Let's practice on the topic of "scale" to understand it better. But what we understand, we don't forget! Let's start by familiarizing ourselves with the task. On a map with a scale of 1:1000, the distance between ponds is 2 cm. What is this distance in reality? To find out, we'll multiply the scale by the distance on the map and convert the result into more comprehensible units of measurement if we see the need. So, two centimeters on the map correspond to twenty meters in reality. Explore and continue on your own. Solution: Real distance = scale x map distance Real distance = 1000 x 2 cm = 2000 cm = 20 m Task: In a garden house model with a scale of 1:100, the house is 3 cm tall. How tall is the real house? Solution: House height = scale x model height House height = 100 x 3 cm = 300 cm = 3 m Task: On a plan with a scale of 1:50, the pool is depicted 4 cm wide. How wide is the real pool? Solution: Park width = scale x map width Park width = 50 x 4 cm = 200 cm = 2 m Task: If the real house length is 10 meters and in the scale model it's depicted as 2 cm long, what is the scale? Solution: Scale = house model length divided by real house length. Scale = 2 cm / 10 m = 2 cm / 1000 cm = 1:500 What's the scale of a map where 6 cm corresponds to 12 km in real life? Solution: Scale = map distance / real distance Scale = 6 cm / 1200000 cm = 1:200000 I hope these examples helped you understand the concept of scale better! Goodbye!

Exploring the World of Scales: A Mathematical Journey

Understanding the concept of scale is crucial not just in mathematics but in our daily lives. From reading maps to constructing models, scales help us represent real-world distances in a manageable way. In this article, we will delve into some new examples and methods to grasp the concept of scale more deeply, complementing the knowledge gained from our video lesson.

Why Scale Matters

Imagine wanting to draw the entire Earth on a piece of paper. Without scaling down the real distances, it would be impossible. This is where the concept of scale comes in handy. It allows us to shrink or enlarge objects or distances while keeping the proportions accurate, enabling us to represent something as vast as the Earth on a small map or a sheet of paper.

New Examples to Consider

1. The Classroom Map

Let's say we want to create a classroom map on a scale of 1:50. If the actual length of the classroom is 10 meters, our map would depict this length as 20 cm. Calculating this is straightforward: Real distance = scale x map distance. Hence, the map length = 50 x 20 cm = 1000 cm or 10 m, bringing our drawing to life with accurate proportions.

2. Scale Model of a Car

If a toy car model uses a scale of 1:20, and the model is 15 cm long, how long is the actual car? Applying our formula, Real length = 20 x 15 cm = 300 cm, or 3 meters. This example shows how scale models help us understand the dimensions of objects too big to fit inside our homes.

3. Scaling Down a Mountain

Representing a mountain in a geography project could seem daunting, but with scale, it’s achievable. If a mountain is 1,000 meters high and we use a scale of 1:1000, the model height would be 1 meter. This manageable size helps us appreciate the mountain’s majesty on a smaller, more comprehensible scale.

Conclusion

Grasping the concept of scale enhances our understanding of the world. It bridges the gap between the unimaginable and the tangible, enabling us to explore, represent, and appreciate objects and distances of all magnitudes. By practicing with different examples and scales, we can develop a deeper understanding of this fundamental concept in mathematics.