Lesson plan of Spatial Geometry: Surface Area of the Cone

Objectives ( 5 minutes )

1. Understanding of the cone surface area Formula: Students should be able to understand the formula for computing the surface area of a cone which is A = Π * r* ( r + l ) where A represents surface area, r represents base radius, l is the slant height.

2.Application of the formula to solve area problems: Students should be capable of applying the cone surface area formula in order to solve real-world problems that involve calculating the surface area. 3. Identification of variables in the formula: Learners should have the knowledge to identify and comprehend the variables( r and l ) and constant( Π ) in a cone surface formula.

Secondary Objectives:

• Development in spatial reasoning: By learning spatial geometry and in particular the cone students should be able to develop the ability to mentally visualize and manipulate three-dimensional shapes.

• Stimulus of logical reasoning : Solving mathematical problem like those involving cone surface area problems require the use of logical reasoning so it can serve as an opportunity for students in improving this skill.

##Introduction ( 10-15 minutes )

1. Relevant prior content review: The teacher should start the lesson by recalling the already learned concepts of space geometry that will be useful for the lesson’s topic. This could involve the definition of cone, its characteristics( radius, height , slant height , base) and the formulas of cone volume. The teacher could do this through an interactive manner asking questions to students to recall and clarify any doubts if needed ( 3 - 5 minutes )

2. Problem situations: The teacher will present to the students 2 problem situations that involve calculating cone surface area. The situations could be for example, finding the surface of a traffic cone the surface area of an ice cream cone. These scenarios should be used to get the student’s interest in the lesson's topic ( 3 -5 minutes )

3.Subject contextualization: The teacher should proceed to explain to the students how cone surface area is relevant and can be used in real life . For example, the calculation of cone surface area is important in fields like Architecture, Engineering, physics and even cooking. The instructor can mention examples of these uses to make it more concrete and interesting for the student ( 2-3 minutes )

4. Topic introduction through curiosities or application: To grab the attention of the student the teacher can present some interesting curiosities or uses about cone surface area. As an example the instructor can mention the formula used to calculate cone surface was discovered by the renowned Greek mathematician Archimedes or about how the formula can be used to figure out the quantity of paint needed to coat a cone in some practical applications ( 2 - 3 minutes)

##Development ( 25-30minutes )

1.**Activity" Building cone surface" :

-**Materials**: card stock, scissors , ruler, pencil, glue

-**Description**:  In this hands on activity students are grouped in group of 3 to 5 students. Each team will receive a cone template ( which can be obtained by cutting out a sector of a circle from cardstock and forming a cone) and  will be tasked with constructing a cone surface using the cardstock. Students will need to mark a central point in the cardstock circle( which will serve as the vertex) and from this point draw line segments to points on the edge circle. Then they will be required to  cut the cone along the line segments and unfold to visualize the cone surface.


**Steps of the Activity**: 


	1- Each student from a group will take a card stock and build a cone
	
	2- With the help of a ruler, students will be required to measure slant height and radius of the base , notind down these measurements.
		
	
3- The students now proceed to cut out the segments which  join the apex of the  cone to the points on the circumference of the base.


4 - Lastly learners will open up the cardstock paper to reveal the cone’s surface. At this time students should be guided to identify which parts represents cone base, slant and lateral surface area.

**Objective**: The main purpose of this exercise is to enable the students to see and manipulate a three-dimensional form of a cone in order to easily understand the formula for the cone’s surface and identify the parts of the  cone used in calculating its area.

2. "Discovering the cone Surface Area Formula " Activity: -Materials : paper, pencils, ruler, and calculator -Description : In this exercise the learners while still in their groups are given the task of figuring out the formula of cone surface by manipulating a paper cone. They are given a paper cone and are instructed to cut open the cone lengthwise along a generatrix and a base so as to get a flat figure. The students should be able to measure dimensions of this flat shape and with the gathered data come up with a possible formula to compute cone surface area.

