Tinkerplots Lesson PDF

Exploring Multiple Representations of a Data Set Using Tinkerplots
Linde
Mathematical Goal
The long-term mathematical goals of the task are for students to reason abstractly and
quantitatively CCSS.MATH.PRACTICE.MP2 as well as construct viable arguments and
critique the reasoning of others CCSS.MATH.PRACTICE.MP3.
o They will achieve this by making predictions, evaluating a data set by justifying
their reasoning rooted in mathematical concepts pertaining to measures of
center mean, median, etc.
o Students will come to understand that different measures of center or attributes
in the data set can be used to justify a claim that they make. Incorporating these
different attributes may result in similar or different claims from their peers, but
it is the reasoning behind the claim that is what students will need in order to
attain reaching the mathematical goal.
o From the various representations that they can create within the realm of
TInkerplots, students will be able to formulate a claim and articulate it with their
peers and justify their reasoning using mathematical concepts like measures of
center and distribution.
o Common Core High School Statistics and Probability:
Interpreting Categorical and Quantitative Data S-ID
Summarize, represent, and interpret data on a single count or
measurement variable (S-ID.A)
Represent data with plots on the real number line (dot plots,
histograms, and box plots). (S-ID.A.1)
Use statistics appropriate to the shape of the data distribution to
compare center (median, mean) and spread (interquartile range,
standard deviation) of two or more different data sets. (S-ID.A.2)
Interpret differences in shape, center, and spread in the context of
the data sets, accounting for possible effects of extreme data
points (outliers). (S-ID.A.3)
Students will be provided the opportunity to engage with this task at a high level
because it will ask them to make predictions and justify their reasoning. The open-ended and
student centered exploration will enable them to go about different ways of answering the
guiding questions, and well as focus their attention to interpreting a data set within Tinkerplots
(US Students). Because most of the work will involve students manipulating data on Tinkerplots,
students will also use the technology as a reorganizer because without it, it would be difficult
or near impossible to arrive at the same goal. The open-endedness, and dynamic aspects will
show further on, but they also provide evidence as to why this will be a lesson where
technology is supporting students investigations in such a way that they may not reach the
same conclusions without it. Students will use their knowledge of mathematical concepts and
Tinkerplots to make conclusions based on various representations measures of center,
distribution, statistical calculations, etc.
Linde
Building on Prior Knowledge

