simpler questions to become familiar with the situation and how averages work. Then we will work our way towards the full formula to help the business owners answer their question above. You will use skills you learned about solving formulas for a particular variable and working with rational expressions.

AVERAGES We will be exploring how basic averages work in this section. This Average is also called the Mean, or Arithmetic Mean. 1. Write a formula which can find the average of two numbers x and y. AVERAGE = 2. Use your formula to find the average of 16 and 34. Show your process. AVERAGE = 3. Explain in words: How does the process of finding the average change if there are 6 numbers to average? 4. Find the average of the six numbers 4, 6, 7, 12, 14, and 17. Show your process.

FREQUENCY TABLES Often very large data sets are averaged. The data sets include many numbers which are the same. A Frequency Table describes how many of each number are included in the set. Examine the following table as an example: Number Frequency The table explains the data set 1, 1, 2, 2, 2, 2, 3, 3, 3. 5. Find the average of the nine numbers above. Show your process. Round your answer to the nearest hundredth. When the data set becomes too large, it becomes too tedious to add all of the numbers one by one. We need a different strategy. Examine the next frequency table, which shows the number of reviews a particular business owner has received of each number of stars. Stars Frequency. Determine how many total reviews this business has received. Show your process.

7. Rather than add up all of those numbers one at a time, we will add them in groups. As an example, if we add up all twelve of the 3s, we should use multiplication (since it represents adding the same number repeatedly). All of the 3s sum to 3 times 12 which is 36. In the following blanks, similarly write the sum of all numbers of each type. Sum of 1s __________ Sum of 2s __________ Sum of 3s ___36___ Sum of 4s __________ Sum of 5s __________ 8. Use your results from the previous two parts to find the average number of stars the business has received. Show your process. Round your answer to the nearest hundredth.

ONE MORE NUMBER To answer our final question, we will need to know what happens to an average if we add one more number. 9. Suppose a list of seven numbers has an average of 12. What is the SUM of those seven numbers? Show your process. 10. Suppose the number 18 is added to the previous list of seven numbers to make eight numbers. What is the new SUM of all eight numbers? 11. What is the new average of all eight numbers? Show your process.

MANY MORE REVIEWS 12. Suppose a business has a current average review of 3.2 stars. This is from 30 customer reviews. Using a similar process to the previous three questions, find the new average review for the business after four new 5-star reviews. Show your process and round your answer to the nearest hundredth. PUTTING IT ALL TOGETHER Suppose a business currently has an average rating of R stars. This average is calculated from N current reviews. 13. Find a formula for the new average rating A that the business will have after receiving X new reviews in a row, all of them 5-star reviews. Try to carefully follow the steps you used in Part 12. 14. If the business wants to know how many 5-star reviews in a row are needed to achieve a desired new rating, the formula in the previous part must be solved for X. Solve your formula in the previous part for X, and show your process. Let’s put our new formula into action!

Kevin’s Tree Service is a small business that currently has ratings given in the table below: Stars Frequency. First calculate the current average review for Kevin’s Tree Service. Show your process. Leave your answer in the form of a fraction. AVERAGE = 16. Now use your formula from Part 14 to calculate how many 5-star reviews in a row are needed for Kevin’s Tree Service to achieve an average review of 4.5. REFLECTION 17. Did this project change the way you think about how math can be applied in the real world? Do you believe this kind of analysis could be important to business owners? Did you expect Kevin’s Tree Service to need that many 5-star reviews to reach its goal? Does what you learned here make you more likely to carefully consider ratings you give for services you receive? Write at least two paragraphs addressing the above questions.

