Lesson Plan | Active Learning | Ratio

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

This stage of the lesson plan aims to establish the necessary foundations for students to not only understand the concept of ratio but also apply it practically in everyday situations and more complex mathematical contexts. By clearly defining the objectives, students will be better prepared to engage in the proposed activities, knowing what is expected of them and how the knowledge acquired can be applied to real problems.

Main Objectives:

1. Empower students to identify and understand the concept of ratio, applying it in different mathematical and everyday contexts.

2. Develop skills in calculating ratios and proportions, focusing on solving practical problems, such as calculating average speed.

3. Encourage critical thinking and the application of mathematical concepts in real situations, promoting student autonomy and confidence.

Side Objectives:

1. Encourage collaboration among students during classroom activities, promoting discussions and exchanges of ideas that enrich everyone's learning.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students through problem situations they may encounter in daily life, prompting them to reflect on how the concept of ratio is applied practically. Furthermore, by contextualizing the importance of ratios in various areas, students are motivated to see the relevance of what they are learning, increasing interest and understanding of the subject.

Problem-Based Situations

1. Imagine that you are in a marathon and need to calculate your average speed to complete the course in the desired time. How would you use the concept of ratio to calculate this?

2. Consider that a cake recipe calls for 2 cups of flour for 1 cup of sugar. If you wanted to make double the recipe, how many cups of flour and sugar would you need? Use ratios to solve.

Contextualization

The ratio is a concept intrinsically linked to our daily lives, whether in the kitchen adjusting recipe proportions or in traffic calculating the average efficiency of a vehicle. Additionally, ratios are fundamental in areas such as economics, engineering, and natural sciences. For example, in engineering, understanding the ratio between the load and the area of a material can determine whether a bridge is safe. This practical applicability makes the study of ratios crucial for understanding and applying mathematics in real situations.

Development

Duration: (70 - 75 minutes)

The Development stage primarily aims to allow students to practically and contextually apply the concept of ratio, which was previously studied at home. The proposed activities aim to solidify students' understanding of ratios and proportions, using everyday situations and playful contexts to facilitate learning and retention of knowledge. Additionally, group activities encourage collaboration and communication, essential for developing social and mathematical skills.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Race of Ratios

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of ratio and proportion to calculate average speeds in various contexts and develop teamwork and communication skills.

- Description: In this activity, students will simulate a Formula 1 competition, where each group represents a team and must calculate the ratio of the average speed of their car in different sections of the circuit. They will use real data of times and distances from past races to calculate the ratios and proportions.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the times and distances data for each group, related to specific sections of a race.

• Ask each group to calculate the average speed of their car for each stretch.

• Use the formula V = S/T, where V is speed, S is distance, and T is time.

• After calculations, ask each group to present their ratios and how they arrived at them.

• Hold a class discussion about the different ratios found and possible calculation errors.

Activity 2 - Mathematical Cooking

> Duration: (60 - 70 minutes)

- Objective: Understand the practical application of ratios and proportions in a daily situation, while developing organizational and calculation skills.

- Description: Students will prepare a recipe in scale, where they will need to calculate the ratios and proportions of the ingredients to adjust the number of servings. They will use an original recipe and have to calculate the amount of each ingredient for 3, 6, and 10 servings.

- Instructions:

• Organize the room into cooking stations, where each station has the necessary ingredients and utensils.

• Distribute a recipe to each group, specifying the amount of ingredients for 1 serving.

• Ask each group to calculate the required amount of ingredients for 3, 6, and 10 servings.

• Groups must use ratios and proportions to adjust the quantities.

• Each group prepares the recipe and, at the end, presents the process and calculations made to the class.

• Promote a tasting of the recipe, discussing how the quantities influence flavor and texture.

Activity 3 - Scale Model Builders

> Duration: (60 - 70 minutes)

- Objective: Apply ratios and proportions practically, developing calculation and construction skills, while promoting creativity.

- Description: In this activity, students will use ratios to build scale models of famous buildings and monuments, such as the Eiffel Tower. They will need to calculate the proportions to replicate the real dimensions on a smaller scale.

- Instructions:

• Divide the class into groups and assign each one a different monument to build to scale.

• Provide the actual dimensions of the monument and the scale they should use.

• Groups calculate the new dimensions for the scale model using ratios and proportions.

• Students build the model using materials like paper, popsicle sticks, glue, etc.

• Each group presents their model, highlighting the ratios and proportions used in the calculations.

• Conduct a vote to choose which group best reproduced the correct proportions.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to consolidate students' understanding of the concept of ratio, allowing them to share their experiences and learnings. The group discussion helps identify potential interpretation errors and correct them collectively, as well as reinforces the applicability of ratios in various contexts. This joint reflection promotes a greater understanding of the theme and stimulates critical and collaborative thinking.

Group Discussion

After the activities are completed, gather all students for a group discussion. Begin the conversation with a brief introduction: 'Now that everyone has had the opportunity to apply the concept of ratio in different contexts, let’s share our discoveries and challenges. Each group will have the chance to present what they did and discuss the ratios found and the strategies used.'

Key Questions

1. What were the main challenges when applying ratios and proportions in the activities we performed?

2. How can the concept of ratio be applied in other everyday situations or in other subjects?

3. Was there any situation where the computed ratio didn't make sense? How did you correct the error?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage of the lesson plan is to ensure that students have a clear and consolidated understanding of the content covered. By summarizing key points, connecting theory to practice, and highlighting the relevance of the topic to real life, we reinforce learning and prepare students to apply what they have learned in diverse contexts. This conclusion also serves to emphasize the importance of ratios as essential tools for critical thinking and problem-solving.

Summary

To conclude, let’s recap what we learned about ratios. Initially, we explored the theoretical concept, understanding that a ratio is a comparison between two numbers. Next, we applied this concept in practical situations such as calculating average speeds in a race and in cooking, adjusting recipes for different serving amounts. Furthermore, we saw how ratios are fundamental in various fields, such as engineering and economics.

Theory Connection

Today's class was designed to seamlessly integrate theory and practice. Through activities like 'Race of Ratios', 'Mathematical Cooking', and 'Scale Model Builders', students could directly apply what they studied at home, solidifying theoretical understanding through practical applications that simulate everyday and professional situations.

Closing

Understanding ratios is essential not only for success in mathematics but also for daily life. The ability to think proportionally and apply ratios in practical situations, such as managing recipes or planning projects, is a valuable skill that prepares them for future challenges, both academic and professional.