Lesson Plan | Traditional Methodology | Ratio

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to establish a solid foundation on the concept of ratio, allowing students to understand its importance and application in various contexts. By clearly describing what a ratio is and how to calculate it, students will develop fundamental skills to solve mathematical problems and everyday situations that involve ratios.

Main Objectives

1. Identify and understand the concept of ratio.

2. Calculate ratios in different mathematical contexts.

3. Solve practical problems using ratio calculations, such as the average speed of a car.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to establish a solid foundation on the concept of ratio, allowing students to understand its importance and application in various contexts. By clearly describing what a ratio is and how to calculate it, students will develop fundamental skills to solve mathematical problems and everyday situations that involve ratios.

Context

To start the lesson on ratios, begin by telling a story or everyday situation that involves comparing two quantities. One example could be the comparison of the amount of sugar and flour in a cake recipe or comparing the distance traveled and time spent on a car trip. Explain that these comparisons are examples of ratios and are very common in various fields of knowledge and in daily life.

Curiosities

Did you know that the ratio is a fundamental concept in several areas of science and engineering? For example, in physics, the ratio between distance traveled and time taken gives us the average speed. In biology, the ratio between the number of predators and prey can determine the balance of an ecosystem. Even in economics, the ratio between supply and demand can influence market prices.

Development

Duration: (40 - 50 minutes)

The purpose of this stage is to deepen students' understanding of the concept of ratio, providing practical and detailed examples. By covering topics such as definition, simplification, and application of ratios, students will be able to identify, calculate, and apply ratios in various mathematical contexts and everyday situations.

Covered Topics

1. Definition of Ratio: Explain that a ratio is a comparison between two quantities, expressed as a fraction. Highlight that the ratio can be written in three forms: a/b, a:b, or a ÷ b. 2. Examples of Ratio: Provide everyday examples, such as the ratio of sugar to flour in a recipe (2:3), or the ratio between distance and time on a trip (100 km in 2 hours = 50 km/h). 3. Simplification of Ratios: Explain how to simplify a ratio by dividing both terms by the greatest common divisor. Use practical examples to illustrate the process. 4. Equivalent Ratios: Show that different ratios can be equivalent. For example, 2:3 is equivalent to 4:6. Explain how to find equivalent ratios by multiplying or dividing both terms by the same number. 5. Practical Application - Average Speed: Explain how to calculate average speed using the formula: Average Speed = Distance / Time. Provide practical examples and solve one or two problems with the students.

Classroom Questions

1. Calculate the ratio of 15 apples to 25 oranges and simplify the ratio. 2. If a car traveled 180 km in 3 hours, what was the car's average speed? 3. Determine if the ratios 4:6 and 8:12 are equivalent.

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage is to review and consolidate students' understanding of the concept of ratio, ensuring that they can apply the knowledge gained to solve practical problems. By discussing the answers in detail and engaging students in reflections and practical examples, this stage reinforces learning and promotes a deeper understanding of the content.

Discussion

• Question 1: Calculate the ratio of 15 apples to 25 oranges and simplify the ratio.

• Explain that the initial ratio is 15/25. To simplify it, it is necessary to find the greatest common divisor (GCD) of 15 and 25, which is 5. Dividing both terms by 5, we obtain the simplified ratio of 3/5. Thus, the ratio of 15 apples to 25 oranges is 3:5.

• Question 2: If a car traveled 180 km in 3 hours, what was the car's average speed?

• The average speed can be calculated using the formula Average Speed = Distance / Time. Substituting the given values, we have Average Speed = 180 km / 3 hours = 60 km/h. Therefore, the car's average speed was 60 km/h.

• Question 3: Determine if the ratios 4:6 and 8:12 are equivalent.

• To check if the ratios are equivalent, we can simplify both and compare them. The ratio 4/6 can be simplified by dividing both terms by the GCD, which is 2, resulting in 2/3. The ratio 8/12 can be simplified by dividing both terms by the GCD, which is 4, also resulting in 2/3. Since both simplified ratios are equal (2/3), we can conclude that the ratios 4:6 and 8:12 are equivalent.

Student Engagement

1. Ask students: Why is it important to simplify ratios? 2. Have students discuss in pairs: Give an everyday example where you use ratios and explain its importance. 3. Question: How can understanding ratios help in other subjects like physics or economics? 4. Suggest to students that they solve the following problem in groups: If a recipe requires 4 cups of flour for every 3 cups of sugar, how many cups of flour are needed for 9 cups of sugar?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the main points covered during the lesson, ensuring that students have a clear and comprehensive view of what they have learned. By recapping the content and highlighting its practical relevance, this stage reinforces the importance of the topic and promotes a deeper and lasting understanding.

Summary

• Definition of ratio as a comparison between two quantities, expressed as a fraction (a/b, a:b, or a ÷ b).
• Practical examples of ratios in everyday life, such as the ratio of ingredients in a recipe or average speed on a trip.
• Simplification of ratios by dividing both terms by the greatest common divisor.
• Equivalent ratios and how to find them by multiplying or dividing both terms by the same number.
• Calculation of average speed using the formula Average Speed = Distance / Time.

The lesson connected theory and practice by presenting the concept of ratio and then applying this concept in everyday examples, such as cooking recipes and average speed calculations. Solving practical problems helped students see the immediate utility of what they learned, facilitating understanding and retention of the content.

The concept of ratio is fundamental in everyday life, as it is often used in practical situations such as cooking, calculating speed, and even in economic and scientific analyses. Understanding ratios allows students to make informed decisions and solve problems effectively in various areas of knowledge and daily life.