SWBAT use a circle to model possible locations in space. Students will understand the meaning of a circle in terms of its properties.

Using circles to represent information about the position of an object. I know where your cell phone is located!

5 minutes

**Team Warm-up**

Using the Slideshow, I display the Warm-Up prompt for the lesson as the bell rings. As I take role and check for homework and required materials, I watch to see that students are following the team warm-up routine and that scribes write a High Quality Answer.

The warm-up asks students define a circle. This will tell me if they have learned anything from previous lessons. Students will elaborate on or refine their answers at the end of the lesson.

Displaying the Agenda and Learning Targets, I tell the class that today we will be learning about a method for locating a cell phone that is more precise than the one we studied in the last lesson (simply narrowing down the caller's location to a region around the nearest cell phone tower). The method depends on the properties of circles.

15 minutes

**Demonstration (5 min)**

I arrange a demonstration using a sound-ranging device, a Texas Instruments Calculator Based Ranger. I set up the sensor at the front of the room and ask a student volunteer to walk in front of itself. I display the calculator screen using on the overhead projector so that the class can see how the device measure's the distance of the student volunteer from the sensor. I ask for student explanations of how the sensor works, and make corrections if needed.

Turning so that the students volunteer is behind me, but I can see the calculator readout, I ask the volunteer to move quietly to a position within the range of the sensor. I ask the class: do I know where the student is, since I positioned the sensor and can read his range from the sensor on the screen? I ask the student volunteer if he or she can change position at all without changing the distance reading on the calculator screen. My goal is to get the class to realize that the student could be located anywhere on an arc that lies within the field of detection of the sensor. I ask someone to define the term 'arc'.

I tell the class that the technology similar to what they have just witnessed is used in a method of locating a cell phone called 'trilateration', except that the sensors use radio waves instead of acoustic waves.

**Team Reading (10 min)**

Displaying the instructions, I ask students to continue the team reading exercise they began in yesterday's lesson. Today, every team needs 2 copies of Reading A, and they must answer questions #3-6 in the time limit.

While the class is working, I circulate. My goal is for every team to realize that the possible locations of a caller based on a range from a single tower is represented by a circle (**MP4**), and it takes ranges from multiple cell phone towers to pinpoint the location of a cell phone. (Students will have an opportunity later in the lesson to see that, in general, three ranges are required). I also want students to be able to convert the time-of-flight of a radio signal to a distance in meters.

At the end of the time limit, I review answers with the class.

10 minutes

Many students have no experience using a map scale, and some will have very limited experience with using a compass. (What is this? *A compass! * What is it for? *Making circles. * No! A compass is a tool for measuring *distance*. And, it is a tool for copying a distance wherever you need it.)

As shown in the Measuring Distance On a Map video, I demonstrate proper use of a compass and map scale for measuring distance (**MP5, MP6**). I then have students try it using scratch paper and the Greeley Map they will use for the next activity. Finally, I show how to use the scale to set their compass to a given distance and have them try it.

20 minutes

Once each team of students has practiced measuring distance on a map, I get them started on the next activity: locating a simulated 9-1-1 caller by trilateration.

Displaying the instructions on the front board, I explain the Rally Coach format for paired work that I want the students to use with this activity. Each pair of students gets a strip of paper with information simulating a call to an emergency dispatch center. As each team finishes performing a trilateration to locate the caller, I bring them the data for the next call.

I have provided two versions of call data: one provides simulated times of flight, such as might be measured by sensors on a cell phone tower. The other simply gives the distance of the caller from each tower.

My goal is for each student to perform at least one trilateration. As students work, I circulate. I pay attention to whether they are performing the procedure correctly, and I coach them on how to use their tools correctly. There are always opportunities to have conversations on how to manage the error that inevitably creeps into measurements in an exercise like this (**MP6**). For example: students will notice that three range circles rarely intersect at a point. I explain that this is due to normal error in measurement (and in constructing the circles), and advise them to use the "center of mass" of the triangle as the caller's most probable location. I praise students who make range rings whose intersections form a tight triangle.

4 minutes

**Team Size-Up**

Displaying the Lesson Close prompt, I ask students to summarize what they learned from the lesson with their team-mates, then select the best answer to write on the board. This activity follows the Team Size-Up routine, which is basically like the team warm-up we used to begin the lesson.

**Homework**

Homework Set 1 problems #12-13 allow students to review and practice the modeling skllls (trilateration) which they learned in this lesson. I also assign Portfolio Problem #1, which students should now have the knowledge and skills to be able to complete (**MP1**).