Surface Area and Volume 1
Surface Area and Volume
Nicole Spangler
The University of Akron
Mr. Farmakidis, M.A.
Integrating and Implementing Technology
5150:638:630
Spring 2012
Surface Area and Volume 2
Name: Nicole Spangler
Lesson Plan Title: Surface Area and Volume
Project Website: http://spanglersurfaceareavolume.wikispaces.com/Home
Subject Area(s): Geometry
Grade Level(s): 10th/11th
Objectives/Indicators: Ohio Mathematical Content Standards
Measurement Standard (grade 8) #10: Use conventional formulas to find the surface area and
volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified
level of precision.
Measurement Standard (grade 11) #4 Calculate distances, areas, surface areas and volumes of
composite three-dimensional objects to a specified number of significant digits.
Measurement Standard (grade 11) #5: Solve real world problems involving area, surface area,
volume and density to a specified degree of precision.
Objectives:
Students will be able to find the surface area and volume of 3D shapes including composite
solids. Those solids include prisms, cylinders, spheres, cones, and pyramids.
The students will be able to apply this concept to real-life objects found in their home, outside or
in the school.
Prior Knowledge/Prerequisites
The students will have to remember the basic area formulas for rectangle, squares, and
triangles. They will have to recall how to find the area of regular polygons (five or more sides)
that was taught in chapter eleven. To be able to find the area of regular polygons, the students
must remember the trigonometry and special triangle theorems from chapter seven. Sine,
cosine, and tangent are the only trig functions needed but the students must be able to take an
angle measure and a side length to find another side length of a right triangle. The special
triangle theorems (30, 60, 90 and 45, 45 90 triangles) have specific measurements to help find
other side lengths. The trigonometry and special triangle theorems are needed to be able to
find the apothem and/or side length of the polygon. Then the formula for polygons with five or
1
more sides is Area = ans where a = apothem, n = number of sides, and s = side length of the
2
polygon. This is needed because surface area and volume formulas have larger letters, which
means that there are formulas inside of formulas. For instance when the volume formula of a
prism is Bh it means that B = area of the base of the polygon and h = height.
Identify and Discuss Pedagogical Decisions
Assessment Test Ch. 12 and surface area and volume project
Pre-Assessment- Review questions on trigonometry, special triangles, and the chapter eleven
test given the week prior.
Formative and Summative Assessments
The students will be evaluated on their understanding and skills on how to find the surface area
and volume of prisms, cylinders, pyramids, cones, and spheres through homework (formative
Surface Area and Volume 3
assessment) from each section, a quiz covering sections 12.1 – 12.3 (formative assessment), a
chapter test (summative assessment) worth 100 points and also the project (summative
assessment) found on the wikispace created. For the project, the students have to find four 3-D
objects around their house, outside or in the school, measure and take a picture with them, and
find the surface area and volume of those objects. They also must find two composite solids
(two together, i.e. ice cream cone = cone and sphere). They again must measure and take a
picture with them and find the surface area and volume of the objects. The students will then
post all their information to their own wikispace created by me. They will review other students’
work and make comments to 2 different peers.
I have chosen these methods as I need to assess the students for the chapter twelve material
and the project because I want the students to see how this information can apply to their
everyday life. They will use technology to upload all of their data and mathematical content and
they will also make postings about their peers’ work. Their work must be uploaded on time and
any links and picture must be visible and work properly. The wikispace will allow other students
to see what items were chosen and allow students to explain why they picked those objects.
They will also need to share what they have learned in choosing the objects they did. I think
that the more students see examples of mathematical concepts, the more they will feel it is
relevant to their life and give them more understanding.
Models of Instruction/Instructional Strategies
The instructional models used will be direct and indirect. The students will be learning the
content for all of the lessons of chapter twelve except two. They will be in the computer lab with
specific notes to be filled in from the on-line learning environment. I will go over the homework
with the students before they start a new lesson. I will also be available while the students are
learning the lessons so that I can clarify or help with a “Quiz Me” or homework question.
Procedures/Activities
The students are in the computer lab and at the beginning of class, we will go over the
homework from the lesson the day before and I will answer any questions the students have.
Then the students begin working on the lesson for the day. One of the activities that the
students are to complete are called “Quiz Me” questions. These questions are integrated into
the lessons through the SoftChalk software. The students are to watch the instructional videos
and fill in the notes for that example. Then they are to work on the quiz me question that follows
the example. These questions can be fill in or multiple choice. They do provide a hint if the
student chooses to use the help. These questions are also part of their notes and should be
filled in on their handout. Once students finish going through the section they are to start
working on the homework assignment that is at the end of each lesson.
