Lesson 8: Tangible Plots
Lesson 8: Tangible Plots [The Data Cycle: Analyze Data]
Objective:
Students will learn how distributions help us organize and visualize data values, and that the shapes of the distributions give us information about the variability of the data.
Materials:

Computer and projector for Campaign Monitoring

Video: Value of Data Visualization found at:
https://www.youtube.com/watch?v=xekEXM0Vonc 
Nutrition facts labels or pictures (collected previously by students)

Food Habits Data Collection handout (from lesson 6, LMR_1.8_Food Habits Data Collection)

3 pieces of tape per student

Poster paper

Dot stickers or sticky notes

Tangible Plot handout (LMR_1.9_Tangible Plot)
Vocabulary:
xaxis, yaxis, visualization, range, minimum, maximum, frequency, distribution, typical, symmetric, range, data points, dotplot
Essential Concepts:
Essential Concepts:
Distributions organize data for us by telling us (a) which values of a variable were observed, and (b) how many times the values were observed (their frequency).
Lesson:

Food Habits Campaign Data Collection Monitoring:

Display the IDS Campaign Monitoring Tool, found at https://tools.idsucla.org
Click on Campaign Monitor and sign in. 
Inform students that you will be monitoring their data collection. This is a good opportunity for teachers to remind students that if their data are not shared, they cannot be used in analysis.

See User List and sort by Total. Ask: Who has collected the most data so far?

Click on the pie chart. Ask: How many active users are there? How many inactive users are there?

See Total Responses. How many responses have been submitted?

Using TPS, ask students to think about what can they do to increase their data collection.



Inform students that today they will be learning how to visualize their data.

Show the Value of Data Visualization video at https://www.youtube.com/watch?v=xekEXM0Vonc, which describes the importance of graphical representations of data. As they watch the video, students should respond to the following in their DS journals:

What is data visualization?

List one example of how visualization can be used to increase data comprehension.


Have a whole class discussion regarding the video’s last statement: “Your message is only as good as your ability to share it.” Ask students:

What does this statement mean?

What makes a good message in terms of data and visualizations?


Have students take out their nutrition facts labels or pictures, and also their Food Habits Data Collection handout (from lesson 6).

On poster paper, make the first quadrant of a coordinate plane. Leave the labels for the xaxis and yaxis blank for now (see step 10).

Distribute 3 pieces of tape to each student. Make sure they fold each piece of tape to make two sticky sides. Have each student tape one sticky side to the back of each label and ask them to have the labels ready to tape onto the poster paper.

As a class, ask students to select 2 numerical variables and 1 categorical variable from the Food Habits Data Collection handout whose data they would like to see in a visualization, which is a picture of the data. For example, students may vote to see a visualization of the following numerical variables: calories per serving, total fat per serving; categorical variable: salty_sweet

Once students select the variables, inform them that they will be creating a plot with the nutrition facts labels for each of the variables they selected.

Create a bargraph of the categorical variable chosen by the students. Begin by showing students how to clearly label the xaxis with the categories. For instance, if salty_sweet is the variable, ask students to identify the categories for that variable. Then mark the yaxis with the label frequency, which simply means the number of times an outcome occurs. Do not put tickmarks on the yaxis. The frequency will be measured by the number of labels plotted.

Have students come up and place their nutrition fact label above the category that describes their snack. Have students stack their nutrition label so that is easy to calculate the frequency. Once all the labels have been placed, create bars with the appropriate height (frequency) for each category. Make sure to leave spaces between the bars, and that bars are the same width.

Ask students to respond to the following questions in their DS journals:

How many data points does this distribution have? Why?

What information is this visualization telling us about [insert categorical variable name] in the snacks we consume?


Use another piece of poster paper to create a distribution for the first numerical variable chosen by the students.

Create a dotplot of the first numerical variable chosen by the students. Begin by showing students how to clearly label the xaxis. For instance, if calories per serving is the variable, ask students for the range of values for calories per serving and determine the minimum and maximum values for the data set. Clearly label the xaxis with adequate intervals and the variable’s name. Then mark the yaxis with the label frequency, which simply means the number of times a value occurs. Do not put tickmarks on the yaxis. The frequency will be measured by the number of labels plotted.

For each value in the data set, put a nutrition facts label above that value on the xaxis. When a value occurs more than once, stack the nutrition facts labels. For example, if there are three nutrition facts labels with 120 calories per serving in the data set, there will be three nutrition facts labels above the 120 mark on the xaxis.

Once all the labels have been placed, ask students to observe the distribution of the data in the dotplot. Ask students to respond to the following questions in their DS journals:

What are the minimum and the maximum values of the data set? Answers will vary by class.

The range is the largest value minus the smallest value. It is one way of measuring the variability of a variable. What is the range, and why do you think this measures the variability? Answers will vary by class. The range measures variability because if the values of the variable are really different, the range will be a big number (because the max and min will be far apart); but if there is little variability, the range will be small. For example, if all of the values were the same, we would have no variability and the range would be 0 because the max and min would be the same number.

How many data points does this distribution have? Why? Answers will vary by class.

What is the amount of [insert variable name] that appears most often in a snack? Why? Answers will vary by class.

What do you think the phrase distribution of the data set means? It shows us how values are distributed. We learn where there are many values, where there are only a few values, and where there are no values at all.

What information is this distribution telling us about the [insert variable name] in the snacks we consume? Answers will vary. We see how the value of [variable name] varies. For example, we can see whether all foods have the same number of calories, or if they differ.

A distribution tells us two things: the values of the variable and the frequency of the values. "Frequency" is just another way of saying "the count." Why is this dotplot a picture of the distribution of [variable name]? Because the location of the labels on the xaxis tells us the values we saw, and the number of labels at that value tells us the frequency for that value.


Review the students’ responses in a class discussion. Ask students to put a check mark next to the answers that were validated, and to revise the answers that need to be corrected.

Use another piece of poster paper to create a distribution for the second numerical variable chosen by the students. Repeat steps 1416 with this variable.

On the first visualization for the numerical variable, show students how to convert the nutrition facts labels into something more readable. Draw another horizontal like on the plot above the nutrition facts labels. Explain that we can represent each label with an item such as a dot sticker or a sticky note.

Then, start with the minimum xvalue on the plot and place the new sticker above the second horizontal axis. Do this for each nutrition facts label in the plot. Once all values have been represented, ask the students how this new plot IS or IS NOT better than the original. Explain that we can call this type of plot a dotplot since we’re using dots to represent each observation.

Distribute the Tangible Plot handout (LMR_1.9). Each student should pick one of the 2 numerical variables plotted on the poster paper. Then, they should complete part 1 of the Tangible Plot handout before leaving class. They will complete part 2 of the handout for homework.

Ask students to think about the statistical questions they came up with. Can the visualizations they created in class help answer their statistical question? If yes, answer the question; if not, what visualization would be appropriate?
Class Scribes:
One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.
Homework
Students will complete part 2 of the Tangible Plot handout (LMR_1.9) and bring it to the next class for assessment.
Students should continue to collect nutritional facts data using the Food Habits Participatory Sensing campaign on their smart devices or via web browser.