# Engaging students: Midpoint

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 Cody Luttrell. His topic, from Geometry: deriving the term midpoint. A1: Being able to find midpoint is a very important skill for students to learn in their geometry class. Some interesting word problems that students may be able to solve would being able to find the “half way point” between two locations. If they were wanting to meet their friend in a town that is equidistant from their town and their friend’s town, they may use midpoint to solve this. Other word problems may include running track, NASCAR, and can even be used in fast food examples. For example, Subway sells foot long sandwiches that are cut in half. How does the Subway worker know where to cut the sandwich where they have equal half’s? The student can find the midpoint of the distance of the sandwich and that is where they should make the cut. Knowing how to find midpoint will aid the student in the rest of their geometry class as well which can lead to more interesting word problems. B1: Knowing how to find the midpoint between two points can greatly aid students in future subjects. One of the most common examples would be finding the vertex of a parabola. If the students looks at the x value for the roots of a quadratic, the student can find the midpoint between the two points which in results will give you the x value for the vertex since the function is even. This can then be applied to physics when dealing with projectiles. Students can find where an object reaches its maximum height if they know its starting point and landing point. The students then will also come across this topic when they get into calculus when they deal with integrals. Using Riemann sums end up using the midpoint formula to help estimate the area under the curve. As seen from above, midpoint can applied to many advanced mathematical or science courses that a student may be enrolled in. C2: Knowing how to find the midpoint between two distances is used in art pieces and architecture around the world. To keep things symmetrical, one must know how to find the line of symmetry which is also the midpoint between the two points. Symmetry is used to make things appealing to the eye, which is a major concept of art in general. In architecture, having to know where the “middle” is located, is very important to keep things structurally sound. The reason for this, is if a building is weighted unevenly on opposite sides of the midpoint, it can create an unbalance which can end up being an unsafe environment. Knowing how to use midpoint can also be applied in theatre. The stage is divided up to left, center, and right stage. Finding the midpoint of the stage can help differentiate where center stage is compared to right and left stage.

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