Algebra 1 Topic 5 Algebra 1 Table of

Algebra 1 Topic 5

Algebra 1 Table of Contents • Recommended Instructional Design and Planning Continuum ……. Slide 3 • Vocabulary …………………………… Slides 4 – 22 • Pre-Requisite Practice Items ……………………… Slides 23 – 46 • Reporting Category Practice Items ………………… Slides 47 – 80

Algebra 1 RECOMMENDED INSTRUCTIONAL DESIGN AND PLANNING CONTINUUM Before Prior to the lesson: Outline content standard(s). Determine learning targets. Anticipate student understanding and misconceptions. Determine prerequisite skills. Plan for learning experiences that target o Rigor o Conceptual Understanding o Procedural Fluency o Application Determine the task students will demonstrate to reach the desired learning targets. Plan instructional delivery methods that will maximize initial engagement and sustain it throughout the lesson. Decide how students will reflect upon, selfassess, and set goals for their future learning. During the lesson: Activate (or supply) prior knowledge and/or spiral back o Warm ups, Bell Ringers, Openers, etc. Tailor lesson experiences to the different needs and ability of the learners. Clarify vocabulary and mathematical notation. Incorporate a variety of higher order questions to encourage and increase critical thinking skills. Continuously check for student understanding and provide feedback. Provide opportunities for students to develop self-assessment and to reflect about their understanding and work. Bring closure to the lesson so that the students can articulate what they have learned. After the lesson: Analyze evidence of student learning to develop intervention, enrichment, and future instruction. Discuss results of assessments with students. Engage students in reflective processes and goal setting. Engage in self-reflection to adapt/modify teaching strategies to improve instruction.

Algebra 1 Vocabulary

Algebra 1 Mathematically Speaking! Choose 3 -4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods. Examples of accuracy • translation vs slide • variable vs letter • addition property of equality vs adding on both sides

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Scatterplot Graphical representation of the relationship between two numerical sets of data

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Positive Correlation •

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Negative Correlation •

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 No Correlation •

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Line of Best Fit The line that comes closest to all of the points in a data set.

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Curve of Best Fit

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Outlier Data •

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Mean A measure of central tendency (the “average”).

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Median A measure of central tendency (the "middle" value).

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Mode A measure of central tendency The value or values that occur most frequently in a data set. If all values occur with the same frequency, the data set is said to have no mode.

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Box Plot A graphical representation of the five-number summary

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Histogram A graph used to display data grouped in a class interval.

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Dot Plot A number line with marks or dots that show frequency.

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Standard Deviation (σ) A measure of the spread of a data set Comparison of two distributions with same mean and different standard deviation values

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Normal Distribution

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Two-Way Frequency Table A frequency table that displays two-variable data in rows and columns in order to help organize and provide greater insight into features of a population being surveyed. A trend, or pattern in the data, can also be examined using a two-way frequency table. Has Kids No Kids Total Has Pets 37 9 46 No Pets 15 15 30 Total 52 24 76

Compiled and/or modified from: http: //www. doe. virginia. gov/instruction/mathematics/resources/vocab_cards/ Algebra 1 Two-Way Frequency Table Has Kids No Kids Total Has Pets 37 9 46 No Pets 15 15 30 Total 52 24 76 Joint Frequency: A joint frequency is the number of responses for a given characteristic. The entries in the cells of a two-way frequency table are joint frequencies. Marginal Frequency is the total number of times a response was given, or the total number of respondents with a given characteristic. This is the sum of either a row or a column. Conditional Relative Frequency allows a comparison to be made for multiple responses in a single row, single column, or table. They are found by dividing the number of responses by either the total number of people who gave that response, the total number of people with a given characteristic, or the total number of responses.

