krit.club logo

Mapping Your Way - Directions and Landmarks

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Maps and Scales: A map is a flat representation of a larger area. Because we cannot draw the actual size of a place, we use a 'Scale' to reduce distances proportionally. Visually, a map looks like a small drawing where a 1 cm1\text{ cm} line might represent a real-world distance of 100 km100\text{ km}.

•

Cardinal Directions: Maps are standardly oriented using four main directions: North (NN), South (SS), East (EE), and West (WW). Visually, imagine a cross: North points to the top edge of the map, South to the bottom, East to the right, and West to the left.

•

Measuring Distance on a Map: To find the real-world distance between two points, measure the distance on the map using a ruler and then multiply it by the scale factor. If two points are 5 cm5\text{ cm} apart on a map with a scale of 1 cm=10 km1\text{ cm} = 10\text{ km}, the ground distance is 50 km50\text{ km}.

•

Grid Systems: Maps are often divided into equal-sized squares called a grid. This helps in locating specific landmarks precisely. For instance, a landmark might be located in grid box B3B3, where BB represents the column and 33 represents the row.

•

Enlarging and Reducing: When a map or picture is redrawn from a 1 cm1\text{ cm} grid to a 2 cm2\text{ cm} grid, it looks bigger. The side of the square doubles, but the area becomes 44 times larger. Visually, a small square of 1 cm×1 cm1\text{ cm} \times 1\text{ cm} fits four times into a larger 2 cm×2 cm2\text{ cm} \times 2\text{ cm} square.

•

Landmarks and Symbols: Landmarks are easily recognizable features like a bridge, a park, or a temple used to guide someone. In a map, these are shown as small symbols or icons (like a small blue wave for a river or a green tree for a forest) to save space while providing clear information.

•

Turns and Angles: Directions can be understood through angles. Turning from North to East is a 90∘90^{\circ} clockwise turn (a right angle). Turning from North to South is a 180∘180^{\circ} turn (a straight line). Visually, these turns follow the corners and edges of a square grid.

📐Formulae

Actual Distance=Map Distance×Scale Value\text{Actual Distance} = \text{Map Distance} \times \text{Scale Value}

Map Distance=Actual DistanceScale Value\text{Map Distance} = \frac{\text{Actual Distance}}{\text{Scale Value}}

Area of a square grid=side×side\text{Area of a square grid} = \text{side} \times \text{side}

Total Area change=(New Side Scale)2\text{Total Area change} = (\text{New Side Scale})^2

💡Examples

Problem 1:

On a city map, the scale is given as 1 cm=200 metres1\text{ cm} = 200\text{ metres}. If the distance between a school and a library on the map is 7 cm7\text{ cm}, what is the actual distance in metres?

Solution:

  1. Identify the map distance: 7 cm7\text{ cm}.
  2. Identify the scale: 1 cm=200 m1\text{ cm} = 200\text{ m}.
  3. Multiply map distance by scale value: 7×200=1400 m7 \times 200 = 1400\text{ m}.
  4. Therefore, the actual distance is 1400 m1400\text{ m} (or 1.4 km1.4\text{ km}).

Explanation:

To convert map distance to real distance, we multiply the units measured on paper by the value assigned to each unit in the scale.

Problem 2:

A square garden with a side of 3 cm3\text{ cm} is drawn on a map with a 1 cm1\text{ cm} grid. If the map is redrawn on a 3 cm3\text{ cm} grid, what will be the area of the garden on the new grid?

Solution:

  1. Side of the garden on original grid = 33 units (3 cm3\text{ cm}).
  2. In the new grid, each unit is 3 cm3\text{ cm} instead of 1 cm1\text{ cm}.
  3. The new side length in centimeters will be 3×3 cm=9 cm3 \times 3\text{ cm} = 9\text{ cm}.
  4. Area of the garden on the new grid = side×side=9 cm×9 cm=81 cm2\text{side} \times \text{side} = 9\text{ cm} \times 9\text{ cm} = 81\text{ cm}^2.

Explanation:

When we change the grid size, the number of grid squares occupied stays the same, but the physical measurement of each square increases, leading to a much larger total area.