SWBAT make graphs based on tables. SWBAT fit lines to data. SWBAT find symbolic rules for lines of best fit and make predictions from the given data.

From scatterplot to predictions. Students plot data, approximate a line of best fit, generate an equation for the line to make predictions.

10 minutes

I begin class by projecting an image of the Water Park Attendance data on the board. I explain the context to students as we look at the table. I tell them to imagine that a local water park would like to consult with them about how many visitors they should plan to have on a sunny summer day based on the number predicted temperature.

I ask students how many people they should advise the water park to expect if the predicted temperature is 75 degrees. Students may come up with different ideas about how to approximate the estimated number of visitors. I ask students, "What's another way we could get a picture of this data?" I let students know that today they will be graphing the water park data in order to make predictions for the company that owns the park.

Before we begin work on the investigation, I might include a conversation here about how to scale the graphs appropriately. I might ask students for tips about how to scale these graphs appropriately. I also discuss dependent and independent variables here. I might ask students, "Is the amount of visitors dependent on the temperature or is the temperature dependent on the amount of visitors?" I usually find this line of questioning to be a good way for students to understand the distinction between independent and dependent variables.

Some students may wonder if they need to start the y-axis at zero. I let them know that sometimes it's ok to start not to start at zero in order to show a trend in the data and this task is one of those times. We discuss what that is and what kind of graph might have to start at the origin.

35 minutes

Next, I let students get to work on creating graphs for their Water Park Predictions. I think it's best to have students work individually on these graphs. Here's why:

- Some students will struggle with scale. Sometimes when they work with other students, they don't play around with the numbers enough to understand what scales will work best.
- Students will be drawing a line of best fit. If they don't have much experience with this, I'll want them to consider where to draw the line on their own so that it reflects their own intuitive thinking.

Issues I watch for as students are working:

- Students may find graphing all the points tedious. They may ask if you if they have to plot them all. I tell them, yes!! They need to see a full "picture" of the data.
- Students may not know how to draw a line of best fit. I might try to guide them in the right direction by asking a question like, "If you had to draw a straight line that best represented the 'trend' of those points, where would you put it?" Sometimes I address this issue with the whole class, asking students to pause on their individual work. I also emphasize to students that there is no one right answer for a line of best fit. This may be a surprising point for them in the context of a math class where they traditionally look for one right answer.
- Students may want to compare their line of best fit to another student's. I encourage this! I like to let them see how other people are handling the situation. I encourage students to inquire about other's reasoning too.
- Students will likely struggle with making an In/Out table
**from their line of best fit**. They may be confused because they already have a table AND new values may be hard to determine from the line of best fit. I address this by letting students know they will look for a rule for their line and a new table will help them to find it. I help them identify ordered pairs on their line, drawing attention to any points that fall evenly at a lattice point.

15 minutes

Some of the discussion relevant to this task will take place while students are working. Still, at the end of class, I save time for discussion. One of the main points I want to hit on is that in this activity, students are able to find linear functions for particular situations. I make the distinction that the original tables of data DO NOT represent functions (I sometimes add a row of data to the original table showing a different number of attendance on a different day with the same temperature), but the line of best fit does represent a function.

I want to help students see how the line of best fit connects to making useful predictions. I might ask students, "Suppose the water park knows next week will be unusually cool with temperatures in the upper 60s. How would your work be able to help them plan for how many people they should expect to have that week?" Again, I bring out the relationships between graphs, rules, tables, and situations.

At the end of class, I give students the opportunity to process their learning by reflecting on today's activity. I ask them to finish class by doing five minutes of free writing in response to the following prompt, "How did you use all the data about weather and the number of visitors to make a prediction?"