Download Moving Mount Spokane

MOVING MOUNT SPOKANE
Enduring Understanding: Develop a better understanding of how the change in a linear dimension
will affect the volume of a figure.
Essential Questions:
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How does a change in one linear dimension affect the volume?
How are units of measure converted within the US system?
How are appropriate concepts and procedures from measurement and algebraic sense used?
How can a conclusion be supported using mathematical information and calculations?
Lesson Overview:
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Before allowing the students the opportunity to start the activity: access their prior
knowledge regarding how to find the volume of a cone. Allow for collaborative time for the
students, possibly activities around the room, discuss with the students.
What would happen if one linear dimension of a cone changes?
What are the relationships that exist among the units of measure for linear dimensions and
volume?
A good warm-up to use would be Ice Cream Dilemma.
How is a problem situation decoded so that a person understands what is being asked?
What is expected when putting together a presentation? What should a person do when
making a presentation? How do you formulate a written persuasive argument?
What mathematical information should be used to support a particular conclusion?
How will the students make their thinking visible?
Use resources from your building.
EALRs/GLEs:
1.1.1
1.2.1
1.2.3
2.2.2
5.1.1
Item Specifications: NS01; ME01; ME02; SR05; MC01
Assessment:
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Use WASL format items that link to what is being covered by the classroom activity
Include Multiple Choice items
Moving Mount Spokane
The engineers in the I Dig It Company of Spokane recently designed a new conveyor belt that
can move 9000 cubic yards of earth per hour. Since this sounds like a great quantity of earth that
could be moved in a day, week or month, we were wondering how long it would take to move Mt.
Spokane! You have been contracted by the I Dig It Company to calculate the amount of earth in Mt.
Spokane and you must determine how long it would take to move Mt. Spokane. You are also to
answer some other relative questions dealing with such a gigantic task.
1. The city of Spokane is approximately 1880 feet above sea level. The base of Mt. Spokane is
approximately 2300 feet above sea level. The top of Mt. Spokane is approximately 5883 feet above
sea level. What is the height of Mt. Spokane from its base? Show all calculations.
2. The diameter of the base is 21 miles and the mountain is cone-shaped. What would be the
volume of earth contained in Mt. Spokane in cubic yards? Show and explain ALL of your
calculations.
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3. The president of the company was told that the diameter of the base of Mt. Spokane was
miscalculated. The actual diameter is half of what was originally told to him. How does this new
information affect your calculation of the volume of Mt. Spokane? Explain your thinking to the
president of the company.
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4. The new conveyor moves 9000 cubic yards per hour. How long would it take to move Mt.
Spokane with the new conveyor? Show and explain ALL of your calculations.
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5. The previous edition of the conveyor used by the I Dig It Company moved 5720 cubic yards of
earth per hour. In addition to the difference in actual time in moving earth, the new conveyor is also
more cost efficient. The older machine cost the company, taking into account all expenses, $64.24
per hour to operate. The new conveyor cost the company $43.54 per hour to operate. How much
cheaper is it to move Mt. Spokane with the new conveyor as opposed to the older machine? Show
and explain ALL of your calculations.
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6. An edge of Cube A is twice as long as an edge of Cube B as shown in the figure below.
Which is the maximum number of smaller cubes that will fit into the interior of the larger cube?
O
O
O
O
A.
B.
C.
D.
2
4
8
16
7. The Great Pyramid at Giza has a square base with sides of length 230 meters and a height of 146.7
meters.
Which is the volume of the Great Pyramid?
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O
O
O
A.
B.
C.
D.
1,650,000 m³
2,590,000 m³
4,950,000 m³
7,760,000 m³
8. The radius of the earth’s orbit is 150,000,000,000 meters.
Which is this number in scientific notation?
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O
O
O
A.
B.
C.
D.
1.5 1011
1.5 1011
15  1010
150  109