Objectives (5 - 7 minutes)

1. Understand the concept of area in geometry: Students will be able to define and explain the concept of area in geometry. They will understand that area is a measure of the amount of space inside a shape and is always expressed in square units.

2. Calculate the area of squares: Students will learn the formula for calculating the area of a square (Area = side²) and practice applying it to various examples.

3. Calculate the area of parallelograms: Students will learn the formula for calculating the area of a parallelogram (Area = base × height) and practice applying it to various examples.

Secondary Objectives:

• Develop problem-solving skills: Students will enhance their problem-solving abilities by applying the area formulas to solve mathematical problems.

• Improve collaborative learning: Through group activities and discussions, students will enhance their collaborative learning skills.

• Foster interest in geometry: By engaging in hands-on activities and games, students will develop an interest in geometry, particularly in the concept of area.

Introduction (10 - 15 minutes)

• The teacher begins the lesson by reminding students of the basic concepts of geometry they have learned so far, such as the definitions of shape, sides, and angles. The teacher also revisits the concepts of square and parallelogram, ensuring that students have a clear understanding of these shapes. (3 - 4 minutes)

• The teacher then presents two problem situations to the class:

  1. "Imagine you are a farmer who needs to decide how much fencing to buy to enclose a square field. How would you calculate the area of the field to determine the amount of fencing you would need?"
  2. "Now, imagine you are an architect designing a floor plan for a room that has a parallelogram shape. How would you calculate the area of the room to determine the amount of flooring you would need?" These scenarios are used to contextualize the importance of understanding the concept of area in real-world applications. (3 - 4 minutes)

• The teacher then expands on the second problem, discussing the importance of understanding the area of parallelograms in real-world applications such as architecture and design. The teacher might mention the use of parallelograms in the design of bridges, buildings, and even in art and fashion. This discussion helps to spark students' interest and curiosity about the topic. (2 - 3 minutes)

• After this, the teacher introduces the topic of the day: "Today, we will be exploring the concept of area in geometry. Specifically, we will be learning how to calculate the area of squares and parallelograms. Understanding the area of these shapes will not only help us solve mathematical problems, but it will also help us in real-world situations, like the ones we just discussed." This introduction sets the stage for the learning objectives and prepares the students for the upcoming activities. (2 - 3 minutes)

• To conclude the introduction, the teacher might share a fun fact or a real-world application related to the topic. For example, the teacher could mention that the concept of area is used in computer graphics to determine the size of a shape on a screen. Or the teacher could share that the largest square-shaped country in the world is Kazakhstan. These extra tidbits of information can help to engage students and make the lesson more enjoyable. (1 - 2 minutes)

Development (20 - 25 minutes)

Activity 1: "Area Race" Game (10 - 12 minutes)

• The teacher divides the class into several groups and distributes a pack of geometrical cards to each group. These cards have various squares and parallelograms drawn on them, with the measurements of the sides and heights provided. (1 - 2 minutes)

• The teacher explains the "Area Race" game rules: Each group has to calculate the area of the shapes on their cards as quickly as possible using the correct formulas. The first group to correctly calculate the area of all their shapes is the winner. (2 - 3 minutes)

• The teacher encourages students to help each other and share their strategies during the game. This fosters collaborative learning and enables students to learn from each other. (1 - 2 minutes)

• Once a group finishes, they need to show their cards to the teacher for verification. If the areas are calculated correctly, they receive a new pack of cards to continue the game. If not, they need to rework and correct their calculations. (2 - 3 minutes)

• The game continues until all groups have correctly calculated the area of all their shapes. The teacher keeps track of the time taken by each group. This adds a fun competitive element to the activity. (2 - 3 minutes)

• After the game, the teacher goes over the solutions with the class, explaining the correct method for calculating the area of each shape. The teacher also addresses any common mistakes made by the students. This step ensures that the students understand the correct application of the area formulas. (2 - 3 minutes)

Activity 2: "Design Your Room" Project (10 - 13 minutes)

• The teacher presents each group with a floor plan of a room that has a shape of a parallelogram. The dimensions of the room are labeled on the plan. The room is assumed to be empty, and the students' task is to determine the amount of flooring needed to cover the room. (1 - 2 minutes)

