Complete Week 9 Package

Transcription

1 Complete Week 9 Package 2015

2 Table of Contents Unit 3 Pacing Chart Day 41 Bellringer Day 41 Activity Day 41 Practice Day 41 Exit Slip Day 42 Bellringer Day 42 Activity Day 42 Practice Day 42 Exit Slip Day 43 Bellringer Day 43 Activity Day 43 Practice Day 43 Exit Slip Day 44 Bellringer Day 44 Activity Day 44 Practice Day 44 Exit Slip Weekly Assessment

3 CCSS Algebra 1 Pacing Chart Unit 3 Unit Week Day CCSS Standards Mathematical Practices Objective I Can Statements 3 Modeling Linear Data 3 Modeling Linear Data 3 Modeling Linear Data 9 Understan ding Functions 9 Understan ding Functions 9 Understan ding Functions CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. CCSS.MATH.PRACTIC E.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. CCSS.MATH.PRACTIC E.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. CCSS.MATH.PRACTIC E.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. The student can determine whether correlation coefficient shows a weak positive, strong positive, weak negative, strong negative, or no correlation. The student can determine whether correlation coefficient shows a weak positive, strong positive, weak negative, strong negative, or no correlation and use the information to make decisions The student can compute the correlation coefficient of a set of linearly related data using Microsoft Excel. I can determine whether correlation coefficient shows a weak positive, strong positive, weak negative, strong negative, or no correlation. I can determine whether correlation coefficient shows a weak positive, strong positive, weak negative, strong negative, or no correlation and use the information to make decisions I can compute the correlation coefficient of a set of linearly related data using Microsoft Excel Page 1

4 CCSS Algebra 1 Pacing Chart Unit 3 3 Modeling Linear Data 3 Modeling Linear Data 3 Modeling Linear Data 9 Understan ding Functions 9 Understan ding Functions 9 Understan ding Functions CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. CCSS.MATH.CONTENT.HSF.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an ex CCSS.MATH.PRACTIC E.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. CCSS.MATH.PRACTIC E.MP6 Attend to precision. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. The student can compute the correlation coefficient of a set of linearly related data using technology. The student can use the computations of the cerrelation coefficient to answer questions and make predictions. I can compute the correlation coefficient of a set of linearly related data using technology. I can use the computations of the correlation coefficient to answer questions and make predictions. 45 Assessment Assessment Assessment Assessment 2015 Page 2

5 Day 41 Bellringer Name Day 41 Interpret the Scatter plots 1. Based on the scatter plot below, which is a better prediction for x when y = 5? 3 or 8? 3. Based on the scatter plot below, which is a better prediction for y when x = 8? 3 or 10? 2. Based on the scatter plot below, which is a better prediction for y when x = 36? 80 or 13? 4. Based on the scatter plot below, which is a better prediction for x when y = 11? 87 or 54? 2015 Page 3

6 Day 41 Bellringer Answer Key Day Page 4

7 Day 41 Activity Take a look at your performance in the consecutive mathematics assignments done every day. Consider 15 assignments beginning from the first one is the term going onwards. Or you may as well consider the last term s consecutive assignments. a). Convert each performance out of 100%. b). Make a table of values showing the number of assignments and the performance in each assignment. c). Generate a scatter plot showing the data above. d). What king correlation does it have? 2015 Page 5

8 Day 41 Activity Answer Keys Day 41: Marks a). The formula for determining the percentage is 100% Total Marks The values should range between 0% and 100%. b). The table should have two rows or columns where the first one has the number (position of the assignment in the list) of the assignments while the seconds one has the performance out of 100. c).this should be composed of dots in the positive quadrant of xy plane with a line of the best fit. d). The correlation should be either positive if the student is improving or negative if the students is dropping in performance. There may be no correlation too when the dots are uniformly scattered in the plane Page 6

9 Day 41 Practice Use the graph below to answer questions 1-3. y x 1. Identify the correlation between y and x in the graph above. (Use negative, positive or no correlation) 2. What could be the value of r among 0.8, -0.79, 0 in the graph above? 3. How do the variables change as one of them varies? 2015 Page 7

10 Day 41 Practice Use the graph below to answer questions 4-6. y 4. Identify the correlation between y and x in the graph above. (Use negative, positive or no correlation) x 5. What could be the value of r among 0.75, -0.76, 0 in the graph above? 6. How do the variables change as one of them varies? 2015 Page 8

11 Day 41 Practice Use the graphs below to answer questions 7-13 March the graph with the appropriate correlation (i) (ii) 2015 Page 9

