LP-W3-Q2-11/21/2011
________________________________________________
Every small positive change we make in ourselves repays us in
confidence in the future.
Alice Walker, b. 1944
American Author
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GEOMETRY 11/21/11
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LESSON PLAN RESOURCES.xlsx2
Chapter 1: Introducing Geometry
Section: 1.8 Space Geometry pg. 75
Objectives:
LA.1112.1.6.1 LA.1112.1.6.2 LA.1112.1.6.5 LA.910.1.6.1 LA.910.1.6.2 MA.912.G.8.6
ASSIGNMENTS:
1. Discussion and Examples with Interactive Practice (KA)
2. Classwork Practice DG workbook PG. 8(WA)
HOMEWORK: 1. SSS pg. 95
2. SSS pg. 119
REMINDER: IT IS YOUR RESPONSIBILITY TO SUBMIT YOUR
NOTEBOOK TO THE TEACHER ON THE ASSIGNED DAY, AND
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GET IT BACK THE NEXT DAY FROM THE METAL CABINET;
SECOND DRAWER.
1. Bell-Ringer
In the Middle Ages, the principal square root of a number x was
estimated to be the average of the values obtained by using the
two expressions:
𝑏
𝑏
√𝑎2 + 𝑏1 = a + 2𝑎 and √𝑎2 + 𝑏1 = a + 2𝑎+1 , where the
number x = a2+ b.
Find the square root of 26 using this method. Then, use the
calculator and compare the answers. Write the conclusion in
complete sentence.
Answer: 26 = 25 + 1 = 52 + 1
X = 26
a=5, b=1
1
√25 + 1 = 5 + 10 = 5.1
5.1+5.095
2
1
√25 + 1= 5 + 11 = 5 + 0.095 = 5.095
= 5.10
2. Vocabulary, definitions and notes.
Space
- The set of all possible points; made up of infinite planes.
2
Isometry
-A transformation that keeps the same size and shape of a
figure but moves it to a new location
Examples of transformations are: reflection, rotation,
translation, glide reflection
Transformation
- a correspondence between two sets of points such that
each point in the preimage has a unique image and that
each point in the image has exactly one preimage.
Preimage
- the original object that is reflected
Image
- the reflection of the preimage
SOLIDS
Examples of Solids:
2.
Bases are congruent and // circles
1.
3
3.
4.
5.
Bases are congruent and // circles
centce
Axis of a cylinder is the line connecting the
centers of two bases.
Lateral Area: LA = Circumference x height
Surface Area: SA = LA + 2(Area of the circle)
Right cylinder: A cylinder whose axis is perpendicular to its bases.
It is not a right cylinder. Why?
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It is not a right cylinder because the axis is not perpendicular
to the bases.
A cylinder is analogous to a prism, except its bases are
circular. A cylinder is not a polyhedron (just like a circle is not
a polygon).
Note: The word cylinder actually refers to any solid shape with
two congruent bases in parallel planes (including prisms and
solids with, say, clover-leaf-shaped bases). The cylinders we
mean here are called circular cylinders.
Volume = (Base area) x (height)
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A polyhedron (Pl. polyhedra) is a solid region formed by the
intersection of several (at least four) planes. The planes
intersect in polygonal faces whose sides are called edges and
whose corners are the vertices of the polyhedron.
Surface Area: Total area of all of the faces of the polyhedron.
Volume: A measure of how much space fits inside a solid
figure, calculated in cubic units.
Simple 6-faced solids: Cube, Rectangular solid, parallelepiped.
Rectangular solid: A polyhedron with six rectangular faces.
Adjacent faces intersect at right angles. A rectangular solid has
three measurements: length, width and height.
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Surface Area: SA= 2(LW + LH +HW)
Rectangular solid
Cube: A rectangular solid with six congruent square faces. A
cube has twelve congruent edges and eight vertices.
Volume: V = (side length)3
Surface Area: SA= 6(side length)2
Parallelepiped: A polyhedron whose six faces are
parallelograms lying in pairs of parallel planes. Rectangular
solids are parallelepipeds whose adjacent faces lie in
perpendicular planes.
height
V= L x W x H
width
length
Prism: A prism is a polyhedron two of whose faces (the bases)
are congruent polygons lying in parallel planes; the other
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faces (the lateral faces) are parallelograms that join
corresponding sides on the congruent polygons. The sides that
join the lateral parallelograms to each other are called lateral
edges.
- A prism is identified by the shape of its bases.
Height: The (perpendicular) distance between the bases (or
rather, the planes containing them).
