# Essential Learning Event 2

### Students make sense of patterns and relationships in observations and data through representation, analysis, and interpretation.

Students make sense of observations or collected data and determine how to represent the data. The presentation of data helps reveal patterns and relationships and allows results to be communicated with others. Student analysis of data helps bring out its meaning and relevance so that it may be used as evidence for the phenomenon or design problem. Interpretation of data helps students identify significant features and patterns, use mathematics to represent relationships between variables, and take into account sources of error.

## Foregrounded Practices for ELE2

SEP4: Analyzing and interpreting data

SEP5: Using mathematics and computational thinking

## Student Use Continuum for ELE2

Foregrounded SEP Level 1 Level 2 Level 3 Level 4
SEP4: Analyzing and interpreting data Students may record, but do not analyze data. Students work with data to organize or group the data in a table or graph. However, students do not recognize patterns or relationships in the natural world. Students work with data to organize or group the data in a table or graph. Students make sense of data by recognizing patterns or relationships in the natural world. Students make decisions about how to analyze data (e.g., table or graph) and work with the data to create the representation. Students make sense of the data by recognizing patterns or relationships in the natural world.
SEP5: Using mathematics and computational thinking Students do not use mathematical skills (i.e., measuring, estimating) or concepts (i.e., ratios). Students use mathematical skills or concepts but these are not connected to answering a scientific question. Students use mathematical skills or concepts to answer a scientific question. Students make decisions about what mathematical skills or concepts to use. Students use mathematical skills or concepts to answer a scientific question.

Note: The levels reflect increasingly sophisticated engagement in the practices and are not grade-level specific. Appendix F in the NGSS provides significantly more detail for each practice that should be integrated as both students and teachers develop greater fluency with each practice.

## Sample Student Actions for ELE2

#### Analyze and Interpret Data (SEP4)

• Students make decisions about how to visually represent data (e.g. graph, illustration, simulation).
• Students construct visual displays of data to show relationships using appropriate tools, technologies and/or models. (SEP2)
• Students describe patterns, trends, and relationships in data. (SEP2)
• Students distinguish between causal and correlational relationships in data.
• Students discuss what graphs, data, and observations tell them about the phenomena under study.
• Students ask questions to determine relationships, including quantitative relationships, between independent and dependent variables (SEP1)
• Students identify sources of measurement error in an attempt to improve accuracy and precision of data.
• Students discuss limitations of tools and readings used in the data collection process and their effects on data accuracy and precision.
• Students apply concepts of statistics and probability to analyze and characterize data (e.g., mean, median, mode, variability, and curve of best fit).
• Students identify additional data that could be collected to test emerging claims and evidence. (SEP3)
• Students evaluate interpretations of data for possible bias, effective sampling, and sufficient representative data. (SEP7)
• Students communicate how the data can be used as evidence to explain a phenomenon. (SEP8)
• Students compare datra sets to evaluate consistency of evidence and revise thinking.
• Students use evidence to design a solution to a problem.
• Students analyze data to identify design features or components of a proposed process or system to optimize it relative to criteria for success.

#### Using Mathematics and Computational Thinking (SEP5)

• Students organize simple data sets to reveal patterns that suggest relationships.
• Students apply mathematical concepts and/or processes (such as ratio, rate, percent, basic operations, and simple algebra) while investigating a phenomenon.
• Students recognize dimensional quantities and use appropriate units in scientific applications of mathematical formulas and graphs.
• Students create algorithms (a series of ordered steps) to solve a problem.
• Students clearly define the system, the components, and quantities that are represented mathematically. (SEP2)
• Students develop and/or use mathematical or computational representations (e.g., equations, graphs, spreadsheets, computer simulations) to depict and describe the relationships between system components. (SEP2)
• Students analyze the mathematical representations and use them to support claims, explanations, or predictions about phenomena. (SEP6)
• Students use simple test cases of mathematical expressions, computer programs, or simulations—that is, compare their outcomes with what is known about the real world—to see if they “make sense.”
• Students use digital tools to analyze very large data sets for patterns and trends.
• Students create, use, and/or revise a computational model or simulation of a phenomenon, designed system, process, or system.
• Use quantitative data to compare two alternative solutions to a problem.
• Create and/or use graphs and/or charts generated from simple algorithms to compare alternative solutions to an engineering problem.

