Question bank: Movements and Location: Grid Meshes

Rafaela started making a map of her neighborhood, which she wanted to divide into equal squares to represent the blocks. However, the streets in the neighborhood form a pattern that does not fit perfectly into squares and rectangles, making the task more challenging. She knows that the footage of each block is very important for the urbanization plans and needs to calculate the area of each space delimited by the streets. For this, she decided to use a grid and estimate the measurements of each square or rectangle formed by the streets. Considering that the streets are represented by lines that delimit the blocks of Rafaela's neighborhood and that Rafaela needs to calculate the area of a space with the lateral measurements being 'x' squares of size 'a' and 'y' squares of size 'b', where 'a' is different from 'b', determine the correct formula to calculate the area of this space on Rafaela's neighborhood grid.

Imagine you are a detective in a mysterious city and need to find a hidden treasure. Following the map, you must leave the blue house, walk 5 blocks to the north, 3 to the east, 2 to the south, and 4 to the west to reach the exact location where the treasure is buried. Draw the route you must follow on the gridded map and then write down what the final coordinates of the place where the treasure is hidden are. Remember that each step you take is worth one block of distance in the north, south, east, or west direction.

At the school's science fair, the 4th-grade students are building a model of the city they studied in Geography. They need to organize the streets, squares, and buildings on a grid, where each square represents a block. Joãozinho has the task of building the school, which is 5 blocks north of the city park. He has already built 3 blocks north of the park and realized he needed to walk 7 blocks east to reach the school. Describe the path Joãozinho took on the grid to reach the school, starting at the park and counting how many blocks he walked north and then east.

Imagine you are in a park that is divided into blocks, like a chessboard. The park's restroom is located in block A3 and you are in block C5. Describe the path you would take to reach the park's restroom. Remember, you can only move up, down, left, or right, one block at a time. Why did you choose this path?

In the city of Jardim Feliz, there is a central square with a special design on the ground made of grid meshes. Children play by walking on these meshes, and each square has an exact size. Ana and Pedro agreed to meet at the square, but they want to choose a point on the grid where they can be the same distance from each other. The grid lines represent the city streets, and they can only walk up, down, left, or right, but cannot walk diagonally. Knowing that each little square is 2 meters on each side, how can Ana and Pedro choose a point on the grid of the square where they are 8 meters apart from each other by walking only up, down, left, or right? Draw a simplified map of the grid and indicate the point where Ana and Pedro should meet, considering that they are at different points on the grid.