Fossil Fuels
Two Weeks
Geometry
Lesson Plan
Teacher:
8th Grade Math Teacher
Grade:
8th Grade
Lesson Title:
Moving Land: How Volume and Slope Shape our Landscape
STRANDS
Geometric Measurements and Dimensions
Modeling with Geometry
LESSON OVERVIEW
Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
The Teachers will introduce the lesson to students as a team with the Unit Hook (see Unit Plan). The math teacher will go over the math rubric for students and
introduce the learning and project objectives for this unit in mathematics. Students will hear a presentation from a professional who is responsible for buying,
inspecting, and burning coal in order to provide power to a local high profile plant. Through building a generator, students will learn how copper, metal, and magnets
can be used to generate electricity and how the volume of the copper wire lends to the strength of the generator. Students will learn about a specific engineering
method, cut and fill, for moving large volumes of land. Students will complete an activity to become familiar with this method. This will assist students in being able to
use this information in their final debate when talking about the affects, whether good or bad, caused from mountaintop removal mining.
MOTIVATOR
Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites,
literature)
Day 1: "Exploring Other Dimensions"
This motivator will utilize the following video clip – “Exploring Other Dimensions” (Appendix A). This clip goes introduces the idea of dimensions beyond our 3dimensional world. It does this by
Day 2: "Mining Operations: Cut and Fill"
This motivator will utilize the following video clip – “Mining Operations: Cut and Fill” (Appendix K). This clips has an entertaining way of students investigating the
irrational number pi. It goes over what we know about pi, as well as what we do not know. This will spark a discussion about the similarity of circles and what knowing
more about pi could do for us technologically and mathematically.
DAY
Objectives
(I can….)
1
I can use volume
formulas for
cylinders,
pyramids, cones,
and spheres to
solve problems.
I can identify the
shapes of twodimensional
cross-sections of
threedimensional
objects, and
identify threedimensional
objects generated
by rotations of
two-dimensional
objects.
I can use
geometric shapes,
their measures,
and their
properties to
describe objects.
I can apply
concepts of
Materials &
Resources
“Exploring Other
Dimensions”
Video Clip
(Appendix A)
“Hypercube”
Handout
(Appendix A)
“Hypercubefacilitators
guide”
(Appendix A)
“Hypercube
Lesson-Other
Dimensions, A
Textbook”
(Appendix A)
iPad
Calculator
Instructional Procedures
Essential Question(s):
1. How can I use volume formulas for cylinders, pyramids, cones, and spheres
to solve problems?
2. How can I identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects?
3. How can I use geometric shapes, their measures, and their properties to
describe objects?
4. How can I apply concepts of density based on area and volume in modeling
situations?
1/2 Project Day – See Unit Plan
The Cost of Creating Energy - Introduction
Set:
The teacher will begin showing the “Exploring Other Dimensions” video clip.
This will introduce students to the idea behind the fourth dimension and what
is may look like to us. Have a discussion afterwards to discuss the hypercube.
Also discuss the common thought that time is the fourth dimension. Have the
students share what they think. Remember that this concept is a bit fuzzy to
them and allow them to give their thoughts.
Teaching Strategy:
1. Assign students to heterogeneous groups of 2-4. Have groups open the
“Hypercube” assignment.
2. Go over Pascal’s triangle and where it is derived from. Talk about where in
nature this pattern occurs and also show them how the powers of 11
coincide. Show the students different ways Pascal’s Triangle is modeled.
3. After you have gone over Pascal’s Triangle, allow the students to work on
their assignment.
4. Students will have a lot of difficult questions, as this is higher order
thinking. Make sure as a teacher, you go over the hypercube handout
Differentiated Assessment
Instruction
Remediation:
Peer Tutoring
Heterogeneous
Grouping
Enrichment:
Peer tutoring
Heterogeneous
Grouping
Formative
Assessment:
Teacher
observations of
opening discussion
Performance
Assessment:
Teacher
observation of
completion of
Pascal’s Triangle
Exit ticket
Summative
Assessment:
Completed
Pascal’s Triangle
density based on
area and volume
in modeling
1/2situations.
