Engaging students: Defining intersection

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 comes from my former student Marlene Diaz. Her topic, from Geometry: defining intersection.

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How could you as a teacher create an activity or project that involves your topic?

Intersection is a term that the students will see for a very long time in math. There are many beneficial activities or projects that students can do that involves intersections. There project will include them to first define the term next find any examples where the term has been used. They will have to show two mathematical examples and five real world examples of intersection. For example, a student can compare a rail road intersecting and two lines intersecting on a graph. Furthermore, they will have to explain each image by answering questions like, how do you know it is intersecting, and can it intersect again. These questions can be answered for different examples. In conclusion, it will allow the student to connect a real-world example to a mathematical term. Since this is a very fast and small concept because we are just defining the term intersection, therefore I will consider this an activity the students can do in their group.


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What interesting things can you say about the people who contributed to the discovery and/or the development of this topic? (You might want to consult Math Through the Ages.)

Girard Desargues was one of the people who contributed to the development of intersection. Desargues was born February 21, 1591 in France. He had significant contribution to mathematics, especially projective geometry. For part of his life he was very known, he met people like Rene Descartes and Pierre de Fermat who have also contributed to the mathematical community. In the 19th century his work was being rediscovered and resulted in the Desargues’s theorem. Desargues’s Theorem states that if two triangles ABC and A′B′C′, situated in three-dimensional space, are related to each other in such a way that they can be seen perceptively from one, then the points of intersection of corresponding sides all lie on one line, provided that no two corresponding sides are parallel. Furthermore, his best and most important work was from 1639 called, “Rough Draft of Attaining the Outcome of Intersecting a Cone with a Plane”. Although, he and his work were forgotten for a long time, he did help the mathematics community with all items rediscovered.


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How has this topic appeared in the news?

One main thing that always appear on the news are traffic and traffic accidents. Some traffic is created when cars are attempting to cross an intersection. At most intersections there are traffic lights that only allow certain traffic to get across the intersection. Traffic lights are very helpful in intersections because it helps traffic get across without putting drivers in danger. The only time traffic accidents can happen at intersections is when a driver ignores the traffic signs, or they are at a stop sign. At stop signs in intersections not all four intersections will have stop signs therefore drivers should be careful in these areas. Intersections, like seen here, appear in the real world and they are something people don’t realize since its just a part of life, but if there are car accidents most happen near or at an intersection. These are some of the headlines some news report when car accidents, “Serious accident renews discussion about dangerous intersection” and “Motorcyclist killed in 5-vehicle crash at intersection with disabled traffic lights in Aurora”.








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