Lesson 8: Spot the Plot

Objective:

Students will be able to identify the appropriate plot types (bar graphs, pictograms, dot plots, histograms, and boxplots) for both categorical and numerical data. They will practice analyzing plots with limited information and formulate questions based on graphical representations. Students will also be formally introduced to the Analyze Data phase of the Data Cycle.

Materials:

Sticky notes
Data Cycle poster [pages 3 & 4] (LMR_U1_L01_B_The_Data_Cycle)
Plot Stations (LMR_U1_L08_A_Plot_Stations) - can be hand-drawn or printed using poster paper or other material; placed around classroom

Advanced preparation required. See Class Setup section for additional details.
Plot Walk handout (LMR_U1_L08_B_Plot_Walk)

Vocabulary:

bar graph dot plot pictogram histogram boxplot Analyze Data (phase)

Essential Concepts:

Different types of data (categorical and numerical) are best represented by different types of plots. Categorical data can be displayed using bar graphs or pictograms to show frequencies of categories. Numerical data can be displayed using dot plots, histograms, or boxplots to show the distribution, center, spread, and shape of the data. Graphs help us visualize and understand patterns in data. The Analyze Data phase of the Data Cycle involves examining data and their graphical representations to identify patterns, trends, and insights.

Lesson:

Class Setup

Advanced preparation required.
- Prior to class starting, use poster paper, construction paper, or any convenient material available to create 5 Plot Stations around the room. All of the plots correspond to a variable from the Candy Culprit dataset. The plot types and the variables that are represented are listed here, but should NOT be included at the actual stations.
  
       ❏ Station 1: Bar Graph - Favorite Candy
       ❏ Station 2: Dot Plot - # of Library Books
       ❏ Station 3: Pictogram - Activity
       ❏ Station 4: Histogram - GPA
       ❏ Station 5: Boxplot - Age
- For your convenience, the plots have been provided in the Plot Stations handout (LMR_U1_L08_A). They can be used as a template for creating by hand or can be printed directly on large poster paper.
LMR_U1_L08_A

	ADDITIONAL SUPPORT: Vocabulary Labels for Diverse Learners For students who are unfamiliar or uncomfortable with plots, consider displaying the name of the plot type on each poster. If additional support is needed, consider adding a small card with a one-sentence definition or key feature of each type of graph (ex. “A histogram groups numbers into bins or intervals.”)

Opening

Lesson Hook: Data Collection with Sticky Notes
1. Have two large axes drawn on the board before class begins.
  1. Plot A: Labeled “Eye Color” (Categories: Brown, Blue, Black, Green, Hazel, Other).
  2. Plot B: Labeled “Number of Siblings” (Number Line: 0 - 10).
2. Action: As students enter, instruct them to place one sticky note on Graph A corresponding to their eye color and one on Graph B for their sibling count.
Once class begins and students are seated, ask two students to briefly review the definitions of categorical and numerical variables from Lesson 5.
1. Numerical Variables: data that can be expressed as numbers that come from a measurement or count.
2. Categorical Variables: data that can be expressed in distinct, non-numeric categories.
Next, pose the following questions regarding the sticky notes they just placed on the board:
1. What two types of variables have we learned about? Answer: Numerical variables and categorical variables.
2. A person’s eye color is what type of variable? Answer: Categorical variable.
3. The number of siblings a person has is what type of variable? Answer: Numerical Variable.
4. In Plot A (Eye Color), does the order of the columns matter? Could we move Blue to the left of Brown? What order makes the most sense to you? Sample answer: The order does not matter. We can choose to place the eye colors in any order we want. It would make sense to order them alphabetically or from most common to least common. Any order would still make sense.
5. In Plot B (Siblings), does the order of the columns matter? Could we move 2 to the left of 1? Explain. Sample answer: The order does matter because there is a number line and numbers have a logical order to them. You would not want to have the value 2 before 1 because it has a greater value, and it is important to be able to show that someone has MORE siblings and also HOW MANY more.
Concept Development

Part 1: Which Plot for Which Variable?
Display the Data Cycle poster with the Pose Questions and Consider Data phases shown (LMR_U1_L01_B, page 3).

