The second lesson of the curriculum unit
Previously, students practiced with hands–on transformations, usage of a digital camera and presentations. The next step is to engage them in the different ways of using translations and / or rotations, including dancing, and music.
For this part I will divide the students in three groups. One group will be those who will pursue careers in engineering, medicine, and such, where the level of math required to succeed in college is very high, and therefore, they will be taking Pre–Calculus/Trig next year and AP Calculus the following year. In other words, this is the group of students who like math or at least they feel very confident with their math skills.
The second group will be composed of those students who like music. They must read and write music at least at a basic level to be able to understand the instructions for this part. Basic vocabulary on music such as a staff (pentagram), notes, chromatic scale, transposition and time delay is also important. If not, these concepts must be addressed prior to the lesson. Another way to do it is coordinating with the music teacher.
The third group is composed by students who like dancing and / or students who are currently in the cheer–leaders group, dancing squad or simply want to be part of this group. A basic knowledge of vocabulary for a square, such as vertices, vertex, diagonal, sides and rotation is necessary. As an anticipatory set, students in the group who will work with music will have to bring a song written in a pentagram. It can be any song that they like, as long as they can read it and play it with their respective instrument.
The activity for this lesson will have three parts, one for each of the groups. There will be 12 questions about applied rotations and translations and a review from the previous lesson. There will be 4 questions per each group. The first 10 minutes will be for to the warm–up. Those who know how to solve their corresponding questions will come up to the board to show their solutions. Showing solutions will take approximately 5 to 10 extra minutes, including the explanation. There are 35 minutes left from the 55 minutes allocated for the lesson.
This time, we will learn the concept of reflecting an entire song (or a phrase of the song) using the pentagram and the song they have brought to class. There are two options for the axis of rotation. One option would be to have the axis of rotation as the third line of the pentagram. In this case, the "song" would be reflected through this third line; therefore, the notes written at the bottom will be at the top o the pentagram and the notes from the top will be at the bottom.
The second option would be to reflect the entire song having the axis of reflection as a line perpendicular to the pentagram and right in the middle of the entire song (or phrase). For this particular case, the ending of the song would be the beginning and the beginning would be the end.
Inviting the music teacher to coordinate this part would be a great example of working as a team. I will contact the parents of my students as well to let them know what their children are doing. It is not out of experimenting but reaching all the students.
We will learn the application of two types of translations in music, under the name of transposition, comparing it to the idea of vertical translation, as well as time delay to compare it with horizontal translation. It is not my intent to teach music instead of math concepts. It is a matter of relating the math concepts with things that students are familiar with.
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