# Lesson 11

Plotting the Weather

## 11.1: California Rain (5 minutes)

### Optional activity

This activity is a review of scatter plots and how to interpret information from a scatter plot.

### Launch

Keep students in same groups. Tell students that they will look at an image, and their job is to think of at least one thing they notice and at least one thing they wonder. Display the image for all to see. Ask students to give a signal when they have noticed or wondered about something. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their group, followed by a whole-class discussion.

Action and Expression: Internalize Executive Functions. Provide students with a graphic organizer, such as a two-column table, to record what they notice and wonder prior to being expected to share these ideas with others.
Supports accessibility for: Language; Organization

### Student Facing

What do you notice? What do you wonder?

### Activity Synthesis

Invite students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After each response, ask the class if they agree or disagree and to explain alternative ways of thinking, referring back to the images each time.

Discuss what each point in the scatter plot represents. Ask students to describe general patterns visible in the plot. Ask, “Is there a pattern of association?” (Yes, it is not linear, but it is possible to say that there is more rain in the winter and less rain in the summer.)

## 11.2: Data Snooping (10 minutes)

### Optional activity

The task statement provides data students can analyze for the remainder of this lesson. It gives the average high temperature in September at different cities across North America. This is only one possible choice for data to analyze. If appropriate, students can instead collect their own data and then continue using it. If so, then the instructions are the same just with the students’ data.

### Launch

Students in same groups of 3–4.

Engagement: Develop Effort and Persistence. Encourage and support opportunities for peer interactions. Prior to the whole-class discussion, invite students to share their work with a partner. Display sentence frames to support student conversation such as: “First, I _____ because . . .”, “I noticed _____ so I . . .”, “There is/is not an association because . . .”, or “I agree/disagree because . . .”
Supports accessibility for: Language; Social-emotional skills

### Student Facing

The table shows the average high temperature in September for cities with different latitudes. Examine the data in the table.

city latitude  (degrees North)   temperature (degrees Fahrenheit)
Atlanta, GA 33.38 82
Portland, ME 43.38 69
Boston, MA 42.22 73
Dallas, TX 32.51 88
Denver, CO 39.46 77
Edmonton, AB 53.34 62
Fairbanks, AK 64.48 55
Juneau, AK 58.22 56
Kansas City, MO 39.16 78
Lincoln, NE 40.51 77
Miami, FL 25.45 88
Minneapolis, MN 44.53 71
New York City, NY 40.38 75
Orlando, FL 28.26 90
San Antonio, TX 29.32 89
San Francisco, CA 37.37 74
Seattle, WA 47.36 69
Tampa, FL 27.57 89
Tucson, AZ 32.13 93
Yellowknife, NT  62.27 50
1. What information does each row contain?
2. What is the range for each variable?

3. Do you see an association between the two variables? If so, describe the association.

### Activity Synthesis

Make sure students understand the information listed in the table. Invite students to share their responses to the last question, then move on to the next activity.

## 11.3: Temperature vs. Latitude (15 minutes)

### Optional activity

In this activity, students use the data from the previous activity and draw a scatter plot and a line that fits the data. The given data show a clear linear association, so it is appropriate to model the data with a line. Students can use a piece of dried linguine pasta or some other rigid, slim, long object (for example, wooden skewer) to eyeball the line that best fits the data. (The line of best fit has a variance of $$R^2=0.94$$.) Even though different answers will have slightly different slopes and intercepts, they will be close to each other.

### Launch

Students in same groups of 3–4. Provide access to pieces of dried linguine pasta.

Representation: Internalize Comprehension. Provide a range of examples and counterexamples for a best fit line. Consider displaying charts and examples from previous lessons to aide in memory recall.
Supports accessibility for: Conceptual processing

### Student Facing

1. Make a scatter plot of the data.

2. Describe any patterns of association that you notice.

3. Draw a line that fits the data. Write an equation for this line.

### Anticipated Misconceptions

If a student is stuck on making the scale on the graph, remind them to look at the range from the previous problem.

### Activity Synthesis

At the start of the discussion, make sure students agree that there seems to be a negative association that looks like a line would fit the data nicely before moving on.

Invite several groups to share the equations they came up with and how they found them. They will likely have slightly different slopes and intercepts. Ask students to explain where those differences come from. (Not everyone chose the same points to guide the trendline they drew for the data.) The differences should be small and the different models give more or less the same information. In the next activity, students will be using the model (equation and graph) to make predictions.

Representing, Conversing: MLR8 Discussion Supports. After students complete their scatter plots from the data, they should meet with a small group of 3–4 students to share and compare. While each student shares, circulate and encourage students to look for commonalities and to discuss their differences in displays. Tell students to generate an agreed on response for the equation and the visual display of the line even though they may have differences. Tell students that one member will share out, but they won’t know who, so they all need to be prepared to share and explain. During the whole-class discussion, amplify use of mathematical language such as “slope”, “intercept”, “equation”, “graph”, and “negative association”. Use this to help students develop their explanations of associations and differences that they see in how the data is interpreted.

Design Principle(s): Cultivate conversation; Maximize meta-awareness