Teacher Burnout Survey Required 1. I currently teach at the ________ level. Mark only one oval. Elementary Middle High 2. I currently have ________ years of experience. Mark only one oval. 05 years 610 years 1115 years 1620 years 20+ years 3. I am _______. Mark only one oval. Male Female Other: 4. 1. Overall, I am completely satisfied with my position of being a teacher. Mark only one oval. Strongly Disagree Strongly Agree 5. 2. If I had to do it over again, I would choose teaching as my career. Mark only one oval. Strongly Disagree Strongly Agree 6 3. In teaching, I am often expected to do tasks that I feel are unreasonable. Mark only one oval. Strongly Disagree Strongly Agree 7 4. The expectations for lesson planning and preparation are difficult to meet. Mark only one oval. Strongly Disagree Strongly Agree 8. 5. I have enough time to complete all of my expected tasks. Mark only one oval. Strongly Disagree Strongly Agree 9. 6. The lack of time related to planning and preparation is NOT a potential burnout area for me. Mark only one oval. Strongly Agree Strongly Disagree 10. 7. The expectations set forth by the state for evaluations are reachable. Mark only one oval. Strongly Disagree Strongly Agree 11. 8. I often feel stressed in trying to meet the expectations for evaluations. Mark only one oval. Strongly Disagree Strongly Agree 12. 9. The expectations for evaluations is NOT a potential burnout area for me. Mark only one oval. . The expectations set forth by the state for standardized testing are reachable. Mark only one oval. Strongly Disagree Strongly Agree 14 11. I often feel stressed in trying to meet the expectations for state standardized testing. Mark only one oval. Strongly Disagree Strongly Agree 15. 12. The requirements of state standardized is NOT a potential burnout area for me. Mark only one oval. Strongly Agree Strongly Disagree 16. 13. There is adequate time spent trying to ensure proficiency in in math and reading. Mark only one oval. Strongly Disagree Strongly Agree 17. 14. It is difficult to meet the demands of proficiency in math and reading. Mark only one oval. Strongly Disagree Strongly Agree 18. 15. The expectations for student performance is NOT a potential burnout area for me. Mark only one oval. Strongly Agree Strongly Disagree 19. 16. I have control over the curriculum that I teach. Mark only one oval. Strongly Disagree Strongly Agree 20 17. I am frustrated with the amount of control I have over the curriculum I teach. Mark only one oval. Strongly Disagree Strongly Agree 21 18. The freedom I have over the curriculum I teach is NOT a potential burnout area for me. Mark only one oval. Strongly Disagree Strongly Disagree 22. 19. I have strong relationships with the parents or guardians of my students. Mark only one oval. Strongly Disagree Strongly Agree 23. 20. The parents of my students have high involvement in their child’s education. Mark only one oval. Strongly Disagree Strongly Agree Strongly Disagree Strongly Agree 24. 21. I am frustrated with the level of involvement my students’ parents have in their child’s education. Mark only one oval. Strongly Disagree Strongly Agree 25. 22. I am expected to use technology in my lessons. Mark only one oval. Strongly Disagree Strongly Agree 26. 23. I receive adequate support for technology integration in my classroom. Mark only one oval. . . . . 27 24. I am frustrated with the expectations of technology integration. Mark only one oval. Strongly Disagree Strongly Agree 28. 25. Technology integration is NOT a potential burnout area for me. Mark only one oval. Strongly Agree Strongly Disagree 29. 26. In my position, I am expected to do too many extra tasks (i.e. bus duty, lunchroom duty, extra meetings, after school supervision). Mark only one oval. Strongly Disagree Strongly Agree Strongly Disagree Strongly Agree 30. 27. The extra tasks (i.e. bus duty, lunchroom duty, extra meetings, after school supervision) I am expected to do lead to disgust for me. Mark only one oval. Strongly Disagree Strongly Agree 31. 28. The extra tasks (i.e. bus duty, lunchroom duty, extra meetings, after school supervision) I am expected to do is NOT a potential burnout area for me. Mark only one oval. Strongly Agree Strongly Disagree 32. 29. There are other areas not listed in this survey that are potential burnout or burnout areas for me. Mark only one oval. . I feel burned out in my profession. Mark only one oval. Strongly Disagree Strongly Agree Powered by Successful Learning Individual Protocol Thank you for agreeing to meet with me today. If you could please sign and date the consent form that allows me to use the information from today’s interview in my research project. As a reminder, this research study is entirely confidential and your name will not be attached to any research data. I have an hour to an hour and half scheduled for our interview today. I want to honor any time constraints that you have today. Finally, I will ask open ended questions today and I will be taking notes and recording our conversation. This interview should feel more like a conversation rather than a question answer session. I want you to feel comfortable elaborating on your responses, and there will be times where I will ask follow-up questions based on your answers. Our first questions are built to help me gain background information about you and your experiences in teaching.

Introduction How long have you been a teacher? What subject matter do you teach? What grades do you teach? Can you describe your first experiences of teaching a class? What is your favorite thing about teaching? What, if anything, would cause you to leave the field of teaching? Researcher notes: Our next few questions will focus primarily on learning. As a teacher you see learning every day. Once again, I will be taking notes and recording your responses. I want you to feel comfortable elaborating on your responses, and I will ask you follow-up questions based on your responses.

Learning What research on learning are you familiar with? Tell me about your experiences with successful learning. What causes learning to take place? How or why do you believe this? How do think learning and communication is linked? Do you think that all teachers believe they way that you do about the link between communication and learning? Why? In your opinion, what must teachers do for students to learn best? How do you perceive other teachers would respond to this question? What do you believe causes students not to learn? What can be done to fix ineffective learning? How can teachers change practice of communication to fix students lack of learning? Researcher notes: Thank you for your responses to the learning based questions. Our next questions will be tied to the role of engagement in the learning process. As you have done with the previous questions, please feel free to elaborate on your answers, and I will ask follow-up questions.

