Grades 5-6 Video Solutions 2025-2025_5-6

Video Transcription

7. Thea rotates a piece of paper divided into 6 equal parts. When the paper is rotated, it is turned clockwise by one part. The original sheet of paper and the result of one rotation are shown in the diagram. What does the sheet of paper look like after 8 rotations?  Pause if you want to try and solve it. The key thing to realize here is that we don't actually have to do all of these rotations out. We don't have to imagine all of them.  Because if we rotate it 6 times, because this shape is a hexagon which has 6 sides, after we rotate it 6 times, it's just going to be back where it started, right?  So after the first 6 rotations, it's going to look like the starting one, the same way that it looked at the start.  And so then if we rotate it one more time, we'll get to this one. So that'll be after the 7th rotation.  And then if we rotate this one more time, and remember we're rotating it clockwise, then we'll get to the 8th one. So if we rotate this one once, which shape do we get?  Well, we can see that, for example, this gray square over here is going to move one over, and we can see that that looks like option A, right?  Because we have this gray square over here moved one over, and then the two black, sorry, gray rectangle, gray triangle, and the two black triangles up here.  So the correct answer is A.

Video Summary

Thea rotates a hexagonal piece of paper, divided into six equal parts, clockwise. After six rotations, the paper realigns with its starting position due to the symmetry of the hexagon. Therefore, after eight rotations, the paper aligns two positions clockwise from the starting point. Observing the movement of the shapes within the hexagon, particularly a gray triangle moving one position clockwise, the paper after eight rotations resembles option A, where the gray triangle and two black triangles are shifted accordingly.

Keywords

hexagon

rotation

symmetry

triangles

clockwise