Algebra 1 Pre-Requisite Practice Items

Pre-Requisites Algebra 1 Formative Assessments MAFS. 6. SP. 1. 1 MAFS. 6. SP. 1. 2 MAFS. 6. SP. 2. 4 MAFS. 6. SP. 2. 5 Questions About a Class Math Test Center Basketball Histogram Analyzing Physical Activity TV Statistics Pet Frequency Chores Data Puzzle Times Shark Attack Data MAFS. 8. SP. 1. 1 MAFS. 8. SP. 1. 2 MAFS. 8. SP. 1. 3 MAFS. 8. SP. 1. 4 Cheesy Statistics Line of Good Fit - 1 Stretching Statistics School Start Time Sleepy Statistics Line of Good Fit - 2 Tuition Music and Sports Two Scatterplots Siblings and Pets Three Scatterplots Two-Way Relative Frequency Table

Pre-Requisites Algebra 1 Illustrative Mathematics Tasks MAFS. 6. SP. 1. 1 MAFS. 6. SP. 1. 2 MAFS. 6. SP. 2. 4 MAFS. 6. SP. 2. 5 Identifying Statistical Questions Electoral College Puppy Weights Puzzle Times Buttons: Statistical Questions Is It Center or Is It Variability? Comparing Test Scores Mean or Median? Statistical Questions Describing Distributions Average Number of Siblings Math Homework Problems MAFS. 8. SP. 1. 1 MAFS. 8. SP. 1. 2 MAFS. 8. SP. 1. 3 MAFS. 8. SP. 1. 4 Birds' Eggs Laptop Battery Charge US Airports, Assessment Variation What's Your Favorite Subject? Texting and Grades I Hand span and height Animal Brains

Algebra 1 Reporting Category Items

Algebra 1 MAFS. 912. S-ID. 1. 1 The data below are the number of beds in a sample of 15 nursing homes in New Mexico in 1988. 44 59 59 60 62 65 80 80 90 96 100 116 120 135 a) Find the minimum and maximum of the data. b) Find the first, second, and third quartiles. c) Make a box plot of the data. a) The minimum data value is 44 beds. The maximum data value is 135 beds. b) The second quartile is 80 beds. The first quartile is 60 beds. The third quartile is 110 beds. c)

Algebra 1 MAFS. 912. S-ID. 1. 1 Billy incorrectly made a box plot for the following data. His work is shown below. Identify and correct his errors. The following data are the amounts of potassium, in grams, per serving in randomly selected breakfast cereals. 25 25 30 30 35 35 40 45 50 55 60 60 60 70 85 90 95 95 105 Billy’s box plot: Billy misidentified the first, second, and third quartiles. The first quartile is 35 grams, the second quartile is 55 grams, and the third quartile is 85 grams.

Algebra 1 MAFS. 912. S-ID. 1. 2 The box plots below display the distributions of maximum speed for 145 roller coasters in the United States, separated by whether they are wooden coasters or steel coasters. Based on the box plots, answer the following questions or indicate whether you do not have enough information. CONTINUE ON NEXT SLIDE

Algebra 1 MAFS. 912. S-ID. 1. 2 1. Which type of coaster has more observations? Explain your choice. A. Wooden B. Steel C. About the same D. Cannot be determined 2. Which type of coaster has a higher percentage of coasters that go faster than 60 mph? Explain your choice. A. Wooden B. Steel C. About the same D. Cannot be determined CONTINUE ON NEXT SLIDE 1. D 2. B

Algebra 1 MAFS. 912. S-ID. 1. 2 3. Which type of coaster has a higher percentage of coasters that go faster than 50 mph? Explain. A. Wooden B. Steel C. About the same D. Cannot be determined 4. Which type of coaster has a higher percentage of coasters that go faster than 48 mph? Explain. A. Wooden B. Steel C. About the same D. Cannot be determined 3. C 4. D

Algebra 1 MAFS. 912. S-ID. 1. 3 The depth of snow at seven different mountain lodges is 18 inches, 20 inches, 26 inches, 22 inches, 85 inches, 18 inches, and 24 inches. Find the mean, median, and mode. Which measure is the most useful for predicting how deep the snow will be at an 8 th lodge? A. mean: 30. 4 in. , median: 22 in. , mode: 18 in. The median is the most useful. B. mean: 22 in. , median: 30. 4 in. , mode: 18 in. The median is the most useful. C. mean: 22 in. , median: 30. 4 in. , mode: 18 in. The mean is the most useful. D. mean: 30. 4 in. , median: 22 in. , mode: 18 in. The mean is the most useful. A

Algebra 1 MAFS. 912. S-ID. 1. 3 Raegan's first five geography test scores are 95, 58, 68, and 61. What misleading statistic could Raegan use to verify the claim that she is earning a good grade in geography? A. the median of 68 B. the mode of 95 C. the mean of 75. 4 D. the range of 37 B

