# Estimate Whole Numbers

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```					Unit 7
Geometry
   Lesson 1
   7-a: Lines and Line Segments
Start a chart in your notes!

A point is             No symbol   Point P
the an
exact
location.
n
A line is a                           line ST
straight path                            or
that goes on
line TS
forever in
both
directions. It
has no
endpoints.
n
A line                         Line
segment is                     segment
a part of a                    MN or line
line. It has                   segment
two                            NM
endpoints.
n
A ray is a part                       ray CD
of a line that
begins at one
endpoint and
goes on
forever in the
other
direction.
n
An angle is                          angle KIM
formed by two
rays that have
a common                             angle MIK
endpoint.
The endpoint                         angle I
is called the
vertex.
n
A plane is            No symbol Plane ABC
a flat
surface
that goes
on forever
in all
directions.

Parallel lines                         Line MN is
are lines in a                MN OP    parallel to
plane that are                         line OP
always equal
distance apart,
never intersect,
and have no
common points.

Intersecting              No symbol Line WZ
lines are                           intersects
lines that                          Line YX at
cross or                            Point A
touch at
exactly one
point.

Intersecting              No symbol Line WZ
lines are                           intersects
lines that                          Line YX at
cross at                            Point A
exactly one
point.

Perpendicular                           Line TU is
lines are lines               TU   AB   perpendicular
that intersect at                       to line AB
a 90 degree
(right) angle.

Skew lines are                   No        line ?? and
not parallel and                 symbol    line ?? are
do not                                     skew
intersect. Skew
lines are in
different
planes.

http://mathworld.wolfram.com/SkewLines.html
Classwork
   Look around the room. Find 3 examples of the following terms.
   Angle
   Ray
   Line
   Line segment
   Parallel Lines
   Intersecting Lines
   Perpendicular Lines
   Skew Lines
   BE VERY SPECIFIC

   Example: Skew: The top line of the chalkboard to the bottom line of the wall with the
whiteboard.
Closure
   Where can we see geometric figures in real
life?
Homework
   H54 Lesson 6.1 (1) and Lesson 6.2 (1-7)
   Lesson 2
   7-b: Angles and Their Measures
What
geometric
ideas do you
see in the face
of a clock?
Circles are
divided into
360
degrees.
We can use
these
degrees to
help
measure
angles.
Complementary Angles
Two angles are complementary if
the sum of their measures is 90
degrees.
Supplementary Angles
Two angles whose measures add up
to 180 degrees.
Vertical Angles: When two lines
intersect, the angles opposite each
other are called vertical angles.
Vertical angles have equal measures.
intersect, the angles next to each
supplementary angles.
Central Angles
   Reflex Central Angle: measure greater than
180 degrees but less than 360 degrees

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   Chapter 10 Animations
   Playing Golf with Angles              Quic kTime™ and a
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   And
   Angles
   http://www.classzone.com/cz/books/msmath_2_n
a/get_chapter_group.htm?cin=4&rg=ani_math&at
=animations&var=animations
Classwork
New Purple 511-515 and 516-520

Biggest Problem of Miners worksheet
Closure
   What angles do you see around the room?
Homework
   Pages 186-187
   Problems (1-20)
   Lesson 3
   7-c : Angles with Transversals
What do you think the measure of each angle
might be? What type of angles are they?

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Measuring angles
   Protractor: tool to measure angles

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What’s My Measure?

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Transversal is a line that intersects
two parallel lines.

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What are the relationships?

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Classwork
   Old Purple page 360-361
   Problems (1-9)

   Pouring Oil Into a Car worksheet
Closure
   If you have a transversal but the two lines
are not parallel, will you have any of the
same relationships?
Homework
   Brontosaurus Band-Aids and Judge Rotten Milk
Worksheets
   Lesson 4
   7-d: Identify and Classify Angles (measure
them)
What’s My Measure??????
   How to Use Protractors
   http://www.amblesideprimary.com/amblewe
b/mentalmaths/protractor.html

   Ninja Angles
   http://www.bbc.co.uk/keyskills/flash/kfa/kfa.
shtml
Copy this link down to find cool
stuff!
   http://jmathpage.com/JIMSGeometrypage.h
tml

   Really cool geometry games online! Take
a peek!
Classwork
   Books Never Written worksheet

   Draw and measure angles if there is extra
time
Closure
   Why do protractors have two sets of
numbers going in different directions.
Homework
   What Happens When Cupid Shoots an Arrow?
Worksheet
   Lesson 5
   7-e: Identify Polygons
   7-f: Identify Polygons in a composite figure
Name each of the shapes
Polygons: A polygon is a closed figure
made by joining line segments, where each
line segment intersects exactly two others.
The following are examples of polygons:

The figure below is not a polygon, since it is not a closed figure:

The figure below is not a polygon, since it is not made of line
segments:

The figure below is not a polygon,
since its sides do not intersect in exactly two places each:
Types of
Polygons