## Teacher Use Continuum for ELE2

Foregrounded SEP Level 1 Level 2 Level 3 Level 4
SEP4: Analyzing and interpreting data Teacher does not provide opportunities for students to analyze data. Students may record data, but do not analyze it. Teacher provides opportunities for students to work with data, which could include organizing or grouping the data. However, these opportunities do not support students in recognizing patterns or relationships in the natural world. Teacher provides opportunities for students to work with data to organize or group the data in a table or graph. These opportunities support students in making sense of data by recognizing patterns or relationships in the natural world. Teacher provides opportunities for students to make decisions about how to analyze data (e.g., table or graph) and work with the data to create the representation. Students make sense of data by recognizing patterns or relationships in the natural world.
SEP5: Using mathematics and computational thinking Teacher does not provide opportunities for students to use mathematical skills (i.e., measuring, comparing, estimating) or concepts (i.e., ratios). Teacher provides opportunities for students to use mathematical skills or concepts but these are not connected to answering a scientific question. Teacher provides opportunities for students to use mathematical skills or concepts that are connected to answering a scientific question. Teacher provides opportunities for students to make decisions about what mathematical skills or concepts to use. Students use mathematical skills or concepts to answer a scientific question.

Note: The levels reflect increasingly sophisticated engagement in the practices and are not grade-level specific. Appendix F in the NGSS provides significantly more detail for each practice that should be integrated as both students and teachers develop greater fluency with each practice.

## Sample Teacher Actions and Instructional Strategies for ELE2

#### Analyze and Interpret Data (SEP4)

• To practice figuring out patterns in the data or graphs give groups of students a data table and sentence strips with various statements about the patterns in the data. Have students decide whether each statement is accurate or inaccurate based on the data table.1
• Model for students how to construct a graph. Talk about what decisions must be made when creating a graph (e.g. bar graph vs. line graph) and the reasons for one choice or another. Point out aspects of graphs that enable others to comprehend patterns in the graph (e.g. reasonable intervals on the axes).1
• Ask students to graph their data to visually represent the patterns in the data. Provide checklists for students to use to ensure their graphs contain key components, such as labels on the axes and a title.1
• Hang posters in the classroom with examples of different types of graphs (bar, line, etc.) that students can reference as they decide what type of graph to construct and as they make their graphs.1
• After students construct a graph for data, ask them to defend their choice of that type of graph. Facilitate a discussion about the differences in how each graph type shows the patterns in the data.1
• Conduct a gallery walk for students to view and critique each other’s data tables or graphs. Encourage students to use sticky notes to ask questions and provide feedback about how well their data tables show the patterns in the data. Give students time to use the feedback to improve their work.1
• Encourage students to support and justify their ideas by referring to the data. Have students not only communicate their opinions and arguments, but also back them up with data.
• Encourage students to look at different aspects of the data displayed in graphs and charts.
• Guide students in evaluating graphs to see if they answer the questions for which they were designed.
• Ask students to vote (thumbs up/thumbs down) whether they agree with a fellow student’s interpretation of the patterns in data.1
• Have students write 1-2 sentences that summarize the pattern(s) in a graph. Provide sentence starters such as “My graph shows...” and “Over time, plant A...”.1
• Provide sentence starters such as “As the amount of ________ increases...” and “We saw that changing _______ caused...”1