12 Day 41 Practice (iii) 7. Positive correlation 8. No correlation 9. Negative correlation 2015 Page 10

13 Day 41 Practice Identify the graph that best describes the r value given below. 10. r = r = r = r = A graphical relationship reveals that the correlation coefficient is 1. Describe the relation between the two variables. 15. A graphical relationship reveals that the correlation coefficient is 1. Describe the relation between the two variables Page 11

14 Day 41 Practice Identify the correlation between the variables described below, The data between amount of fuel in a vehicle and distance travelled. 17. The data between the amount of water in a tank and the height of the water. 18. The data between the temperature and the number of stretch of the wind on different days. 19. The data between the age and the height of students. 20. The data between the amount of wheat fed in the mill and the volume of wheat flour produced Page 12

15 Day 41 Practice Answer Keys Day 41: Answers 1. Positive correlation As the value of x increases, y increases too 4. Negative correlation As the value of x increases, the value of y decreses. 7. (ii) 8. (i) 9. (iii) 10. (i) 11. (iii) 12. (ii) 13. None 14. The variables have a perfect positive linear correlation 15. The variables have a perfect negative linear correlation 16. Negative correlation 17. Positive correlation 18. No correlation 19. Positive correlation 20. Positive correlation 2015 Page 13

16 Day 41 Exit Slip Day 41 What is the difference between a correlation of 0.5 and 0.9 and how that would look on a scatter plot? What is the difference between a correlation of 0.9 and -0.9 and how that would look on a scatter plot? 2015 Page 14

17 Day 41 Exit Slip Answer Key Day Both.5 and.9 would be positive but the points with a correlation of.9 would be much closer to the line of best fit. 2. Both +.9 and -.9 would be very close to the line of best fit, but +.9 would have a strong positive trend and -.9 would have a strong negative trend Page 15

18 Day 42 Bellringer Day 42 Choose the most appropriate Correlation Coefficient a.) b.) c.) 2.1 d.) -2 a.) -2 b.) 1.2 c.) d.) a.) b.) 2.1 c.) 0.9 d.) -1 a.) -1 b.) -0.3 c.) d.) Page 16

19 Day 42 Activity Answer Key Day a c c d Page 17

20 Day 42 Activity Take a 16 oz. plastic beaker and make a small hole at the bottom so that it can allow, only, the drops of water out. Fill it with water and find out if the hole allows drops of water out. Mark the initial level of water then fill it slightly beyond it so that you get ready to investigate the number of drops immediately the water gets to that level. 1. Record the number of drops after each ounce is lost. This should be a table having two rows and at least 11 columns. The first row has the total number of drops recorded after every loss of one ounce of water. 2. Draw a scatter plot showing the height of the water in the beaker against the total number of drops after every drop of water. Draw the line of the best fit too Page 18

21 Day 42 Activity 3. Observe and state the number of points lying on the line of the best fit Page 19

22 Day 42 Activity 4. What is the correlation between the height of the water in the beaker and the total number of drops after every loss of 1 ounce? 5. Explain your answer in 4 above Page 20

23 Day 42 Activity Answer Keys Day 42: 1. The table should have at least 11 columns with two rows. The difference between the successive values in the first row should be the same or different by 1 only in a few cases. 2. The graph should be a typical xy plane with points represented by dots that lies on the same line. The horizontal and vertical axis should be labelled as Total number of drops and height of water respectively. The graph should lie within the first quadrant only. 3. All points lies on the line of the best fit (except one or two, not more) The slope of the line is negative and all the points lies on the line of the best fit (except one or two, not more) Page 21

24 Day 42 Practice 1. A researcher carefully computes the correlation coefficient between two variables and gets r = What does this value mean? 2. It has been noted that there is a positive correlation between the U.S. economy and the height of women's hemlines (distance from the floor of the bottom of a skirt or dress) with shorter skirts corresponding to economic growth and lower hemlines to periods of economic recession. Comment on the conclusion that economic factors cause hemlines to rise and fall. 3. Given a set of paired data (x, y) a. if y is independent of x, then what value of a correlation coefficient would you expect? b. if y is linearly dependent on x, then what value of a correlation coefficient would you expect? 4. A researcher has a large number of data pairs (age, height) of humans from birth to 18 years. He computes a correlation coefficient. Would you expect it to be positive or negative? Why? 5. Given the following data: X Y a. Construct a scatterplot. b. Compute the correlation coefficient, r Page 22

25 Day 42 Practice 6. Given the following data: X Y a. Construct a scatterplot b. Compute the correlation coefficient, r Page 23