3:Triangle
5: Pentagon
6: Hexagon
7: Heptagon
8: Octagon
9: Nonagon
10: Decagon
11: Undecagon
12: Dodecagon
by 4 segments called sides. Each side
intersects exactly two sides, one at
each endpoint, and no two sides are
part of the same line. All angles add
up to be 360 degrees.
Parallelogram
   Opposite sides of a parallelogram are
parallel and equal in length.
   Opposite angles are equal in size.
Rectangle
   Opposite sides of a rectangle are parallel
and equal in length.
   All angles are equal to 90°.
Rhombus (Diamond)
   All sides of a rhombus are equal in length
   Opposite sides are parallel.
   Opposite angles of a rhombus are equal.
   The diagonals of a rhombus bisect each
other at right angles.
Square
   Opposite sides
of a square are
parallel and all
sides are equal
in length.
   All angles are
equal to 90°.
Trapezoid

   A trapezoid has one pair of opposite sides
parallel.
   A regular trapezoid has non-parallel sides
equal and its base angles are equal, as
shown in the diagram
   Another name for it is trapezium
Concave and Convex
   Concave Polygons have at least one
interior angle that is greater than 180                                                                                                       QuickTime™ and a
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degrees.                                         Quic kTime™ and a
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   Convex Polygons have all interior angles
less than 180 degrees.
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Concave or convex?
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Classwork
   New Purple 531-532
   Problems: 1- 22
   Checkpoints: 4, 10, 22
Closure
   What shapes do you see represented in the
classroom?
Homework
   Pages 192-193
   Problems (1-13)
   Lesson 6
   7-g: Identify and Classify Triangles
   7-h: Sum of Interior Angles
What are the differences between
the two triangles?
A triangle is a closed plane figure
bounded by three line segments.
2 Ways to Classify Angles
   Way 1 is by its angles
   Way 2 is by it sides

   Let’s explore more in depth!
Classifying Triangles by its Angles
   Acute: An acute-angled triangle has all
angles less than 90º
   Obtuse: An obtuse-angled triangle has one
angle greater than 90º. That is, one angle
is obtuse.
   Right: A right-angled triangle has one
angle equal to 90°. That is, one angle is a
right angle.
What are these?
Classifying Triangles by its Sides
   Scalene: A scalene triangle has no equal
sides.
   Equilateral: An equilateral triangle has all
sides equal.
   Isosceles: An isosceles triangle has two
sides equal.
What are these?
Sum of the interior angles in a
triangle equal 180 degrees.
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Classwork
   New Purple
   Pages 524-526
   Problems: 1-34
   Checkpoints: 5, 9, 15, 21, 26, 34
Closure
   What do you think the angles of a
Homework
   Pages 198-199
   Problems (1-15)
   Lesson 7
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Explore Some Shapes
   http://www.learnalberta.ca/content/mejhm/i
ndex.html?l=0&ID1=AB.MATH.JR.SHAP&I
D2=AB.MATH.JR.SHAP.SHAP&lesson=ht
ml/object_interactives/shape_classification/
explore_it.html

   Classzone.com
Quic kTime™ and a

   Chapter 10: Polygons and Angles               decom pres sor
are needed to s ee this picture.
Classwork
   Old Purple
   Pages 384-385
   Problems: 1-22
   Checkpoints: 3, 8, 14, 19, 22
Closure
   Is a rectangle a square?
   Is a square a rectangle?
   I’m confused!
Homework
   Pages 204-205
   Problems (1-8)
   Lesson 8
   7-j: Relationship between Interior Angles and
Polygons
   The angles in a triangle add up to 180
degrees.
degrees.
   You can use a formula to determine the
measures of the interior angles.

   Draw the diagonals from one vertex in
several regular polygons to form triangles.
Number of   Number of      Total angle         Measure of
Angles      Triangles      measure             each angle

3         1 or (3-2)   (1 x 180), or 180    (180/3), or 60

4         2 or (4-2)   (2 x 180), or 360    (360/4), or 90

5         3 or (5-2)   (3 x 180), or 540   (540/5), or 108

6         4 or (6-2)   (4 x 180), or 720   (720/6), or 120

n           (n-2)        (n-2) x 180        (n-2) x 180
divided by n
Classwork
   Practice drawing and measuring angles!
Closure
   What is your favorite part of geometry?
   Why?
Homework
   Page 207 Problems (1-8)
   Lesson 9
   7-k: Legs and Hypotenuse
   7-l: Pythagorean Theorom
The Pythagorean Theorem
   The Pythagorean Theorem was one of the earliest theorems known
to ancient civilizations. This famous theorem is named for the
Greek mathematician and philosopher, Pythagoras. Pythagoras
founded the Pythagorean School of Mathematics in Cortona, a
Greek seaport in Southern Italy. He is credited with many
contributions to mathematics although some of them may have
actually been the work of his students.

