Which+brand+should+I+buy?

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**Adapted From:** “Understanding Box Plots” in Garfield & Ben-Zvi (2008) **Reference**: Garfield, J. & Ben-Zvi, D. (2008) //Developing students’ statistical reasoning: Connecting research and teaching practice// (pp. 226-228). Dordrecht: Springer.
 * Which Brand Should I Buy? **

**CCSS-M Content Standards: 6. SP (1-5), 7.SP.3 and 7.SP.4** **CCSS-M Practices: 2, 3, 5, and 7**

**Task:** ***Note: This task requires some familiarity with //TinkerPlots.// Also, students will work in groups for this activity.**
 * 1) Students are seated in groups of 2-3 to foster collaboration and discussion during the activity. Teacher launches the activity by asking students, “Suppose you’re at the store, and you were in the mood for some raisins. There are two brands that offer the same size boxes, and they’re sold for prices that differ by only a nickel. You’re pretty hungry, so you want the box with the highest number of raisins, no matter the cost! Do you think it matters which box you choose? Do you expect that the boxes would have the same number of raisins in them?” Teacher facilitates a brief discussion with the students as they share their answers.
 * 2) Teacher passes out one box of raisins to each student and asks them to count the number of raisins they have in their box. Half of the class receives Brand A and half receives Brand B. Once every student has counted their raisins, the teacher writes the numbers of raisins up on the board in two columns-one for Brand A and one for Brand B.
 * 3) Teacher asks the students to create dot plots of the data on paper for the two competing brands and discuss in their groups what they observe about the data. Teacher asks, “What information can you gather from these plots about the two brands of raisins?” and conducts a brief discussion with the class. Teacher asks the students if the dot plots give them a good way to compare the two sets of data.
 * 4) Teacher asks students to now create box plots of the two datasets in // TinkerPlots // and has students work in groups to talk about how they would compare the two sets. Discussions could include:
 * Comparing where “most” of the data are
 * Comparing where the “middle halves” are
 * Comparing the means and medians of the data
 * Comparing the different parts of the boxplots and interpret what the values mean in the context of their investigation
 * 1) Teacher brings class back together as a whole group and has groups share what they discussed. A discussion follows on how boxplots help compare by showing differences in the center and spread of the numbers of raisins per box for each brand. They discuss possibilities of why there may be a difference in number of raisins per box between and among brands and whether their samples of data helps them make inferences about all boxes of raisins by the brands they sampled.

**PD Agenda:** **Length of session:** //2 hours// **Materials needed**: Computer with //TinkerPlots//; Two brands of small boxes of raisins ***Note: Facilitators will model how the lesson should be carried out in the classroom with pedagogical discussions interwoven throughout. All time lengths listed below following each component of the activity are estimates and not strict time allotments.** > Discussions could include: > Questions might include:
 * 1) Participants (teachers) are seated in groups of 2-3 to encourage discussion and collaboration.
 * 2) Facilitators conduct a brief tutorial on //Tinkerplots// with participants to help them become familiar with the graphical representations of data available on the software. This will be done with an abstract set of data (out of context, so that the focus is on learning the technology). (20 minutes)
 * 3) Once participants feel comfortable with the software, the facilitators conduct the class activity as the teachers would with their students. Facilitators launch the activity by asking the participants, “Suppose you’re at the store, and you were in the mood for some raisins. There are two brands that offer the same size boxes, and they’re sold for prices that differ by only a nickel. You’re pretty hungry, so you want the box with the highest number of raisins, no matter the cost! Do you think it matters which box you choose? Do you expect that the boxes would have the same number of raisins in them?” Participants share their answers. (5 minutes)
 * 4) Each participant then receives a box of raisins and counts the number of raisins are in it. Half of the participants receive Brand A and half receives Brand B. Once every participant has counted their raisins, the facilitators write the numbers of raisins up on the board in two columns-one for Brand A and one for Brand B. (10 minutes)
 * 5) Facilitators ask the participants to create dot plots of the data on paper for the two competing brands and discuss in their groups what they observe about the data. (15 minutes)
 * 6) Facilitators conduct a class discussion with guiding questions including:
 * What information can you gather from these plots about the two brands of raisins?
 * What information do the dot plots give you?
 * Do the dot plots provide a useful way to compare the two sets of data? If so, why? If not, why not?
 * 1) Participants then create box plots of the two data sets in // TinkerPlots // and work in groups to talk about how they would compare the two sets using this graphical display. (20 minutes)
 * Comparing where “most” of the data are
 * Comparing where the “middle halves” are
 * Comparing the means and medians of the data
 * Comparing the different parts of the box plots and interpret what the values mean in the context of their investigation
 * 1) As participants are working, the facilitators circulate to monitor and select participant strategies to highlight in the whole group discussion that will follow. Facilitators will also decide on an appropriate sequence for group presentations that will promote the goal of the lesson.
 * 2) A whole group discussion follows on how box plots help compare by showing differences in the center and spread of the numbers of raisins per box for each brand. They discuss possibilities of why there may be a difference in number of raisins per box between and among brands and whether their samples of data helps them make inferences about all boxes of raisins by the brands they sampled. As participants present, facilitators allow time for questions from other participants and facilitators for any needed clarifications. Facilitators should ensure the group fully communicates their approach and justifies their inference. If evidence is not presented nor questioned by others, the facilitators should guide the presenters to provide their justification. (30 minutes)
 * 3) After presentations, facilitators holds a discussion about the task. (20 minutes)
 * What did you like about the task? Not like?
 * What was challenging?
 * What did you think about the other approaches presented?
 * Would you modify this task for your classroom? If so, how? If not, why?
 * What do you anticipate your students to like about this task? Dislike?
 * Is the task engaging enough for students? Explain.
 * What are some problems that may arise during the implementation of this task?
 * What are some misconceptions students might have during this task?
 * What could you do to alleviate some of these problems/misconceptions without taking away from the discovery?

**Why the task would promote conceptual understanding of this topic and if it lays the foundation for other topics in statistics:** With this activity, students learn the importance of repeated samples and the inferences they can make based on the variation (or lack thereof) observed in their samples. With a focused comparison of two visual representations of data, students have an opportunity to discuss strengths and weaknesses of each representation. Through their explorations of their samples using technology, students also have the opportunity to pose and address questions related to measures of center, distribution and spread as they work to draw conclusions about the variation among and/or between different brands of the same foods. This lays a foundation for further study of those descriptive measures of data and how those measures help us make comparisons among data sets. It also provides a real-world context in which data can give us information that affects our decision-making.