Graphing lesson plan

TITLE

Graphing Atmospheric Data as Scatterplots

AUTHOR

Kirstin Neff

TOTAL TIME

15-20 minutes

GOALS

Students will graph quantitative data collected while heading up-mountain in a scatterplot format to help them discuss and make sense of the relationships between atmospheric variables and elevation.

LEARNING OBJECTIVES

Students will be able to:

• Identify variables and choose two to compare in a graph

• Identify independent and dependent variables.

• Identify, label and scale the axes of a scatterplot graph

• Locate and record scatterplot points using a dataset with multiple variables

• Describe the relationship between the chosen variables using their scatterplot

NEXT GENERATION SCIENCE STANDARDS

3-ESS2-1. Represent data in tables and graphical displays to describe typical weather conditions expected during a particular season.[Clarification Statement: Examples of data could include average temperature, precipitation, and wind direction.]

HS-LS2-2. Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales. [Clarification Statement: Examples of mathematical representations include finding the average, determining trends, and using graphical comparisons of multiple sets of data.]

Science and Engineering Practices:

1. Asking questions

• (3-5) specify qualitative relationships

• (6-8) specify relationships between variables, and clarifying arguments and models

• (9-12) formulating, refining, and evaluating empirically testable questions

4. Analyzing and interpreting data

• (3-5) introduces quantitative approaches to collecting data and conducting multiple trials of qualitative observations. When possible and feasible, digital tools should be used.

• (6-8) extend quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis.

• (9-12) introduce more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data.

5. Using mathematics and computational thinking

• (3-5) extend quantitative measurements to a variety of physical properties and using computation and mathematics to analyze data

• (6-8) identify patterns in large data sets and using mathematical concepts to support explanations and arguments.

• (9-12) use algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions.

6. Constructing explanations (for science) and designing solutions (for engineering)

• (3-5) use evidence in constructing explanations that specify variables that describe and predict phenomena

• (6-8) construct explanations supported by multiple sources of evidence consistent with scientific ideas, principles, and theories

• (9-12) generate explanations that are supported by multiple and independent student-generated sources of evidence consistent with scientific ideas, principles, and theories

7. Engaging in argument from evidence

• (3-5) critique the scientific explanations proposed by peers by citing relevant evidence about the natural world

• (6-8) construct a convincing argument that supports or refutes claims for explanations about the natural world

• (9-12) use appropriate and sufficient evidence and scientific reasoning to defend and critique claims and explanations about the natural world. Arguments may also come from current scientific or historical episodes in science.

Crosscutting Concepts:

1. Patterns: Observed patterns of forms and events guide organization and classification, and they prompt questions about relationships and the factors that influence them.

2. Cause and effect: Mechanism and explanation. Events have causes, sometimes simple, sometimes multifaceted. A major activity of science is investigating and explaining causal relationships and the mechanisms by which they are mediated. Such mechanisms can then be tested across given contexts and used to predict and explain events in new contexts.

ARIZONA SCIENCE STANDARDS

Grade 6, Strand 1: Inquiry Process (each consecutive grade level has similar inquiry standards that become more rigorous as the grades progress)

Concept 3: Analysis and Conclusions PO 1. Analyze data obtained in a scientific investigation to identify trends. PO 2. Form a logical argument about a correlation between variables or sequence of events (e.g., construct a cause-and-effect chain that explains a sequence of events).

Concept 4: Communication PO 1. Choose an appropriate graphic representation for collected data PO 2. Display data collected from a controlled investigation. PO 3. Communicate the results of an investigation with appropriate use of qualitative and quantitative information. PO 5. Communicate the results and conclusion of the investigation.

INSTRUCTIONAL PROCESS

Materials

• All students should have their field notebook, which includes pre-made pages for a data sheet and 3 pages of blank graphs with x and y axes. The data sheet should be filled with data collected while going up the mountain. Students who are missing data measurements should copy the values from their group mates before beginning the exercise.

• Depending on the schedule, it may be necessary to collect the Sky Center data points as part of the lesson, in which case the atmospheric meters and IR thermometers are necessary.

• All students will need a writing implement (preferably erasable).

Setup

• A location should be chosen for this exercise where students can sit and write comfortably in their field notebooks while facing the instructor.

• It might be useful for the instructor to have their own blank set of axes to demonstrate with, but it is not necessary. Usually there is at least one student in the group whose graph is done well and can be used as an example.

Introduction/Engagement

Essential Questions How can scientists use graphs to visualize data and examine relationships between variables?

Student Misconceptions Begin by asking students to raise their hand if they have made a graph before. Ask them what kind of graphs they have made in the past. This will give you an idea of how much previous experience the students have with graphing. If none have made a graph before, ask if they’ve ever seen one, and what type. If the students are unfamiliar with graphs, explain that it is a way to compare and contrast two or more variables by making a picture to see if there is a relationship between the variables.

Some common misconceptions:

• The only kind of graph is a bar graph.

• Numbers can be written anywhere along an axis, regardless of scale.

• An axis has to start at zero.

