# here - Ed101 ```Galin Ma
February 2009
Ms. Jennifer Jordan
Math
1 Hour
1. Content Area: Geometry
Students learn the relationships between shapes, both two dimensional and three
dimensional. Specifically in this lesson, I will describe the relationships between the
surface area and volume of rectangular objects, prisms, and cylinders.
2. Topic: I will be going over the basic formulations of three dimensional rectangles,
rectangular prisms, and cylinders. Students will also learn how to approximate the surface
area and volume of different objects without using any tools for measurement. They will
also learn how to calculate surface area and volume given only the dimensions of the
object.
3. Goals: To understand the relative volumes of objects in real life compared to theoretical
calculations. Students should be able to calculate the dimensions of objects and have a
general idea of the formulas needed to find the volume and surface areas of objects. They
should differentiate between the properties of cylindrical and non-cylindrical shapes.
4. Objectives:
 My students will be able to
o calculate the volume and surface area of a cylinders, three dimensional
rectangles, and prisms
o estimate the volume and surface area of objects by sight and without any
calculations
o Understand the formulas length times width times height, r^2pi times
height
o Identity real life objects, such as buildings, balls, and soda cans as specific
three dimensional objects
o Measure objects to find their surface area and volume based on the
dimensions
5. Technology, materials and aids: I will use my laptop and a borrowed electronic
projector to project a PowerPoint presentation on shapes and objects. I will also supply
materials and objects such as coke cans, books, and people for students to measure. There
will also be worksheets copied for each student in the class focusing on group activities.
Students will also need:
 Calculators for calculating volume and surface area
 Meter sticks to measure objects
 Foot-long rulers to measure smaller objects
 Pen and pencil to work on handouts
6. Procedures/methods:
a. Overview: My lesson will review concepts taught by Ms. Jordan from previous
lessons, but also add a constructivist approach to it. I will integrate media, group
activities and real life connections to concepts already learned by the students. My
job will be to make the math concepts more relatable and personal to their
everyday lives. I will do so by first starting with an activity about identifying and
estimating certain objects’ volumes and surface area and then moving on to a
PowerPoint review session of the concepts. Also I will then show videos online of
interesting comparisons of stars and planets to show aspects of volume and
surface area. I will wrap up by facilitating a group discussion and listening to the
students’ responses to questions I pose at the end to make sure the class
understands.
b. Introduction: I will begin by introducing the topic by an activity involving
estimating the actual volumes of different buildings and objects. These exhibits
will be shown on PowerPoint. The objects will consist of a small office building,
a book, and large living room. The students will discuss as in groups to what they
think the correct volume is and each winning group will get candy as a reward.
There will be 5 different objects so that there will be an opportunity for each team
c. Activities:
1. The first activity will be the activity mentioned in the introduction.
This will serve as an icebreaker to the rest of the lesson. The activity
surface area and volume relate to real life and its applications.
2. The second activity will be an overview of the concepts taught
beforehand by Ms. Jordan. Slides of the different formulas will be
shown on the slide as well as a few practice questions to make sure the
material is understood by the class.
3. Next I will pull up the website I made with Dreamweaver, which will
have more material specifically about rectangular prisms, cylinders
and rectangular prisms.
4. On the website there will be videos of the largest rectangular prisms in
the world (Skyscrapers). The videos will have information about their
dimensions.
5. Given the dimensions of the Prudential Center, what will the volume
be?
6. The class will separate into groups of three or four to work on a
worksheet to compare which object is bigger given certain dimensions.
7. Discuss the answers as a class.
8. End with a video on the sizes of planets and stars in the universe
located on the Dreamweaver so that the students can have an idea of
how big some planets are.
d. Follow-up: Give out a worksheet that they would take home and complete that is
a comprehensive overview of shapes, volume and surface areas. The questions
will focus more on real-life scenarios and applications. The worksheet will be
collected the next day by Ms. Jordan.
7. Technology Frameworks:
 1.14 Use various number formats (e.g., scientific notation, percentages,
exponents) as appropriate.

Use a variety of technology tools (e.g., dictionary, thesaurus, grammar-checker,
calculator) to maximize the accuracy of work.

Plan, design, and develop a multimedia product to present research findings and
creative ideas effectively, citing sources.
8. Assessment: After reviewing concepts about pyramids, rectangular prisms, and spheres,
students should be able to solve for volumes and surface areas given certain dimensions
of the objects. They should also intuitively find certain dimensions of objects given
incomplete information about its measurements. Students should also have an
understanding about the relative size of real-life objects; they should be able to estimate
the areas and have a general understanding of the relative sizes of different objects,
especially skyscrapers and planets.
The teacher will test the students’ knowledge by orally asking the students to estimate the
size of different objects, for example, skyscrapers, cars, books, and planets. Students
should understand that a books’ volume will vastly different from that of a car,
skyscraper, and a planet.
Also, the teacher should test the students’ conceptual knowledge of the mathematical
content of finding surface areas and volumes. Having the students work individually, in
groups or as a class on the quiz provided will give a general assessment of the class’s
progress. The quiz has both questions that test basic understanding of the topic and
advanced understanding that requires intuitive thinking and problem solving. The quiz is
provided below and correct answers are in bold. There are also additional practice
problems on the website that test students’ understanding as they move along in the web
page.
Calculate the missing information for the following of a rectangular prism:
1) l = 9 m, w = 2 m, h = 3 m, V =?
a) 54 m^3
b) 64 m^3
c) 128 m^3
d) 54pi m^3
2) l = 6.8 m, w = 5.4 m, h = 2 m, V= ?
a) 74.44 m^3
b) 146.88 m^3
c) 73.44 m^3
d) 146.88pi m^3
3) V = 30 cm^3, w = 5 cm, h = 2 cm, l = ?
a) 3 cm
b) 5 cm
c) 2 cm
d) sqrt(12) cm
4) A = 48 mm^2, l = 6 mm, h = 4 mm, w =?
a) 4 mm
b) 8.5 mm
c) 1 mm
d) 2.4 mm
Calculate the missing information for the following of a sphere given the following
dimensions:
1) r = 6cm, V = ?
a) 506.22 cm^3
b) 506.22 cm^2
c) 904.32 cm^3
d 904.32 cm^2
2) Circumference = 25.24 in, V = ?
a) 60 in^3
b) 52.86 in^3
c) 54.32 in^3
d) 54.32 in^2
3) V = 225 in^3, Diameter = ?
a) 5.23 in
b) 69.22 in
c) 3.77 in
d) 2.33 in
4) A = 64pi cm^2, r = ?
a) 4 cm
b) 5 cm
c) 3.8 cm
d) 2.2 cm
Calculate the missing information for the following of a pyramid given the following
dimensions:
1) b = 9m, h = 3m, S = sqrt(90), V = ?
a) 81m^3
b) 9 m^3
c) 162 m^3
d) 25 m^3
2) b = 9.70m, h = 2.43m, S = 10m, V = ?
a) 76.21 m^3
b) 43.29 m^3
c) 32.57 m^3
d) 26.84 m^3
3) S = ?, h = 3 cm, b = 8 cm V = ?
a) S = 6.54 cm^2, V = 64 cm^3
b) S = 8.54 cm^2, V = 64 cm^3
c) S = 8.54 cm^2, V = 96 cm^3
d) S = 6.54 cm^2, V = 96 cm^3
4) A = 48 in^2, S = 3 b = ?
a) 8 in
b) 4 in
c) 6 in
d) 10 in
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