Context

Theoretical Introduction

The study of functions is a main area of mathematics, concerning the relationship between two variables. A function can be thought of as a 'machine' that receives an input, called an independent variable, and produces an output, called a dependent variable.

Associated with this idea are the 'inputs and outputs of functions', which are, respectively, the values you feed into a function and the results it produces. This concept is a powerful tool for understanding and describing phenomena in the real world.

For example, think of a function as a cake recipe: the ingredients are the inputs, the recipe is the function, and the finished cake is the output. If you change the inputs (say, using milk chocolate instead of dark chocolate), the output - the cake - will be different.

Context

Functions are present in various everyday situations and in various areas of knowledge. From economics, where we can relate the price of a product and the quantity consumers are willing to buy, to physics, where we can relate the time it takes for an object to fall with its speed.

In the world of programming, the concept of function input and output is extremely relevant. Computer programs are essentially disguised functions that take inputs, such as mouse clicks or keyboard inputs, and produce outputs, such as graphics on the screen or sounds through the speaker.

Practical Activity: Function Maze

Project Objective

Create and solve a maze composed of different mathematical functions with the aim of deepening the understanding of functions, inputs and outputs, as well as improving teamwork, communication, time management, and problem-solving skills.

Detailed Project Description

Students will be divided into groups of 3 to 5 people, and each group will create a maze board representing a sequence of functions that must be solved to progress through the maze and reach the exit.

Each position on the board will be a function, and each function will have an input and an output determined by the group. The output of one function will be the input of the next function in the maze sequence. The goal is to create a challenging and interesting maze using a variety of functions.

Required Materials

• Large grid paper
• Colored pens
• Calculators
• Reference books or internet access to research functions

Detailed Step-by-Step

1. Each group receives a large grid paper and colored pens.

2. Next, they create a maze that traverses the grid paper, where each cell represents a different function. They should choose interesting and varied functions, each with a specific input and output.

3. The functions should be arranged so that the output of one is the input of the next.

4. After the maze is ready, the groups should exchange their mazes and try to solve them, calculating the outputs of the functions and moving through the maze according to these outputs.

5. Finally, the groups should review and discuss each other's solutions, providing feedback for the learning process.

Project Deliverables

At the end of the project, each group must present the created function maze and a detailed report on the maze creation and resolution process. The report should address the following points:

1. Introduction: Contextualization of the concept of functions, importance in the real world, and the project's objective.

2. Development: Details on the theory of functions used, detailed explanation of the activity, the methodology followed to create and solve the maze, along with the difficulties faced and how they were overcome.

3. Conclusions: Reflection on the main learning points of the project, the significance of the functions used in the maze, and the teamwork process.

4. Bibliography: References to the materials consulted during the project, such as books, websites, videos, among others.

The report should be submitted in digital or printed format, according to the teacher's preference, and should contain 5 to 10 pages. The function maze should be submitted along with the report. It is recommended that the report be written after all project stages have been completed, so that all points can be accurately addressed.