Context
Theoretical Introduction
The logarithmic function is an important mathematical concept and is a fundamental element in many fields of science. Basically, the logarithm of a number is the exponent that we need to apply to a certain base to obtain this number. The base is given by a positive number different from 1.
A key concept is the inversion between the exponential function and the logarithmic function. That is, if the exponential function is expressed as y = b^x, the logarithmic function will be expressed as x = log_b(y), where 'b' represents the base, 'x' the logarithm and 'y' the number.
Understanding the graph of a logarithmic function is fundamental to understand the relationship between the logarithm and the base and the number. These graphs are characterized by a curve that starts on the Y axis and grows in a decelerated manner as it moves to the right on the X axis.
Contextualization
Logarithms have a wide range of practical applications ranging from performing complex calculations to modeling phenomena in physics, biology, economics and many other disciplines. For example, in physics, logarithms are used to calculate the magnitude of earthquakes on the Richter Scale. In biology, they help in understanding population growth.
Understanding how the logarithmic function behaves and how to represent it graphically is, therefore, a very important skill not only for mathematics, but for various other areas of knowledge that are based on calculations and quantitative analyzes.
Practical Activity
Activity Title: Bringing Logarithms to Life
Project Objective
The main objective of this project is to lead students to understand logarithmic functions and their graphical representation in a practical and engaging way.
Detailed Project Description
In this project, the groups will assume the role of teachers and must develop an "interactive whiteboard" that explains the logarithmic functions and graphically demonstrates their behavior.
The interactive whiteboard should allow the user to change the base of the logarithm, as well as the number, and see how these changes are reflected in the graph. In addition, the groups must create a mini video tutorial explaining how their interactive whiteboard works and how to use it to understand logarithmic functions.
Required Materials
- Cardboard or brown paper
- Colored pens
- Pencils and eraser
- Ruler and compass
- Video editing and recording software (a smartphone can be used)
Detailed Step-by-Step to Carry Out the Activity
-
Interactive Whiteboard Assembly: The groups should use cardboard or brown paper to create their interactive whiteboard. On the board, there should be a space to insert the base of the logarithm and the number, and another space for the graph of the logarithmic function.
-
Drawing the Graph: Using the colored pens, the groups should draw the basic graph of a logarithmic function, clearly indicating the axes and their respective values.
-
Interactivity: The groups should think about how to make the graph interactive. One suggestion is to create moving arrows that can be placed on the graph to indicate the base and the number, and show how this affects the shape of the graph.
-
Video Tutorial: Finally, the groups must create a video tutorial explaining how to use the interactive whiteboard, including practical examples to illustrate the concept of logarithmic functions. The video should be short (around 5 minutes) and easy to understand.
Project Deliverables
At the end of the project, each group must deliver:
- The interactive whiteboard on logarithmic functions.
- The video tutorial explaining the concept of logarithmic functions and how to use the interactive whiteboard.
In addition, each group must write a written document containing:
- Introduction: Relevance of the theme and objective of the project.
- Development: Theory of logarithmic functions, detailed explanation of the project, methodology used and results obtained.
- Conclusion: Lessons learned, main points of the project and conclusions.
- Bibliography: Research sources used for the project.
In this document, it is important that students show how the practical activity connects with the theoretical concept, illustrating how the logarithmic functions were applied in the creation of the interactive board and how they were able, from the activity, to better understand the theme.
