Lesson plan of Area: Rectangle and Parallelogram

Objectives (5 - 7 minutes)

1. Understanding the concept of the area of a rectangle and a parallelogram.

   • Students should understand that the area of a rectangle is calculated by multiplying its length by its width, while the area of a parallelogram is calculated in the same way.
   • It will be emphasised that the length of a rectangle is the side that is perpendicular to the width, whereas in a parallelogram, the length can be any of the sides.

2. Applying the concept of area to find the area of rectangles and parallelograms.

   • Students should be able to use the area formula to calculate the area of rectangles and parallelograms.
   • Practical examples will be provided so that students can apply the formula and calculate areas.

3. Differentiating between rectangles and parallelograms.

   • Students should be able to distinguish between rectangles and parallelograms by identifying their unique characteristics.
   • Visual and practical examples will be provided to help students identify and differentiate between the two.

Secondary Objectives:

• Developing logical thinking and problem-solving.

  • By working through problem situations that involve the area of rectangles and parallelograms, students will be encouraged to think logically and develop their problem-solving skills.
  • This will be fostered through hands-on activities and classroom discussions.

• Encouraging active participation and teamwork.

  • In order to achieve the proposed Objectives, students will be encouraged to actively participate in the lesson by asking questions, sharing ideas and working in teams to solve problems.

• Fostering an interest in mathematics.

  • The teacher will endeavor to present mathematics in an engaging and interesting way, using practical examples and real-life situations to demonstrate the applicability of the concepts of area of rectangles and parallelograms.

Introduction (10 - 15 minutes)

1. Review of previous concepts (3 - 5 minutes):

   • The teacher will begin the lesson by asking students to review the concepts of perimeter and area, which were discussed in previous lessons.
   • This review is crucial to ensure that students have a solid foundation before moving on to the main topic of the lesson: area of rectangles and parallelograms.

2. Problem situation (3 - 5 minutes):

   • The teacher will present two problem situations to spark students' interest:
     1. The first problem situation could be calculating the amount of wallpaper needed to cover the walls of a rectangular or parallelogram-shaped room.
     2. The second problem situation could be calculating the area of a football pitch, which is a rectangle, and the area of a rugby pitch, which is a parallelogram.
   • The teacher will encourage students to think about how to solve these problems, but will not provide the solution immediately.

3. Contextualisation (2 - 3 minutes):

   • The teacher will explain that calculating area is an essential mathematical skill used in a variety of everyday situations, from planning spaces (as in the wallpaper example) to engineering and architecture.
   • It will be highlighted that understanding the area of rectangles and parallelograms is fundamental to these practical applications.

4. Introducing the topic (2 - 3 minutes):

   • The teacher will introduce the topic of the lesson - Area: Rectangle and Parallelogram - explaining that the study of area of plane figures is one of the fundamental concepts in mathematics.
   • To capture students' attention, the teacher could share some interesting facts, such as:
     1. The fact that the formula for the area of a rectangle (length x width) is one of the simplest and most widely used in mathematics.
     2. The story behind the name "parallelogram", which comes from the Greek "para" (beside) and "gramma" (line), because the opposite sides of a parallelogram are parallel.
   • The teacher will conclude the Introduction by stating that by the end of the lesson, students will be able to calculate the area of rectangles and parallelograms and apply this knowledge to practical situations.

Development (20 - 25 minutes)

1. Activity 1: Constructing Rectangles and Parallelograms (10 - 12 minutes)

   • The teacher will divide the class into groups of 3-4 students, and each group will be given a set of toothpicks and modelling clay.
   • The teacher will explain that each toothpick represents one unit of length, and that the modelling clay will be used to attach the toothpicks and form the shapes.
   • The teacher will guide students to construct rectangles and parallelograms of different sizes and shapes, varying the length and the width.
   • During the activity, the teacher will circulate around the room, helping groups as needed and encouraging discussion about the characteristics and differences between rectangles and parallelograms.
   • Once the shapes have been constructed, the teacher will ask each group to measure the length and width of their shapes and calculate the area using the area formula for a rectangle or parallelogram (length x width).
   • The students will be encouraged to compare the areas of their shapes and discuss how changing the length or width affects the area.

2. Activity 2: Solving Problems (10 - 12 minutes)

   • The teacher will present students with two problems to solve in groups.
     1. Problem 1: "A gardener is planning to fence off a triangular area in his garden. He has three wooden stakes of different lengths. He knows that the area of a triangle is half of the product of its base and its height. How can he use his stakes to measure the area of the triangle?" (This question is designed to lead students to apply the concept of the area of parallelograms, which is similar to that of triangles.)
     2. Problem 2: "A student is trying to calculate the area of a football pitch, but he only has a measuring tape that measures up to 20 metres. How can he use the measuring tape to calculate the area of the pitch, given that a football pitch is in the shape of a rectangle and its dimensions are 100 metres long by 60 metres wide?" (This question is designed to challenge students to apply the area formula for a rectangle in a creative way.)
   • The groups will have a set amount of time to discuss and present their solutions. The teacher will encourage students to explain their reasoning and to check that their solutions make sense.