Algebra 1 MAFS. 912. S-ID. 1. 3 Rachel is applying for a summer job. The six current employees earn $9. 00, $9. 50, $10. 00, $10. 50, $11. 00, and $25. 00 per hour. In the interview, the boss tells Rachel that the average hourly wage is $12. 50. Is the boss's statement misleading? Why or why not? A. Yes, because no one makes that exact amount. B. Yes, because only one employee makes at least $12. 50. C. No, because $12. 50 is the mean, which is the most reliable average. D. No, because $12. 50 is the median, which is the most reliable average. B

Algebra 1 MAFS. 912. S-ID. 1. 3 By how much does the outlier in the following data set increase the mean of the data set? Round your answer to the nearest hundredth if necessary. {10, 14, 15, 20, 25, 27, 29, 30, 114} A. 21. 25 B. 14. 25 C. 10. 31 D. 22. 5 C

Algebra 1 MAFS. 912. S-ID. 1. 3 The number of calls received by a technical support center during 22 randomly selected days is listed. Identify the outlier, and describe how it affects the mean and the standard deviation. 50 57 77 66 50 57 82 70 62 64 69 77 66 53 72 51 88 98 65 11 68 88 A. The outlier is 11. The outlier in the data set causes the mean to decrease from about 17. 4 to about 13 and the standard deviation to increase from 65. 5 to about 68. 1. B. The outlier is 11. The outlier in the data set causes the mean to decrease from about 68. 1 to 65. 5 and the standard deviation to increase from about 13 to about 17. 4. C. The outlier is 88. The outlier in the data set causes the mean to increase from about 17. 1 to about 17. 4 and the standard deviation to increase from 64. 43 to about 65. 5. D. The outlier is 88. The outlier in the data set causes the mean to increase from 64. 43 to about 65. 5 and the standard deviation to increase from about 17. 1 to about 17. 4.

Algebra 1 MAFS. 912. S-ID. 1. 3 The following data represents the ages of tenants in a particular apartment building. 54, 37, 30, 37, 55, 38, 43, 37, 28, 53, 39, 30, 41, 34 Part A: Find the minimum and maximum values and the first, second, and third quartiles for the age data. Part B: If the 55 -year-old tenant moves out and a 56 -year-old person moves in, how will this affect a box-and-whisker plot of the data? The new maximum will be 56. Part C: To the nearest whole percent, what percent of the tenants are 30 years old or older? To the nearest whole percent, what percent are 43 years old or older? Explain 30 years or older: 87%; 43 years or older: 27%

Algebra 1 MAFS. 912. S-ID. 1. 3 Ms. Katz made the box-and-whisker plot below to show the distribution of her students’ scores on their last science test. All of the scores were different and one score was an outlier. Which statement describes the most likely effect on the mean and median test scores when the outlier is removed? A. The mean score increases and the median score decreases. B. Both the mean and median scores decrease. C. The mean score decreases and the median score increases. D. Both the mean and median scores increase. D

Algebra 1 MAFS. 912. S-ID. 1. 2 The box-and-whisker plots show the distribution of test scores for two students for a semester. What conclusion can you make about the data? A. Overall, Jim had better scores than Suresh, and Jim was more consistent in his scores. B. Overall, Jim had better scores than Suresh, and Suresh was more consistent in his scores. C. Overall, Suresh had better scores than Jim, and Jim was more consistent in his scores. D. Overall, Suresh had better scores than Jim, and Suresh was more consistent in his scores. D

Algebra 1 MAFS. 912. S-ID. 1. 1 The ages of the U. S. Presidents that were inaugurated during the 1900 s are given below. Ages at Inauguration 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 46 Look at the box-and-whisker plot of these data below. What, if anything, is wrong with this box-and-whisker plot? A. The value of Q 1 is incorrect. B. The median is incorrect. C. The value of Q 3 is incorrect. D. The box-and-whisker plot is correct. C

Algebra 1 MAFS. 912. S-ID. 1. 2 What is the best measure of center to use to compare the two data sets? Data Set A Data Set B A. Median B. Either the mean or the median C. Interquartile range D. Either the standard deviation or the interquartile range A

Algebra 1 MAFS. 912. S-ID. 2. 5 A group of men and women were polled about whether they go to the gym regularly. The joint and marginal relative frequencies corresponding to the results are shown in the two-way table. YES NO TOTAL MEN 0. 4 WOMEN 0. 3 TOTAL 0. 7 0. 3 0. 6 0. 4 1 D