• The teacher provides the students with a catalog of floor materials, each with a different price per square unit. The students' goal is to choose the most cost-effective flooring option based on the area and the price per square unit. (1 - 2 minutes)

• The teacher encourages the students to use their knowledge of the area of parallelograms and the cost of flooring to make the most informed decision. (1 - 2 minutes)

• Once the groups have determined the amount and type of flooring necessary, they present their choices to the class, explaining the reasoning behind their decision. This activity promotes critical thinking and real-world application of the area concept. (3 - 4 minutes)

• The teacher concludes the project by facilitating a class discussion about the different choices made by the groups. The teacher also explains the correct choice, emphasizing the importance of accurate area calculations in real-life scenarios. (2 - 3 minutes)

These activities not only provide a hands-on and fun approach to learning the area of squares and parallelograms, but they also enhance students' problem-solving, decision-making, and collaboration skills. The competitive element in the game and the real-world application in the project make the learning experience engaging and memorable for the students.

Feedback (8 - 10 minutes)

• The teacher initiates a group discussion, asking each group to share their solutions or conclusions from the "Area Race" game and the "Design Your Room" project. Each group is given up to 2 minutes to present their work. (4 - 5 minutes)

• The teacher then facilitates a discussion comparing the different solutions presented by the groups. This discussion highlights the variety of approaches to problem-solving and reinforces the concept that there can be multiple correct methods to calculate the area of a shape. The teacher also emphasizes the importance of checking and rechecking calculations for accuracy. (2 - 3 minutes)

• Following this, the teacher asks the students to reflect on their learning experience and consider the following questions:

  1. "What was the most important concept you learned today?" This question encourages students to reflect on the key learning points of the lesson, reinforcing the main objectives of the lesson.
  2. "What questions do you still have about calculating the area of squares and parallelograms?" This question allows the teacher to gauge the students' understanding of the topic and identify any areas that may require further clarification or reinforcement in future lessons. (1 - 2 minutes)

• The teacher then provides feedback on the students' performance in the activities, praising their efforts and highlighting areas of improvement. The teacher also addresses any common mistakes made by the students, providing corrective feedback to ensure understanding. This feedback stage is crucial in reinforcing the learning objectives and in guiding the students towards a better understanding of the topic. (1 - 2 minutes)

• To conclude the feedback session, the teacher asks the students to take a moment to reflect on their learning experience. The teacher then asks the students to share their reflections, reinforcing the key learning points and providing closure to the lesson. (1 - 2 minutes)

The feedback stage is an essential component of the lesson as it provides an opportunity for the students to synthesize and reflect on their learning. It also allows the teacher to assess the effectiveness of the lesson and make any necessary adjustments for future lessons.

Conclusion (5 - 7 minutes)

• The teacher begins the conclusion by summarizing the main points of the lesson. They reiterate the concept of area in geometry, emphasizing that it is a measure of the amount of space inside a shape and is always expressed in square units. The teacher then reviews the formulas for calculating the area of squares (Area = side²) and parallelograms (Area = base × height), emphasizing the importance of using the correct units in the calculations. (2 - 3 minutes)

• The teacher then explains how the lesson connected theory, practice, and real-world applications. They emphasize that the theoretical understanding of the concept of area was reinforced through hands-on activities like the "Area Race" game and the "Design Your Room" project. The teacher also highlights how the real-world applications of calculating the area of squares and parallelograms, such as in farming, architecture, and design, were brought to life through these activities. (1 - 2 minutes)

• The teacher suggests additional materials for the students to further their understanding of the topic. These materials could include online geometry games, interactive area calculators, and worksheets on calculating the area of squares and parallelograms. The teacher might also recommend books or educational videos that provide more in-depth explanations of the topic. (1 minute)

• Lastly, the teacher wraps up the lesson by discussing the importance of understanding the concept of area in everyday life. They explain that knowing how to calculate the area of a space can be useful in many real-world situations, from planning a garden to designing a room layout. The teacher also emphasizes that learning this concept is not just about solving mathematical problems, but it also helps to develop critical thinking, problem-solving, and decision-making skills. (1 - 2 minutes)

The conclusion stage is crucial as it provides a summary of the lesson, reinforces the key learning points, and helps to connect the theoretical knowledge with practical applications. It also serves as a bridge to future learning by suggesting additional resources for further study.