Lesson Plan | Active Learning | Absolute Value and Number Order

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The objectives stage is crucial for clearly establishing what students should achieve by the end of the lesson. By outlining specific objectives, it helps to focus students' attention on the essential skills that need to be developed. This section also serves to align expectations and proposed activities to achieve the desired outcomes.

Main Objectives:

1. Understand the difference between the value of a number and its absolute value.

2. Calculate the absolute value of a number.

3. Order rational numbers in ascending and descending order, identifying the largest and smallest.

4. Recognize and operate with negative numbers.

Side Objectives:

1. Develop critical thinking skills when comparing the relative value of numbers.
2. Promote collaboration among students during practical activities.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the lesson's theme, using problem situations they may encounter in everyday life or in more playful contexts. The contextualization helps to show the relevance of the content, linking it to practical and real situations, thus increasing interest and awareness of the usefulness of what they are learning, as well as preparing them for practical applications during activities in the classroom.

Problem-Based Situations

1. Imagine that you are in a math competition and you receive the following task: order the following numbers in ascending order, but you can only see their absolute values. The numbers are -5, 7, -9, 3, -2. How would you solve this challenge?

2. Consider that you need to score points in a game where the distance traveled is measured in meters, and points are awarded every 5 meters. If you move 12 meters forward and then retreat 8 meters, how many points would you earn? And what if you started 8 meters behind the starting point?

Contextualization

The absolute value and ordering of numbers are essential mathematical skills in many everyday situations, from calculating distances to understanding personal finance. For example, on a map, coordinates are used to determine the exact location of a place, and often these coordinates include negative values. Additionally, in music, the intervals between notes are represented by integers and fractions, and knowing how to order them and understand their absolute values is fundamental in music theory.

Development

Duration: (65 - 75 minutes)

The Development stage is designed to allow students to practically and playfully apply the concepts of absolute value, ordering of numbers, and recognition of negative numbers studied previously. Through group activities, students are challenged to use theoretical knowledge creatively and to solve real or simulated problems, thus promoting active and collaborative learning.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - The Race of Secret Numbers

> Duration: (60 - 70 minutes)

- Objective: Practice ordering rational numbers in ascending and descending order, using the knowledge of absolute value as a guide.

- Description: In this activity, students will be divided into groups of up to 5 people and will participate in a 'race' to decipher a mathematical code. Each group will receive a series of envelopes, each containing a set of cards with rational numbers. Some cards will only have the absolute value of the number, and others will have both the number and its absolute value. The challenge is to order the cards in ascending and descending order, using only the absolute value when necessary.

- Instructions:

• Form groups of up to 5 students.

• Distribute the envelopes with the cards to each group.

• Explain that they must order the cards into two rows on the classroom floor, one in ascending order and the other in descending order.

• Allow them to discuss and plan their strategy for 10 minutes.

• Start the countdown of 30 minutes for the task.

• At the end, each group presents their solutions and explains the reasoning used.

• Conduct a brief class discussion about the different strategies used by the groups.

Activity 2 - The Mystery of the Missing Numbers

> Duration: (60 - 70 minutes)

- Objective: Develop the ability to work with negative numbers and absolute value in a problem-solving context.

- Description: Students will have to solve a mathematical mystery that involves discovering the 'missing' negative numbers. Each group will receive a series of clues that will lead them to discover the location and value of numbers on a 'corrupted' number line. Using the concept of absolute value, they will need to order the numbers and identify the missing ones.

- Instructions:

• Divide the class into groups of up to 5 students.

• Give each group a set of clues and a partially complete number line.

• Students must use the clues to find out the missing numbers and their correct order.

• Each group has 10 minutes to analyze the clues before starting to fill in the line.

• Allow 40 minutes for solving the mystery.

• Conclude with a discussion on how the absolute value helped in solving the problem.

Activity 3 - Builders of Mathematical Bridges

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of absolute value in solving a practical engineering problem, reinforcing the understanding of negative and positive numbers.

- Description: In this activity, students will work in groups to design and build a bridge using popsicle sticks and rubber bands. Each group will receive a set of cards that contain absolute values of distances that must be respected when building the bridge. Students will need to calculate the real distances (including negative numbers) from the absolute values to effectively build the bridge.

- Instructions:

• Organize students into groups of up to 5.

• Distribute the materials (sticks and rubber bands) and the challenge cards.

• Explain that they must use the absolute values to calculate the real distances needed.

• Groups have 10 minutes to plan the construction based on the absolute values provided.

• Allow 50 minutes for building the bridge.

• At the end, each group presents their bridge and explains how they applied the concept of absolute value in the construction.

• Discuss the different approaches and solutions found by the groups.

Feedback

Duration: (10 - 15 minutes)

This feedback stage is vital to consolidate students' learning, allowing them to articulate what they have learned and reflect on the practical application of mathematical concepts. Additionally, group discussion helps develop communication and collaboration skills, essential for teamwork and a deeper understanding of the content.

Group Discussion

To start the discussion, the teacher should ask each group to share their experiences and discoveries throughout the activities performed. It is suggested that each group present a brief summary of the problem they faced, how they solved it, and which strategies were most effective. The teacher should encourage students to reflect on the application of the concept of absolute value and the importance of negative numbers and their ordering.

Key Questions

1. What were the biggest challenges in trying to order the numbers using only their absolute values?

2. How did the concept of absolute value help you to understand and solve the proposed problems?

3. Was there any situation in which the order of negative numbers drastically influenced the outcome of the activity?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion stage is critical to ensure that students consolidate the knowledge acquired during the lesson. By summarizing key points, the teacher helps students reinforce their memory and understanding of the discussed content. Additionally, by discussing how the theory was applied in practice and the importance of concepts in everyday life, this stage reinforces the relevance of what was learned, encouraging students to become more engaged with the subject and value mathematical learning.

Summary

In the conclusion of the lesson, the teacher should summarize and recap the main points discussed about absolute value and ordering of numbers. It is essential to revisit how to calculate absolute value, the difference between value and absolute value, the ordering of rational numbers, and the manipulation of negative numbers.

Theory Connection

During the lesson, the theory about absolute value and the order of numbers was linked to practices like solving problems in groups, where students applied theoretical knowledge directly to practical and playful situations. The connection between theory and practice was established through examples from everyday life, reinforcing the relevance and usefulness of the mathematical concepts covered.

Closing

Finally, it is important to highlight the relevance of the concepts of absolute value and order of numbers in everyday life, from simple applications such as measuring distances to more complex situations such as solving mathematical problems or understanding musical notes. Understanding and manipulating these concepts is fundamental to the development of mathematical skills and critical thinking for students.