26 Day 42 Exit Slip Day 42 What does the correlation coefficient tell you about the relationship between two variables? 2015 Page 24

27 Day 42 Exit Slip Answer Key Day 42 The measure of the strength and direction of the linear relationship between two variables Page 25

28 Day 43 Bellringer Day 43 Graph and Calculate Correlation Coefficient 1. A company wants to predict the annual value of its total sales based on the national income of the country where does business is. The relationship is represented in the following table: x y x represents the national income in millions of dollars and y represents the company's sales in thousands of dollars in the period from 1990 to 2000 (inclusive). 1. Make a scatter plot of the data. 2. Draw the line of best fit on the scatter plot 3. Find the correlation coefficient. 4. What would be the prediction of the company's sales if the national income would be 325 million in 2017? 2015 Page 26

29 Day 43 Bellringer Answer Key Day & Page 27

30 Day 43 Activity Use Excel to calculate the Correlation Coefficient. General Scenario: Dr. Truong wants to examine the relation between the amount of television that people watch and how happy they are. Ten adults participate in her study. Each participant records the total number of hours of TV that he or she watches for a particular week. In addition, at the end of the week, each participant completes a questionnaire that measures the person s overall happiness. The questionnaire scores can range from 0 (extremely unhappy) to 10 (extremely happy). The results from Dr. Truong s experiment are listed below. Participant Number Hours of TV Watched Happiness Score 1. Enter the data from the table above into an Excel spreadsheet. Label row 1 of columns A, B, and C with Participant Number, Hours of TV Watched, and Happiness Score, respectively. 2. Find the mean, median, and mode using the Function Shortcuts in Excel. 3. Find correlation coefficient using the =correl( tool and round your answer to the hundredths place. Describe the association between the TV watching and happiness. Don t just say that the correlation is positive or negative. Explain what your correlation tells you about how these two variables are associated with each other Page 28

31 Day 43 Activity Answer Key There it is, a strong negative correlation coefficient. This tells us that as the number of hours of TV watched goes up, the happiness score goes down. Because the correlation coefficient is close to -1, there is a high probability of causation. Teacher Note: There are step by step instructions on the presentation for day Page 29

32 Day 43 Practice Use Excel to calculate the Correlation Coefficient. General Scenario: Dr. Rouke wants to examine the relation between the hours practiced and performance on an athletic task: free-throw shooting in basketball. Ten adults have agreed to participate in his study. Prior to shooting free throws, each participant completes a survey that asks how many hours they practiced. Scores range from 0 (hours) to 9 (hours). After this survey, each participant shoots 10 free-throws and the number of baskets made is recorded. The results from Dr. Rouke s study are listed below. Participant Number Hours Practiced Free-throw Performance 4. Enter the data from the table above into an Excel spreadsheet. Label row 1 of columns A, B, and C with Participant Number, Hours of TV Watched, and Happiness Score, respectively. 5. Find the mean, median, and mode using the Function Shortcuts in Excel. 6. Find correlation coefficient using the =correl( tool and round your answer to the hundredths place. Based solely on the correlation coefficient, what would you conclude about the relation between hours practiced and free-throw performance? Based on the scatterplot, what conclusion do you reach? 2015 Page 30

33 Day 43 Exit Slip Day 43 For the pairs of variables below, indicate what you would expect for the direction (positive, negative, scattered) and the strength (none, weak, moderate, strong) of the association. Be ready to justify your answer. a. Height and arm span Positive, Strong b. Height and shoe size Positive, Moderate c. Height and GPA Scattered, None d. SAT score and college GPA Positive, Moderate e. Latitude and average January temperature of American cities Negative, Moderate f. Lifespan and weekly cigarette consumption Negative, Moderate g. Serving size and calories of fast food sandwiches Positive, Moderate h. Air fare and distance to destination Positive, Moderate 2015 Page 31

34 Day 43 Exit Slip Answer Key Day 43 These answers will vary depending on the student s background information. The most important part is that they have the positive and negative correct and that they can justify the answers Page 32

35 Day 44 Bellringer Day 44 Write the line of best fit from the scatter plot Page 33

36 Day 44 Bellringer Answer Key Day Page 34

37 Day 44 Activity Name 1 A study compared the number of years of education a person received and that person's average yearly salary. It was determined that the relationship between these two quantities was linear and the correlation coefficient was Which conclusion can be made based on the findings of this study? 3 As shown in the table below, a person s target heart rate during exercise changes as the person gets older. 1) There was a weak relationship. 2) There was a strong relationship. 3) There was no relationship. 4) There was an unpredictable relationship. 2 The relationship of a woman s shoe size and length of a woman s foot, in inches, is given in the accompanying table. Which value represents the linear correlation coefficient, rounded to the nearest thousandth, between a person s age, in years, and that person s target heart rate, in beats per minute? The linear correlation coefficient for this relationship is 1) 1 2) 3) 0.5 1) 2) 3) ) ) Page 35

