Lesson Plan | Active Learning | Quadrilateral: Rhombus

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)

In the Objectives stage, the aim is to clearly establish what students should learn and which competencies they should develop during the lesson. This phase is crucial for directing students' focus and ensuring they understand the expected outcomes of their learning. Furthermore, by setting clear and specific objectives, students can better organize their previous study process and maximize the effectiveness of class time, focusing on application and practical problem-solving.

Main Objectives:

1. Empower students to identify and describe the essential characteristics of a rhombus, including the definition that all its sides are equal.

2. Develop skills in calculating measures of sides and angles in rhombuses through practical exercises.

3. Enable students to solve problems involving rhombuses, focusing on the application of the geometric properties of this quadrilateral in various contexts.

Side Objectives:

1. Encourage critical thinking and analytical skills among students when addressing complex geometric problems.
2. Promote collaboration and communication among students during practical activities.

Introduction

Duration: (15 - 20 minutes)

The Introduction phase is designed to engage students from the start, using problem situations to facilitate the review of previously studied content and to make immediate connections with practical applications of the rhombus. The contextualization serves to demonstrate the relevance and ubiquity of rhombuses in the real world, increasing students' interest and curiosity about the topic.

Problem-Based Situations

1.  Situation 1: Ask students to imagine that they are designing a playground where the paths should be paved with rhombus-shaped tiles. How could they calculate the amount of material needed using the properties of rhombuses?

2.  Situation 2: Challenge students to think about how a jeweler could use the geometry of rhombuses to create an intricate pattern in a necklace, considering the precise measurements and angles so that all the rhombuses in the design are identical.

Contextualization

The rhombus is a shape frequently found in both nature and designs created by humans, due to its symmetry and aesthetic properties. For example, the arrangement of cells in many types of fruits, such as lychees, displays patterns that can be analyzed through the properties of rhombuses. Additionally, this shape is popular in tile patterns and jewelry, where precision in measuring angles and sides is crucial for the beauty and functionality of the design.

Development

Duration: (70 - 75 minutes)

The Development stage is crucial for students to apply the knowledge acquired at home in a practical and interactive manner. This section allows them to explore different scenarios and problems involving rhombuses, promoting teamwork, creativity, and critical thinking. The activities are designed to be challenging and fun, ensuring that students can consolidate their learning through direct practice and real problem-solving.

Activity Suggestions

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

Activity 1 - Rhombuses in the Amusement Park

> Duration: (60 - 70 minutes)

- Objective: Develop skills for calculating the area in geometric figures and apply knowledge of geometry in a creative and practical project.

- Description: In this activity, students will be challenged to create a map for an amusement park, where all paths must be decorated with rhombus-shaped tiles. They should calculate the required amount of tiles and plan the arrangement to ensure that the design is aesthetically pleasing and functional.

- Instructions:

• Form groups of 5 students.

• Draw a sketch of the amusement park on a large sheet of paper, marking areas for rides, snack bars, and rest areas.

• Decide where the paths will go and draw them on the map.

• Calculate the area of each path and use the property of all sides being equal of the rhombus to determine how many tiles will be needed.

• Present the final project to the class, explaining the mathematical reasoning and design choices.

Activity 2 - Building a Rhombus Quilt

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of geometry to solve a practical design and proportion problem, stimulating creativity and teamwork.

- Description: Students will design a patchwork quilt using colored paper to create a pattern that involves rhombuses. They will need to calculate the dimensions of the rhombuses so that all pieces fit perfectly, simulating sewing a real quilt.

- Instructions:

• Organize into groups of up to 5 students.

• Each group receives colored paper and scissors.

• Choose a pattern that involves rhombuses and decide on the dimensions of the rhombuses so that all fit without leftovers.

• Cut the paper rhombuses and assemble the pattern onto a large base sheet of paper.

• Discuss the importance of precise measurements and present the final work to the class.

Activity 3 - Rhombus Puzzle Challenge

> Duration: (60 - 70 minutes)

- Objective: Promote understanding of the properties of rhombuses and their applicability in complex geometric constructions, fostering problem-solving skills and teamwork.

- Description: In this challenge, students will receive various rhombuses cut from cardstock. They must use these pieces to form larger geometric figures, such as stars or other polygons, exploring the properties of the angles and sides of the rhombuses.

- Instructions:

• Divide into groups of no more than 5 people.

• Distribute cut cardstock in the shape of rhombuses to each group.

• Challenge them to assemble different geometric shapes using all the rhombuses provided.

• Each group must calculate the angles necessary for the rhombuses to fit perfectly into the desired shapes.

• Present the created shapes and discuss the difficulties and strategies used.

Feedback

Duration: (10 - 15 minutes)

The purpose of this feedback stage is to allow students to articulate what they learned and how they applied the acquired knowledge. Group discussion helps consolidate learning, allows for the exchange of ideas and strategies among students, and reinforces the practical application of mathematical knowledge in real situations. This stage also serves as an informal assessment of students' understanding of the topic studied.

Group Discussion

At the end of the activities, gather all the students for a group discussion. Start with a brief introduction about the importance of sharing discoveries and strategies used during the activities. Encourage each group to explain their solutions, challenges faced, and what they learned about the properties of rhombuses. This is an opportunity for students to reflect on the application of mathematics in the real world and how geometry can be used in different contexts.

Key Questions

1. What were the biggest challenges in calculating measurements and angles of the rhombuses during the activities?

2. How did the properties of rhombuses help in solving the proposed problems?

3. Are there situations in everyday life where you could apply what you learned today about rhombuses?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion section is to consolidate the learning acquired throughout the lesson, connecting theoretical concepts with the practical applications discussed during the activities. This stage is essential for reinforcing students' understanding of the topic and ensuring they perceive the relevance of mathematical knowledge in real situations. Furthermore, it is an opportunity for students to reflect on how they can apply what they learned in their daily lives and in future academic or professional situations.

Summary

 Class Summary: During today's class, we explored the rhombus in depth, a quadrilateral with equal sides, addressing its geometric properties, such as internal angles and symmetry relationship. We reviewed how to calculate the area and perimeter of the rhombus and applied that knowledge in practical activities involving everything from designing an amusement park to creating a patchwork quilt.

Theory Connection

 Connection Theory and Practice: Today's lesson was structured for students to apply theoretical knowledge in practical and real situations, such as in jewelry design and construction of geometric patterns. This demonstrates the relevance of the study of rhombuses not only as a mathematical concept but as a useful tool in various areas of knowledge and everyday life.

Closing

 Importance of the Rhombus: Understanding the properties of rhombuses and how to calculate their measures is crucial not only for mathematics but also for practical applications in design, architecture, and art. The ability to solve problems using these geometric concepts allows students to develop more critical and analytical thinking skills, essential in many careers.