Engaging students: Using the undefined terms point, line, and plane

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Dorathy Scrudder. Her topic, from Geometry: using the undefined terms point, line, and plane.

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A1. What interesting word problems using this topic can your students do now?

“Given the marching band coordinates shown in the picture, plot the points on the Cartesian coordinate plane and connect the points to show the line of where the band member will march.” This is an engaging warm up problem for the students because the problem covers all three aspects of the topic while engaging the students who are not normally the subject of the example. Normally, as teachers, we focus on involving the athletes due to stereotypes but we forget there are other students who are not interested in sports or math so they do not stay engaged in the lesson. Using band coordinates allows the band members to feel appreciated and they also get to help explain the marching process to their classmates who may not know how the band creates such intricate designs on the football field. The students should be able to plot the points on the plane and connect the lines before the main lesson. This will allow the teacher to scaffold the students into making connections between the undefined terms of point, line, and plane.



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B1. How can this topic be used in your students’ future courses in mathematics or science?

This topic will be continuously used in every following math class and most science classes. Students will be expected to know how to find an equation of a line and graph the line on a plane in all future math courses. They will also be expected to plot points in both polar and rectangular coordinates. A lesson in using the undefined terms of point, line, and plane will come in use for multiple facets of their educational journey. Learning how to plot points on a plane should come fairly easy at this point. Students should be able to label their x and y axis and therefore can plot points. Graphing lines on a plane is a bit more difficult. Students will need to learn how to find the slope and understand what it means. With that information, the students will be able to graph a line when given two points, a point and a slope, and a y-intercept (a point) and a slope. Students will hopefully be able to transfer this knowledge to other topics and courses.


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C2. How has this topic appeared in high culture (art, classical music, theatre, etc.)?

This topic has appeared in high culture through art, theatre, and dance. An artist must know their canvas they are working with. Whether the canvas is an actual canvas, a piece of clay, or a pile of scrap metal they will be welding together, the artist must understand the concept of how points, lines, and planes work together to create a masterpiece. A lighting designer must work with a director of a play to know where to point a spotlight, when to follow an actor walking in a line, and to know what altitude the spotlighted actor would be at (for example, if the actor is on a platform or flying in a harness). A dance choreographer must also be conscientious of points, lines, and planes so that the dancers can create formations that are pleasing to the eye. A dancer must understand points and lines so that he or she can move their body with the music and show the audience the lines and contorts of their body.


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