2
I can use volume
formulas for
cylinders,
pyramids, cones,
and spheres to
solve problems.
I can identify the
shapes of twodimensional
cross-sections of
threedimensional
objects, and
identify threedimensional
objects generated
by rotations of
two-dimensional
objects.
I can use
geometric shapes,
their measures,
and their
properties to
before you have this lesson with the students. Try to prepare for the
types of questions they will have.
5. Make sure they have finished their Pascal’s triangle by the time they have
finished this day’s lesson. If they have not, have them finish it for
homework.
“Exploring Other
Dimensions”
Video Clip
(Appendix A)
“Hypercube”
Handout
(Appendix A)
“Hypercubefacilitators
guide”
(Appendix A)
“Hypercube
Lesson-Other
Dimensions, A
Textbook”
(Appendix A)
iPad
Calculator
Summarizing Strategy:
As an exit ticket, have students summarize their findings. Ask students how we
can try to imagine the 4th dimension. What would we be able to do if time
really is the fourth dimension?
Essential Question(s):
1. How can I use volume formulas for cylinders, pyramids, cones, and spheres
to solve problems?
2. How can I identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects?
3. How can I use geometric shapes, their measures, and their properties to
describe objects?
4. How can I apply concepts of density based on area and volume in modeling
situations?
Set:
The teacher will begin by asking students to pull up their work from the
previous lesson. Have them write down any questions they may have at this
point. Open up dialogue with the students. Allow them to share some of their
questions if they are comfortable. Allow other students to try and answer the
questions. Allow them to debate what they have discovered so far about the
proposed fourth dimension.
Teaching Strategy:
1. Allow students to go back to their groups from the day before and
continue working on their hypercube assignment. Remind them that it
will be due at the end of the day.
2. Circulate around the room and answer student questions. Today they
should have a better grasp of the concept than they did the previous
day.
3. Near the end of class, be sure to collect the finished assignments.
Summarizing Strategy:
Remediation:
Peer Tutoring
Heterogeneous
Grouping
Enrichment:
Peer tutoring
Heterogeneous
Grouping
Formative
Assessment:
Teacher
observations of
opening discussion
and debate
Performance
Assessment:
Teacher
observation of
completion of
Pascal’s Triangle
Exit ticket
Summative
Assessment:
Completed
Hypercube
Assignment
As an exit ticket, have the student answer the following questions:
1. How do you think Pascal’s Triangle helps us grasp and calculate the
fourth dimension?
2. Do you think we live in four-dimensional world? Explain
describe objects.
I can apply
concepts of
density based on
area and volume
in modeling
situations.
3
I can use volume
formulas for
cylinders,
pyramids, cones,
and spheres to
solve problems.
I can identify the
shapes of twodimensional
cross-sections of
threedimensional
objects, and
identify threedimensional
objects generated
by rotations of
two-dimensional
objects.
I can use
geometric shapes,
their measures,
and their
properties to
iPad
Internet
Calculator
Essential Question(s):
1. How can I use volume formulas for cylinders, pyramids, cones, and spheres
to solve problems?
2. How can I identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects?
3. How can I use geometric shapes, their measures, and their properties to
describe objects?
Set:
Have students to write down what type of pool they would have in their
backyard if they could pick. What would it look like, and where would they
place it? Allow students to open a discussion about their dream pool. After
the short discussion, ask them to write down how much water they think
their pool will hold.
Teaching Strategy:
1. Allow students some time to research the Internet. Have them choose
two pools they would like to purchase, one above ground and one
below ground.
2. Calculate the volume for each of these pools. The measurements of
the pool will be listed online and must be provided in the student’s
work.