   The Pythagorean Theorem is Pythagoras' most famous
mathematical contribution. According to legend, Pythagoras was so
happy when he discovered the theorem that he offered a sacrifice
of oxen. The later discovery that some numbers were irrational
greatly troubled him. It is even said that the man who proved some
numbers were irrational was drowned at sea by Pythagoras.
Doesn’t sound very rational to me!
   The Pythagorean Theorem is a
containing a right angle. The
Pythagorean Theorem states that:
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“The area of the square built upon
the hypotenuse of a right triangle is
equal to the sum of the areas of the
squares upon the remaining sides.”
2      2       2
a +b =c
   The lengths of the
two shorter sides
of the right                QuickTime™ and a
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are a and b. The
length of the
longest side, the
hypotenuse, is c.
   Classzone.com
   Chapter 11
   Animations
   The Pythagorean Theorem
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Classwork
   New Purple
   Pages 590-592
   Problems: 1-29
   Checkpoints: 5, 11, 17, 24, 29
Closure
   What is the formula and how does it work?
Homework
   Pages 482-483
   Problems (1-15)
   Lesson 10
   7-m: Coordinate Planes
What is this? What does it
represent?
http://www.learningwave.com/lwonlin
e/algebra_section2/alg_coord.html

http://www.shodor.org/interactivate/ac
tivities/MazeGame/
Classwork
   New Purple
   Pages: 315-316
   Problems: 1 - 40
   Check Points: 10, 22, 30, 40
Closure
   How are the quadrants labeled?
Homework
   Pages 310-311
   Problems (1-21)
   Lesson 11
   7-n: Similar and Congruent
   7-o: Transformations
   7-p: Transformations in Coordinate Planes
Which ones are which?

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Which ones are which?

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Similar: So what are the
measurements?
Are these the same figures? What
happened to them?
Types of Transformations
(changes)
   Translations: you can slide a figure along a
straight line

   Rotations: you can turn the figure around a
point

   Reflections: you can flip the figure over a line

   Blue: original figure   Red: transformed figure
Slide 6 to
the right!

Original
Figure

    A (-5, 6)
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New Figure

    A (1, 6)
    B (1, 3)
    C (4, 3)
Rotate 90
degrees to the
right around
point B!

Original
Figure

A (-5, 6)
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New Figure

A (-2, 3)
B (-5, 3)
C (-5, 0)
Reflect or
flip over a
line of
symmetry

Original
Figure

     A (-5, 6)
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New Figure

     A (3, 6)
     B (3, 3)
     C (0, 3)
Slide 7 to
the right and
down 8!

Original
Figure

    A (-5, 6)
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New Figure

    A (2, -2)
    B (2, -5)
    C (5, -5)
   Classzone.com
   Chapter 10
   Animations
   Translations, Reflections, and Rotations

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Classwork
   New Purple
   Pages 558-561
   Problems: 1 - 20
   Checkpoints: 4, 8, 16, 20
Closure
   When do we see transformations in real
life?
Homework
   You Choose one group
   Pages 414-415 Problems (1-18)
   or
   Page 419 (1-4) and 421 (1-6)
   Lesson 12
   7-q: Parts of a Circle
What are the parts of a circle?
Vocabulary

   Circle: a special closed figure made up of all the
points in a plane that are the same distance from
the point called the center.
   Chord: a line segment with endpoints on a circle
   Diameter: a chord that passes through the center
of the circle
   Radius: a line segment with one endpoint at the
center of the circle and the other on the circle.
http://www.mathgoodies.com/lesso
ns/vol2/geometry.html
Closure
   Do you think Sir Cumference and the First
Round Table is a good way to introduce the
parts of a circle to a class of 4th grade GT
Math students? Why or why not?
Homework
   Model/Label a
circle with chord,   Make a model of a
arc,                 circle, label all
circumference        parts!
   Be creative!                  Center
   Lesson 13
   7-r: Classifying Solids Prisms and Pyramids
   7:s: Euler’s Formula V-E + F = 2
   7:t: Nets
What do
you see?

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http://www.harcourtschool.com/jin
gles/jingles_all/1what_am_i.html
   In the mood for a tune?
Types of Solid Figures (pull them out)
Shape of Base   Figure with One Base                                                                    Figure with Two
Congruent Bases
Triangular Pyramid                                                   Triangular Prism

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Rectangular Pyramid                                                      Rectangular Prism
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Cone                                                Cylinder
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Hexagonal Pyramid                                                     Hexagonal Prism

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http://www.bgfl.org/bgfl/custom/re
sources_ftp/client_ftp/ks2/maths/3
d/index.htm Copy Chart first!
Name of shape         Number of bases   Number of   Number of
and faces        edges       vertices

Cone
Cylinder
Triangular Pyramid
Triangular Prism
Rectangular Pyramid
Rectangular Prism
Pentagonal Pyramid
Pentagonal Prism
Hexagonal Pyramid
Hexagonal Prism
Euler’s Formula
   http://www.math.ohio-
state.edu/~fiedorow/math655/Euler.html
Classwork
   New Purple
   Pages 633-635
   Problems: 1 - 26
   Checkpoints: 8, 13, 19, 22, 26
Homework
   Pages 430-433 (1-10)
Closure
   What is the difference between pyramids
and prisms?

```
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