Contextualization

Hello, little mathematicians! Let's embark on an adventure full of discoveries and learning. Imagine that you are on a trip and need to move from one place to another. Have you ever stopped to think how this is possible? Mathematics can help us better understand how we can move from one point to another.

When we talk about displacement, we are referring to the change in position of something or someone. Every day, we are constantly moving. When we are at home and go to school, for example, we are displacing ourselves. And how is mathematics involved in this? Well, mathematics helps us understand the distance we travel, the time it takes to cover that distance, and the speed at which we move.

Introduction

Now that we know what displacement is, let's learn about a very important word: vector. A vector is a quantity that has direction, sense, and magnitude. This may seem complicated, but it's simpler than it seems.

Imagine you are in a car and want to go to a friend's house. First, you need to know the direction, whether it's right or left. Then, you need to know the sense, whether it's forward or backward. Finally, you need to know the distance you will travel, that is, the magnitude. And that's what a vector tells us: where, in which direction, with what sense, and at what distance we are moving.

Now, let's talk about something you probably use every day: GPS. Did you know that GPS also uses mathematics to calculate displacement? That's right! When you enter the address of where you want to go in the GPS, it calculates the distance, time, and speed you will travel. And it does this using the concepts we are learning: displacement, vector, and mathematics.

So, are you ready to get your hands dirty and discover how mathematics helps us understand the displacement of objects and people? Let's go!

Practical Activity

Activity Title: "The Great Mathematical Journey"

Project Objective:

• Understand the concept of displacement, vector, speed, and time through a practical experience.
• Apply these concepts in real displacement situations.

Project Description:

In this activity, we will simulate a car trip using the concept of displacement, vector, speed, and time. Each group will have to plan a trip, determining the displacement, vector, speed, and time taken to reach the destination.

Required Materials:

• A printed or drawn map of a fictional city (can be made of cardboard or on the floor);
• Toy cars (or any other object that can represent the vehicle);
• Ruler and stopwatch (can be on the phone);
• Paper and pencil for notes.

Step by Step:

1. Group Formation: Students will divide into groups of 3 to 5 members. Each group will be responsible for planning their own trip.

2. Destination Choice: Each group must choose a destination in the fictional city.

3. Trip Planning: With the map in hand, students must trace the path they will take, defining the directions (north, south, east, west), the senses (forward, backward), and the distance traveled.

4. Determination of the Vector: After defining the path, the group must determine the vector of the trip. Remember, the vector is the combination of direction, sense, and magnitude (distance).

5. Calculation of Time and Speed: Now, it's time to calculate how long it will take to reach the destination and the average speed. For this, students must measure the distance on the map with the ruler and then determine the time it would take to cover the same distance with the toy car. With this data, they can calculate the average speed using the formula: speed = distance / time.

6. Project Presentation: Each group must present their planning to the class, explaining how they arrived at the vector, time, and speed.

7. Trip Execution: Finally, each group will put the planning into practice, following the path determined on the map with the toy car. During the trip, they must measure the time taken and, in the end, check if the calculated average speed was the same.

Remember, the most important thing is to have fun while learning! Bon voyage, little mathematicians!

Delivery Format:

Each group must submit a written or drawn report, containing the map of the fictional city with the trip planning, notes on the vector, time, and speed, and a brief explanation of what they learned from the activity. The report must be submitted to the teacher at the end of the week.