Lesson Plan | Technical Methodology | Problems with Scientific Notation

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to ensure that students understand the importance of scientific notation, both in academic contexts and in the job market. By developing practical skills in converting and manipulating numbers in scientific notation, students will be better prepared to solve real-world problems and interpret data in scientific and technological disciplines. This brings them closer to the job market, where these skills are often required.

Main Objectives

1. Understand scientific notation and its importance in scientific and technological contexts.

2. Learn to convert numbers to scientific notation and vice versa.

3. Perform basic mathematical operations (addition, subtraction, multiplication, and division) using numbers in scientific notation.

Side Objectives

1. Develop the ability to solve practical problems involving scientific notation.
2. Apply scientific notation in the interpretation of scientific and technological data.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to ensure that students understand the importance of scientific notation, both in academic contexts and in the job market. By developing practical skills in converting and manipulating numbers in scientific notation, students will be better prepared to solve real-world problems and interpret data in scientific and technological disciplines. This brings them closer to the job market, where these skills are often required.

Contextualization

Scientific notation is an essential tool in various fields of knowledge, such as physics, chemistry, and astronomy. It allows very large or very small numbers to be represented in a more practical and manageable way. Imagine trying to calculate the distance between stars or the mass of subatomic particles without scientific notation— it would be almost impossible! This lesson will address how to use this powerful tool to simplify calculations and solve complex problems.

Curiosities and Market Connection

Scientific notation is widely used in the job market, especially in fields such as engineering, information technology, and finance. For example, engineers use scientific notation to calculate forces and pressures in structures, while data scientists use it to analyze large volumes of data. Curiosity: The number of cells in the human body is approximately 37 trillion, which in scientific notation is represented as 3.7 x 10^13. Without this notation, manipulating such large numbers would be much more difficult.

Initial Activity

Start the lesson with a provocative question: How would you represent the distance from Earth to the Sun (approximately 150 million kilometers) in a way that facilitates calculations? Then, show a short video (3-5 minutes) that visually and dynamically explains the importance of scientific notation in everyday and scientific situations. The recommended video is 'What is Scientific Notation?' from the 'Numberphile' channel on YouTube.

Development

Duration: 40 - 45 minutes

The purpose of this stage is to ensure that students understand and can apply scientific notation in a practical and relevant way. By engaging in collaborative and challenging activities, students consolidate their understanding and develop essential skills for solving real-world problems. The construction and use of a manual scientific notation calculator reinforce the concepts learned and promote creativity and collaboration.

Covered Topics

1. Introduction to scientific notation
2. Conversion of numbers to scientific notation and vice versa
3. Basic mathematical operations (addition, subtraction, multiplication, and division) with numbers in scientific notation
4. Practical applications of scientific notation in the job market

Reflections on the Theme

Guide students to reflect on how scientific notation simplifies the representation and manipulation of very large or very small numbers, and how this is essential in various fields of knowledge and the job market, such as in physics, engineering, and information technology.

Mini Challenge

Maker Challenge: Building a Scientific Notation Calculator

In this activity, students will build a basic calculator that performs operations with numbers in scientific notation using simple materials like cardboard, paper, markers, and a ruler. The calculator will be a manual tool that helps students understand and apply the concepts of scientific notation.

Instructions

1. Divide the class into groups of 4 to 5 students.
2. Distribute the necessary materials for each group: cardboard, paper, markers, ruler, and scissors.
3. Explain that each group should create a manual calculator with the following functionalities:
4. An area to input the base number (from 1 to 10).
5. An area to input the exponent (power of 10).
6. A system to perform basic operations (addition, subtraction, multiplication, and division) between two numbers in scientific notation.
7. A space to display the final result in scientific notation.
8. Guide students to discuss as a group how they will design and assemble the calculator, encouraging creativity and collaboration.
9. After construction, each group must present their calculator to the class, explaining how it works and demonstrating a calculation example.
10. Encourage the exchange of ideas among groups, highlighting the different approaches and solutions found.

Objective: Develop practical and collaborative skills by applying the concepts of scientific notation in building a manual tool that facilitates mathematical calculations.

Duration: 30 - 35 minutes

Evaluation Exercises

1. Convert the following numbers to scientific notation: 4500, 0.0078, 1230000.
2. Convert the following numbers from scientific notation to decimal form: 3.4 x 10^5, 2.1 x 10^-3, 6.02 x 10^23.
3. Perform the following operations using scientific notation: (2 x 10^3) + (3 x 10^2), (4 x 10^-4) - (1 x 10^-5), (5 x 10^6) * (2 x 10^2), (9 x 10^8) / (3 x 10^4).
4. Describe a practical situation where scientific notation would be useful and explain how you would use this notation to solve a problem.

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to consolidate learning by promoting reflection and discussion about the content addressed. By recapping the main points of the lesson and connecting theory with practice, students reinforce their understanding and recognize the relevance of the topic in real contexts. The discussion allows students to share their experiences and doubts, enriching the learning process.

Discussion

Promote an open discussion with students about the topics covered in the lesson. Ask them how scientific notation can be used in different subjects and in the job market. Encourage them to reflect on the activities carried out, especially the construction of the manual calculator. Ask what they found most challenging and how they overcame those challenges. Discuss how the fixation exercises helped consolidate their knowledge and invite them to share examples of everyday situations where scientific notation would be useful.

Summary

Summarize and recap the main contents presented during the lesson. Highlight the importance of scientific notation for simplifying the manipulation of very large or very small numbers. Remind students of the steps to convert numbers to scientific notation and vice versa, as well as to perform basic mathematical operations with those numbers. Reinforce the connection between theory, practice, and real applications, and how this was evidenced in the activities developed.

Closing

Briefly explain the importance of scientific notation in everyday life and in various careers, emphasizing how this skill can be a differential in the job market. Conclude the lesson by thanking the students for their participation and encouraging them to continue practicing and applying what they learned in practical situations and in other subjects. Make it clear that the ability to use scientific notation is valuable and widely applicable in various fields of knowledge.