#### Using Mathematics and Computational Thinking (SEP5)

• Provide opportunities for students to perform calculations on their gathered data, such as finding the mean (average) of several trials of data.1
• Engage older students in using computer programs such as excel to analyze large data sets from scientific organization (e.g. NASA, NOAA).1
• Create activities in which students are given a scientific question and must decide how to use mathematical or computational thinking to address the question.1
• Use various tools to gather data such as graduated cylinders, thermometers, balances, etc.1
• Have older students decide whether to represent their data in different ways such as using ratios, percents, etc.1
• Engage students in investigations that require them to use mathematical operations (e.g. subtract quantities to determine the volume of an object).1
• Teach students the skills they can use to summarize data such as determining the measures of center (mean, median, and mode), identifying range, outliers, quartiles, and so on, as they are appropriate.
• Teach students the correct statistical terms so they have the words necessary to clearly convey their thinking; terms such as axis, range, median, correlation, interval, and so on, should become part of their vocabulary.

## Questions to Promote the Use of the SEP and CCC in ELE2

#### Analyze and Interpret Data (SEP4)

##### Trends and Patterns
• Are there places where the data are concentrated or clumped?
• What trends are visible in the data?
• Are there data points that have unusual values?
• Which two values are being compared?
• What are we seeing in the data? (CCC Patterns)
• What patterns do you see in the data or graph? (CCC Patterns)
• Is there a pattern to this data? How can I organize and display my data to show this pattern? (CCC Patterns)
##### Statistical Calculations
• What is the range, mean, median, mode, and so on? How does it help you understand the the data?
• What level of accuracy is required in your analysis?
• How confident are you in the precision or accuracy of your data?
##### Validity and Potential Bias
• How confident are you in the data and why?
• Would the data be the same if the sample was…?
• How might we reduce sources of error in future iterations?
##### Sense Making (Meaning of Data)/Data Interpretation (What is the data saying? What does it mean?)
• Do you have enough background information to analyze this data?
• What additional data might we need to collect?
• Is there extra, unnecessary data?
• Are these values consistent with your predictions?
• Why might there be an increase/decrease in the data?
• How might this data change if...? (CCC Cause and Effect)
• What is the most appropriate way to summarize your findings?
• Based on this data, what will happen in the future? (CCC Cause and Effect)
• For what other data sample might you use a similar graph?
• What is the relationship between the data sets? Why do you think there is a relationship?
• What can you infer or conclude from the data? Why?
• Does our data support this cause and effect relationship? (CCC Cause and Effect)
• What does the data tell us about how nature works at this scale? What does the data tell us about how the system changes at different scales? (CCC Scale, Proportion, and Quantity)
• What kind of data can help us understand this system? What does the data tell us about the system? (CCC System and System Models)
• What does the data tell us about the effect of energy on this system? What does the data tell us about the matter in this system? (CCC Energy and Matter)
• What does the data tell us about how changes to this structure affect its function? (CCC Structure and Function)
• What does the data tell us about what affects the stability of this system? (CCC Stability and Change)

#### Using Mathematics and Computational Thinking (SEP5)

• How can we use mathematics to measure the rate of change in this system? Can mathematics describe the balance that keeps it stable? (CCC Stability and Change)
• How can computers be used to analyze stability and change in this system? (CCC Stability and Change)
• How can we use math to measure and describe the function? (CCC Structure and Function)
• How can computers be used to study how the structure affects the function? (CCC Structure and Function)
• How can we use math to quantify the energy and matter in this system? (CCC Matter and Energy: Flows, Cycles, and Conservation)
• How can computers be used to track matter or energy in this system? (CCC Matter and Energy: Flows, Cycles, and Conservation)
• How can we use math to model how this system works? (CCC System and System Models)
• How can we use computer models to understand this system? (CCC System and System Models)
• How can we use mathematics to describe and measure this scale? How does mathematics help us understand what happens if this gets bigger or smaller (or increases or decreases)? (CCC Scale and Proportion)
• How can we use computers to see how this changes as it gets bigger or smaller? (CCC Scale and Proportion)
• How can we measure the relationship between the cause and effect? How can we model it with mathematics? (CCC Cause and Effect)
• How can we make a computer model of this cause and effect relationship? (CCC Cause and Effect)
• How can we use mathematics to represent this pattern? (CCC Patterns)
• How can we use a computer to find or visualize patterns in the data? (CCC Patterns)

## Assessment Task Formats for ELE2

#### Potential Task Formats: Analyzing and Interpreting Data (SEP4)

Relevant definitions:

• A pattern of evidence from data is what the data say (“The population of white-colored moths disappeared in cities,” or “The birds’ tail feathers are whiter in the mountains than in the city”)

1

Present students with recorded observations of the natural world, then

• Ask them to describe a pattern or relationship they can infer from the observations.