3. You will also calculate the area of the yard that will be covered and
the ratio of the area of the pool to the whole yard.
4. Draw a figure showing the amount of yard along with one of the pools
you have chosen from online. Include all measurements as well as the
yard to pool ratio.
5.
Summarizing Strategy:
Remediation:
Peer Tutoring
Heterogeneous
Grouping
Enrichment:
Peer tutoring
Heterogeneous
Grouping
Formative
Assessment:
Teacher
observations of
opening discussion
Performance
Assessment:
Teacher
observation
student work
Exit ticket
Summative
Assessment:
Completed Pool
Project
describe objects.
4
I can use volume
formulas for
cylinders,
pyramids, cones,
and spheres to
solve problems.
I can identify the
shapes of twodimensional
cross-sections of
threedimensional
objects, and
identify threedimensional
objects generated
by rotations of
two-dimensional
objects.
I can use
geometric shapes,
their measures,
and their
properties to
describe objects.
I can apply
concepts of
“Mining
Operations-Cut
and Fill” Video
Clip
(Appendix B)
“Cut and Fill”
Handout
(Appendix B)
iPad
Calculator
As an exit ticket, have the student answer the following questions:
1. What role does area play in putting in a pool to your backyard?
2. What role does volume play in putting in a pool into your backyard?
3. What will happen to the volume of land that will need to be dug up
for your pool?
Essential Question(s):
1. How can I use volume formulas for cylinders, pyramids, cones, and spheres
to solve problems?
2. How can I identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects?
3. How can I use geometric shapes, their measures, and their properties to
describe objects?
4. How can I apply concepts of density based on area and volume in modeling
situations?
½ Project Day – See Unit Plan
The Cost of Creating Energy – Learning from a STEM
Professional
Set:
The teacher will begin showing the “Mining Operations: Cut and Fill” video
clip. This will show students about the cut and fill method is used to get to
coal that is embedded in the mountaintop, and how the earth is moved in
order to get to that coal. Teacher will then begin a discussion about how
much land needs to be moved, and what is done with the land. How do
engineers figure the amount of land they will be moving? The teacher will
then talk about volume and how it will play a role in this process. Have the
students down how they think volume will be found.
Teaching Strategy:
1. Assign students to heterogeneous groups of 2-4. Have groups open
the “Cut and Fill” assignment.
2. Next, the teacher will go over the definition of cut and fill, and walk
through the beginning of the document with the students. This
explains how professions use the cut and fill method and why.
3. Have students Begin working on the assignment. Explain that this will
Remediation:
Peer Tutoring
Heterogeneous
Grouping
Enrichment:
Peer tutoring
Heterogeneous
Grouping
Formative
Assessment:
Teacher
observations of
opening discussion
Performance
Assessment:
Teacher
observation of
estimates and
graphs
Exit ticket
Summative
Assessment:
Cross-sectional
graphs with
estimated area
rectangles
density based on
area and volume
in modeling
situations.
take several days to complete, and like engineers and architects must
also do, they will work in groups in order to complete this task. The
numerous amounts of calculations mean that it will be easy to make a
few small calculation errors. For this reason they will each individually
complete this assignment while working together in groups. This way
they can compare answers and locate mistakes.
4. The teacher should circle the room, answering questions and clearing
up any misconceptions. Students will find the verbiage and look of the
task to be challenging at first. Once an understanding of the goal is
met, they will feel more comfortable.
5. Make sure the students save all their work before they leave class.
They will continue this task when they return the next day.
6. By the end of the first day, the students should have a mental grasp
on the objective of the cut and fill project, and should have correctly
drawn in all of the rectangles for each of the cut and fill crosssectional areas in order to begin calculations the next day.
Summarizing Strategy:
7. As an exit ticket, have students summarize their findings. Ask students
how we can estimate surface area for each cross-section.
