SWBAT calculate the topographic gradient and the direction of stream movement in topographic maps

In this lesson, students cover two things. First, we explore how to mathematically calculate the gradient for topographic profiles before moving on to figuring out the direction of stream movement. Two important concepts covered in one lesson!

This is a lesson with two *mini-objectives*. First, students explore what defines a **gradient** in relation to topographic maps by doing a few calculations based on the equation provided in their Earth Science Reference Tables [ESRT]. Then, in the second part of class, I teach students about how stream flow looks in a topographic map, as well as the *trick* to figure it out quickly and easily when looking at a topographic map on a piece of paper. Both are relatively straightforward, which is why I condensed this information into a single lesson. If you feel you need to, feel free to extend this out over two days.

[**Note**: For embedded comments, checks for understanding (CFUs), and key additional information on transitions and key parts of the lesson not necessarily included in the below narrative, please download the comments in the following document: 7.13 - Topographic Maps II (Entire Lesson w/comments). Additionally, if you would like all of the resources together in a PDF document, that can be accessed as a complete resource here: 7.13 - Topographic Maps II (Entire Lesson)[PDF]. Finally, students may need their Earth Science Reference Tables [ESRT] for parts of the lesson (a document used widely in the New York State Earth Science Regents course) as well.]

10 minutes

Students come in silently and complete the (attached) Do Now. In this case, the Do Now is a review of material and some "hot standards" from earlier in the weathering and erosion portions of the unit. After time expires (anywhere from 2-4 minutes depending on the type of Do Now and number of questions), we collectively go over the responses (usually involving a series of cold calls and/or volunteers), before I call on a student and ask them to read the objective out loud to start the lesson.

As a general note, the Do Now serves a few purposes:

- It serves as a general review of the previous day's material;
- It is a re-activation of student knowledge to get them back into "student mode" and get them thinking about science after transitioning from another content area or alternate class;
- as a strategy for reviewing material students have struggled with (for example, using this as a focused review for material that they have struggled with on unit assessments or recent quizzes); and,
- It is an efficient and established routine for entering the classroom that is repeated each day with fidelity (I never let students enter the classroom talking. While it may seem potentially severe to have students enter silently each day, this is both a school wide expectation and a key component of my classroom. In many respects, I find that students readily enjoy the focus that starting with a quiet classrooms brings each day).

10 minutes

Post Do Now, the first section entails students being able to identify and calculate the gradient. From looking at the first page of the resource, students see that the formula for calculating the gradient is actually on the first page of their Earth Science Reference Tables [ESRT]. In a topographic map, the **gradient** is defined as the slope, or the change in elevation over a specific distance.

I feel the best and most authentic way to teach this skill is to model it directly in the same context students will see it. Traditionally, they'll be exposed to 2D images and asked to calculate the change in slope or gradient based on two factors: (1) the change in elevation; and (2) the horizontal distance. The first deliverable for students, figuring out the difference in elevation (*change in field value*, for those utilizing the wording of the equation), requires calculating the change in elevation via the contour interval. For example, in modeling the first problem for students, I show them that there are four (4) contour lines between points *X* and *Y*. If no contour interval is given, then it falls on the students to actually calculate it. In this case, there are two listed elevations near the top of the hill at 400 and 500, respectively. Since there are five (5) jumps between them, that means that each contour interval is 20 meters, as the difference in elevations, 100 meters (500 - 400 = 100) is distributed over five (5) contour lines. So, 100/5 = 20 meters for each contour line. Since there are four (4) contour lines, that is a total elevation of 80 meters

The second value, the horizontal distance, is much more straightforward. In this, all one needs to do is utilize a ruler or straight edge (a piece of paper also works remarkably well, especially if you *plot* the dots and compare to the listed scale) and match up the distance in the image with the provided scale. In the same problem, it is a distance of 2 kilometers. That means that solving the gradient becomes relatively simple - 80 meters /2 kilometers = 40 meters/kilometer. More directly, the elevation averages about a 40 meter change in elevation for every kilometer in horizontal distance.

15 minutes

The Practice I section in this lesson is, like the vast majority of questions found in all of my classwork and homework, is 100% Regents-based, and is one of two practice-based sections that students will uncover through the course of this lesson. All of the questions come from prior Regents examinations. Likewise, as I try to generally do with all of my lessons, the questions are mostly organized to get increasingly more difficult and increase in complexity, which is why the harder questions tend to come toward the end. For whatever reason, the Regents loves to ask questions about source regions and air masses, so I truly think the practice is worthwhile, considering this is something they'll see over and over and over again in the future.

