Here we talk through components involved in understanding what *line graphs* are, how to read them, and some aspects overall for how to interpret them. This is **not** a list of questions to ask every time your students work with *line graphs*, but rather a resource of skills regarding *line graphs* that we need to help our students gain over time.

*What are line graphs?*

A *line graph* plots a quantitative attribute, in which there is a specific order to the data (e.g., ordered by time), along each of the axes to investigate the local changes of the data between the attributes. The line is an indication of what a case value reasonably could have been if it had been collected. If desired, a third attribute may be included within the formatting of the data points.

*How do we read line graphs?*

**What attribute is on the x-axis (often can be time)? What attribute is on the y-axis?****What is the range of the quantitative values on the x-axis? On the y-axis?**

**Tuva tip:** Besides just reading the lowest and highest values on the y- and x-axes, students can adjust the size of the axes by moving the “T” bars at each end to see if that is the full extent of the data, and/or look at the data values in the corresponding attribute columns in the Table View (below graph).

**Where does the x-axis start? The y-axis start?**

**Tuva tip:** While many graphs have axes setup to start at 0, this is not always the case. The range of values on the y-axis should be relevant to data being plotted, for example if a value of 0 is unrealistic (like when looking at parts per million of carbon dioxide in the air) then the scale should not start at 0. Similarly, the range of values on the x-axis should be relevant to the data being plotted, for example as many line graphs are timeseries data when only looking at data of the 20th century it would not make sense to start at 0. Therefore, it is important for students to look at the start values of the axes.

**Are there multiple lines on the graph? If so, what does each line on the graph represent?**

**Tuva tip:** Knowing what is actually represented on the graph is an important step before you can successfully interpret the data. Look for legends or the Case Cards to understand what is being plotted.

**What do high and low values on the x-axis mean for the subject being represented? On the y-axis?**

**Tuva tip:** Before students find the maximum and minimum values of the data, it can be helpful for them to think about what high and low values would mean for the subject to help them better interpret the data.

**Moving from left to right (x-axis) and up to down (y-axis), do the values tend to increase or decrease?**

**What are the maximum values?**

**Tuva tip:** Always use the context of the data for framing all data interpretation related questions. For example, rather than asking “What are the maximum values?” ask questions like “What is the highest value of cumulative vertebrate extinctions?” or “What is the most recent year of record is there data about the cumulative vertebrate extinctions?”

**What are the minimum values?**

**Tuva tip:** Similar to the maximum value questions, always use the context of the data for framing all data interpretation related questions.

**What is the first and last value for each category/line?**

**Tuva tip:** If there are multiple categories/lines it is helpful to determine the maximum and minimum values for each line.

*How do we notice and interpret patterns using line graphs?*

**“V” or “W/M” or “J” shapes in the line?**

**Tuva tip:** Looking at the path of the line to see if there are “V” (peaks and valleys, pink), “W/M” (repeated peaks and valleys, red), or “J” (an increasing trend, blue) shapes can cue students in to patterns in the data for interpretation. Following up with questions about what these shapes could mean in terms of what is happening within the data is an important step to help them make the connection between an observed shape and the resulting interpretation of the data.

**Cyclical (repeated up and down) patterns in a line?****Places where the line(s) reach a threshold and seem to level off?**

**What is the direction of change among the first few data points in the series? Middle few data points? Last few data points?**

**Tuva tip:** Have the students articulate the direction and extent of local changes in the data. This helps your students make the connection between data values at small scale changes (but beyond individual data points) and whether the relationship is positive, negative, or no relationship. This also helps them think about how much of a change is happening in each section (e.g., gradually, abruptly, small ups/downs, etc.).

As our eyes are typically drawn first to the end of the line, it can help to explicitly ask about other parts of the series. For example, having them look at the start (positive, red), middle (negative, blue), and end (no change, yellow) of the number of honey bee colonies over time in the US can help cue them into interpreting these data. Have the students use the Annotate / Arrows or the Stats / Add Movable Line on X- Y features to help with this.

**What is the sequence of change between the attributes?**

**Tuva tip:** Have the students use their knowledge of the changes at the beginning, middle, and end of the series of data to make interpretations about the sequences of change between the attributes. This provides a start for them discussing how things are changing in relation to one another throughout the scale of the axes.

**Are there long term (across all the data) or short term (across only some of the data) trends of the lines?****What is the direction of the relationship between the attributes?**

**Tuva tip:** Have the students use their knowledge of the direction of the axes, scale of axes, and maximum/minimum values for each attribute to articulate the pattern in the data about as values along the y-axis attribute increase what happens to the values of the x-axis attribute. Do they also increase, do they decrease, or do they not change? This helps your students make the connection between the data values and whether the relationship is positive, negative, or no relationship and how that is related to the context of the data.

**Is the rate of change in the data the same throughout the data, or does it vary?**

**Tuva tip:** Once the students have identified the direction of change, then they can look at the rate of change in a line graph. They do not need to calculate the slope per se for each connection between points, but instead can look at the overall steepness of the line to get a general sense of the rate of change. For example, the rate of decrease in honey bee colonies since their peak in 1949 has not be consistent over time (blue arrows from different time points). This is important for interpreting the patterns in the data. Have the students use the Annotate / Arrows or the Stats / Add Movable Line on X- Y features to help with this.

**If applicable, how does the rate of change vary across the data?**

**How do the series relate to each other?****Are there places where the lines cross each other or come close to one another?**

**Tuva tip:** To understand how attributes relate to one another it can be helpful to determine if there are places where the case values are close in space. When analyzing two series on the same axis this can provide valuable information about how to interpret the data. For example, overall Boston has more snowfall than Baltimore, but there are some years when that was not the case (e.g., 1979, 2010).

**NOTE**, when analyzing multiple attributes across different y-axes (which is purposefully not an option in Tuva) it is imperative to know that the spatial location of the lines on a graph should not be inferred to mean anything about the relationship between the data. This is because the scales are completely separate across multiple y-axes, and thus the x,y coordinate systems are different.

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