Origami and Math: Exploring Volume

Origami, the art of paper folding, is more than just a fun and creative hobby. It can also be a powerful tool for learning mathematical concepts, particularly geometry. By folding paper, students can visualize and manipulate shapes, gaining a deeper understanding of their properties.

One such concept that can be explored through origami is volume. Volume refers to the amount of space a three-dimensional object occupies. In this blog post, we'll use origami to create two simple shapes – a box and a square base pyramid – and then calculate their volumes.

Origami Box

Let's start with the origami box. It's a simple shape that's easy to make, even for beginners.

Instructions:

1. Begin with a square sheet of paper. Fold it in half diagonally to create a triangle, then unfold.
2. Fold the bottom two corners up to meet at the top point of the triangle. You should now have a kite shape.
3. Fold the top flap down to meet the base of the kite. This will create a rectangle.
4. Flip the paper over and repeat step 3.
5. Now you have a square with four flaps. Fold each flap inwards to create the sides of the box. The box should be open at the top.

You've now created an origami box!

Calculating the Volume:

To calculate the volume of the box, we'll use the formula: Volume = Length x Width x Height

The length and width of the box are equal to the side length of the original square sheet of paper. The height is the depth of the box, which is equal to the length of the flaps folded inwards.

For example, if the original square sheet of paper has a side length of 10 cm and the flaps are folded inwards to a depth of 5 cm, the volume of the box would be:

Volume = 10 cm x 10 cm x 5 cm = 500 cm³

Origami Square Base Pyramid

Now let's move on to the origami square base pyramid. This shape is a bit more complex, but it still provides a great opportunity to learn about volume.

Instructions:

1. Begin with a square sheet of paper. Fold it in half diagonally to create a triangle, then unfold.
2. Fold the top two corners of the square down to meet the center point of the base. You should now have a shape that resembles a kite.
3. Fold the bottom two corners of the square up to meet the center point of the base. You should now have a shape with four flaps.
4. Flip the paper over and fold the top flap down to meet the base. You should now have a shape that resembles a pyramid.
5. Fold the remaining three flaps inwards, tucking them underneath the base to create a square base pyramid.

You've now created an origami square base pyramid!

Calculating the Volume:

To calculate the volume of the square base pyramid, we'll use the formula: Volume = (1/3) x Base Area x Height

The base area of the pyramid is equal to the area of the square base. The height of the pyramid is the perpendicular distance from the apex (the top point) to the base.

For example, if the side length of the square base is 8 cm and the height of the pyramid is 6 cm, the volume of the pyramid would be:

Volume = (1/3) x (8 cm x 8 cm) x 6 cm = 128 cm³

Conclusion

Origami provides a fun and engaging way to teach students about volume and other geometric concepts. By manipulating paper and creating three-dimensional shapes, students can develop a deeper understanding of these concepts and see how they apply to the real world. This activity is particularly beneficial for visual and kinesthetic learners, as it allows them to learn through hands-on experience.