Pentagonal Prism
Volume: V = Base Area x height
Lateral Area (LA): The area of the lateral faces of a prism.
Surface Area: SA = LA + 2(Base Area)
Right Prism: A prism whose lateral edges are perpendicular to
the planes containing the bases of the prism.
Right triangular prism
Lateral area (for right prism):
LA = Perimeter of base x height
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Special type of prisms: Parallelepipeds are prisms with a
parallelogram base. Rectangular solids and cubes are right
prisms with a rectangular (or square) base.
Pyramid: A pyramid is the set of all points along segments
that join a polygonal base with a vertex not in the plane of the
base.
-If the base is a polygon with n edges, the pyramid has n+1
faces: one base and n triangular lateral faces.
-Height: The distance from the vertex to (the plane that
contains) the base.
(𝒃𝒂𝒔𝒆 𝒂𝒓𝒆𝒂)(𝒉𝒆𝒊𝒈𝒉𝒕)
-volume: V=
𝟑
Pyramid with trapezoid base
Base
Regular pyramid: A pyramid with two properties:
1. The base is a regular polygon.
2. The line joining the vertex and the center of the base is
perpendicular to (the plane of) the base. All lateral faces
are congruent isosceles triangles.
- Slant height: The length of the altitude of one of the
lateral faces. The Pythagorean Theorem tells us that
(apothem of base)2 + (height)2 = (slant height)2
-Lateral area: LA =
(𝒃𝒂𝒔𝒆 𝒑𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓)(𝒔𝒍𝒂𝒏𝒕 𝒉𝒆𝒊𝒈𝒉𝒕)
𝟐
- Surface area: SA= LA + Base area
8
Square Pyramid
(Regular Pyramid)
Tetrahedron: A regular triangular pyramid; tetrahedron has
four triangular faces, four vertices, and six edges.
___________________________________________
Cone: A cone is analogous to a pyramid, except the base is a
circle.
Volume: V =
=
(𝒃𝒂𝒔𝒆 𝒂𝒓𝒆𝒂)(𝒉𝒆𝒊𝒈𝒉𝒕)
𝟑
𝝅 𝒓𝟐 𝒉
𝟑
Right cone
Slant height: The length of the shortest segment from the
vertex to a point on the perimeter of the circular base. The
segment is perpendicular to the tangent to the circle at the
point where the segment hits the circular base. Pythagorean
Theorem states that (radius)2 + (height)2 = (slant height)2 =
= π(radius)(slant height)
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Sphere: A sphere is the three-dimensional equivalent of a
circle: the set of all points in space equidistant from a fixed
point called the center. The common distance is called the
radius.
-Hemisphere: Half of a sphere
-Volume: V = 4π(radius)3/3
-Surface area: SA = 4π(radius)2
Sphere
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WWW MATH RESOURCES
PARENT CONTACT LOG.xlsx
MONTHLY RESTROOM PASS.xlsx
MEETINGS CALENDAR.xlsx
NOTEBOOK CHECKING.xlsx
VERIFICATION QUARTERLY GRADES.xlsx
DAILY CLASS BEHAVIOR LOG.xlsx
GRADING SCALES.xlsx
HOMEWORK LOG.xlsx
INTERIM ASSESSMENTS BBA-WINTER RECORDS.xlsx
WWW.KUTTASOFTWARE.COM
GRADE RECORDS PER SECTION.xlsx
LESSON PLAN RESOURCES.xlsx
http://www.dadeschools.net/calendars/11-12/11-12_el-sec.pdf
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web: sbaldoquin, sb223266
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GIZMO RESOUCES
MATH RESOURCES ONLINE
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http://ehandbooks.dadeschools.net/policies/90/csc_sec.pdf
TEXTBOOK MATH RESOURCE
GIZMO RESOUCES\Math Exploration Guides\Algebra
11
STRATEGIES AND PRACTICES
PROVIDE HINTS AND FEEDBACK
INTERACTIV E PARTICIPATION
HAVING STUDENTS TEACH WHAT THEY LEARNED TO SOMEONE ELSE
BLOOM TAXONOMY (CONGNITIVE DOMAIN)
1. KNOWLEDGE
Name
2. COMPREHENSION
Recognize
3. APPLICATION
Sketch
4. ANALYSIS
Dif ferentiate
TEACHING RESOURCES & MATERIALS
DOCUMENT CAMERA
WHITE BOARD
MARKERS
COMPASS
PROTRACTOR
CARDBOARD
PAPER
RULER
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