Contextualization
In this project, we will explore the fascinating world of 'Operations with Ratios'. But before we dive into this mathematical adventure, it is important to understand exactly what a ratio is. Simply put, a ratio is a way to compare the quantity, size, or number of one thing to the quantity, size, or number of another thing. In mathematics, we express a ratio through a fraction. For example, the ratio of 2 to 3 can be written as 2/3.
Operations with ratios are very important and often used in our daily lives without us even realizing it. To explore this in more detail, we need to understand how ratios work and how they relate to fractions. A ratio, as mentioned earlier, can be expressed as a fraction, and just like fractions, ratios can be multiplied and divided. Having a solid understanding of how to perform these operations is essential to mastering more advanced topics in mathematics and many other disciplines.
Now let's contextualize the concept of ratios in real-life situations. A classic example is the scale on maps. For instance, a ratio of 1:1000 on a map means that every 1 cm on the map corresponds to 1000 cm (or 10 meters) in reality. Another example is a car's speed, which is usually expressed as a ratio (kilometers per hour or miles per hour). These are just two examples, but ratios are present in many everyday contexts, demonstrating the importance of this concept.
To deepen your knowledge of ratios and operations with ratios, we recommend the following resources:
- Khan Academy: Ratios, Rates, and Percentages
- Só Matemática: Ratio and Proportion
- Mundo Educação: Ratio and Proportion
Use these resources as a starting point for our project and explore other materials you may find. Remember, the goal is to understand and apply the concept of ratios effectively.
Practical Activity: 'The Race of Ratios'
Project Objective
The objective of this project is to apply the concepts of operations with ratios in a playful context, simulating a car race where speed is represented through ratios. Students will calculate the speeds of the cars and, with that, determine the winners of the race.
Project Description
Each group of 3 to 5 students will be responsible for organizing and calculating the speeds of a car race. Each group member will be a driver who will 'race' a certain distance. Each driver's speed will be represented by a ratio (distance/time).
Students should calculate the ratios, perform operations with them, and represent them as fractions. They should also compare the ratios to determine the race winner.
Additionally, the groups should present a detailed report of the race, including the calculation of the ratios, the operation with the ratios, and the analysis of the results.
Necessary Materials
- Paper and pen for calculating the ratios.
- Stopwatch to measure the time of each 'race'.
- Ruler or measuring tape to measure the distance covered.
Step by Step
-
By drawing lots, each group member will receive a ratio that will represent the speed of their 'car' in the race (e.g., 2/3, 4/5, 6/7...).
-
The race distance should be 100 meters (or a value predetermined by the teacher). Each student will 'race' the determined distance.
-
With the help of a stopwatch, the time of each 'race' should be recorded.
-
Based on the drawn ratios and the recorded time, students should calculate the speed of each 'race'.
-
After calculating all speeds, the groups should compare the ratios and determine the race winner.
-
Finally, the groups should prepare a detailed report of the race, including an explanation of the ratio calculations, the step-by-step operations performed, and the analysis of the results.
Project Deliverables
The delivery of this project will consist of a report that will be divided into four parts: introduction, development, conclusion, and bibliography.
In the Introduction, group members should contextualize the project theme, explaining, for example, what ratios are and how they were used in the car race. They should also explain the importance of operations with ratios and their applicability in the real world.
In the Development, students should explain in detail the step-by-step process of the project. It should include the methodology used for ratio calculation, the execution of the 'races', the operation with the ratios, and the determination of the winner.
In the Conclusion, students should summarize the main learnings from the project execution. They should indicate what they learned about operations with ratios and how they applied them in the execution of the 'races'.
In the Bibliography, students should indicate all sources used for the project, whether books, internet sites, videos, etc. It is important to cite all sources consulted.
During the report elaboration, students should pay attention to clear and objective communication, prioritizing detailed explanation of the processes and reflection on the results obtained.