In terms of student work habits, I tend to sometimes make this decision in the moment, and as a response of what I know about the students and how they're processing the material on, but I'll either ask them to work independently, in partners, or (sometimes) give them the option. Usually, before starting practice, we tend to go over some steps for self-help ("What should you do if you're stuck?"), and I might reference a previously used multiple-choice or free response strategy in order to build their skills while simultaneously learning content (as an example - one popular one we always use - "If you aren't sure what the right answer is, see if you can eliminate some wrong answer choices"). I tend to circulate for compliance and then hone in on specific students while they're doing this.

After about 10 minutes, we go over their responses. Students who finish early are encouraged to work on the exit ticket (resource below) and double-check their responses. We use a combination of strategies (active voting, cold calling, popsicle sticks, volunteers) to go over the responses, where students correct their work and ask any clarifying questions.

10 minutes

The second section of the lesson details how to calculate the Direction of River Flow. Similar to calculating gradient, finding the direction of river flow is best done via a model. As noted in the *Reflection *in this section, I do feel that this lesson deserves more than the *trick* (see *Reflection* for more context here) that's commonly taught (although it is useful) - it's important to develop or have some visual anchor for students to attach their learning to. So I usually do something to the effect of building a small Play-Doh hill and having students see, when a small stream of water is passed over, that the water will quickly seek out the lowest elevations. I use the analogy of an electron - just as electricity moves through the path of least resistance, water flows through the path with the lowest elevation. So any valleys that have water running through them (or valleys made by running water) are going to have slightly lower elevations than their surroundings. So, students can understand the *trick* which is what the Regents exam usually asks them about - contour lines bend upstream. In other words, contour lines passing through a river usually *point* in such a way that the line is pointing toward a higher elevation. This is somewhat odd for students to grasp initially, as water always flow downhill. So the direction the contour lines are *pointing *is actually the **opposite** direction the stream is flowing!

While this initially seems confusing, when students are able to visualize (and practice) this information, it quickly becomes easy for them to understand the relationship between the curve of the contour line and the direction of stream flow. As in the previous section on gradients, after demonstrating this, I like to model this process directly for students on the first page of the Direction of River Flow resource.

10 minutes

The Practice II section in this lesson is the second part of the Regents-based work that students see in this lesson. All of the questions come from prior Regents examinations. Likewise, as I try to generally do with all of my lessons, the questions are mostly organized to get increasingly more difficult and increase in complexity, which is why the harder questions tend to come toward the end. For whatever reason, the Regents loves to ask questions about source regions and air masses, so I truly think the practice is worthwhile, considering this is something they'll see over and over and over again in the future.

In terms of student work habits, I tend to sometimes make this decision in the moment, and as a response of what I know about the students and how they're processing the material on, but I'll either ask them to work independently, in partners, or (sometimes) give them the option. Usually, before starting practice, we tend to go over some steps for self-help ("What should you do if you're stuck?"), and I might reference a previously used multiple-choice or free response strategy in order to build their skills while simultaneously learning content (as an example - one popular one we always use - "If you aren't sure what the right answer is, see if you can eliminate some wrong answer choices"). I tend to circulate for compliance and then hone in on specific students while they're doing this.

After about 10 minutes, we go over their responses. Students who finish early are encouraged to work on the exit ticket (resource below) and double-check their responses. We use a combination of strategies (active voting, cold calling, popsicle sticks, volunteers) to go over the responses, where students correct their work and ask any clarifying questions.

5 minutes

In the last few minutes of class, I have students complete the daily Exit Ticket. For the sake of time, I have students grade them communally, with a key emphasis on particular questions and items that hit on the key ideas of the lesson (Note: This usually manifests as students self-grading, or having students do a "trade and grade" with their table partners). After students grade their exit tickets, they usually pass them in (so that I can analyze them) and track their exit ticket scores on a unit Exit Ticket Tracker.

After students take a few seconds to track their scores, we usually wrap up in a similar way. I give students time to pack up their belongings, and I end the class at the objective, which is posted on the whiteboard, and ask students two questions:

- Do you feel that you mastered the objective for the day?
- Can you reiterate one thing you learned about (in this case, information on calculating the gradient or the direction of river flow, etc.)?

Once I take 2-3 individual responses (sometimes I'll ask for a binary "thumbs up/thumbs down" or something similar), I have students leave once the bell rings.