Introduction[edit | edit source]
This is a kinesthetic math activity for students learning about the circumference, surface area, and volume of a sphere. Kinethetic learning is a method of learning that connects the position and movement of body parts with a concept or idea; i.e. learning through a physical activity.
For this activity, students "draw" a sphere with light using their arms and a camera set with a long shutter speed to take a photo of the sphere drawn. By having students stand in the same position and draw the sphere with their arms extended horizontally at their sides, it helps them to understand the correlation between diameter and the rest of a sphere. In this case, their two extended arms are the diameter of the sphere drawn. Once the sphere is drawn, students can measure their arm span to know the exact diameter of their sphere and are then able to calculate the circumference, surface area, and volume of the said sphere.
What is Shutter Speed and How Does it Work?[edit | edit source]
Shutter speed affects how long the shutter covering the lens of your camera will stay open when taking a picture and how much light will enter the lens. In other words, how long it takes the camera to capture and process a picture. With a short shutter speed, the picture will be taken quickly and will be darker as very little light was allowed to pass through to the lens. With a longer shutter speed, the picture will be taken slowly with a longer delay from pressing the button to capture the image to viewing the end result. A longer shutter speed allows for more light to pass through to the lens, and will result in a lighter, often almost completely white, picture.
Since a longer shutter speed allows for more light to pass through, it is preferable at night or in dark rooms. Creative photographers have taken advantage of this setting to "draw" with light in a dark area.
Some examples:
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A group of people writing out "smile" with sparklers.
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A spinning carnival ride.
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Traffic in a city.
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Someone spinning with a sparkler.
This project works similarly to how these photos were taken. The next sections explain how to set up your camera or phone to have a long shutter speed, in what way students need to move the lights in order to successfully draw a sphere, and how to calculate the circumference, surface area, and volume of the sphere they drew using the length of their arm span.
How to Adjust the Shutter Speed on a Phone or Camera[edit | edit source]
Each model of phone and camera is different, so be sure to research what will work for you if the methods featured in the videos below are not applicable to you.
A Samsung Galaxy s10 is used in the phone setting video and a Nikon Coolpix Model# S9700 is used in the camera setting video. Most Android phones have a similar set-up as the s10, however Apple, Google, or the product of any other company may be different. In short, if you own or have access to a smart phone with a decent camera then it should allow you to adjust the shutter speed.
Taking the Photo[edit | edit source]
Have the student find one or two light sources to use in the photo. These can be anything from another phone to a sparkler; any object that emits light will work. Once the student is ready, be sure to have someone operate the camera or set a timer for the camera to automatically take the picture.
Note: Due to the longer shutter speed the lens will be open longer. This means that if the camera or phone taking the picture is not on a steady surface such as a tripod or leaning against a book (or something similar) then the image will be blurry. It is important to keep the camera steady for the entire duration of the camera processing the photo!
Pick a dark room or any area at night and determine where the student will stand. Line up the camera so that the picture will capture the full body of the student. Once this is one, have the student hold their light source(s) in their hands. If there are two sources, have one in each hand. If there is one, pick a hand to hold it in. Then, have the student move/wave their arms in the same fashion featured in the video below. The video on the left is the pattern for two light sources, and the video on the right is for one light source. It may take a few trials before you get adequate results.
The results of both methods:
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A sphere drawn with two light sources.
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A sphere drawn with one light source.
Math Activity[edit | edit source]
Now that your student has a photo of the sphere they drew with light, have them measure their arm span using a tape measure or string paired with a ruler. The arm span of the person who drew the spheres above is 62 inches (157.5 cm), making this the diameter of the spheres. The radius of a sphere is half of the diameter, making the radius of our example 31 inches (78.7 cm).
Circumference of a Sphere
The formula for the circumference of a sphere is πd. π = 3.14 and d = diameter.
This means that our circumference is 3.14 x 62 inches = 194.7 inches
Surface Area of a Sphere:
The formula for the surface area of a sphere is 4πr^2. π = 3.14 and r= radius.
This means that our surface area is 4 x 3.14 x (31 inches)^2 = 12,076.3 inches^2
Volume of a Sphere
The formula for the volume of a sphere is (4/3)πr^3. π = 3.14 and r = radius.
This means that our volume is (4/3) x 3.14 x (31 inches)^3 = 124,725 inches^3