38 Day 44 Activity Name 4. What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? 6 The points in the scatter plot below represent the ages of automobiles and their values. Based on this scatter plot, it would be reasonable to conclude: 1) ) ) 4) 5 What could be the approximate value of the correlation coefficient for the accompanying scatter plot? 1) Age and value have a coefficient of correlation that is less than zero. 2) Age and value have a coefficient of correlation that is equal to zero. 3) Age and value have a coefficient of correlation that is between zero and ) Age and value have a coefficient of correlation that is greater than Which value of r represents data with a strong negative linear correlation between two variables? 1) 2) 3) 4) 1) 2) 3) 4) Which value of r represents data with a strong positive linear correlation between two variables? 1) ) ) ) Page 36

39 Day 44 Activity Name 9 The relationship between t, a student s test scores, and d, the student s success in college, is modeled by the equation. Based on this linear regression model, the correlation coefficient could be 1) between and 0 2) between 0 and 1 3) equal to 4) equal to 0 10 A linear regression equation of best fit between a student s attendance and the degree of success in school is. The correlation coefficient, r, for these data would be 1) 2) 12 Which graph represents data used in a linear regression that produces a correlation coefficient closest to? 1) 2) 3) 3) 4) 11 Which calculator output shows the strongest linear relationship between x and y? 4) 1) 2) 3) 4) 2015 Page 37

40 Day 44 Activity Name 13 Which scatter diagram shows the strongest positive correlation? 1) 14 In the physics lab, Thelma determined the kinetic energy, KE, of an object at various velocities, V, and found the linear correlation coefficient between KE and V to be Which graph shows this relationship? 1) 2) 2) 3) 3) 4) 4) 15 Determine which set of data given below has the stronger linear relationship between x and y. Justify your choice Page 38

41 Day 44 Activity Name 16 A nutritionist collected information about different brands of beef hot dogs. She made a table showing the number of Calories and the amount of sodium in each hot dog. a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest hundredth. b) Explain what the correlation coefficient suggests in the context of this problem Page 39

42 Day 44 Activity Name Answer Key ; The correlation coefficient for the plot must be positive, eliminating answers (1) and (2). The correlation is rather strong, so the correlation coefficient should be closer to 1. 6 The correlation coefficient for the plot must be negative Since the coefficient of is greater than 0,. 10 Because the slope of the linear regression equation of best fit is positive (0.5), the correlation coefficient must be positive. 11 (4) shows the strongest linear relationship, but if,. The Regents announced that a correct solution was not provided for this question and all students should be awarded credit. 12 If the correlation coefficient (r) is negative, the line of best fit must have a negative slope, eliminating answers (2) and (3). The nearer r is to, the more closely the data cluster around the line of best fit. Answer (4) has a tighter fit than answer (1). 13 Answer (2) has a negative correlation. Answer (4) has no correlation. The closer the data cluster around the line of best fit, the stronger the correlation. Answer (1) has a tighter fit than answer (3). 14 (2) is the only graph that shows a positive correlation. 15 Set B has the stronger linear relationship since r is higher. 16. The correlation coefficient suggests that as calories increase, so does sodium Page 40

43 Day 44 Practice Use the information below to answer questions 1-9. I teacher would like to investigate if the weight of students affects their performance in class. He therefore carry out a study by sampling out 15 student in grade 9, measure their weight and gets the performance in mathematics from their past term reports. Weight(lbs.) Performance(%) Draw a scatter plot to represent the data above 2. Find the equation of the line of the best fit Page 41

44 Day 44 Practice 3. Determine the correlation coefficient of the variables. 4. Identify this type of correlation. 5. From the correlation, how is the change in performance when the weight of the student increases? 6. Interpret the slope of the graph 7. Explain why interpretation of the slope is applicable or not applicable to real life situation. 8. From the results what was the conclusion of the teacher Page 42

45 Day 44 Practice 9. Why the conclusion? Use the information below to answer questions A researcher in interested in determining the linear relationship between the consumption of water and the number of people in each house hold. After the study, he found that the correlation coefficient was Identify the type of correlation 11. What is the effect on the amount of consumption of water with increase in the number of people in each house hold? 12. State if true of false. The decrease in the number of people in a house hold drastically decreases the amount of consumption of water. 13. Explain your answer above Page 43

