Transcript Volume01_Powerpoint

21st Century Lessons
Volume of Right,
Rectangular Prisms
6.G.2.
Mrs. Thompson
Level 1
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Lesson Overview (1 of 3)
Lesson Objective
Lesson Objective: SWBAT calculate the volume of right,
rectangular prisms using unit-cube, spatial analysis and volume
formulas: V = lwh and V = Bh
Student- Friendly Objective:
I will be able to develop and utilize the formula for the volume of
right, rectangular prisms.
Lesson Description
This lesson was designed to teach volume within the confines of an
engaging, relatable scenario. As it is an introduction into the most basic of
volume formulae, the lesson is structured to be broadly accessible. Future
lessons or problems involving the volume of right, rectangular prisms may
necessitate more focused bands of differentiation, especially on the
advanced end.
One option is choosing to arrange student groups and pairings by
diversifying skill levels. This spectrum within each group may allow the
teacher to circulate among groups more equally in terms of time assistance.
Again, future lessons on this concept might lend themselves better to
homogenous skill set groupings.
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Lesson Overview (2 of 3)
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Materials
Classwork handout (double-sided), Homework handout (double-sided), Key To
Leave page, Powerpoint does include sound clips… speakers optional
Scaffolding
This lesson was crafted to proceed in a deliberate, concrete fashion. The
classwork work-sheets that accompany it are procedural in nature. Diverse
student groupings should also assist in access. Student-specific scaffolds
would be up to teacher discretion.
Enrichment
The homework offers some levels of enrichment in terms of unit pricing etc. A
subsequent volume lesson would lend itself better to having advanced
students really stretch the concept of volume. Again, this is a concept-intro
lesson.
Online Resources for
Absent Students
olume formula explained:
http://mathvillage.info/node/111
http://www.mathsisfun.com/fractions_multiplication.htmllying
http://www.mathsisfun.com/multiplying-decimals.html
Lesson Overview (3 of 3)
Common Core
State Standard
6.G.2.
Solve real-world and mathematical problems involving area, volume
and surface area of two- and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and right prisms.
Before and After
This lesson logically falls after skills in perimeter and area have been taught. It introduces
students to the concept of volume and associated formulas. I would follow up this lesson
with a class focused on students applying the formula to both concrete and theoretical
problems. Then it would make sense to have lessons that really tie all the geometric
measures together…perhaps in a project.
Topic Background
The concept of volume was utilized by ancient Greeks and Babylonians for many purposes. While specific formulas can
be attributed to individuals (Euclid is often linked to volume of a sphere although it is believed to have existed much
earlier), it is nearly impossible to identify the ancient individual to first calculate the volume of rectangular prisms.
Perhaps the most famous account of volume discovery involved Archimedes of Syracuse who determined how to
calculate the volume of irregular shapes.
Lean more about it…
http://en.wikipedia.org/wiki/Archimedes
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Lesson Vocabulary
Prism
A solid object that has two identical ends and all flat sides. The cross section is the same
all along its length. The shape of the ends give the prism a name
Right, Rectangular Prism
A solid (3-dimensional) object which has six faces that are rectangles.
Volume
The amount of 3-dimensional space an object occupies. Capacity.
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Warm Up/Do Now
OBJECTIVE: SWBAT develop and utilize the formula for the
volume of right, rectangular prisms.
A) Explain why the figure at left happens to be
called a Right, Rectangular Prism.
B) Think of 3 examples of these prisms that
you encounter in everyday life.
C) What geometric term do we use to describe
the space inside 3-dimensional figures?
D) Why is such space measured in cubic units
rather than square units like when
measuring Area?
Agenda
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Agenda
OBJECTIVE: SWBAT develop and utilize the formula for the
volume of right, rectangular prisms.
1) Warm Up: Independent (10 Min)
2) Launch:
Teacher Guided Problem (15 Min)
3) Explore:
Partner/Group Investigation (30 Min)
4) Summary: Independent (5 Min)
5) Practice:
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Homework
Problem Launch
Jamal started a Boston business, City Crave,
selling chocolate bars made using his
grandmother’s recipe. He wants to ship the
bars to a candy store in Los Angeles.
Agenda
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Jamal has 3 shipping box options.
No vertical
stacking or
bars will
break.
What are some important things for Jamal to consider?
First, he needs to know how much space is inside each box !
Agenda
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Measuring Area Vs. Measuring Volume
Remember that when we wanted to find the space
inside a 2-dimensional, flat shape, we determined
how many 1 x 1 squares fit into that shape.
Area of rectangle is
18 units2
3
units
6 units
Well, to find the space inside of Jamal’s boxes
(3-dimensional prisms), we will use 1 x 1 x 1 cubes
instead of flat squares. Don’t worry yet about the fact that
his candy bars are not cubes…focus on box space.
Agenda
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1 X 1 X 1 cube
How many cubes will fill each box ?
(these boxes are on CW page #1)
Agenda
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CW Page #1
•
•
1 Problem – Many Brains
Work with your partner(s) on
problem #1.
Pencils down when you reach
the sign.
6 minutes on the clock!
Click on the timer!
Agenda
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CW Page #2
1 Problem – Many Brains
Work with your partner(s) on problem #2.
• Discuss why the formula is
followed by units3.
• Pencils down when you
reach the sign.
2 minutes on the clock!
Click on the timer!
Agenda
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CW Page #2
1 Problem – Many Brains
Work with your partner(s) on problem #3.
• Make sure to assist one another
if needed.
• Pencils down when you reach the
sign.
7 minutes on the clock!
Click on the timer!
Agenda
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Summary, Key to Leave, HW
Name:
1) Provide a definition for volume. How
is it different than area and
perimeter? (think units)
3) Calculate the volume of the prism.
Show all work. Measured in cm.
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2) What is the formula for the volume of
Right, Rectangular Prisms?
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Challenge - Given a right, rectangular prism
with a volume of 120 cm3, length of 12
cm, and width of 5 cm, determine the
prism's height.
Agenda
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