2

Describe an investigation, the phenomenon under investigation, and one or more recorded observations from the investigation, then

• Ask students to organize, represent, and analyze the data in at least two different ways, and
• Ask students to compare how the representations and analyses help them to identify patterns in the data.

3

Describe an investigation, the phenomenon under investigation, and one or more recorded observations from the investigation, then

• Ask students to use grade-level appropriate mathematics and/or statistics to analyze patterns the data, and
• Ask students to draw conclusions supported by their mathematical analysis.

4

Describe an investigation, the phenomenon under investigation, and recorded observations from the investigation that are directly relevant to explaining the phenomenon, then

• Ask students to organize the data and describe how this organization helps them to analyze the data, and
• Ask students to identify and describe the patterns they see in the organized data, and/or
• Ask students to student to describe how the patterns of evidence in the data help to explain the phenomenon.

5

Describe an investigation, the phenomenon under investigation, a hypothesis about the phenomenon that the investigation was intended to test, and multiple recorded observations from the investigation, then

• Ask students to organize the data and describe how this organization helps them to see whether the evidence supports the hypothesis, and
• Draw a conclusion about whether the data are consistent with the hypothesis.

6

Describe an investigation, the phenomenon under investigation, and recorded observations from the investigation from multiple groups of investigators, then

• Ask students to organize (e.g., tabulate, graph, or statistically summarize) the data, and
• Ask students to identify outliers in the different data sets, and
• Develop hypotheses about what sources of error might have caused the outliers.

7

Present a causal explanation of a phenomenon developed from either an experiment or from a simulation, empirical data from the experiment or simulation, then

• Ask students to decide whether the data presented provide causal or correlational evidence, and
• Ask students to assess whether the data are consistent with the causal explanation presented.

8

Describe an investigation, the phenomenon under investigation, one or more recorded observations from the investigation, the results of analyses, and an interpretation of the data, then

• Ask students to assess whether the interpretation is consistent with the data and the analysis, or
• Ask students to evaluate how the interpretation is affected by variation or uncertainty in the data.

#### Potential Task Formats: Using Mathematics and Computational Thinking (SEP5)

1

Present students with multiple objects, then

• Ask students to construct quantitative attributes (e.g., measurements of heights) of the objects, and
• Display the data using simple graphs.

2

Present students with a dataset from an investigation, the question the investigation is intended to answer, then

• Ask students to identify features of the dataset (e.g., range, average) that should be analyzed in order to answer the question.

3

Present students with a textual description and measured quantities of an observable scientific phenomenon, then

• Ask students to develop a grade-level appropriate equation or algorithm that corresponds to the textual description, and
• Explain how the equation or algorithm represents the textual description.

4

Present students with a textual description, measured quantities of data, and a grade-level appropriate mathematical equation of an observable scientific phenomenon, then

• Ask students to make a prediction about the state of the phenomenon in the future that the equation can be used to support, and
• Ask students to write an explanation for the prediction, using the mathematical model as supporting evidence.

5

Engage students in using a simulation of an observable scientific phenomenon, then

• Ask students to compare the simulation results with real-world data, and
• Write an argument for whether or not the simulation makes sense using the comparison as supporting evidence.

6

Present students with a large data set from an investigation, the question the data are intended to answer, and computer tools (e.g., a spreadsheet) for analyzing the data set, then

• Ask students to develop statistical summaries of the data set that help them answer the question about the dataset.