5
Project Day – See Unit Plan
The Cost of Creating Energy – Building a
Generator
6
Project Day – See Unit Plan
The Cost of Creating Energy – Debating Mountaintop
Removal Mining Research
7
I can use volume
formulas for
cylinders,
pyramids, cones,
and spheres to
solve problems.
I can identify the
shapes of twodimensional
cross-sections of
threedimensional
objects, and
identify threedimensional
objects generated
by rotations of
two-dimensional
objects.
I can use
geometric shapes,
their measures,
and their
“Cut and Fill”
Handout
(Appendix B)
iPad
Calculator )
Essential Question(s):
1. How can I use volume formulas for cylinders, pyramids, cones, and spheres
to solve problems?
2. How can I identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects?
3. How can I use geometric shapes, their measures, and their properties to
describe objects?
4. How can I apply concepts of density based on area and volume in modeling
situations?
½ Project Day – See Unit Plan
The Cost of Energy – Researching the Generator
Set:
The teacher will begin by asking the students to revisit the cut and fill
assignments what was started on day 4. At this point they should understand
their objective and have their graphs sectioned into rectangles that are all
10ft in width. The heights will depend on their assessment of the land and
which whole number on the graph with which the land best lines up. Ask the
students before you being to discuss what they are to be calculating during
today’s lesson, and how this will lend to finding the overall volume. Use this
to drive instruction of area as a 2-dimensional measurement and volume as a
3-dimensional measurement. Talk about what type of units they should have
when finished with the area and clear up any misconceptions.
Teaching Strategy:
Remediation:
Peer Tutoring
Heterogeneous
Grouping
Enrichment:
Peer tutoring
Heterogeneous
Grouping
Formative
Assessment:
Teacher
observations of
opening discussion
Performance
Assessment:
Teacher
observation of
estimates and
graphs
Area Calculations
made by students
Exit ticket
Summative
Assessment:
Cross-sectional
graphs with
estimated area
rectangles and
estimated areas
properties to
describe objects.
1. Assign students to heterogeneous groups of 2-4. Have groups open
the “Cut and Fill” assignment.
2. Have students begin calculating the area of each cross-section. They
need to have a way to organize the cut and fill in order to keep those
calculations separate from one another. This will take the majority of
the class period.
3. The teacher should circulate and assist students as they have
questions. Remind students to compare their calculations with other
students. They should not be exactly the same as this is a way of
estimating, but they should be relatively close.
4. Make sure students are using the correct units and have viable
answers. This will keep them from having to redo calculations at the
end of this project, therefore keeping them on schedule.
I can apply
concepts of
density based on
area and volume
in modeling
situations.
8
I can use volume
formulas for
cylinders,
pyramids, cones,
and spheres to
solve problems.
I can identify the
shapes of twodimensional
cross-sections of
threedimensional
objects, and
identify threedimensional
objects generated
by rotations of
“Cut and Fill”
Handout
(Appendix B)
iPad
Calculator
Summarizing Strategy:
As an exit ticket, have students summarize their findings. Ask students
what methods could make more accurate estimates than the method we
are using.
Essential Question(s):
1. How can I use volume formulas for cylinders, pyramids, cones, and spheres
to solve problems?
2. How can I identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects?
3. How can I use geometric shapes, their measures, and their properties to
describe objects?
4. How can I apply concepts of density based on area and volume in modeling
situations?
Set:
The teacher will begin by having students share some of their findings from
this point about the areas found in each cross section. Explain that today they
will be finding the total volume that is being cut and the total volume that is
being filled and comparing the two numbers. Ask students to write down how
they will be able to find the volume of each cross section if they have already
figured the area, and what units will be used. After allowing the students time
to answer the question, ask students to share some of their answers. Use this
to steer the students in the correct direction for today’s objectives of finding
and comparing the total volume of cut and total volume of fill. Clear up any
Remediation:
Peer Tutoring
Heterogeneous
Grouping
Enrichment:
Peer tutoring
Heterogeneous
Grouping
Formative
Assessment:
Teacher
observations of
opening writing
assignment
Teacher
observations of
opening discussion
Performance
Assessment:
Teacher
observation of
volume estimates,
graphs, and cost
cutting
suggestions
Exit ticket
two-dimensional
objects.
misconceptions for the students. Next discuss what the contractor will have
to do if the cut volume is higher then the fill volume and visa versa. Explain
what this means in terms of the contractor’s plans and costs.
