Lesson Plan | Active Methodology | Logarithmic Function: Graph

Premises: This Active Lesson Plan assumes: a 100-minute class duration, prior student study both with the Book and the beginning of Project development, and that only one activity (among the three suggested) will be chosen to be carried out during the class, as each activity is designed to take up a large part of the available time.

Objective

Duration: (5 - 10 minutes)

This part of the lesson plan is crucial for building a strong understanding of logarithmic functions. By setting clear and targeted objectives, students can focus their learning effectively. With the knowledge gained in this stage, students will be able to apply theoretical concepts in practical situations during class, promoting a solid understanding of the subject. This focused and objective-driven approach is vital for the success of the flipped classroom methodology.

Objective Utama:

1. Help students accurately identify the graph of a logarithmic function.

2. Teach students how to draw the graph of a logarithmic function based on a given equation.

3. Enable students to extract values and interpret information directly from the graph of a logarithmic function.

Introduction

Duration: (10 - 15 minutes)

The introduction phase aims to engage students and revisit previously learned concepts, creating a direct link between theory and practice. Problem-based situations stimulate critical thinking regarding the real-world applications of logarithmic functions, preparing students for hands-on work during class. Contextualizing the learning adds depth, illustrating the relevance and widespread use of logarithmic functions across various disciplines.

Problem-Based Situation

1. Imagine an investor wanting to figure out how long it will take for their money to double with a continuous interest rate. How can a logarithmic function assist in solving this issue?

2. Consider a scientist studying the concentration of a chemical in a reaction over time. How can we use the logarithmic function to model the concentration changes? What steps do we need to take to determine the parameters of this function using experimental data?

Contextualization

The logarithmic function plays a significant role in various fields, such as economics for calculating compound interest and biology for examining population growth under specific conditions. Its historical significance in science, tracing back to the time of Napier and its impact on simplifying astronomical calculations, makes this topic intriguing, showcasing how mathematics enriches our understanding of the world.

Development

Duration: (75 - 80 minutes)

The development stage is key to translating theoretical knowledge into practical skills. By engaging students in hands-on group activities, this phase aims to strengthen their understanding of logarithmic function graphs, fostering interaction, collaboration, and meaningful learning experiences. Opting for just one activity helps ensure depth and significance in the learning process.

Activity Suggestions

It is recommended that only one of the suggested activities be carried out

Activity 1 - Logarithmic Treasure Hunt

> Duration: (60 - 70 minutes)

- Objective: Enhance skills in interpreting and analysing logarithmic graphs, while promoting teamwork and practical application of theoretical concepts.

- Description: In this fun activity, students will be split into groups of up to 5 members to embark on a mathematical 'treasure hunt,' where each 'treasure' is a specific point on a logarithmic function graph that they need to identify and analyze. Each group will receive a treasure map with clues describing the characteristics of logarithmic graphs (like asymptotes, intersections, and curve behaviour). They'll use these clues to find and pinpoint the correct locations on actual logarithmic graphs displayed on large sheets of paper.

- Instructions:

• Divide the class into groups, allowing for a maximum of 5 students per group.

• Provide each group with their treasure map and printed logarithmic graphs.

• Students should use the clues to identify specific points on the graphs, such as where the function crosses the Y-axis or approaches an asymptotic line.

• Each group will present their findings to the class, explaining how they used the clues to deduce the points and what those points signify within the context of logarithmic functions.

Activity 2 - Logarithmic Graph Builders

> Duration: (60 - 70 minutes)

- Objective: Promote visual and tactile comprehension of logarithmic graphs, enhance teamwork abilities, and ensure practical application.

- Description: Groups of students will get the chance to build graphs of various logarithmic functions from given equations. Using materials like rope, nails, and wooden boards, they will create physical models of the graphs. Each group will be assigned different logarithmic equations along with materials to display their graphs on a large bulletin board. The goal is to create a gallery of logarithmic graphs for everyone to explore and discuss.

- Instructions:

• Distribute different logarithmic equations to each group.

• Provide equipment like rope, nails, hammers, and wooden boards.

• Guide students in using the materials to represent the given logarithmic function, ensuring nails are secured at key points and connecting them with rope to shape the curve.

• Allow other students to visit the gallery of graphs for analysis and discussions.

Activity 3 - Logarithms in the Real World

> Duration: (60 - 70 minutes)

- Objective: Enhance the ability to apply mathematical concepts in practical situations while boosting analytical and presentation skills.

- Description: This activity focuses on using logarithmic functions to tackle real-world problems. Each group will receive unique scenarios, like predicting radioactive decay, modelling population growth, or calculating pH levels. They will solve these problems using logarithmic graphs and calculators, culminating in a presentation of their findings.

- Instructions:

• Present different real-world scenarios involving logarithmic functions to each group.

• Provide logarithmic graphs and calculators to the students.

• Instruct students to leverage the graphs to model and resolve the posed challenges.

• Each group will present their solution, detailing the steps they took and illustrating how logarithmic functions relate to their scenario.

Feedback

Duration: (15 - 20 minutes)

This feedback segment is vital for cementing students' learning, allowing them to exchange ideas and deepen their understanding of the practical applications of the concepts studied. Group discussions enable a sharing of perspectives and clarification of queries, strengthening both collective and individual comprehension of the material. Moreover, reflecting on practical tasks allows students to internalise the significance of logarithmic graphs and their uses.

Group Discussion

Kick off the group discussion with a brief recap of the activities undertaken, inviting students to share their experiences while working with logarithmic graphs. Encourage each group to showcase their findings and any challenges faced. Prompt students to explore how the concepts learned can be applied in real-life contexts and discuss how logarithmic graphs can be employed to solve practical problems.

Key Questions

1. What challenges did you encounter while identifying specific points on the logarithmic graphs during the activity?

2. In what ways would you leverage your understanding of logarithmic functions to address challenges in fields like economics or biology?

3. What insights have you gained about the behaviour of logarithmic functions, and how can this knowledge benefit you in real-life situations?

Conclusion

Duration: (5 - 10 minutes)

The aim of this conclusion stage is to reinforce and summarise the knowledge acquired during the lesson, ensuring students have a solid understanding of the logarithmic function and its graphical representation. Additionally, it seeks to highlight the connection between theory and practice, illustrating how mathematical learning is relevant in practical and everyday contexts. This final reflection solidifies learning and inspires students by demonstrating the real-world utility of the skills developed.

Summary

In this closing segment, we will revisit the key concepts of the logarithmic function, focusing on its graphical representation, identification of critical points, and interpretation. We will discuss how students utilised these concepts during practical activities that challenged them to construct and interpret graphs derived from logarithmic equations while tackling real-world problems.

Theory Connection

Today's lesson effectively bridged the theoretical knowledge of logarithmic functions with their practical applications through interactive learning methods. By incorporating activities that simulate real situations, students gained a better appreciation for the relevance of mathematical concepts beyond academic settings, underscoring the importance of mastering and applying mathematics.

Closing

The logarithmic function, with its broad range of applications, from population studies to economics, is key to numerous fields. Grasping and manipulating its graphs not only enhances mathematical comprehension but also equips students to tackle real and complex challenges they may face in their academic and professional journeys.