Question bank: Movement of Objects and People

In the city of Mathematics, there is a square with four sculptures at different points, A, B, C, and D, which are used as reference points to indicate directions. João walks 20 steps north from point A to point E. Then, he walks 15 steps east to point F. Next, he decides to return to point A, but instead of following the way back, he walks 30 steps west and 5 steps south, ending up at a point we will call G. Considering that each of João's steps is the same size and he does not take steps diagonally, what is the total distance, in steps, that João travels from point E to point G, passing through point F? Consider that he travels the shortest distance possible between two points.

Imagine that you and your friend are playing a game of following a path in a park. You start walking from a bench, go straight to a large bush, turn around, and return to the bench. During the game, you write down the directions you take, such as 'forward,' 'turn right,' or 'turn left.' Thinking about the things you encountered along the way and the directions you took, how would you describe the path you took? Remember to consider the landmarks, which are fixed places like the bench and the bush, that help you understand where you went.

João is playing in the park and decides to walk in a straight line from the bench where he is sitting to the slide. After the displacement, he realizes that the bench is now exactly behind him, in the same direction and sense that he was initially sitting. Considering that the bench did not move and that João moved in a straight line, how can we describe João's movement from the bench to the slide and what is the spatial relationship between the slide, the bench, and the point where João was initially sitting?

Imagine that you and your friend are playing cops and robbers in the park. You decide to have a race, but before starting, you need to think of a starting point and a finish line. You choose the ice cream kiosk as the starting point. The finish line will be the toy scale, which is on the other side of the park. Now, you will run, but each of you chooses a different path to get to the toy scale. After running for a bit, you realize that to reach the toy scale, you need to change direction a few times. You also notice that the position of the big tree and the colorful slide will help you know if you are going in the right direction. Thinking about this, describe how you should follow the directions of these reference points, like the big tree and the colorful slide, to get to the toy scale, starting from the ice cream kiosk.

João is at the playground and wants to reach the newspaper stand, which is 10 steps away. He takes 3 steps forward, then 2 steps back, and finally takes 5 more steps forward. Based on this, describe how João moved around the playground and explain the reference points he used to decide the steps he took.