46 Day 44 Practice Use the information below to answer questions A laboratory expert is growing a culture of bacteria for further investigation. He founds that the decrease in temperature greatly decreases the growth of the culture while increase in temperature drastically increases the multiplication process. 14. What is the correlation between the rate of growth of culture and the increase in the degree of coldness? 15. Identify the possible correlation coefficient for the relationship in 14 above among r = 0.95, r = 0, r = 9.6 and r = What is the correlation coefficient between the rate of growth of culture and the increase in the degree of hotness? 17. Identify the possible correlation coefficient for the relationship in 14 above among r = 0.95, r = 0, r = 9.6 and r = Page 44

47 Day 44 Practice 18. The expert would like to maintain the relative size of culture after the growing to the required size. Between a freezer and warm container, which one is the best for storing the culture? 19. Explain your answer in 18 above. 20. In which situation can we have the correlation coefficient of 1 when the results does not reflect the true real life situation? 2015 Page 45

48 Day 44 Practice Answer Keys Day 44: y = 0.24x Around Weak positive correlation 5. Increase in weight leads to an increase in performance 6. There is an increase of 0.24% marks for each increase in weight 7. This is not true because the weight and the performance do not have a strong linear correlation 8. The weight of the student has insignificant effect (very little) effect on the performance of the student 9. The performance and the weight has a very weak linear correlation hence the later cannot be used to determine the performance Page 46

49 Day 44 Practice 10. Moderate positive correlation 11. Increase in the number people in a house gradually increases the consumption of water 12. False 13. The two variables do not have a perfect strong linear correlation rather a moderate one hence the decrease in the number of people in a house hold will decrease gradually and not drastically the consumption of water. 14. Strong negative correlation 15. r = Strong positive correlation 17. r = freezer 19. A freezer has very low temperatures which does not favor the growth of the culture 20. In situations where the independent variable is not the only factor that affect the change in the dependent variable Page 47

50 Day 44 Exit Slip Day 44 Which graph represents data used in a linear regression that produces a correlation coefficient closest to 1? a) b) c) d) 2015 Page 48

51 Complete Week 9 Answer Key Day 44 C 2015 Page 49

52 Algebra 1 Teachers Weekly Assessment Package Unit 3 Created by: Jeanette Stein 2015 Algebra 1 Teachers 50

53 Algebra 1 Common Core Semester 1 Skills Number Unit CCSS Skill 15 3 S.ID.6 Find the line of best fit 16 3 S.ID.6 Predict future events given data 17 3 S.ID.8 Calculate Correlation Coefficient with technology 18 3 S.ID.9 Understand the difference between Causation and Correlation 51

54 Unit 3 Weekly Assessments 52

55 Week #9 1. The accompanying table shows the enrollment of a preschool from 1980 through Write a linear regression equation to model the data in the table. 2. Find the inverse of the function. y = 3x 7 Year (x) Enrollment (y) Create a scatterplot and a table for the Average Cost of a Loaf of Bread. Use the graph to predict the cost in Be sure to label your scatterplot appropriately. In 1930 a loaf was 9 cents, 1940 a loaf was 10 cents, 1950 a loaf cost 12 cents, 1960 a loaf cost 22 cents, 1970 a loaf was 25 cents, 1980 a loaf cost 50 cents, 1990 a loaf cost 70 cents, and in 2008 it was $2.79 Cost in 2050 = 53

56 4. Match the following correlation coefficients with the approprite graph. r =.86 r =.90 r =.80 r =.10 54

57 Unit 3 - KEYS Weekly Assessments 55

58 Week #9 KEY 1. The accompanying table shows the enrollment of a preschool from 1980 through Write a linear regression equation to model the data in the table. 2. Find the inverse of the function. y = 3x 7 y = x Answers will vary: y = 1.15x Create a scatterplot and a table for the Average Cost of a Loaf of Bread. Use the graph to predict the cost in Be sure to label your scatterplot appropriately. In 1930 a loaf was 9 cents, 1940 a loaf was 10 cents, 1950 a loaf cost 12 cents, 1960 a loaf cost 22 cents, 1970 a loaf was 25 cents, 1980 a loaf cost 50 cents, 1990 a loaf cost 70 cents, and in 2008 it was $2.79 Year Cost Cost in 2050 = Answers will vary 56

59 4. Match the following correlation coefficients with the approprite graph. r =. 10 r =. 90 r =. 86 r =