Prior to this lesson, students will having familiarity with measures of center, statistical
calculations, and time spent in Tinkerplots. Because it is likely that students will already have
been exposed to mean and median, this lesson isnt focused on teaching them what they are,
but rather building on what they know about them and how they affect interpreting data sets.
In other words, it puts the measurements they are familiar with into context and will give them
a chance to determine when it is best to use them. Students will have had experience with
statistical measurements like IQR and standard deviation to help them reach the goal of being
able to interpret data using mathematical concepts that they are familiar with. I plan to do this
activity following a lesson pertaining to box plots and other measurements within Tinkerplots.
This will be somewhat of a tie-together for students to really ground their understanding in the
concepts that they have been working on previously. Without lowering the cognitive demand, I
may ask students to recall what they have been learning over the past week. Students will have
come to realize that there are many ways to reach the same conclusion, or sometimes similar
pathways lead to differing conclusions. Using various representations within Tinkerplots,
students will use their prior knowledge to go forth in this lesson. I think that because there are
many ways to go about the task, I do not want to curtail their thinking when it comes to
applying mathematical measures to the data set or direct them toward a particular way of
going about the investigation.
Task Setup
As students are coming into class, I will have them open their notes from the previous
week and review them as everyone is getting settled. To introduce the task, I will display the
follow paragraph on the projector for students to read,
Researchers have studied and debated the benefits and drawbacks of teens and parttime jobs for more than 2 decades. Many researchers, including those on government
panels like the National Commission on Youth, praise part-time work and say it
contributes to the transition from youth to adulthood. Other studies have found
significant negative consequences to students working over 20 hours a week. Source
This will be done to engage them in the data that they are about to see in Tinkerplots, but I
want them to have some background knowledge about where the information is coming
from. To tie it into math concepts, I will tell students that I want them to consider what we
have been discussing in class the past week as they are about to begin this investigation. I
will then tell them that I will pass out a worksheet and I want them to make a prediction
about the leading question at the top of their page. After they have made their prediction,
they can proceed with the investigation.
Linde
The Task
After the setup, students will continue with the worksheet provided and complete the
investigation based on the US Students data. The task itself connects to the mathematical goal
because students are using their prior knowledge of measures of center, box plots, and other
statistical measures to reason quantitatively to evaluate the data. I feel that this task requires
high level thinking because there really isnt a particular way to go about finding a solution.
Students have to use their prior knowledge and determine how they will answer the leading
question of the investigation to determine what the result will be. The open-endedness is a
main focus for the task because students have to be able to support their claim themselves. It
would be trivial if the data portrayed the mean and median significantly lower for students that
have jobs compared to those that do not. This requires students to utilize all the mathematical
resources that they have been familiarize themselves with to arrive at a conclusion.
Tinkerplots is the medium as to how students will arrive at this answer because it
provides them with a way to manipulate data and easily explore attributes that students may
consider to be a factor in their answer. This provides students with something much more than
an amplifier because the focus of the task would be centralized on creating the graphs as
opposed to interpreting them. Being able to plan the units of measurement on the graphs and
also construct box plots enables students to focus on what the data is actually telling them as
opposed to putting all their energy into constructing the graph in the first place. We spoke all
semester that math students have difficulty making connections between the calculations and
what they actually represent aside from an algorithm to find a value. Tinkerplots helps to
provide students to see these connections in a real data set.
(See Investigation with US Students Data worksheet)
Investigation with US Students Data

In this investigation, you will determine an answer to the following question based on the data.
Do students with jobs spend fewer hours per week doing homework?
*Make a Prediction and Explain Your Reasoning:
Open the US Students file in Tinkerplots.

Click on the attribute HomeWork from a data card ad drag it to the x-axis of the plot.
Use the various plot tools along with your investigation to explore attributes that may have an
effect on students school work.
1. Describe the distribution of the time students spend on homework each week.
2. Explore additional attributes to look at different dimensions pertaining to students homework

time. What attributes did you look at, and what conclusions can you draw from them?
3. Based on the data, what evidence did you find to confirm or reject your prediction? Explain
your reasoning.
Extension:
4. Using the various plot tools along with your investigation, do the students who spend more
time on homework tend to get better grades? Be sure to describe the mathematical concept
that you used to arrive at this conclusion.
Linde
Solving the Task

