Contextualization
Mathematics is a powerful tool used to describe and analyze the world around us. Within this vast field of study, a fundamental concept is ratio. Ratios are used to compare quantities of things or measurements. They are useful for understanding proportions and relationships between numbers.
A ratio is a way to compare quantities or measurements. Essentially, it is a fraction, or a division between two numbers. When we say the ratio of 10 to 2, we are saying that 'for every 10 of one thing, we have 2 of another'. This can be expressed as the fraction 10/2 or the quotient 5.
Ratios are used in many aspects of daily life, from the kitchen to the classroom. They are used in various disciplines such as Physics, Chemistry, Economics, Engineering, among others. It is common to use ratios to compare ingredients in a recipe, calculate the speed of a car, or even understand the efficiency of a certain process.
In the kitchen, for example, the ratio is used to determine the proportion of ingredients in a recipe. In Physics, ratios are used to calculate speed (distance/time), density (mass/volume), and many other concepts. In Economics, ratios are used for evaluating companies and understanding the cost-benefit relationship of an investment.
To deepen the study of ratios, you can consult the following resources:
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Video: 'Ratio and Proportion' (Khan Academy Brazil). Available on YouTube
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Book: 'Elementary Mathematics: Ratio and Proportion' (Carla Silva and Fernando Miranda). Available on Amazon
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Website: 'Ratios and Proportions' (Just Mathematics). Available at somatematica.com.br
Practical Activity
Activity Title: Scratch-off of Ratios
Project Objective
This project aims to develop students' understanding of the concept of ratio through a game. Participants will also work on their communication skills, time management, problem-solving, and teamwork.
Detailed Project Description
Each group of 3 to 5 students will receive a 'Scratch-off of Ratios' - a set of cards with a ratio problem on each of them. These problems will be based on real-world situations. For example, a card may say: 'You have 10 apples and 5 oranges. What is the ratio of apples to oranges?'
The students will scratch off the space below the problem to reveal the answer. Before scratching, however, they must calculate the ratio on their own and reach a consensus within the group. If they scratch and the group's answer is correct, they will earn points. If the answer is wrong, they will lose points.
The groups will make a list of all the ratios they calculated, as well as those of the corresponding problems. This list will be used later to write the project report.
Required Materials
- Cardboard cards or heavy paper
- Material to cover the answers on the cards (scratch-off ink, stickers, etc.)
- Pencils and paper for students to make calculations and notes
- Stopwatch or clock to control the time for each round
Detailed Activity Steps
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Divide the students into groups of 3 to 5.
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Distribute the 'Scratch-off of Ratios' to each group.
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Each group will have a certain amount of time to calculate the ratio of each problem before scratching and checking the answer.
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The students will write down all the calculated ratios and those corresponding to the problems.
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The groups will continue to solve problems until all cards have been used.
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With all the problems solved, the groups will have to prepare a final report.
The written report should include:
- Introduction: Describe the concept of ratio, its real-world application, and the project's objective.
- Development: Explain the theory behind the ratio and how it was applied in the activity. Describe the activity in detail and present the results obtained (the calculated ratios). Discuss any difficulties and how the group overcame them.
- Conclusions: Summarize the main points, explain what was learned, and draw conclusions about the project.
- Bibliography: List the sources used to prepare for the activity.
Remember, the idea of this project is not just to get the answers right, but to work as a team, understand the concept of ratio, and how it applies in various situations in our daily lives.
This project should take two to four hours to complete and has a one-week deadline for the final report submission.
