Context

In our daily lives, we constantly deal with units of measurement. We use them to define time, calculate distances, buy groceries at the supermarket, measure our height, and many other things. The use of these units helps us better understand the world around us and enables us to make more informed decisions. Therefore, it is extremely important that we learn about the different systems of units and the correct way to convert them.

We have developed this project to address the theme of 'Unit Systems' in a somewhat playful, fun, and practical way. We want you to understand not only the academic importance of the theme but also how it applies in the real world. The teaching of Mathematics, contrary to what many believe, should transcend exercise sheets and connect directly with students' reality.

Introduction

Unit systems are sets of measurement units used to express quantities such as distance, time, volume, among others. There are different unit systems around the world, such as the International System of Units (SI), which is the most widely used system globally. However, in some countries, other systems are still used, such as the imperial system in the United Kingdom and the American system in the United States.

The SI consists of seven fundamental units of measurement (second, meter, kilogram, ampere, kelvin, mole, and candela) and various prefixes indicating multiples and submultiples of these units. Learning to convert between these units and their multiples/submultiples is an essential skill in various scientific and technical disciplines.

The ability to convert units is also extremely useful in everyday life. For example, it can help understand which is the best price at a supermarket (comparing the price per unit of different brands or packaging sizes), calculating the time needed to travel a certain distance, among many other applications.

Practical Activity: Mathematical Market

Project Objective

The objective of this project is to apply knowledge about unit systems and conversions in a practical context, through a shopping simulation at a supermarket. This activity will allow students to apply the skills learned in the classroom in a real-world scenario, promoting collaboration, communication, and time management.

Detailed Project Description

Students will be divided into groups of three to five members. Each group will be designated as a 'family' that needs to go to the supermarket to shop. The activity consists of selecting products, considering the different units of measurement and prices, and deciding which one has the best cost-benefit.

For example, a product may be cheaper, but the size or unit of measurement may make it not the most economical option. Students will need to convert the units, adjust the prices, and then decide which product to take.

Necessary Materials

1. List of products with prices and units of measurement (provided by the teacher).
2. Calculators.
3. Notebook or paper to make calculations.
4. Internet access for research, if necessary.

Activity Step by Step

1. The teacher distributes the list of products with prices and units of measurement to each group.
2. The groups must then analyze the available products and decide what to buy, taking into account the price and unit of measurement of each item.
3. Students must show their calculations and decisions, explaining the reason for each choice. Explanations should be logical and based on their calculations.
4. After deciding on all products, the group must calculate the total cost of the purchases.

At the end of the project, each group must submit a report addressing the following topics:

1. Introduction: Explain the purpose of the project, the relevance of learning unit systems, and how they are used in everyday life.
2. Development: Present the calculations made for unit conversion and the methodology used to decide which products to buy. Additionally, discuss the results obtained and the difficulties encountered during the process.
3. Conclusions: Summarize the main points of the project, what was learned, and what conclusions were drawn from the activity. Also include reflections on the importance of understanding unit systems in everyday situations.
4. Bibliography: Indicate the sources they relied on to work on the project such as books, web pages, videos, etc.

Note: The recommended time for the execution of this activity is two to four hours per student. The project deadline is one week from the start date.