Algebra 1 MAFS. 912. S-ID. 2. 5 A survey of 120 students about which sport, baseball, basketball, football, hockey, or other, they prefer to watch on TV yielded the following two-way frequency table. What is the conditional relative frequency that a student prefers to watch baseball, given that the student is a girl? Round the answer to two decimal places as needed. Baseball Basketball Football Hockey Other Total Boys 18 14 20 6 2 60 Girls 14 16 13 5 12 60 Total 32 30 33 11 14 120 A. 11. 67% B. 23. 33% C. 43. 75% D. 53. 33% B

Algebra 1 MAFS. 912. S-ID. 2. 5 Which of the following statements are supported by the survey data in the two-way frequency table? Right-handed Left-handed Total Males Females Total 82 79 161 23 16 39 105 95 200 q The joint relative frequency that a person surveyed is female and left-handed is about 0. 168, or 16. 8%. q The conditional relative frequency that a person surveyed is female, given that the person is righthanded, is about 0. 4907, or 49. 07%. q The joint relative frequency that a person surveyed is male and is right-handed is about 0. 41, or 41%. q The conditional relative frequency that a person surveyed is right-handed, given that the person is male, is about 0. 5093, or 50. 93%. q The marginal relative frequency that a person surveyed is left-handed is about 0. 195, or 19. 5%.

Algebra 1 MAFS. 912. S-ID. 1. 2 The annual salaries (in thousands of dollars) of 15 randomly selected employees at two small companies are given. Indicate the shape of the data distributions. Then, compare the center and spread of the data and justify your method of doing so. Company 1: 22, 36, 37, 37, 39, 42, 45, 46, 150, 200 Company 2: 21, 37, 38, 38, 39, 42, 45, 46, 47, 48, 62, 250 The salary distributions for both companies are skewed right. Since the data sets are skewed right, the centers should be compared using the medians and the spreads should be compared using the interquartile range. The median salary of company 1 is $42, 000 and the median salary of company 2 is $45, 000. The first quartile for company 1 is $37, 000 and the third quartile is $46, 000. The spread of the salaries at company 1 is $46, 000 - $37, 000 = $9000. The first quartile for company 2 is $38, 000 and the third quartile is $47, 000. The spread of the salaries at company 2 is $47, 000 - $38, 000 = $9000. The center salary at company 2 is higher, while the spread of the salaries of the two companies are the same.

Algebra 1 MAFS. 912. S-ID. 1. 2 What is the best measure of spread to use to compare the two data sets? Income of ten recent graduates from college A (in thousands of dollars per year): 0, 35, 38, 39, 45, 47, 50, 51, 52 Income of ten recent graduates from college B (in thousands of dollars per year): 29, 35, 36, 37, 38, 39, 41, 42, 46, 400 A. Median B. Either the mean or the median C. Interquartile range D. Either the standard deviation or the interquartile range C

Algebra 1 MAFS. 912. S-ID. 3. 9 What kind of correlation would you expect from the ordered pair (student’s hair color, student’s college grades)? A. no correlation B. negative correlation C. positive correlation D. none of these A

Algebra 1 MAFS. 912. S-ID. 1. 3 The ages of ten employees at a small company are shown below. 30, 32, 35, 38, 38, 40, 45 If the data set were expanded to include a new employee who is 20 years old, how would the mean of the data set change? A. The mean decreases by 2 years. B. The mean decreases by about 1. 6 years. C. The mean increases by about 1. 6 years. D. The mean does not change. B

Algebra 1 MAFS. 912. S-ID. 2. 6, S-ID. 3. 8 Weather data were recorded for a sample of 25 American cities in one year. Variables measured included January high temperature (in degrees Fahrenheit), January low temperature, annual precipitation (in inches), and annual snow accumulation. The relationships for three pairs of variables are shown in the graphs below (Jan Low Temperature – Graph A; Precipitation – Graph B; Annual Snow Accumulation – Graph C). CONTINUE ON NEXT SLIDE

Algebra 1 MAFS. 912. S-ID. 2. 6, S-ID. 3. 8 Part A: Which pair of variables will have a correlation coefficient closest to 0? Explain your choice: A. Jan high temperature and Jan low temperature B. Jan high temperature and Precipitation C. Jan high temperature and Snow accumulation B D. None of the above Part B: Which of the above scatterplots would be best described as a strong nonlinear relationship? Explain your choice. C Part C: For the city with a January low temperature of 30°F, what do you predict for the annual snow accumulation? Explain how you are estimating this based on the three graphs above. About 10 inches

