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# Performance Task: Analyzing the Powerball Lottery

Lesson 7 of 7

## Objective: SWBAT use what they've learned throughout the semester to examine the Powerball lottery.

In the previous lesson, I described the kind of work periods that run for a day or two at the end the semester. Now it's time to assess students on what they've learned and can do. At the end of each unit, I try to give students some kind of performance task, and some sort of traditional-looking exam. Because it's the end of the semester, I'm assessing a set of learning targets from all units throughout the semester.

In this lesson, I share the performance task half of what this end-of-semester assessment looks like. The other half will take the form of a standardized test, and its exact form depends on the students I have in each section I'm teaching. If most students need to pass the Algebra 1 Regents exam (our state test in New York), I'll simply use a practice exam. Otherwise, I'll use Problem Attic to create an exam made up of questions related to this course.

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Here is today's assessment task: Analyzing the Powerball Lottery. Students arrive knowing to expect this assessment today, so as they arrive, I provide a copy of the assignment, and I tell them that calculators, computers, paper, and colored pencils are available. From there, it's a work period, and students will accomplish as much as they can. I expect students to be able to complete this task in 75 minutes. It's a lot of work, but a fair amount based on my expectations of what they've learned so far this year. That said, if any students want more time, I'll allow anyone who asks to come after school to finish up. There is also an extension task that I describe at the end of this lesson. There probably won't be time to fit the extension in while finishing everything else, so it's most likely that that would happen outside of class as well.

This task covers Student Learning Targets from throughout the semester. It also requires that students use the research skills I've tried to help them cultivate this semester - reading data from web sites, and using the tools they've studied to make sense of what they see.

I hope that the task is self-explanatory. It's split into five parts, and on the assignment, I identify for students the learning targets that will be assessed. Solutions to each part are used in the parts that follow. As students work, I move actively around the room, for two reasons. The first is that I want students to know that I'm available to answer any clarifying questions they have about the work. The other is that part of the way I assess this task is by watching students work and listening to their conversation. I make sure to have my clipboard handy to take notes on who is able to make sense of the task, and who is most helpful to their colleagues.

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Above, I note that each part of this assignment is an assessment of different Student Learning Targets (SLTs) from throughout the semester. These SLTs are posted around the room and are on student progress reports, so at this point everyone should be familiar with the targets. Once students are working, I circulate to provide this rubric, so everyone knows how they'll be assessed.

Missing from this rubric is a detailed description of how to achieve each specific grade. I go back and forth about this: sometimes it's useful to tell students how to get a 2, 3, or 4 on an assignment, but other times, the result of trying to do so results in having so many words on the page that it's hard for students to make sense of what they're supposed to do. So this is an example of a minimal rubric that informs students "How to Demonstrate Mastery" of each SLT, and provides space for me to give feedback specific to the work I receive from each student.

In general, the fewer SLTs I'm assessing on an assignment, the more detail I'll provide on how to earn specific grades on each one. With seven different SLTs here, I've opted to make it more of a checklist. Additionally, "empty" rubrics like this serve another purpose in my teaching practice. The first time I give an assignment, I'm not always certain about the levels of work I'll get from kids or the kinds of mistakes they might make, so it's hard to know exactly what to say on a rubric. After grading an assignment a few times however, common errors start to emerge, and in future years, I'm able to revise the rubric to include more detail, based on student work I've seen in the past.

For now, it's pretty binary. I look at each component, and try to decide whether or not a student knows what they're doing. As I've mentioned above, I also talk to kids as they work, which informs my grading. I ask questions to help me figure out what students know, and I keep track of my observations. When it is time to grade, my observations and student work will both factor in.

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There are two optional extensions that are not included on the original handout. This is because I want the base-level of work to be manageable within one class period, and also for the simple practical reason that I like to keep my handouts to one double-sided sheet of paper as often as possible.

Some students will want to dig a little deeper into their study of how lotteries work, and others have started doing a higher level of work than earlier in the semester, and they'll want to improve their grades on other SLTs.

Students may want to improve their grades on some the Unit 2 Learning Targets:

- 2.3: I can represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- 2.4: I can distinguish between correlation and causation.
- 2.5: I can fit a linear function to data that suggests a linear association.
- 2.6: I can interpret the slope and the intercept of a linear model in the context of the data.

For these students, here is another data set: http://www.lottoreport.com/ticketcomparison14.htm. This data shows the number of lottery tickets sold by date, along with the jackpot for that date. Students can create a scatter plot to compare these two variables, create a regression model of their choice, and interpret their model in context. Then, they can have a conversation with me in which they identify the correlation between these two variables and identify whether this represents a causal relationship or not.

For a more open-ended extension than that, I refer students I refer students to this article: "Here's When Math Says You Should Start to Care About Powerball". This is more for kids who demonstrate an interest in the material beyond their grades. It's interesting from both a mathematical perspective and a more sociological one (see the comments), and makes a great conversation starter for students who want to go that route.

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- UNIT 1: Statistics: Data in One Variable
- UNIT 2: Statistics: Bivariate Data
- UNIT 3: Statistics: Modeling With Exponential Functions
- UNIT 4: Statistics: Using Probability to Make Decisions
- UNIT 5: Trigonometry: Triangles
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- UNIT 7: Trigonometry: The Unit Circle
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- LESSON 1: Capture-Recapture and an Intro to Probability
- LESSON 2: Flipping Coins and Exponential Decay
- LESSON 3: Counting Problems, Combinations and Permutations
- LESSON 4: Solving Probability Problems and Learning Target Check In
- LESSON 5: Probability Distributions and Expected Value
- LESSON 6: Differentiated Days: Finishing Up The Semester or Extending Your Work
- LESSON 7: Performance Task: Analyzing the Powerball Lottery