Objectives (5 - 7 minutes)

1. Understanding the concept of Volume: The students will be able to define and understand the concept of volume as it applies to three-dimensional figures, specifically cones and spheres. They will learn that volume refers to the amount of space occupied by an object.

2. Comparing and Contrasting Cones and Spheres: The students will be able to identify the similarities and differences between cones and spheres in terms of their properties and how these properties affect their volume.

3. Calculating the Volume of Cones and Spheres: The students will be able to apply the appropriate formulas to calculate the volume of cones and spheres, using the knowledge of their properties. They will also learn to convert the units of volume where necessary.

Secondary Objectives:

1. Developing Problem-Solving Skills: Through the application of the volume formulas, students will enhance their problem-solving and critical thinking skills.

2. Promoting Collaborative Learning: The flipped classroom methodology will encourage students to work together in groups, promoting collaborative learning and enhancing their communication skills.

Introduction (10 - 12 minutes)

1. Recap of Prior Knowledge: The teacher begins by reminding students of the fundamental concepts of geometry, such as the definition of three-dimensional figures, their properties, and the concept of measurement. This includes a quick review of the formulas for the area of a circle and the base of a cone. The teacher also reviews the metric units of volume like cubic centimeters, cubic meters, and liters.

2. Problem Situations: The teacher presents two problem situations to the students. The first involves a scenario where the students need to fill a cone with ice cream and a sphere with chocolate. They are asked which container will hold more. The second problem involves a construction project where the students need to decide how much paint would be needed to paint a water tower (a sphere) and a traffic cone (a cone).

3. Real-World Applications: The teacher discusses how the concept of volume is used in real-world situations. They explain that understanding volume is important for architects, engineers, and designers who need to know how much space an object will take up. The teacher also explains that volume is used in industries like food and beverage, where the amount of product that can be contained in a package is important.

4. Topic Introduction: The teacher introduces the topic of the day - Volume: Cones and Spheres. They grab the students' attention by discussing interesting facts related to the topic. For instance, they could mention that the Great Pyramid of Giza, one of the largest pyramids in the world, is essentially a cone, and its volume was calculated by ancient architects. Another interesting fact could be that the Earth is not a perfect sphere, and its volume is calculated using intricate mathematical formulas.

5. Curiosity-Stimulating Questions: The teacher presents two curiosity-stimulating questions to the students. The first one asks, "Can you guess which figure, a cone or a sphere, has more volume if they have the same base and height?" The second question asks, "Why do you think volume is an important concept in our everyday life, not just in mathematics?"

6. Video Assignment: The teacher assigns a video for the students to watch at home. The video will explain the concepts of volume, and how to calculate the volume of cones and spheres. It will also provide examples and practice problems for the students to work on. The teacher provides a link to the video and asks the students to come prepared with any questions they might have after watching it.

Development

Pre-Class Activities: (15 - 20 minutes)

1. Video: Introduction to Volume: The students are expected to watch a 10-minute video at home, providing an introduction to the concept of volume and how to calculate the volume of cones and spheres. This video is an essential precursor to the in-class activities and will ensure that students have a basic understanding of the topic. The video will also introduce the students to some of the necessary formulas for calculating volumes. The teacher will provide the link to the video in the previous session.

2. Online Quiz: After watching the video, the students will partake in an online quiz, which will check their understanding of the concepts taught in the video. The quiz will be conducted via a learning management system (LMS) or any other suitable online platform. The teacher will review the results to identify areas where students might be struggling and provide additional assistance in the classroom.

3. Note-Taking: Besides the online quiz and video, the students are also expected to make notes about the key concepts and formulas presented in the video. This will help them recall the information during the in-class activities.

In-Class Activities: (25 - 30 minutes)

1. Activity 1: Comparing Cones and Spheres (10 - 12 minutes)

   a. The teacher divides the class into small groups of 3-4 students. Each group is given several cones and spheres of different sizes and materials. They are also given a measuring tape, a scale, and a container of water.

   b. The students are asked to measure and record the height and the radius (in the case of a cone) or the diameter (in the case of a sphere) of each object and then calculate the volume using the formula for cones (1/3 * π * r^2 * h) and spheres (4/3 * π * r^3).

   c. Next, the students are asked to place each object in the water container and observe how much water the object displaces. The students are then asked to discuss and compare the volumes they calculated with the actual volumes (the amount of water displaced by each object).

   d. This activity allows students to see the practical application of volume and the accuracy of their calculations.

   e. The teacher then facilitates a group discussion during which each group presents their findings and compares the volumes of the cones and spheres. The teacher uses this discussion to reinforce the concept that the volume of a cone is one-third the volume of a cylinder with the same base and height, and the volume of a sphere is two-thirds the volume of a cylinder with the same base and height.

2. Activity 2: The Volume Race (15 - 18 minutes)

   a. The teacher prepares a "Volume Race" game for this activity. They create a set of cards, each containing the dimensions of a cone or a sphere and a corresponding question about its volume.

   b. The students remain in the same groups as before. Each group, in turn, will draw a card, read the dimensions aloud, and then calculate the volume. The first group to correctly answer the question gets a point.

   c. The game continues with each group taking turns until all the cards have been used. The group with the most points wins.

   d. This activity not only provides the students with more practice in calculating the volume of cones and spheres but also adds a fun and competitive element to the lesson, increasing engagement.

   e. After the game, the teacher encourages a class discussion about the strategies used by different groups to solve the problems and any difficulties they encountered. The teacher provides feedback, clarifies any misconceptions, and provides additional explanations where necessary.

Post-Class Activities: (5 - 7 minutes)

1. Reflection and Review: At the end of the class, the students are asked to take a few minutes to reflect on what they've learned during the lesson. They are then asked to write down the answers to the following questions in their notebooks:

   a. What was the most important concept learned today?

   b. Which questions have not yet been answered?

   c. How can the concept of volume be applied to real-world situations?

2. Homework Assignment: The students are assigned homework that will further their understanding of the volume of cones and spheres. The homework task involves calculating the volumes of a set of cones and spheres at home using the formulas learned in class. The teacher provides the necessary dimensions for each figure. The students are also required to explain the steps they took to arrive at the answer. This will not only reinforce the concepts learned but also promote self-study and independent learning.