Surface Area of a Sphere Lesson (80 mins)
Objectives
Students will be able to understand the surface area formula of the sphere (4πr²) through hands-on practice.
Students will be able to apply the formula to find the curved surface of a sphere and solve related problems.
Before class (on-line)
Students watch a video demonstrating how to find the curved surface area of a sphere (orange) through peeling off its skin (see below).
Students watch video(s) demonstrating how to apply the surface area formula to solve problem(s) (see below).
Students answer the question that follows the videos to check their understanding.
Teacher's preparation
Prepare an orange for every two students in class, or alternatively teacher can ask students to bring their own fruit with a spherical shape.
Bring a few knifes if necessary (in case some students cannot tear open the orange skin by hands).
In-class
Review students on-line pre-learning (5 mins)
Who has done the pre-learning? and who has not? (Teacher has to develop strategies to encourage students to pre-learn, and consistent routines to handle students who do not pre-learn)
Which question is poorly answered? What have students missed or misunderstood?
Re-explain the common mistakes made by the students to the whole class.
For well answered questions, teachers don't need to cater anymore, as students have already grasped the concept.
Hands-on demonstration of curved surface area of sphere using oranges (30 mins)
Have students work in groups of 2 and give them an orange. Draw the shape of the orange (which should be a circle) on a piece of paper 4 times. In case teachers don't want to "prime" the thinking of students, just ask them to draw a few circles on the paper with the same size of the orange.
Have students eat the orange by peeling off its skin and do not throw the skin away.
Have the students arrange the pieces of orange skin in the circles, and ask them
How many circles are filled?
Measure the diameter / radius of the orange. What is the total curved surface area of the orange?
Will bigger or smaller pieces of skin get better results? Why?
If the radius of a sphere is r, what is the total curved surface area of the sphere? If students bring their own fruit, the use of variable r will be even more meaningful as the induction concept is also involved.
Cleaning up students' table (5 mins)
Ask students: Are there ways of re-using the orange skin besides throwing them into the rubbish bin?
Applying the formula to solve problems (25 mins)
Deliver worksheets (can be electronic versions in case of an e-Learning setting classroom) for students to work out and preferably be in groups. Since the worksheet has a greater proportion of more difficult problems (students have pre-learn the basic concept already) and students will need the space time to discuss with each other.
Encourage students to ask if the group cannot solve a particular problem.
Walk among the groups to see if students (especially the shy ones) have problems.
Based on the data collected from the on-line pre-learning platform, teachers already "know" who is struggling in learning the topic, and therefore can seize the time to approach them and provide individual guidance.
Rounding up: Students demonstrate their work (15 mins)
Have a representative from each group come out to blackboard and share their solutions to the problems. In the case of an e-Learning classroom, tablets / iPads and classroom management tools can be used to show student's work on the projector screen.
Comment and feedback on student's work, give praise when students demonstrate their understanding or show creative solutions, encourage students if they make mistakes which is part of the learning process.
Collect the completed worksheets from students. Teachers can decide whether
students check their own solutions against those written on the blackboard or shown on the projector screen before handing in, or
mark the collected worksheets on his own