The following are hypothetical student responses for the worksheet and observations I made
along the way:
Student 1:
I notice that this student has constructed a box plot right away (it was the most recent think we
worked on in class), and he seems amused. I ask him what he is observing with the data and he
says, I wonder who spends 26 hours/week doing homework, thats a lot! I want him to make
sure that he is observing the mathematical concepts about the box plot so I press him to
articulate what he is noticing. He says that most students spend less than 10 hours doing
homework a week. I ask him why he thinks that is and he points to the boxes on the graph and
says because half is in here. I want to make sure he is really clear about this so I ask half of
what. He responds with half of the students homework time is here. I ask one more thing of
him before I move on, Consider the other 50 percent of the data, how does this have an effect
on the distribution.
Linde
Student 2:
I notice that this student has already made a dot plot of the homework data along the x-axis.
She also placed the mean and median measures on the graph. She tells me that it is interesting
that the two measures are so close together. I ask, Can you tell me why you think that is?
After some thinking, the students recalls the discussion we had in class earlier in the week
about balancing data like a scale. She says, They both almost balance! I respond with, Can
you tell me more about that? The students looks at the data again, and says,
Student 3:
As I make my way to the third student, his graph catches me eye. It appears that he has
dividers pulled up on his graph which is something that we had briefly touched on when
investigating what box plots are comprised of. I ask the student what he is noticing about the
distribution about homework, and he says that there are a lot at the end of the data. I proceed
to question why that is so, and how can he prove it to me. He says because this part (pointing
to the section representing the final fourth of the graph) is the biggest. I follow up with, can you
tell me what that means, and he says, that the shaded section is the largest section so it is the
most. I then ask the student to look at the data on the graph and tell me what he is seeing. He
Linde
says that there are the most points at 10 and them at 15. I further question him to think about
the data as an entire set. Because he sees that the fourth quartile is the largest spanning
section, he initially thought that it would be most common for students to do 10-26
hours/week doing homework. After looking at it for a while the student looks at me and says,
most of the data is over here (pointing to the left side of the graph). I ask him if he can tell me
how that relates to dividers. He thinks for a moment and then says, Oh! Its divided evenly! I
ask him what he means by that and he recalls that the quartiles are split evenly so a fourth of
the data is in each divider. I ask him how that relates why the fourth section is so large, the
student looks at his graph and says, it is more spread out, but they have the same number of
points in it as the others. I am convinced that he now understands where he was led astray and
tell him to write down his observations about the distribution.
As this student moves onto the second portion of the task, he clicks on the Job attribute and
tells me that there are less people with jobs than students with jobs. I ask him what that means
for the distribution, and he thinks for a while and begins to write something on his worksheet
as I move around to the other students.
Linde
Student 1
As I make my way back to this student, I observe that he is wrapping up with question
three and the following is displayed on his screen. From what the student has written on his
sheet, I do not feel the need to intervene with his exploration and let him continue on.
Linde
Student 2
Student 1:
This is the graph that I observed of this students response to the extension question.
Linde
Student 2
Student 3

*Make a Prediction and Explain Your Reasoning: I think that students with jobs spend fewer hours
doing homework each week because they are spending time working when they could be doing their
homework.

The IQR shows that half the students do their homework between 3 and 10 hours/week. The data is
mostly on the left because the tail is shorter for the first quartile. It seems like in general, students do no
more than 10 hours of homework/week. The mean and median are close together, so it is a good
measure to say that the average student does about 8 hours of homework each week.
I looked at job, and job hours in conjunction with homework. Even though the means are practicually
the same between having a job and not, the median of the students that do have a job is almost the
same as the mean whereas students that dont have a job have a much lower median. This means that
the weight of the students that do more than the average has more of a pull. I also looked at job hours
to see if that had an effect with people that do more or less hours of homework, but that really wasnt
telling. I would have thought that people with a job that spend less time doing homework have more
hours at their job, but this wasnt true.
your reasoning.
From the data, I would say that students with a job actually spend more time doing homework on
average compared to students without a job. This is because the data is more consistent with the mean
and median practically being the same, so it is well balanced. Also the IQR is about the same for the 2
box plots, so I would say that because 50 percent of people that have job do more homework than
those that do not have a job.
Extension:
From the box plots, I would conclude that students who spend more time doing homework, do not get
better grades. In fact, students in the C category seem to be the ones the spend the most time on
average because their median and mean is the highest. This could be because they have to work really
hard at school.

*Make a Prediction and Explain Your Reasoning: I do not think that students with jobs spend fewer
hours doing homework each week because I have a job and I still spend a lot of time doing homework
each week.

From looking at the graph, it appears that most students in the data set spend 10 hours/week doing
homework. I put the mean and median on the graph and they are 8.16 and 7.5. This makes sense
because there is a lot of data clumped together on the left side, but the mean is a little higher because
the bigger values have more of an effect.
I looked at job and gender to determine if that did anything to the distribution to the time that students
spend doing homework. It seems like boys that have a job spend less time doing homework, whereas
the balance is pretty even for people that do not have a job. The most people with a job spend 10 hours
a week doing homework, whereas the most for people without a job spend 3 hours.
your reasoning.
Based on the graphs, I would say that students spend about the same amount of time doing homework
each week because the range and IQR are basically the same for both students with and without jobs.
Extension:
4. Using the various plot tools along with your investigation, do the students who do spend more
People with jobs are all over the graph when it comes to grades and time spend on homework
However, I noticed that people that dont have a job are in the A/B-B-B/C categories. Even though the
time spend on homework isnt very telling. I think that there might be a correlation between grades and
not having a job.

