Lesson Plan | Traditional Methodology | Operations: Decimals

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to present the specific goals of the lesson to the students, clarifying what is expected for them to learn and be able to do by the end of the session. This initial guidance is essential to prepare students for the content that will be addressed and to motivate them to focus on the key elements of operations with decimal numbers.

Main Objectives

1. Understand the operations of addition, subtraction, multiplication, division, and exponentiation of decimal numbers.

2. Apply operations with decimal numbers in everyday situations such as calculating expenses in a store.

3. Develop the ability to solve mathematical problems involving decimal numbers accurately and efficiently.

Introduction

Duration: (10 - 15 minutes)

 The purpose of this stage is to capture the students' attention and situate them on the importance of the topic in everyday life. By presenting a familiar context and some curiosities, we aim to spark students' interest and motivation to learn about operations with decimal numbers. This helps to prepare the ground for the more technical explanations that will follow.

Context

 Good morning, students! Today we are going to learn about operations with decimal numbers. Have you noticed how we use decimals in our daily lives? For example, when we go to the store, the prices of products usually have decimal places, and we need to know how to add, subtract, multiply, and divide these values correctly to avoid making mistakes in our spending. In addition, decimals are present in many other situations, such as reading temperatures, measurements, and even in the money we keep in our piggy banks.

Curiosities

 Did you know that the concept of decimal numbers has existed for over 4000 years? It was used by the ancient Egyptians and Babylonians, and today it is fundamental to financial math and science. For example, without decimal numbers, it would be very difficult to perform accurate calculations in fields like engineering and medicine.

Development

Duration: (50 - 60 minutes)

 The purpose of this stage is to provide students with a detailed and practical understanding of operations with decimal numbers. Through clear explanations, demonstrative examples, and practical questions, students will be able to see how operations are performed step by step and apply this knowledge in real-life problems. This ensures they develop essential skills for math and everyday life.

Covered Topics

1. Addition of Decimal Numbers: Explain how to align decimal numbers by the comma before performing the addition. Use simple examples, like 2.3 + 1.45. 2. Subtraction of Decimal Numbers: Detail the importance of aligning the numbers by the comma and explain how to perform the subtraction, including the need to 'borrow' when necessary. Use examples like 5.6 - 2.78. 3. Multiplication of Decimal Numbers: Address multiplication temporarily ignoring the comma, multiplying as if they were whole numbers. Then, explain how to count and position the decimal places in the result. Use examples like 3.2 x 4.5. 4. Division of Decimal Numbers: Explain how to move the comma of the divisor to turn it into a whole number and do the same with the dividend. Then perform the division normally. Use examples like 7.5 ÷ 1.25. 5. Exponentiation of Decimal Numbers: Address exponentiation with decimals, explaining how to multiply the decimal number by itself the number of times indicated by the exponent. Use examples like (1.2)^3. 6. Application in Everyday Situations: Demonstrate how these operations are used in real situations, such as calculating the total cost of purchases at the store. Use examples that involve multiple operations, like calculating the total cost for 3 items with decimal prices and applying a percentage discount.

Classroom Questions

1. Calculate the sum: 3.56 + 7.89 + 0.45. 2. Solve the subtraction: 15.6 - 8.75. 3. Multiply: 2.4 x 3.5. 4. Divide: 12.5 ÷ 0.5. 5. Calculate the exponentiation: (1.1)^4.

Questions Discussion

Duration: (20 - 25 minutes)

 The purpose of this stage is to review and consolidate the knowledge acquired by the students during the lesson. Through a detailed discussion of the resolved questions, students have the opportunity to clarify doubts, reinforce concepts, and share their resolution strategies. Engaging with reflective questions helps connect the learned content with practical situations, promoting a deeper and lasting understanding.

Discussion

• Explain that to calculate the sum 3.56 + 7.89 + 0.45, it is necessary to align the numbers by the comma and add each column of digits, starting from the right. The result is 11.90.

• For the subtraction 15.6 - 8.75, align the numbers by the comma. Since 8.75 has more decimal places, add a zero to the end of 15.6 to get 15.60. Perform the subtraction column by column, 'borrowing' when necessary. The result is 6.85.

• In the multiplication 2.4 x 3.5, temporarily ignore the commas and multiply the numbers as whole numbers (24 x 35 = 840). Then count the total number of decimal places in the factors (1 + 1 = 2) and place the comma in the product, resulting in 8.40.

• For the division 12.5 ÷ 0.5, move the comma of the divisor one place to the right to turn it into a whole number (5). Do the same with the dividend, changing 12.5 into 125. Perform the division normally: 125 ÷ 5 = 25.

• In the exponentiation (1.1)^4, multiply 1.1 by itself four times: 1.1 x 1.1 = 1.21, 1.21 x 1.1 = 1.331, 1.331 x 1.1 = 1.4641.

Student Engagement

1. Ask the students how they aligned the decimal numbers for addition and subtraction. 2. Discuss the importance of counting the decimal places in multiplication and how this affects the result. 3. Ask the students to explain the process of moving the comma in division and why this is necessary. 4. Request that students share everyday situations where they used operations with decimal numbers. 5. Ask students how understanding these operations can help them in other subjects and real-life situations.

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the main points addressed during the lesson, ensuring that students have a clear understanding of the concepts and their practical application. By reinforcing the importance and relevance of the topic, we aim to motivate students to apply this knowledge in their everyday lives.

Summary

• Alignment of decimal numbers by the comma for addition and subtraction.
• Multiplication of decimal numbers temporarily ignoring the comma and adjusting the decimal places in the result.
• Division of decimal numbers moving the comma of the divisor and the dividend to turn the divisor into a whole number.
• Exponentiation of decimal numbers by multiplying the decimal number by itself the number of times indicated by the exponent.
• Application of operations with decimal numbers in everyday situations, such as calculating the total cost of purchases in the store.

The lesson connected theory and practice by providing detailed explanations of operations with decimal numbers and then demonstrating these operations in real situations, like purchase calculations at the store. This allowed students to see the direct application of mathematical concepts in their daily lives.

Understanding operations with decimal numbers is essential for various everyday activities, such as shopping, calculating discounts, measuring ingredients in recipes, and managing personal finances. Also, this knowledge is fundamental for professional areas such as engineering, medicine, and science, where precision in calculations is crucial.