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Estimate Whole Numbers

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					Unit 7
Grade 5
 Geometry
   Lesson 1
   7-a: Lines and Line Segments
Start a chart in your notes!

Description Examples   Symbol      Read

A point is             No symbol   Point P
the an
exact
location.
Descriptio       Examples   Symbol   Read
n
A line is a                           line ST
straight path                            or
that goes on
                                      line TS
forever in
both
directions. It
has no
endpoints.
Descriptio Examples   Symbol   Read
n
A line                         Line
segment is                     segment
a part of a                    MN or line
line. It has                   segment
two                            NM
endpoints.
Descriptio        Examples   Symbol   Read
n
A ray is a part                       ray CD
of a line that
begins at one
endpoint and
goes on
forever in the
other
direction.
Descriptio       Examples   Symbol   Read
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.
Descriptio Examples   Symbol    Read
n
A plane is            No symbol Plane ABC
a flat
surface
that goes
on forever
in all
directions.
Description        Examples   Symbol   Read

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.
Description    Examples   Symbol     Read

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

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

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

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.
Adjacent Angles: When two lines
intersect, the angles next to each
other are adjacent. They are
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
                                             decom pres sor
                                    are needed to s ee this picture.
   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
4: Quadrilateral
5: Pentagon
6: Hexagon
7: Heptagon
8: Octagon
9: Nonagon
10: Decagon
11: Undecagon
12: Dodecagon
Quadrilaterals: a plane figure formed
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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                               Qui ckTi me™ and a
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                       are ne ede d to see thi s pi cture.
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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
    quadrilateral add up to be?
Homework
   Pages 198-199
   Problems (1-15)
   Lesson 7
   7-i: Quadrilaterals
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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.
   The angles in a quadrilateral add up to 360
    degrees.
   What about other polygons?
   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 206 Read carefully
   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
    statement about triangles
    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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    triangle, the legs,   are neede d to see this picture.

    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)
       QuickTime™ and a                 B (-5, 3)
        decompressor                    C (-2. 3)
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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)
       QuickTime™ and a             B (-5, 3)
        decompressor                C (-2. 3)
are neede d to se e this picture.
                                    New Figure

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

                                          Original
                                            Figure

                                         A (-5, 6)
       QuickTime™ and a                  B (-5, 3)
        decompressor                     C (-2. 3)
are neede d to se e this picture.
                                        New Figure

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

                                         Original
                                           Figure

                                        A (-5, 6)
       QuickTime™ and a                 B (-5, 3)
        decompressor                    C (-2. 3)
are neede d to se e this picture.
                                        New Figure

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


                  Quic kTime™ and a
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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
    diameter, radius,
    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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                are neede d to see this picture.
  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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