I can use
geometric shapes,
their measures,
and their
properties to
describe objects.
Summative
Assessment:
Completed Cut
and Fill
Assignment
Teaching Strategy:
1. Assign students to heterogeneous groups of 2-4. Have groups open
the “Cut and Fill” assignment.
2. Have students begin calculating the volume of each cross-section. This
will go more quickly then finding the area, but the students will have
several questions to answer concerning their findings after they have
finished calculating the total volume cut and total volume fill for the
lot of land at which they are looking. Make sure their units are
correct.
3. Allow the students to continue working together to sort through some
of the tougher questions. Do not answer the questions for each
student but be sure to lead them in the correct direction.
4. Students should finish their cut and fill assignment today with all units
correctly identified and all questions answered in the assignment. Let
students know that tomorrow they will be presenting their findings to
the class.
I can apply
concepts of
density based on
area and volume
in modeling
situations.
Summarizing Strategy:
As an exit ticket, have students summarize their findings. Ask students what
factors they control and do not control in determining ways for the contractor
to cut costs on this project.
9
Debate Day – See Unit Plan
The Cost of Creating Energy – Debating Mountaintop
Removal Mining
10
I can use volume
formulas for
cylinders,
“Cut and Fill”
Handout
(Appendix B)
Essential Question(s):
1. How can I use volume formulas for cylinders, pyramids, cones, and spheres
to solve problems?
2. How can I identify the shapes of two-dimensional cross-sections of three-
Remediation:
Peer Tutoring
Heterogeneous
Formative
Assessment:
Teacher
observations of
pyramids, cones,
and spheres to
solve problems.
I can identify the
shapes of twodimensional
cross-sections of
threedimensional
objects, and
identify threedimensional
objects generated
by rotations of
two-dimensional
objects.
I can use
geometric shapes,
their measures,
and their
properties to
describe objects.
I can apply
concepts of
density based on
area and volume
in modeling
situations.
iPad
Calculator
dimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects?
3. How can I use geometric shapes, their measures, and their properties to
describe objects?
4. How can I apply concepts of density based on area and volume in modeling
situations?
½ Project Day – See Unit Plan
The Cost of Energy – The Debate
Set:
The teacher will begin by allowing students to look over their findings in
preparation for their presentation. Give students a chance to ask you final
questions about any confusions or misconceptions. Let them know the order
in which they will be presenting and tell them they will not be allowed to
work on their assignment or presentation while other classmates are
presenting.
Teaching Strategy:
1. Students will present to the class on their findings. All should be
relatively similar. Allow students to ask those presenting questions if
they have any.
2. Summarize this project with the students. How were their
findings similar and what were some differences? How did their
suggestions to cut cost compare to one another?
3. Discuss what were the best options for cost cutting. What do
contractors face on a daily basis when trying to be cost efficient?
What happens when mistakes are made and who has to suffer the
cost of these mistakes?
Summarizing Strategy:
As an exit ticket, have students summarize their findings. Ask students why cut
and fill is an excellent way for professionals to make estimates and create
plans. In what ways can technology improve this process? In what ways can
technology leave room for mistakes?
Grouping
Enrichment:
Peer tutoring
opening discussion
Performance
Assessment:
Presentation
Exit ticket
Heterogeneous
Grouping
Summative
Assessment:
Completed Cut
and Fill assignment
STANDARDS
Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
G.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
G.GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of twodimensional objects.
G.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
G.MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot)