Rigorous Curriculum Design Authentic Performance Tasks


 Sabrina Burns
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1 Rigorous Curriculum Design Authentic Performance Tasks 1 of 14 Subject Grade/Course Unit of Study Duration of Unit Math 8 th Grade/ Math Unit 6 Scatter plots and statistics 34 Weeks Engaging Scenario Directions: Incorporate the five elements of effective scenarios: current situation; student challenge; student role; intended audience; product or performance. S Comparing Movie Opening Weekend amount to total movie lifetime gross. C Create a Scatter Plot of recent opening movies R You are a movie critic and analyze total gross on opening weekends. A You need to inform an evaluation panel P Scatter Plot presentation You are a movie critic. You have a 5 minute segment to present on the Today Show on movie opening weekend gross income to measure the monies eventual success. You will need t from o investigate and gather data to describe the gross amount movies have earned on opening weekend and gross amount they earned since they came out. You will construct your findings in a scatter plot form. Priority Standards or Learning Outcomes 8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negatives association, linear association, and nonlinear association.
2 2 of 14 Supporting Standards or Supporting Outcomes Statistics and Probability 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.SP.4 4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Expressions and Equations 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed. 8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. 3 8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Interdisciplinary Connections  Technology  English
3 3 of 14 Unwrapped Concepts (students need to know) Unwrapped Skills (students need to be able to do) DOK Levels Construct 8.SP.1 Interpret 8.SP.1 Scatter plots for bivariate measurement data 8.SP.1 2 Investigate 8.SP.1 Describe 8.SP.1 Patterns of association between two quantities 8.SP.1 Patters of association between two quantities 8.SP.1 Clustering Outliers Correlation Linear/nonlinear association 8.SP Unit Vocabulary Terms Unwrapped Priority Standards Concepts Supporting Standards Concepts and Other UnitSpecific Terms Scatter Plot Outliers Correlation Association Data Bivariate Data Clustering Frequency Linear Equation Trend Line TwoWay Table Relative Frequency Categorical Data Line of Best Fit Slope Linear/Nonlinear Association
4 Performance Task Synopses Directions: 1) Brainstorm three or four possible performance tasks. Refer to Sample Roles and Products for ideas. 2) Write a synopsis for each selected task and list the tasks in a learning progressions sequence. 4 of 14 Task 1: Construct and analyze a scatter plot to show a movie s opening gross income to measure the movie s eventual success. Task 2: Using the collected data, students will answer follow up questions about their findings. Draw and analyze the trend line on final movie gross amount. Task 3: Pick 10 recent movies, investigate, analyze, and contrast a new scatter plot for the total final gross amount the movies made on opening week and interpret and describe the top 3 movies eventual success to present to the today show. Performance Task # 1 In Detail Directions: 1) Copy the unwrapped Priority Standards skills, related concepts, and matching Bloom levels specific to this task. 2) Copy any additional concepts and skills from supporting standards and unit vocabulary terms specific to this task. 3) Describe the task in full detail. Check that the task directly reflects the level of rigor for each targeted skill and related concept(s). S: Which standard(s) (priority/supporting) will the task address? 8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negatives association, linear association, and nonlinear association. 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Q: What essential Question(s) and corresponding Big Idea(s) will this task target? How does the number of tweets relate to English grade? 8.SP.1 U: Which unwrapped specific concepts and skills will this task target? 8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negatives association, linear association, and nonlinear association.
5 5 of 14 A: How will the students apply the concepts and skills? What will they do and/or produce? Students will investigate and gather data to interpret and describe the total gross amount movies have earned on opening weekends, and final gross amount. Students will complete a table, and construct a scatter plot with their findings. R: What resources, instruction, and information will students need in order to complete the task? Students will need to have instruction to introduce the task and preview what is expected of them. Students will need access to a computer in order to research the different movies. E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills the standard(s)? Students will create a finished product listing their movie findings in scatter plot form. The evidence of learning will be the finished product and correctly answered follow up questions. D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Research will be available in simplified form in order accommodate all learning needs. Students will be strategically grouped, with different amounts of teacher instruction provided to each group, depending on student learning needs. Also, follow up questions will be leveled in order to accommodate struggling learners, while also providing additional challenge for advanced learners. Task 1 Full Description: In opening weekends, a movie s opening gross income is often quoted as a way of measuring the movie s eventual success. Can you predict a movie s total gross income from its opening weekend count? In this lesson students will investigate if there is a pattern between the opening weekend data and the final gross total income of the movie. Students will construct graphs and tables in order to interpret predictions and patterns on opening weekend and final gross total income. Students will also answer followup questions to further their understanding and make predictions. Here s data on 14 movies that you might have seen. I ve included the gross amount that they earned on their opening weekend and the gross amount that they have earned since they came out. I also included The Avengers and WreckIt Ralph, but did not give its longterm gross income.
6 6 of 14 Title Opening Gross Total Gross Opening Date Harry Potter and the Deathly Hallows Part 2 $169,189,427 $381,011,219 7/15/2011 The Hunger Games $152,535,747 $396,022,168 3/23/2012 SpiderMan 3 $151,116,516 $336,530,303 5/4/2007 The Twilight Saga: New Moon $142,839,137 $296,623,634 11/20/2009 The Twilight Saga: Breaking Dawn Part 1 $138,122,261 $281,287,133 11/18/2011 Pirates of the Caribbean: Dead Man's Chest $135,634,554 $423,315,812 7/7/2006 Harry Potter and the Deathly Hallows Part 1 $125,017,372 $295,983,305 11/19/2010 Dr. Seuss' The Lorax $70,217,070 $177,412,055 3/2/2012 The Vow $41,202,458 $122,776,350 2/10/2012 Spaceballs $6,613,837 $38,119,483 6/26/1987 Fahrenheit 9/11 $23,920,637 $119,114,517 6/25/2004 The Descendants $23,920,637 $171,481,108 2/9/2011 Marvel s The Avengers $207,438,708 4/4/2012 WreckIt Ralph $49, 038,712 11/2/2012 Using the data collected, you will determine whether there is a correlation between the Opening Gross and the Total Gross incomes for movies. 1. On the next page, use the grid to create a scatter plot. The horizontal axis will represent the Opening weekend income of each film. The vertical axis will be the Final gross income of the movie. Plot the data from above on the next page s grid. If you have gathered additional movie data, be sure to plot it as well.
7 (in millions) 8.MATH.APT.UNIT 6 7 of 14 (in millions) 2. Is the relationship between Opening weekend income and the film s final income a linear association or something else? Describe the relationship between the two variables. 3. Make a prediction, based on the correlation, for what you think The Avengers and WreckIT Ralph will earn for their Lifetime Gross. Justify your prediction. 4. Given the point (40, 120) interpret its meaning within the context of this graph.
8 8 of 14 Performance Task # 1 Scoring Guide Advanced (Possible 4) Demonstrates knowledge of standard(s) being assessed with no errors. Makes connections to other areas of school or life Provides example(s) as part of explanation 3 Proficient Students will correctly construct a scatter plot. Students correctly describe association between the two variables. Students will make a reasonable prediction. Demonstrate knowledge of standard(s) being assessed. (minimal to no errors, ie. minor computation errors) Correctly justifies their answers when required. 2  Progressing Demonstrate partial knowledge of standard(s) being assessed with justification. 1  Beginning Demonstrate minimal knowledge of standard(s) being assessed. 0  No response or shows no knowledge or relation to the standard being assessed. Comments: Peer Evaluation (optional): SelfEvaluation: Teacher s Evaluation: Comments regarding student s performance: Interdisciplinary Connections and Related Priority Standards Specific to Task #1 Technology English 21 st Century Learning Skills Specific to Task #1 Check all those that apply for each task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other
9 9 of 14 Performance Task # 2 In Detail Directions: 1) Copy the unwrapped Priority Standards skills, related concepts, and matching Bloom levels specific to this task. 2) Copy any additional concepts and skills from supporting standards and unit vocabulary terms specific to this task. 3) Describe the task in full detail. Check that the task directly reflects the level of rigor for each targeted skill and related concept(s). S: Which standard(s) (priority/supporting) will the task address? 8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negatives association, linear association, and nonlinear association. 8.SP.4 4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Q: What essential Question(s) and corresponding Big Idea(s) will this task target? How does the number of tweets relate to English grade? 8.SP.1 U: Which unwrapped specific concepts and skills will this task target? 8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negatives association, linear association, and nonlinear association. A: How will the students apply the concepts and skills? What will they do and/or produce? Students will investigate and gather data to interpret and describe the total gross amount movies have earned on opening weekends, and final gross amount. Students will construct and predict a trend line based off of their scatter plot from task 1. R: What resources, instruction, and information will students need in order to complete the task? Students will need to have instruction to introduce the task and preview what is expected of them. Student will need their data from task 1. Students will need access to a computer in order to research the different movies.
