Map My Path: Graph Points to Represent Problems

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Objective

Represent real-world and mathematical problems by graphing points on the coordinate plane.

Big Idea

Map your path to find your way with this coordinate plane.

Warm-up

10 minutes

To warm up, I review the story that we read last week, A Fly on the Ceiling, by Julie Glass.

I ask students:

What was the problem in the story? 

Have any of you had similar problems? 

Why did Descartes use the grid to help him solve his problem?  (I explain how Descartes was able to use the grid to locate a particular item in his house.)

I ask students to hypothesize how a grid is useful in today’s world. Students report out, and I make an anchor chart. This can then be used later, at the end of the mini-unit, for students to create their own relationships over time problem/graph.

Guided Practice

20 minutes

For this Guided Practice, I told kids that our Principal, Mrs, Hunter, used a coordinate plane to make a map of the area near our school. Each unit on the map, or grid, represents 1 block. A typical city block is 100,000 square feet or about 16 to 17 blocks per square mile.

I tell the students that in our nearest city (Wilmington), the blocks are much shorter than the blocks in Washington. D.C. though. (I recently visited D.C. for the M.T.P. project.) Our class then walks the equivalent of a block outside. We also participate in a program called The Walking Classroom; it incorporates walking for exercise with content delivered via podcasts. Each student has their own audio player and headphones.

Once back inside, I ask students to identify which ordered pair represents the location of each place included on the map. In this way they describe a possible route from the School to the Deli and from the School to the Park.

(Think Aloud/Modeling): To locate the ordered pair for the Deli, you start at the origin, (0,0). You move along the x-axis 2 units. Then be sure to move up the vertical line parallel to the y-axis until you reach the point that represents the Deli at (2,9). We then repeated the process to find the ordered pairs for the: School, Park, Library, and Store.

At this point, students understood that to find a possible route from one point to another, you try to find a route by moving horizontally right or left first, and then vertically up or down. To assist with this, we used a hand signal of a horizon line, as students were not confident about which line was which. 

Independent Practice

15 minutes

Students determined the ordered pair for where each student lived. This was a review, and I knew that students would be very successful with this. Then, students described paths from certain students' houses to others.

Closure

15 minutes

We then used our paths to work with a table partner. One partner from each group read their description aloud to their partner, and the other partner traced the route according to their directions. Students then worked to create their own graphs with paths to their own friends' houses for another person to follow for continued practice. Below you'll find a really simple path. What's most important here is the path and the language, and not how pretty the path is. I think sometimes teachers let students do projects, which is wonderful, but then too much time is spent on the projects being aesthetically pleasing, and not related enough to content.