LMR_U1_L01_B
Reveal and highlight today’s phase of interest: Analyze Data (LMR_U1_L01_B, page 4). Explain that this is where detectives start trying to answer their statistical questions by looking for patterns in data.
Introduce the next activity as a Plot Walk and inform students that they are “Evidence Analysts” today. During the Plot Walk, the detectives will visit 5 different stations around the room with different plots displayed. They might notice that a key piece of evidence is missing: the variable name. Explain that their mission will be to:
1. Determine which variable from our Candy Culprit Suspect dataset might be shown in each plot.
2. Classify that variable as either numerical or categorical.
3. Challenge: Record the official name of the plot if they know it.
Randomly assign students to 5 different teams of roughly equal size and distribute the Plot Walk handout (LMR_U1_L08_B) to each student (3 pages – 2 stations per page).

LMR_U1_L08_B
Instruct students to fill out the questions in the “With your team:” section of each table. They will fill out the “With your teacher:” section during the whole class discussion after. Two word banks are provided at the top of each page to help guide the activity.
Assign each team to a starting station. They will rotate through the other stations in increasing order. For example, if a team begins at Station 3, their sequence will be: Station 3, Station 4, Station 5, Station 1, Station 2.
Each team will spend 4 to 5 minutes at each station.
1. They will observe the plot displayed, sketch what it looks like, and then answer the questions for the corresponding Station # on their handout.
2. Encourage students to discuss their ideas quietly with their group members.

Once the timer finishes, signal students to move to the next station and reset the timer. Continue until all groups have visited each of the 5 plot stations.

ADDITIONAL SUPPORT:
Guided Instruction for Diverse Learners
After the students have visited their first station, pause the activity and ask one group to share their observations about the plot displayed at their station. This can help students clarify the expected output.
Ask:

What did you guess for the variable at Station [X]?
What did you guess for the type of variable at Station [X]?
What statistical question did you come up with?

Part 2: The Big Reveal

Once students have visited all the stations and completed their handouts, engage the class in a whole group discussion about what they observed at each station.
1. Reveal the actual variable that corresponds to each station’s plot (or confirm student guesses).
  1. Station 1: Favorite Candy
  2. Station 2: Library Books
  3. Station 3: Activity
  4. Station 4: GPA
  5. Station 5: Age
2. Next, discuss and confirm the names of each plot type, as well as if it should be used for categorical or numerical variables.
  1. Station 1: A bar graph places cases into different categories.
  2. Station 2: A dot plot allows us to see individual data values, typically numerical ones.
  3. Station 3: A pictogram gives a visual representation of different categories.
  4. Station 4: A histogram allows us to group numerical values into bins, or intervals.
    1. NOTE: Discuss and highlight the similarities and differences between Station 1 (bar graph) and Station 4 (histogram). Both of these plots use bars to show frequencies. What is different about how the bars are placed next to each other at each station? Sample answer: The bars at Station 1 (bar graph) do not touch each other and there is a space/gap between each bar. The bars at Station 4 (histogram) do touch and there are no gaps between them.
    2. Why does the spacing between bars matter? Sample answer: Histograms show a number line where any spaces between numbers would matter. For example, having a gap between the numbers 2 and 3 would mean that there were no data values recorded that were greater than 2 and less than 3 (ex. 2.3, 2.75). Since the categories in bar graphs do not have an order and you would not be able to be on the cusp between 2 categories, continuous bars are not necessary.
  5. Station 5: A boxplot divides numerical values into 4 segments (quarters or fourths).
    1. This plot might be the most unfamiliar to students. It does not have dots or bars.
    2. Why is it still useful? It divides the data into four equal parts and is great for seeing how spread out the ages are.
Highlight a few of the statistical questions students generated for each plot, emphasizing how the visual prompted the question.

Closing
Exit Ticket: Ask students to write down the name of one plot that is suitable for categorical data and one plot that is suitable for numerical data. Which graph would they use to show “Favorite Ice Cream Flavors” and which would they use to show “Heights of Students”?
Key Takeaway: Creating plots and observing their values are parts of the Analyze Data phase of the Data Cycle.
Transition: Announce that in the next lesson, students will practice creating a bar graph on paper and in CODAP.

Lesson 8: Spot the Plot