Engagement How would describe engagement? How does your definition vary from your colleagues? Do you use any engagement strategies in your teaching? Which ones? How have your strategies impacted your students’ learning? What role does engagement in content play in learning? How does this role affect the overall impact of learning? Tell me a story about a time where you had total engagement in your classroom. Researcher notes: Thank you for your responses on the engagement based questions. Our next sets of questions will look at the role that relationships and communication techniques play in the learning process. We will continue to follow the same procedure as we have been where you are welcome to elaborate as much as you would like on your answers, and I will ask follow-up questions.

Relationship Tell me about the types of relationships you have with your students. What does it mean to have student to teacher relationships? Do you place an importance on student to teacher relationships? If so, what do you believe is important about student to teacher relationships? How can student to teacher relationships impact learning? How do you feel your relationships with student’s impacts their learning? Can you share with me an example about a time when you had a strong relationship with a student or students? Researcher notes: Communication Tell me about how you speak to your class. When you speak to your class verbally, what speech mechanisms are important for optimal learning to take place? Why are these important? Can you think of an example where you may have felt aggressive in your communication with students? How can a teacher be too aggressive with their classroom? Has there ever been a time where a student just did not respond to you in the way you expected? If so, describe. What is your opinion of a teacher’s use of humor in the learning process? How can humor enhance or detract from learning? Researcher notes: In this final section I want to allow you to have the opportunity to share with me any other information that you feel I should consider in my research project. These last few questions will conclude the interview process. Conclusion Do you think teacher input is valuable in learning research? In what ways can teachers help researchers learn about strong instructional practices that impact learning? Are there other ideas you would like to add? Thank you for your help with our project. Do you have any questions for me about this research? Again, thank you so much for your participation in my interview today. Are there any final comments that you would like to make that would help me in this research project or the field of education as a whole?

Paper For Above Instructions

The application of averaging formulas in educational contexts is significant as it allows educators and administrators to understand how performance metrics can be summarized and interpreted. In this paper, I will explore how averaging works through mathematical principles, applicable to both student performance evaluations and quantitative analyses required for education professionals. This exploration is based on a project encompassing various aspects of averaging and discussing their implications in educational environments.

Understanding Averages

Averages, or means, are fundamental concepts in mathematics that quantify a set of values by providing a central tendency. In its simplest form, the average of two numbers can be calculated using the formula:

A = (x + y) / 2

For instance, if we find the average of 16 and 34, we proceed with the calculation:

A = (16 + 34) / 2 = 25

This simple calculation illustrates the process of finding an average, which remains consistent regardless of the number of values involved. When averaging six numbers, for example, we simply sum the six values and divide by six, ensuring our understanding extends to larger sets.

Calculating Averages with Larger Data Sets

In cases where datasets comprise numerous repetitions of values, frequency tables become essential. These tables facilitate the process of calculating averages for larger datasets without tedious individual additions. For example, if we have a frequency table indicating the number of reviews for various ratings, we can compute the average more efficiently:

• Number 1s: If there are 5 ratings of 1 star, then the contribution to the sum is 1 x 5 = 5.
• Number 2s: If there are 4 ratings of 2 stars, then we calculate 2 x 4 = 8.
• Number 3s: Adding the previously calculated 36 from 3-star ratings.
• Number 4s: If there are 3 ratings of 4 stars, the total contribution is 4 x 3 = 12.
• Number 5s: If there are 2 ratings of 5 stars, then 5 x 2 = 10.

Combining these contributions allows us to find the total and calculate the average effectively.

The Impact of Additional Reviews on Averages

Understanding how an average shifts upon adding new data points is crucial. For instance, if a business has an existing average of 3.2 stars from 30 reviews, we can compute the new average after obtaining four additional 5-star reviews:

New Total Reviews = 30 + 4 = 34

Current Total Stars = 3.2 * 30 = 96

New Total Stars = 96 + (5 x 4) = 96 + 20 = 116

New Average = 116 / 34 = 3.41 stars

Formulating for Future Reviews

In deriving a formula for new averages based on additional reviews, let’s assume a business currently has an average rating R with N reviews. The new average \(A\) after receiving \(X\) additional 5-star reviews can be expressed as:

A = (R N + 5 X) / (N + X)

Using this formula, businesses can calculate the necessary number of 5-star reviews to hit their desired average ratings through rearrangement and resolution of X.

Conclusion

The exploration and application of averaging formulas in educational contexts equip both teachers and administrators with the necessary tools to understand performance data critically. This understanding influences instructional practices and enhances communication with stakeholders. The project highlights the necessity of transparency and accuracy in performance evaluations and the potential effects on a business's reputation. Knowledge of how averages are calculated and the impact of additional ratings can significantly shape educational policy and pedagogical approaches moving forward.

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