-Steps of activity:

1-Each member from a team will build a cone from paper.	

2- The students are instructed to cut open the paper cone lengthwise along a slant height as well as the base to get a  flat figure.	


3-The students are expected to measure the flat figure ( base radius and slant height)  and with the data found they should try to work on a formula to calculate the surface area.

4- Students should confirm if the formula they developed is the one provided by the teacher in the beginning of class. 

**-Objective**: This activity is mainly to boost student creativity and their problem solving skills as they also reinforce their understanding of cone’s surface area formula.

##Return ( 5- 10minutes )

1.Group Discussion( 5 - 7 minutes ):

• The teacher should gather all students together and facilitate a discussion of solutions obtained from each team for the given problems

• The instructor can start by inviting each group to briefly discuss their solutions and or methods used.

• The teacher should open the floor to the class to allow the students to comment on the different approaches used, challenges faced and how they overcame them and the lessons learned.

-The teacher should encourage participation from all the students by asking questions that promote reflection and discussion and by encouraging students to question and respond each other.

• The purpose of the activity is to allow students learn from one another, develop their communication and reasoning skills and solidify the understanding of the lesson's topic.

2.Review of Learning( 3 -4 minutes):
-After the group discussions, the teacher must quickly review the formula for cone surface and the steps taken when solving problems that involve calculating the area.

• The teacher may proceed to ask students to confirm if they can apply what was learned to solve another problem similar to those given in the activity

• The students must be given a chance to work out the problem independently or in their groups with the teacher being available to explain and guide if need be.

• The purpose is to allow students assess their own learning to find any learning gaps that need to addressed in a subsequent lesson.

3.Reflection( 2-4 minutes):

• To end the lesson the teacher should request learners take a minute each to reflect personally on the questions:

  1-Which concept learnt today stood out the most?

  2- Which questions remain unanswered?

• The teacher can call on some students to present their reflections with the rest of the group after the minute of self reflection.

• The teacher should attentively listen to students responses and if most of the learners still have a number of unanswered questions the instructor can plan to revisit the concepts in a subsequent lesson.

-The purpose of this is to allow students consolidate their understanding of lesson topic, identify any areas that need further review and to help them reflect upon their own learning journey.

##Conclusions ( 2-3 minutes)

1.Summary of Content ( 3-5 minutes):

• The teacher can start the Conclusion by summarizing the important points of the lesson recalling the definition, characteristics ( radius, slant height, base ) and the formula for calculating the surface area for a cone ( A = π*r ( r + l) )
• The teacher should stress the importance of understanding and correctly applying the formula and also the ability of visualizing and manipulating 3-D forms associated with the formulas.
• The instructor can do so by engaging with the learners asking them to recall and if need be clarifying any doubts they might have.

2. Connection between theory, practice and application:

• The teacher should then emphasize the connection between theory ( the formula for the cone surface area) the practice ( building the cone activity and problem solving) and real world practice ( examples of when cone surface are is used , like in architecture, Engineering , physics and cooking) -The instructor can highlight how the class has allowed the students to not only understand a mathematical concept but also to see it at work and learn its practical importance.

3. Recommended Material ( 2 - 3minutes):

-The teacher can suggest supplementary material for those students who may want to delve deeper into the topic of cone’s surface areas. -These materials could include video explanations, websites containing maths problems to be solved, Math textbooks with sections dedicated to spatial Geometry among others.

• The instructor can upload these suggested resources in the school’s virtual learning, environment or email them to students.

4. The importance of the topic in everyday life ( 1 - 2minutes):

• Finally, the teacher should reinforce the significance of cone surface areas in everyday situations. -The teacher can remind students that spatial geometry can be found in a number of life scenarios from making a cake recipe ( which may involve calculating surface area of cone shaped cake pans) to construction of buildings and bridges ( which rely on precise area and volume computations.)

• The instructor can close the lesson emphasizing that by learning how to find the surface are of a cone, they have acquired a useful skill that can serve them in various areas of their lives.