Algebra 1 MAFS. 912. S-ID. 3. 9 Which statement regarding correlation is not true? A. The closer the absolute value of the correlation coefficient is to one, the closer the data conform to a line. B. A correlation coefficient measures the strength of the linear relationship between two variables. C. A negative correlation coefficient indicates that there is a weak relationship between two variables. D. A relation for which most of the data fall close to a line is considered strong. C

Algebra 1 MAFS. 912. S-ID. 1. 3 The data set below shows 15 students’ scores on a test. Describe the shape of the data distribution if the student who scored 100 is not included in the data set. 70 72 73 74 74 75 75 76 77 77 78 80 100 A. The data distribution is skewed right. B. The data distribution is symmetric. C. The data distribution is skewed left. D. It is impossible to determine the shape of the data distribution B

Algebra 1 MAFS. 912. S-ID. 2. 6 A

Algebra 1 MAFS. 912. S-ID. 2. 6 A. B. C. D. D

Algebra 1 MAFS. 912. S-ID. 3. 9 Price, One Pound Red Delicious Apples $0. 99 $1. 29 $1. 19 $1. 09 $0. 99 $1. 29 $1. 19 Price, One Gallon Whole Milk $2. 59 $2. 89 $2. 69 $2. 55 $2. 69 $2. 98 $2. 79 A. There is a strong positive correlation between the price of apples and the price of milk. There is a likely cause-and-effect relationship because shoppers often buy both apples and milk at the same time. B. There is a very weak positive correlation between the price of apples and the price of milk. There is a likely cause-and-effect relationship because shoppers often buy both apples and milk at the same time. C. There is a strong positive correlation between the price of apples and the price of milk. There is not a likely cause-and-effect relationship because other factors, such as transportation costs, likely affect both apple and milk prices. D. There is a very weak positive correlation between the price of apples and the price of milk. There is not a likely cause-and-effect relationship because other factors, such as transportation costs, likely affect both apple and milk prices.

Algebra 1 MAFS. 912. S-ID. 2. 6 Joshua is making home-made cards to send to friends and family and to sell at the local craft fair. This scatter plot shows the total number of cards he had made after each hour he worked on the task. Using this information, what is the best prediction of the number of cards Joshua can make in 11 hours? A. 54 B. 39 C. 19 D. 29 B

Algebra 1 MAFS. 912. S-ID. 2. 6 This graph shows the scatter plot of a data set and a line of fit. What is the residual plot for this data set and line? A. B. C. A

Algebra 1 MAFS. 912. S-ID. 2. 6 The table below shows 6 students' overall averages and their averages in their math class. Overall Student - Average 92 98 84 80 75 82 Math Class Average 91 95 85 85 75 78 If a linear model is applied to these data, which statement best describes the correlation coefficient? A. It is close to -1. B. It is close to 1. C. It is close to 0. D. It is close to 0. 5 B

Algebra 1 MAFS. 912. S-ID. 2. 6 Make a scatter plot of the data. Sketch a line that appears to best fit the data. Then write the equation of the line. 3 6 5 2 7 4 8 1 2. 5 4. 5 2. 5 6. 5 3. 5 7 3 D

Algebra 1 Acknowledgment: The Reporting Category Practice Items in this presentation have been compiled and/or modified from various free internet sources. Some of these web sources are listed below: JMAP M 2 Mid-Module Assessment Task – Engage. NY M 2 End-of-Module Assessment Task – Engage. NY Rochester City School District https: //www. acpsd. net/cms/lib/SC 02209457/Centricity/Domain/2344/Foundations%20 Final%20 Exam%20 Study%20 Guide%202018. pdf https: //whitefish. eupschools. org/cms/lib/MI 17000152/Centricity/Domain/7/Stat%20 Review. pdf http: //awtreyms. blogs. com/clody/files/hw_measures_of_central_tendency_and_variation. doc http: //www. semo. edu/pdf/Math_Elementary_Data_Analysis. pdf http: //www. westbrowardhigh. org/ourpages/auto/2017/4/25/34351262/EOC%20 Review%20 Statistics. pdf