Contextualization

Theoretical Introduction

The theme in question deals with the comparison between fractions, an extremely important concept in mathematics. Fractions are ways of representing quantities that are not whole, that is, they are divided into pieces. For example, when we eat half of a pizza, we are eating a pizza divided into 2 equal parts, that is, 1/2 of the pizza.

Saying that one fraction is smaller, equal, or greater than another is making a comparison between fractions. For example, if we have the fractions 1/3 and 1/2, we can affirm that 1/2 is greater than 1/3, because if we divide a pizza into two equal parts, each part will be larger than if we divide it into three equal parts.

To compare fractions, we can use various methods. One of these methods is to find equivalent fractions, where two fractions are equivalent when they represent the same quantity. Another method is to compare fractions with the same denominator or numerator.

Theme Contextualization

Understanding and comparing fractions is necessary for daily activities such as cooking, shopping, dividing tasks, among others. Imagine that you need to divide a cake for a party. If you divide the cake into 10 parts and eat 2, you ate 2/10 or 1/5 of the cake. But if your friend eats 3 slices, he ate more than you, right?

In the financial market and in sectors such as engineering and civil construction, fractions are also present. Think about dividing a plot of land into equal parts or calculating interest on a financial investment, for example. In all these situations, it is crucial to have a good understanding of fractions.

Practical Activity

Name: "The Great Fraction Race"

Project Objective

The practical application of this project aims to provide students with a greater understanding and familiarity with the concept of fractions and their comparison.

Project Description

Students will be divided into groups of 3 to 5 members and will have to organize a car race where each car moves a fraction of the track per turn. The car that completes the track first wins.

Each group must produce:

1. A race track divided into equal parts (preferably 10, to facilitate).
2. Simple models of cars made of paper, cardboard, or similar material.
3. Fraction cards that will determine the distance each car will travel on each turn.

Each group must produce a written report at the end of the project, based on and directly connected to the activities carried out in the project.

Necessary Materials

1. Pencil, ruler, and eraser
2. Paper or cardboard to make the race track and car models
3. Colored pencils or markers
4. Scissors
5. Post-its or papers to write the fractions

Step by Step

1. Each group draws and colors a race track on paper or cardboard. The track must be divided into equal parts (for example, 10 parts).

2. Next, the students create different car models for each group.

3. The students then write fractions on the post-its or papers. The fractions can range from 1/10 to 1/2 to prevent the race from ending too quickly.

4. Now, the race begins. In each turn, a representative from each group draws a post-it and moves the car of their group according to the fraction drawn. For example, if they drew 1/3, they move the car to one-third of the track.

5. The game continues until a car reaches the end of the track.

6. During the game, students should note which fractions were more advantageous, that is, which allowed the cars to advance more on the track.

7. At the end of the game, students should prepare a report on the activity.

In the report, students must:

1. In the Introduction, contextualize the theme, its relevance and real-world application, as well as the purpose of the project.

2. In the Development, explain the game in detail, indicate the methodology used, and finally, present and discuss the results obtained. Explain which fractions proved to be the most advantageous in the race and why. Explain how equivalent fractions behaved in the game.

3. In the Conclusion, recap the main points, explain the learnings obtained, and draw conclusions about the project.

4. In the Bibliography, indicate the sources that were referenced in the project development.

The final report aims to bring together the knowledge acquired during the project execution, allowing students to demonstrate their understanding of the concept of comparing fractions and equivalent fractions.

The final project delivery will consist of the produced game, the notes taken during the game, and the final report. The project must be delivered one week after the start date.