Identify and Discuss Technological Decisions
Resources
The resources that I need are a computer, the Internet, and the You Tube videos created. I also
used SoftChalk software to create the on-line learning environment. I used the textbook’s extra
examples from each lesson to create my notes, videos, and quiz me questions. I used iMovie,
PowerPoint, and Sound Stage to create all of my instructional videos. Then I uploaded those
videos to Vimeo first. Once I found out the filter could not be bypassed at school for the Vimeo
videos, I had to upload them to You Tube and then modify the website. The resources help the
students to feel like they are still in my classroom watching me go through the examples even
though they are not watching me personally. The quiz me questions are interactive and help the
Surface Area and Volume 4
students recognize if they understand the material on their own. The wikispace used for the
project will allow the students to upload their real-life objects that they took the surface area and
volume of. They will be able to see other objects from their peers and learn more about what is
around them in their everyday life.
Technology Resources
The first piece of technology that I decided on using was the SoftChalk software. I watched a
demonstration on how this software works and decided that it would work great for my on-line
learning environment. This software allowed me to create the notes that would fit the lessons
while allowing me to upload my videos as widgets. With SoftChalk I was also able to add quiz
me questions that are interactive with the students and will also keep their overall score while
they are working through the lesson.
I used a wikispace for my students to be able to show their real-life solids and how they found
the surface area and volume of the figures. They are able to upload pictures, files, links and
videos if they choose to make one. They will also communicate with their peers on their work
and what they have discovered. The students will be evaluated on their mathematical
computations, the shapes chosen, and the discussion posts.
iMovie, PowerPoint, Sound Stage, and You Tube were all technology resources used to create
and upload the instructional videos. I had to create the objects and every line of mathematical
content using PowerPoint. Then I used Sound Stage to record my voice and make the movie of
the instruction. I used iMovie to then edit the beginning and end of each movie and upload it to
You Tube. The movies were then used in the form of a widget on SoftChalk using the embed
code from You Tube.
Evidence of Delivery
Surface Area and Volume 5
Samples of Student Artifacts
To see the work of my students on their project go to http://spanglersurfaceareavolume.
wikispaces.com/Home
Surface Area and Volume 6
Examples of a student test:
Surface Area and Volume 7
Surface Area and Volume 8
The break down of the grades was as follows. Out of 50 students there were 15 A’s, 15 B’s, 13
C’s, 5 D’s, and 2 F’s. The average was 84.97% and I was pretty happy with the results. I felt
that the students (for the most part) showed their understanding of the content and learned well
from the on-line learning environment.
Surface Area and Volume 9
Lesson Reflection
My thought process was to first think about how I taught the lessons in years past. I would be
directly involved in the students learning process but I didn’t really let them discover on their
own. I knew that I needed a great on-line learning environment for another class in my master’s
program but instead of just implementing one lesson through technology I implemented five. I
used TPACK to make sure that I was integrating technology the right way and not just to say
that I used technology in my classroom. I wanted an environment that my students were
interested in, one that they did not need constant direction and an environment that was also
interactive. This led me to the SoftChalk website and after a little research I downloaded a free
trial of the software. I used the content that I had used when I would directly teach the lesson
and implemented that information into the software. I chose to make the lessons interactive so
that the students would be able to realize if they understood the information. The movies are full
of information and I made sure that I chose a program where the students would be able to
pause, stop, start, or rewind if needed. What I did not realize when I created this on-line
learning environment was that the movies I originally created in Vimeo would not work at the
school. I talked to the technology department and they told me that there was no way to
unblock certain videos and not all from Vimeo. What I then had to do was change all the videos
to You Tube and change the widgets in the program. With this finally done, I was able to
implement this with my students.
When I plan out my lessons with technology, I have to keep in mind TPACK. I want to make
sure that the students understand the content provided and learning with the technology. In
integrating technology, I made sure to go over all the instructions and what was expected. I
showed the website and how all of the features worked. I also made sure that there was plenty
of time for the students to investigate and be familiar with the website so they could know what
was expected of them.
I measure the impact that the technology has had on my students by the formative and
summative assessments that have been used in the classroom. The wikispace allows me to be
able to see what they have learned from what they see and use everyday. The students always
want to know “When are they ever going to use this?” and this project demonstrates that in
many different ways. The students are also able to communicate with each other in a way that
they have not in my class before. Others who would normally remain silent can speak out and
share their ideas. I have also talked with different students about what they thought and their
opinions. The students really enjoyed the site and being able to watch the videos as much as
they want, wherever they want. They also liked how the site was interactive and how they
would know if they understood the information.