10 10 of 14 E: What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills the standard(s)? Students will create a line of best fit using their scatter plot. Students will make reasonable predictions on certain movies earnings. The evidence of learning will be the finished product and correctly answered follow up questions. D: How can I differentiate the application and/or evidence to meet the varying needs of my students? Research will be available in simplified form in order accommodate all learning needs. Students will be strategically grouped, with different amounts of teacher instruction provided to each group, depending on student learning needs. Also, follow up questions will be leveled in order to accommodate struggling learners, while also providing additional challenge for advanced learners. Task 2 Full Description: Movie critics can influence the public on spending their money on certain movies. Trends can also guide a producer s decision in which genre of movies they want to invest their money on and produce. Which movie would you give 2 thumbs up to? Do you watch movies based on what the expert say about it? Now is your chance to see if you believe the trend. You will have to construct and interpret a trend line to describe the amount of money a movie will gross for any opening weekend total. Finally, you will need to answer followup questions about the data you have gathered and make predictions, and estimations based on the trend line. Use your scatter plot from task 1 to answer the following questions. 1. Draw a line of best fit on your graph. Describe below how you decided where to draw the line. 2. Now, using the line of best fit, make new predictions for The Avengers and Wreck It Ralph. Collect the actual data from the website. Which prediction was more accurate, the prediction from the correlation or using the line of best fit?.
11 11 of Based on the data how much would you expect movies to make in gross that had opening weekends of $60 million, $80 million, $100 million, and $180 million? How did you determine your estimates? $60 $80 $100 $ Using your predictions from #3, construct a new scatterplot. (Make sure you label EVERYTHING!!) The movie, Man of Steel, grossed $116,619,362 during its Opening Weekend. Using this scatterplot, make a prediction for the Lifetime Gross for this movie. Explain the method used to make the prediction. 5. Now go back and check the actual data for Man of Steel. You can get this data from the Internet website Describe how close your prediction was to the actual lifetime gross. Did it follow the association, or would it be considered an outlier?
12 12 of 14 Performance Task # 2 Scoring Guide Advanced (Possible 4) Demonstrates knowledge of standard(s) being assessed with no errors. Makes connections to other areas of school or life Provides example(s) as part of explanation 3 Proficient Students make a reasonable estimate on opening weekend gross. Student correctly constructs a trend line. Students correctly use their estimate to create a linear equation. Demonstrate knowledge of standard(s) being assessed. (minimal to no errors, ie. minor computation errors) Correctly justifies their answers when required. 2  Progressing Demonstrate partial knowledge of standard(s) being assessed with justification. 1  Beginning Demonstrate minimal knowledge of standard(s) being assessed. 0  No response or shows no knowledge or relation to the standard being assessed. Interdisciplinary Connections and Related Priority Standards Specific to Task #2 Technology Language Arts 21 st Century Learning Skills Specific to Task #2 Check all those that apply for each task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other
13 13 of 14 Performance Task # 3 In Detail Directions: 1) Copy the unwrapped Priority Standards skills, related concepts, and matching Bloom levels specific to this task. 2) Copy any additional concepts and skills from supporting standards and unit vocabulary terms specific to this task. 3) Describe the task in full detail. Check that the task directly reflects the level of rigor for each targeted skill and related concept(s). Optional. Pick 10 recent movies (within the past month), investigate the data from the website for opening weekend gross, then create and analyze a new scatterplot for the final gross amount the movies made on opening weekend. Make sure to interpret and describe the association Performance Task # 3 Scoring Guide Advanced (Possible 4) Demonstrates knowledge of standard(s) being assessed with no errors. Makes connections to other areas of school or life Provides example(s) as part of explanation 3 Proficient Students correctly create a table for the top 10 new movies. Students correctly construct a new scatter plot for the top new movies. Students correctly justify their answers using mathematical reasoning. Demonstrate knowledge of standard(s) being assessed. (minimal to no errors, ie. minor computation errors) Correctly justifies their answers when required. 2  Progressing Demonstrate partial knowledge of standard(s) being assessed with justification. 1  Beginning Demonstrate minimal knowledge of standard(s) being assessed. 0  No response or shows no knowledge or relation to the standard being assessed.
14 14 of 14 Interdisciplinary Connections and Related Priority Standards Specific to Task #3 Technology Language Arts 21 st Century Learning Skills Specific to Task #3 Check all those that apply for each task: Teamwork and Collaboration Initiative and Leadership Curiosity and Imagination Innovation and Creativity Critical thinking and Problem Solving Flexibility and Adaptability Effective Oral and Written Communication Accessing and Analyzing Information Other
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