• Both axes must have the same scale

• It is possible to graph a qualitative variable on a scatter plot (ex. Location name)

Learning Structure

This exercise is primarily individual, with students each creating their own graph in their own field notebook. However, students who are struggling with concepts should be encouraged to talk to a neighbor whose graph is correct and compare and contrast their graphs in order to see the best way forward. If no neighbor is able to help, then the instructor should guide the student toward a more correct graph by asking questions about the choices the student made. If all students are struggling with the same concept, the instructor might use their own graph to demonstrate a better way.

Exploration

Step-by-Step Description

Once you have established the students’ previous experience with graphing and explained what a scatter plot graph is, it’s time to begin graphing. The steps for this exercise are as follows:

1. Have students examine their completed data sets and look for any patterns or trends they see in the data. Are there any variables that are always increasing or always decreasing? What are two variables that would be interesting to compare? Let the students choose which variables they want to compare (ex. Pressure vs. elevation, pressure vs. humidity, temperature vs. elevation). Have them hypothesize what the relationship between the variables will be, and why they think that.

2. Once the group has chosen the two variables they want to graph, have them look at the graph on the page after their datasheet and ask them to identify the x and y axes.

3. Ask which of the variables will be the independent variable—the variable that they think would be the same no matter what. Instruct them to put that variable on the x-axis. Tell them to first label the x-axis (put the name of the independent variable below the axis).

4. Next, ask them how they will mark-off the x-axis. What range of numbers should be included on the axis? What are the minimum and maximum values of the variable we are graphing? Some students will chose to start their axis at zero, and some will choose to start at or just below the minimum value. Either is fine. Ask them how they will spread out their numbers over the axis? Will they count by ones, twos, fives, or tens? They should create an axis with a fairly evenly spaced scale. If they haven’t done this, ask them to compare with a neighbor who has a proper scale, or ask them to think about how much is between each of their marks.

5. Once most students have successfully created an x-axis with a label and a proper scale, ask them to do the same in labeling the y-axis. Continue to have the students compare their graphs and make sure that both variables are labeled and marked off with value labels. Give individual time to students who are taking longer so as to catch them up to the group. Ask them why they labeled it the way they did, if the spacing of the marks makes sense, etc.

6. Once most students have labeled both axes, ask them to use their data sets to draw 4 points on the graph—one point for each location heading up the mountain. Each point should be located where the values for each variable at that location cross. A good way to do this is to find the value for the variable x, and put your finger on that value on the x-axis. Then, look at the value for the y variable at the same site, and slide your finger straight up to be even with that value on the y-axis. Then draw a dot where your fingertip is. Do this for each location, and at the end you will have 4 dots on your scatterplot. Spend individual time with students who are having trouble, and have people compare with their neighbors.

7. When most the students have finished plotting their points, ask them to look for a while at their graphs and describe any pattern they see in the data. Do the points seem to make a line that goes up from left to right (positive correlation)? Or down from left to right (negative correlation)? Do the points not make a clear line (common when plotting temperature data, which sometimes increases with elevation due to warming throughout the day)? If so, discuss why this might be. If there is a clear relationship, ask the students, why might this relationship exist? Ex. Why do pressure and humidity both go up as we go up the mountain? Why do you think that? What physical things are causing this relationship? etc. How do their findings differ from their hypotheses (or perhaps how were their hypothesis correct)?

8. In the space below their axes, there is a fill in the blank sentence asking them to write down the relationship between x and y as shown in their graph (ex. As [variable x] increases/decreases, [variable y] increases/decreases). Below that they are asked to answer why they think this is the case. After discussing it as a group, have the students fill in the blanks and answer the question.

9. If there is more than 3 minutes of time left, ask students to choose their two more variables to graph next on the next empty set of axes in their field notebook, and help them individually in doing so while encouraging them to compare their work with neighbors. If there is no time left, ask them to take a couple minutes later during down time to pick two different variables and make their own scatterplot on the next set of empty axes in their field notebook.

Application

Why does it matter?

• Ask the students about the difference between trying to explain the relationship between their chosen variables before and after making the graph. Was it easier or harder looking at the data in a graph versus in a datasheet?

• Ask them if they can think of any other topics in which it might be useful to make a graph (ex. money, sports)

Extensions and/or Follow-up Activities Ask them to make another graph in their field notebook on their own time.

Assessment

How will you know if students "got" it?

• They can make a second graph on their own

• They can explain why they labeled their axes the way they did

• They can explain why there are 4 dots on the graph

• They can correctly explain the relationship between the variables graphed

For those who don’t “get it:”

• Have them compare their graph with a neighbors whose is more correct, so that they can discuss the differences between their graphs.

• Spend individual time with them asking them why they have labeled/plotted their graph as they have (while advanced students are working on the next step). Once you have caught them up, give them a hint on the next step to try to bring them up to speed.

RESOURCES

This lesson plan includes a section to discuss when scatterplots are useful, which could be added if the time for this lesson is ever expanded.

REFLECTION

In order to fit this lesson in a 15-minute rotation period, you have to move pretty fast, so keep the time in mind and move on to the next step as soon as most students get it. Spend individual time with others to bring them up to speed.