Grades 3-4 Video Solutions 2023-2023_3-4

Video Transcription

Problem number 22. Chloe has two machines. When she puts a square sheet of paper in machine R, it turns the paper 90 degrees clockwise, as shown in the  picture. When she puts the paper in machine S, it stamps the paper with a club symbol. In which order are the machines used to produce the result shown?  For this problem, we'll work backwards. Here is the final picture. It has a club symbol that is rotated, and also we have this little square in the corner that  can help us also track the orientation of the paper. Notice that machine S prints the club symbol right side up. So in order to get to this point, the paper  had to be rotated after it was stamped. So the most recent machine was machine R, and since it turns the paper clockwise, we're going to turn it  counterclockwise. And we have this image. Here the clubs is right side up, so this must be right after it was stamped, before it was rotated again. So the  machine before that was machine S. And before machine S, the paper was blank. Here, this corner comes in helpful. Compared to the original paper, we see  that it was rotated once clockwise to get this small black square to the upper left corner. So the first machine was machine R. So the order that we have  is R, S, R. This is answer B.

Video Summary

Chloe uses two machines, R and S, to transform a square sheet of paper. Machine R rotates the paper 90 degrees clockwise, while machine S stamps a club symbol on it. To determine the sequence used to obtain a final image with a club symbol noticeably rotated, we work backwards. Initially, the paper appears rotated, indicating the last machine used was R. Before this, the club symbol was stamped by machine S. The initial paper orientation was achieved by first using machine R. Thus, the sequence of machine usage is R, S, R, corresponding to answer B.

Keywords

machine R

machine S

paper transformation

rotation

club symbol