Contextualization

Theoretical Introduction

Mathematics has several applications in our daily lives, and one of these applications is in relation to measurements. When we talk about measurements, we are referring to quantities that can be understood through numbers, and these are present in various situations in our daily lives, such as when we measure the amount of water we consume, the weight of food, the distance between one place and another, among other situations.

Measurements include key concepts such as directly and inversely proportional quantities, which are used in many practical situations. Directly proportional quantities are those that increase or decrease in the same proportion, while inversely proportional quantities are those that, when one increases, the other decreases, and vice versa.

Another important application is in relation to the recognition that all empirical measurement is approximate. This means that no matter how precise our measuring tools are, there will always be a degree of uncertainty associated with them. It is important to understand this idea in order to have a realistic view of the measurements and data we deal with on a daily basis.

Practical Contextualization

But why is it important to learn about measurements? First, understanding measurements is essential because we use them in many daily activities. For example, cooking requires you to measure ingredients; building a house involves measuring areas and volumes; and if you like to travel, you will have to deal with measurements of distance and time.

In addition, measurements are essential in professions in sectors such as engineering, fashion, cooking, health, and many others. This means that no matter where students end up working, they are likely to use measurements in some way in their careers.

To learn more about the topic, we suggest the following sources:

• Book: "Mathematics: Context & Applications", by Luiz Roberto Dante. Editora Ática.
• Video: YouTube - Matemática Rio: Directly and Inversely Proportional Quantities
• Video: YouTube - Matemática Zup: Approximations and estimates

Practical Activity

Activity Title: Measuring the World Around Us

Project Objective

The objective of this activity is to apply the concepts learned about measurements, directly and inversely proportional quantities, and the idea that all empirical measurement is approximate, in practical and everyday situations.

Project Description

Students will be divided into groups of 3 to 5 members, who must choose an everyday scenario where measurements are applied. Possible scenarios might be: a cooking recipe, building a model house using cardboard, a travel itinerary, among others.

Required Materials

• Paper and pen for notes and calculations.
• Access to the internet for research.
• Various materials according to the scenario chosen by the group (ingredients for a recipe, cardboard, tape, glue, among others).

Step by Step

1. Within the group, discuss and choose a scenario in which you would like to work.
2. Research this scenario and identify the measurements and quantities present in it.
3. Document the steps of the process, indicating where and how measurements and quantities are used.
4. Apply the concepts of directly and inversely proportional quantities in these situations, recording your observations.
5. Remember to consider the idea that all empirical measurement is approximate and discuss how this applies to the chosen scenario.
6. Prepare a detailed final report of the project.

Final Report and Project Deliverables

After completing the practical part of the project, each group must prepare a final report. This document must contain four main sections:

1. Introduction: Contextualize the chosen topic, its relevance and application in the real world, and the objective of this project.
2. Development: Explain the theory behind the key themes of the project, explain the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.
3. Conclusions: Relate back to your main points, explaining the lessons learned and the conclusions drawn about the project.
4. Bibliography: State the sources that were used to work on the project, such as books, web pages, videos, etc.

Remember that this document is a fundamental component of the activity. It will be used to reflect on what was learned, to document the project, and to share your findings. Value each section and strive to make a clear, objective, and well-founded document.

The project must be submitted within a week from the date of its assignment. Remember to organize your time, divide tasks among the group members, and seek collaboration and teamwork.