Building a Parking Lot Part 2
Name: Lisa Fefferman
Title of Lesson: Building a Parking Lot Part 2
Date of Lesson: 5th 6 weeks, Monday of Week 4
Length of Lesson: 50 mins
Description of Class: Geometry
Source of Lesson:
TEKS addressed:
a) Basic understandings.
(1) Foundation concepts for
high school mathematics. As presented in Grades K-8, the basic understandings
of number, operation, and quantitative reasoning; patterns, relationships, and
algebraic thinking; geometry; measurement; and probability and statistics are
essential foundations for all work in high school mathematics. Students
continue to build on this foundation as they expand their understanding through
other mathematical experiences.
(2) Geometric thinking and
spatial reasoning. Spatial reasoning plays a critical role in geometry; shapes
and figures provide powerful ways to represent mathematical situations and to
express generalizations about space and spatial relationships. Students use
geometric thinking to understand mathematical concepts and the relationships
among them.
(4) The relationship between
geometry, other mathematics, and other disciplines. Geometry can be used to
model and represent many mathematical and real-world situations. Students
perceive the connection between geometry and the real and mathematical worlds
and use geometric ideas, relationships, and properties to solve problems.
(b) Geometric structure:
knowledge and skills and performance descriptions.
2) The student analyzes
geometric relationships in order to make and verify conjectures. Following are
performance descriptions.
(A) The student uses
constructions to explore attributes of geometric figures and to make
conjectures about geometric relationships.
(d) Dimensionality and the
geometry of location: knowledge and skills and performance descriptions.
(1) The student analyzes the
relationship between three-dimensional objects and related two-dimensional
representations and uses these representations to solve problems. Following are
performance descriptions.
The Lesson:
I. Overview
The students will their design of a parking lot and
find the volume and surface area. They must use their prior knowledge of each
definition to do so. They will then find that with different shapes, if the
area and the height stay the same, the volume will also stay the same. Finally
the students will find the surface area of a cylinder, by flattening the
stadium, and then thy will find the formula of a right cylinder.
II. Performance or learner outcomes
The students will be able to:
á
Write a verbal
definition of surface area
á
Connect the concepts
of area, perimeter, volume, and surface area
á
Use the verbal
definition of surface area to find the surface area of a right cylinder
á
Use what they know
about right cylinders to find the formula
III. Resources, materials and supplies needed
á Calculator
IV. Supplementary materials, handouts
á The of each groups dimensions of their stadium and their parking lot.
Five-E Organization
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Teacher Does |
Student Does |
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Engage: (5 mins) Bring in two coke boxes; a traditional one (close to a
square) and a fridge pack box (more of a rectangle shape). Tell the class
that they each contain 12 cans of coke. The length of the traditional box is
4, and the width is 3, with a height of 1. The fridge pack has a length of
12, a width of 2, and a height of 1. |
Students will listen to the teacher. |
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Questions:
1. What is the area of the two boxes? 2. What is the volume? 3. Which box would cost the company more? Why? |
Expected Student Response: 1. A= 12 for both 2. V= 12 for both 3. The company would rather use the traditional box because
they use less material. In other words the surface area is smaller. |
Decision Point Assessment (DPA) – What is the definition of Surface Area?
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Explore: (15 mins) The amount of material covering the container is the
surface area. In other words it is the area of the base plus the sum of areas
of lateral faces (show example from engagement). Use the models you designed for the parking lot. We now
need to pour concrete into the lots. We will pour enough concrete that the
lot is 3 feet deep. |
Students will listen to the teacher for directions. |
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Questions:
1. Find the volume of your lot. 2. Find the surface area. |
Expected Student Response: Answers will vary depending on students design. |
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DPA: The teacher will walk around the classroom to make sure that they stay on task and to guide them when necessary.
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Explain: (10 mins) Discuss results with the class. Questions: 1. Why does the volume stay the same? 2. What is the relationship between the perimeter and the surface area? |
Expected Student Response: 1. The volume is the same because the it is the area time the height, and we all have the same area and the same height. 2.
Both the perimeter and the surface area change when the
shape changes, even though the area and the volume stay constant. |
DPA – The teacher will make sure all the students understand the definition of surface and its relationships to area.
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Extend / Elaborate: (20
mins) Now letŐs look at our stadium. The base of the stadium is circle. Therefore itŐs shape is a cylinder. Questions: 1. To find the surface area of the stadium, thing of how it would look if you were to flatten it. What would it look it? 2. Now find the surface area of the stadium. 3. Looking at everyoneŐs results and work, can you guys find a simplified formula for the surface area? |
Expected Student Response 1. It would have a circle on the top, a circle on the bottom, and a rectangle in the middle. 2. Answer will vary with students dimensions. 3. SA = Lateral Area +2B |
DPA – The teacher will work with the students to find the formula of surface area of a right cylinder.