*Make a Prediction and Explain Your Reasoning: I dont think that students spend that much less time
doing homework as students that dont have jobs. This is because I have a job and I still spend enough
time to complete my homework for school. I think that most other students with jobs do the same.

The data is clumped together at the beginning and more spread out at the end. It seems like most
students do 10 hours of homework/week. But almost a good range of students do anywhere from 3 10
hours of homework/week because that it the IQR of the data.
I clicked on the job attribute and noticed that there were more students with jobs in the lower half of
the data as opposed to the upper half. I think this means that students with jobs, spend less than the
average student spends on homework. Even though the highest point is with a student with a job, I still
think this because there are 16 students with a job in the lower half, and 10 in the upper half.
your reasoning.
Students with jobs can spend less than or more than the average student. I would say that there are a
few more students with jobs that spend less than the average student spends on homework, so I would
say that students with a job do spend less time on homework if they have a job. I looked at the
distribution and the mean to help me.
Extension:
Students that spend a lot of time doing homework, dont really get the best grades. There is one
students that spends 26 hours a week doing homework and is in the A/B range, but most students that
get A/Bs do 2-10 hours/week of homework. I would say that because most of the data for all of the
students is positions heavily to the left, that doing less homework might mean that you get better
grades.
Linde
Expectations for Students

I would like this to be an individual investigation for this lesson. While students are exploring, I
want them to take notes on the worksheet provided about what attributes and mathematical concepts
they are incorporating into their claims. I would like students to partner up and share their findings with
each other. By doing so, this will build some confidence in the students reasoning when sharing the
evidence they discovered to support their claim. If they fault, their peer can help them to consider other
implications or press for further understanding. This will allow the extension to the next class for
students to engage with the task and to consider how their peers approached the same data.
I will evaluate the students understanding during the task by walking around and
observing what they are doing with the data. I will also collect their worksheets as a formative
assessment to determine what types of nuances students may have discovered during the
investigation and how it compared to their initial prediction. The discussion we will have the
next day will also help me determine where the students are at in terms of understanding
distribution of the data and evaluating claims. Understanding distribution will involve the
implications that the amount of data, location of the mean and median, box plot calculations,
and the attributes that the students used to arrive at their conclusions will all be factors in this
assessment. I want students be able to evaluate a data set, and clearly articulate why they
chose a particular side that is rooted in mathematical concepts. If I feel as though students are
not looking at enough information, I may push them to consider a component that they hadnt
touched on.
Extending to the Next Day

The next class students will bring their findings to class with them and we will discuss
whether or not students think that it is a good idea for high school students to have jobs while
in school. They will be asked to justify their reasoning based on mathematical concepts relating
to measures of center, and statistical calculations. Approximately 3 students will be asked to
display what they did in their investigation on the overhead and explain how they arrived at
their conclusion based on reasoning quantitatively (this may also be a chance to discuss
qualitative attributes as well). Their peers on the opposing side will construct arguments and
critique the work of the students. Together they will attain the second part of the mathematical
goal. I will be sure that students make explicit what mathematical concepts they used in this
endeavor. For example, explain why they chose to evaluate the data based on mean as
opposed to median. Overall, I want students to see that they can reach the same conclusion by
different mathematical techniques and sometimes answers arent straight forward, but it is
important to evaluate data and decipher where you stand based on concrete evidence.

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Exploring Multiple Representations of a Data Set Using Tinkerplots

Building on Prior Knowledge

Investigation with US Students Data

Open the US Students file in Tinkerplots.

2. Explore additional attributes to look at different dimensions pertaining to students homework

Solving the Task

Investigation with US Students Data

Open the US Students file in Tinkerplots.

Investigation with US Students Data

Open the US Students file in Tinkerplots.

Investigation with US Students Data

Open the US Students file in Tinkerplots.

Expectations for Students

Extending to the Next Day

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