Are+you+a+sleeping+sheep+or+a+turbo-charged+cheetah?

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**Are you a sleeping sheep or a turbo-charged cheetah?** **Adapted From:** “Sleeping Sheep or Turbo-Charged Cheetah” from //New Zealand Curriculum Guides: Senior Secondary// **Reference:** Teaching and learning activities. In // New Zealand Curriculum Guides: Senior Secondary. // Retrieved September 24, 2012, from @http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/Teaching-and-learning-activities.

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

**Task:** ***Note: This task requires some familiarity with //TinkerPlots.// Also, students will work in partners for this activity.** > (May have to refresh page to get applet to work.) This interactive activity measures reaction times for how quickly the player tranquilizes the sheep as they leave the pen. Details on how the game works are described in the.
 * 1) Teacher sets up the activity by asking students, “Are you a sleeping sheep or a turbo-charged cheetah?”
 * 2) Teacher facilitates discussion about reaction time.
 * 3) Teacher then explains that "today we are going to see who has a faster reaction time, you or your partner."
 * 4) Teacher introduces students to the Sheep applet found at: @http://www.bbc.co.uk/science/humanbody/sleep/sheep/reaction_version5.swf
 * 1) Teacher allows students time to investigate the activity and further discuss how the experiment might work. Other ideas include giving students extended time to explore the activity and come up with the plan.
 * 2) Once students have had a chance to explore the activity and generate some ideas on how to collect reaction times, teacher brings the class back together for a discussion.
 * 3) Teacher discusses plans generated by various pairs of students and decides on a class plan of how reaction times will be measured.
 * 4) After the class has decided how they will collect the data, students should individually collect the correct amount of data points (as decided in class).
 * 5) Once data has been collected, teacher has students enter their data and their partner’s data into //TinkerPlots// and explore how they can decide who has the faster reaction time. Each pair of students should be working with just one computer.
 * 6) The goal here is for students to make an informal inference while comparing two data sets by reasoning through who they think has the faster reaction time and justifying their reasoning using what they have found in //TinkerPlots//.
 * 7) Once students have generated inferences, pull the class back together to share findings.

