Week 7 Activity

My activity is inspired by Sarah Chase's activity with numbers 3x4, 3x5, and 4x5. In the beginning, I didn't exactly understand the meaning of her activity, but after I followed the steps in the video and assumed the same posture, I realized how it worked. Then I wondered if it was possible to present the least common multiple by moving footprints.

Therefore, I used 3x3 grids to design the positions of the footsteps. Initially, I drew both the starting positions in the middle of the grids, speculating that the feet would end up in the same position in the final steps, just as her arms did in the video. 

However, this approach failed. Then I thought that perhaps having the feet in the same horizontal line would also make sense, but I still wanted to try another method to achieve the initial premise.

So I changed both final footsteps (3 and 4) to the middle grid, and then it was successful.

After that, I also tried 3x5 and 4x5 and got the same result. 

Therefore, I discovered two things:

1. The numbers are not necessarily, but the position is.
2. Wherever you place the last step in the first round (for example, 3x4, where 3 and 4 are the last steps), the final position (least common multiple, 12) of the footsteps will return to the position you set in the first round.

Curriculum idea

1. The extended activity is based on problem-solving.
2. Utilizing the concepts of 'factors and multiples' to integrate with physical education.
3. Observing the positions of factors, multiples, greatest common factors, and least common multiples on each record paper, and brainstorming ideas for designing various dance steps paired with music.