# Engaging students: Finding the volume and surface area of a pyramid or cone

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 Natalie Moore. Her topic, from Geometry: finding the volume and surface area of a pyramid or cone.

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

A great thing that first came to my mind was using manipulatives, especially for finding surface area. I would prefer to use legos as a manipulative, but that will not work very well when trying to find surface area of a pyramid or a cone. Using the traditional math manipulatives will work fine for these types of shapes. I always loved using manipulatives as a student. However, we did not use them at all, from what I can remember, in high school and most of middle school. It would be great to bring more manipulative use into the high school classrooms. It makes learning more fun for the students, and it also helps the student with retaining the information better. In regards to finding the volume of a pyramid or cone with manipulatives, it will be a little more of a challenge. Instead of maybe using manipulatives though, I was thinking about a different fun activity. The activity I have in mind will not necessarily tell us the exact volume of these shapes, but it will give the students an idea of what volume is. That way, once students have an understanding of volume, once they have a formula, it will be easier for them to use it and it apply it to a problem. The activity I have in mind is taking large versions of these shapes and filling them up with a different object and counting how many of that object can fit into different sizes of the shapes. For example, I would use a camping tent to represent a pyramid. I would have two or three different sizes of tents. I would then see how many students can fit in each sized tent. That way, they can see X amount of students can fit in one tent while Y amount of students fit in a different sized tent. For cones, I would do the same type of thing but the object I would use would be an ice cream cone and see how many scoops can fit into various sizes.

How can this topic be used in your studentsâ€™ future courses in mathematics or science?

Surface area, mainly just area, and volume show up all the time in other math classes, especially calculus based courses. In these types of higher level thinking courses, students will not necessarily have to find the area or volume of shapes, but if a student has to answer a word problem involving area and/or volume and they do not of a good grasp on these concepts, it will be harder for them to solve the word problem. There are times too where the student will have to solve the area or volume of a specific shape, and it will not always be something as simple as a square or rectangle. We need to make sure as teachers that we are doing all we can to instill these concepts into the students since they will need to know them for classes later on.

How does this topic extend what your students should have learned in previous courses?

Before students will learn about the volume and surface area of pyramids and cones, they will typically learn about finding the area of rectangles and squares since those are the easiest to work with. Students are taught pretty early on how to find area of squares, rectangles, triangles, and circles. As they get older, they will learn about other shapes as well, especially 3-d shapes. After students have the basics of area down, then they will begin to learn about surface area and volume of these 3-d shapes. This is taking what they already know and taking it a step further to deepen their understanding.