3. Discussion and Reflection (5 - 6 minutes)

   • After the problems have been solved, the teacher will lead a class discussion about the solutions found by the groups.
   • The teacher will highlight the main points discussed during the activities, reinforcing the understanding of the concept of area of rectangles and parallelograms.
   • The teacher will also encourage students to reflect on how the hands-on activity and the problems they solved relate to the theory learnt in the Introduction to the lesson.
   • To conclude, the teacher will recap the most important concepts discussed during the lesson and prepare students for the next stage of the lesson plan: guided practice.

Feedback (10 - 12 minutes)

1. Group discussion (3 - 4 minutes):

   • The teacher will ask each group to share their solutions or conclusions from the constructing rectangles and parallelograms activity and the problem-solving activity.
   • Each group will have a maximum of 2 minutes to present. During the presentations, other groups will be encouraged to ask questions and provide constructive feedback.
   • The teacher will facilitate the discussion, ensuring that all groups have a chance to share and that the comments are respectful and relevant to the topic.

2. Connecting to the theory (2 - 3 minutes):

   • After all the presentations, the teacher will review the theoretical concepts discussed in the lesson, highlighting how they apply to the solutions or conclusions presented by the groups.
   • The teacher will emphasise the importance of understanding the theory in order to be able to apply it effectively when solving practical problems.
   • The teacher will also take this opportunity to clarify any misunderstandings that may have arisen during the activities.

3. Individual reflection (3 - 4 minutes):

   • The teacher will ask students to reflect individually on what they have learnt in the lesson.
   • The teacher will provide some guiding questions, such as: "What was the most important concept you learnt today?" and "What questions do you still have?"
   • The students will have one minute to think about their answers. They can make notes of their reflections if they wish.
   • After the thinking time, the teacher will ask students to share their answers, if they feel comfortable doing so. The aim is to allow students to process the material covered and to identify any areas where they may need further practice or clarification.

4. Feedback and closing (2 - 3 minutes):

   • To close the lesson, the teacher will ask students for feedback on the lesson. This could include what they enjoyed, what they found challenging and what they think could be improved.
   • The teacher will thank the students for their participation and will reinforce the importance of the concept learnt for mathematics and for everyday life.
   • The teacher may also suggest additional resources for students who wish to deepen their understanding of the topic, such as books, online videos or interactive maths websites.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes):

   • The teacher will recap the main points covered during the lesson, reiterating the definition of the area of a rectangle and a parallelogram, the formula for calculating the area of both shapes, and the characteristics that differentiate these two geometrical shapes.
   • The teacher will remind students that the area of a rectangle and a parallelogram is calculated by multiplying the length by the width, and that in a rectangle the length is perpendicular to the width, whereas in a parallelogram the length can be any of the sides.
   • It will also be reinforced how the concept of area is applied in practical, everyday situations, such as in determining the amount of wallpaper needed to cover a room or in measuring the area of a sports field.

2. Connecting Theory to Practice (1 - 2 minutes):

   • The teacher will explain how the lesson connected the theory, the practice and the applications of the concept of area of rectangles and parallelograms.
   • It will be emphasised that the construction of the plane figures using toothpicks and modelling clay allowed students to visualise the characteristics of these shapes and to understand how the length and the width affect the calculation of the area.
   • Furthermore, solving the proposed problems provided students with the opportunity to apply the theory in practice, reinforcing the understanding of the concept of area and of how to calculate it.

3. Extra Materials (1 - 2 minutes):

   • The teacher will suggest additional materials for students who wish to further their knowledge about the area of rectangles and parallelograms.
   • These materials could include maths textbooks, educational websites and videos that explain in more detail the calculation of area and its applications.
   • The teacher could also encourage students to explore online geometry tools, where they can manipulate the shapes and calculate their areas interactively.

4. Importance of the Topic (1 minute):

   • To close the lesson, the teacher will highlight the importance of the topic covered for everyday life and for mathematics as a whole.
   • It will be emphasised that calculating area is not only a mathematical skill, but also a useful tool in a variety of professions and everyday situations.
   • The teacher will conclude by stressing that understanding the concept of area of rectangles and parallelograms is fundamental to solving practical problems that involve calculating the areas of plane figures.