**PD Agenda:** **Length of session:** 2.5 hours **Materials needed:** Computer with Internet access and //TinkerPlots,// and the ***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. ** > Some other possible questions for opening discussion: > (May have to refresh page to get applet to work.) This interactive activity measures reaction times for how quickly the player tranquilizes the sheep as they leave the pen. Details on how the game works are described in the. (5 minutes) > Things students should consider include: > Important questions to answer together are: > Questions might include:
 * 1) Participants (teachers) are seated in groups of 4 to encourage discussion and collaboration and to easily pair up for this activity.
 * 2) (If necessary, depending on level of participants and place in the PD) 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). (25 minutes)
 * 3) Facilitators set up activity by asking participants, “Are you a sleeping sheep or a turbo-charged cheetah?”
 * 4) Facilitators tell participants that this activity will be about reaction times and asks them if there are any opening discussion questions they may ask their students. For example, you might ask: “What is a reaction?” (10 minutes)
 * What types of things do we react to?
 * What would you consider reaction time?
 * How could you measure reaction time?
 * Why might fast reaction times be important?
 * 1) Facilitators explain that "today we are going to see who has a faster reaction time, you or your partner."
 * 2) Facilitators introduce participants to the Sheep applet found at: http://www.bbc.co.uk/science/humanbody/sleep/sheep/reaction_version5.swf
 * 1) Facilitator allow participants time to investigate the activity and further discuss how the experiment might work. Other ideas include giving participants extended time to explore the activity and come up with the plan. (20 minutes)
 * 2) After the participants have had a chance to explore the activity, facilitators have participants generate questions students should consider before collecting data. (15 minutes)
 * How they will measure reaction time – use the sheep reaction time activity.
 * Will they allow a practice run?
 * How will they deal with penalty shots?
 * How do we know everyone has done the same thing during our trial period? //In trialing this task, some students just ignored sets of data where they had scored 3.0 penalty times, meaning they shot the tranquilizer when there wasn’t a sheep running. This meant that it took a little longer but more importantly the data then wasn’t reliable as not everyone had performed under the same conditions.//
 * 1) Once participants have had a chance to explore the activity and generate some ideas on how to collect reaction times, facilitators bring everyone back together. Group decides on a class plan of how reaction times will be measured. Facilitators have participants anticipate questions that might be important when deciding on how to collect the appropriate data. (15 minutes)
 * Will we allow a practice run?
 * How will we deal with penalty shots? Will we ignore them? What happens to the average if we include them?
 * Will we use the time to tranquilize each sheep or the average time of each set of five?
 * How many pieces of data will we collect?
 * Is it important to keep the data in order? Why or why not?
 * 1) A suggested plan might be to ignore penatly shots and only take the time to tranquilize each sheep. Average time of each set of 5 should not be used because if there is a penalty shot, the average will be skewed. Rather, run the activity until you have collected 30 pieces of data. (15 minutes to collect data as decided)
 * 2) Once data has been collected, facilitators have participants enter their data and their partner’s data into //TinkerPlots// and explore how they can decide who has the faster reaction time. Each pair of participants should be working with just one computer. (30 minutes)
 * 3) The goal here is for participants to make an informal inference while comparing two data sets by reasoning through who they think has the faster reaction time and justifying their reasoning using what they’ve found in //TinkerPlots//. Some possible explorations are listed below.
 * 4) As participants are working, facilitators circulate to monitor and select participant strategies to highlight. Facilitators will also decide on an appropriate sequence for the presentations that will promote the goal of the lesson. For example, the facilitators might select a pair who fully separated the data to present first, then a pair who used bins, then a pair who used divider lines, then a pair who looked at means and or medians, then a pair who used box and whisker plots, and finally a pair who used box and whisker plots with measures of center, for example. The sequence will vary depending on the approaches created by the participants.
 * 5) Once participants have finished generating inferences, facilitators pull everyone back together to share findings. (25 minutes)
 * 6) As participants present, facilitators allow time for questions from other participants for any needed clarifications. Facilitators should ensure each pair fully communicates their approach and justifies their inference. If evidence is not presented nor questioned by others, facilitators should ask something like, “How did you justify that participant A had a faster reaction time than participant B?”
 * 7) After presentations, facilitators hold 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 would your students 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?
 * What sort of things could you reflect on as a teacher for this activity? As a student?
 * What are possible extensions of this task? (Ideas: Other reaction activities: @http://www.serendip.brynmawr.edu/bb/reaction/reaction.html Time series investigation- have you improved over time? Forming conjectures about what the average time is to be considered a bobbing bobcat, turbo-charged cheetah, etc.; Comparison across genders- use averages of each student- very useful if you don’t have the same number of boys and girls in the class- could bring up discussion of how to approach situations when you have samples of different sizes.)
 * What concept could this task lead into investigating next?
 * It is important to note at some point during this conversation that before implementing these types of tasks, teachers need to feel comfortable not only with the math behind the task, but also with the technology. Multiple approaches are possible- some that may be correct, some incorrect and some more efficient than others. It is the job of the teacher to be prepared to not only answer questions, but redirect if necessary.

**Why the task would promote conceptual understanding of this topic and if it lays the foundation for other topics in statistics:** This task promotes understanding of informal inference by having students compare two real data sets and develop data-based arguments to support their reasoning. The use of technology in this task not only enhances the interest level of the task, but also encourages the students to approach the data in a variety of ways. Finally, this task lays the foundation for considering informal inferences on data sets of different sizes, as suggested in the extension tasks, and also promotes a better understanding of formal inference later by having students learn to consider the context when making inferences about the population at hand.

From this set of data:

A fully separated plot

Bins with counts

Bins with percentages

Fully separated with mean and/or median

Fully separated with divider lines

Box and Whisker Plot

Box and Whisker Plot with mean and/or median

The above is just for one student’s set of data. Let’s say the students decide to compare box and whisker plots. Their discussion may generate the following:

Student A’s Box and Whisker Plot with median

Student B’s Box and Whisker Plot with median

Student A: “It looks like my median reaction time is 0.277 and yours is 0.284. So, your median reaction time is higher than mine.”

Student B: “Yes, that’s right. And the middle 50% of your data falls between 0.240 and 0.30, while mine falls between 0.280 and 0.340. So it looks like I have a faster reaction time than you overall.”

Student A: “I think you’re right!”

*These are a few of the many examples participants may generate from their exploration. As the PD leader, you must be familiar with as many as possible and anticipate what they might come up with. This requires the PD leader to have a full understanding of the math behind the task and how to arrive at the goal: to get students to visually compare two sets of data and make a justified inference on who has the faster reaction time.