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4.2

Activity

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

In this activity, students begin developing their plan to predict the temperature. First, they must clearly define the two variables they will be comparing, latitude and temperature, while limiting the impact of other factors by, for example, restricting themselves to locations within a specific geographical area. During this activity, students make sense of the ways different factors influence each other as they narrow the scope of their model (MP1).

Launch

Keep students in the same groups. Tell students, “Andre and Lin want a reliable way of predicting the temperature in different locations. That is, they want a function where you input a location and get an output with the temperature at that location. But what type of location should they use?”

Ask students if they can explain exactly what latitude is. Latitude may have been discussed in the previous activity as one of the factors that can influence the temperature. Students should understand that latitude is a way to measure how far north or south of the equator a place is located. The unit of measurement is degrees north or degrees south. If possible, demonstrate latitude on a physical globe.

Draw a sphere (representing Earth) for all to see and indicate the circle representing the equator. Draw a quarter circle starting somewhere on the equator and ending at the North Pole. A location on the equator is at 0 degrees north (or south), and the North Pole is at 90 degrees north. Note that the angle made by the arc is a 90-degree angle. Since North America lies entirely north of the equator, all latitudes there have units of degrees north.

In this activity, students look at locations at 47.6 degrees north. Ask students where on the highlighted quarter circle this latitude is located. Then draw in the corresponding longitude circle (parallel to the equator) to show that there are many locations that have the same latitude.

<p>A sphere. </p>

<p>A sphere. </p>

Activity

None

Andre says, “I think temperature is a function of the latitude of the location, as long as we keep the time the same when we are measuring the temperature. I know that the temperature varies from summer to winter and throughout the day. By fixing the time, we remove that variability.”

Lin says, “Good idea to fix the time. Now what if we have 2 places with the same latitude? Look at this weather map for Washington State. Seattle and Spokane have the same latitude but different temperatures.”

What do Andre and Lin mean?

<p>A map of Washington state, line of latitude 47 point 6 through Spokane and Seattle. Seattle is 44 degrees Fahrenheit, Spokane is 35 degrees Fahrenheit.</p>

Student Response

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Building on Student Thinking

Activity Synthesis

The purpose of this discussion is to establish that a first step to making a mathematical model is to define the variables and the relationship you want to model with precision.

Here are some questions for discussion:

Why is it sometimes challenging to use functions to represent real-world situations? (Real-world situations often have more than 2 variables involved.)
What are other variables we can “fix” or standardize to be able to predict temperature from latitude? (Elevation: we could choose locations that have similar elevations, Ocean currents: we could choose locations in the same geographic area [like the same continent])

Remind students that models are not perfect representations of the situation. Fixing the variables we are not focusing on, like how Andre suggested to fix the time for temperature, makes it so our model for temperature and latitude will be more reliable.

4.3

Activity

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Copy (from Blackline Masters)

Is There an Association Between Latitude and Temperature Handout

Activity Narrative

In this activity, students determine that they can assume that there is a relationship between latitude and temperature and that data can be collected to define that relationship. As an important step of mathematical modeling, they think about what data they need to collect, how they can collect it, and what methods will help them to analyze the data (MP4). This step is often done for students to save time, but it is non-trivial and worthwhile for students to complete this step.

Launch

Keep students in the same groups. Discuss the following questions as a class.

“Is temperature a function of latitude? Why or why not?” (No, temperature is not a function of latitude because multiple locations on the same latitude can be different temperatures even when other variables, like time, are fixed.)
“Is it reasonable to assume that there is a relationship between temperature and latitude?” (Yes, since latitude is a measure of how far a location is from the equator, and generally the farther a location is from the equator, the lower the temperature.)

Depending on the time available, for the first question either tell students to pick a continent for their latitudes and a month for average temperatures to collect data for or assign a specific continent and month. The following instructions assume the continent of North America and average temperature in September were chosen.

Once a choice of continent and month is made, give a copy of the data collection sheet to each group. As a class, develop a list of 20–30 cities or locations in North America to gather data. Make sure the cities are from a variety of latitudes, since that is what is being analyzed.

Representation: Internalize Comprehension. Activate or supply background knowledge. Provide examples of variables that have an association for students to use as a reference. Check for understanding by selecting a few students to share other possible situations that may have an association between the variables.
Supports accessibility for: Memory, Organization

Activity

None

Data collection:
1. Latitude
2. Temperature
Complete the table to collect your data. Your table should include the cities or locations chosen, the latitude (in degrees north), and the temperature (in degrees Fahrenheit).

Student Response

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Building on Student Thinking

If students are given a choice of continent and choose one crossed by the equator, they will need to make a choice about how to represent the latitudes above and below the equator. Consider asking:

“Can you explain how the equator impacts your data?”
“How could you represent that some latitudes are north of the equator while others are south of the equator?”

Activity Synthesis

The goal of this discussion is to make sure students understand the next steps in analyzing their data. Here are some possible discussion questions:

“What can we do with our data to see if there is an association?” (We can make a scatter plot and fit a trendline to the data.)
“What are some things we kept in mind when we chose our cities?” (We chose many cities so there would be enough data. We selected cities from a variety of locations to have varied values.)

Remind students that while real-world data does not always fit the definition of a function, modeling the situation with a function is a useful way of analyzing the data and seeing trends.

In the next lesson, students will analyze the class data or the provided data to see if there is an association.