Teacher Technology Companion for Grade 5 Geometry

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Teacher Technology Companion for Grade 8 Geometry
Overall Expectations: (Ontario Mathematics Curriculum, rev. 2005)
► 8m40: demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric
properties in the real world;
► 8m41: develop geometric relationships involving lines, triangles, and polyhedra, and solve problems involving lines and triangles;
► 8m42: represent transformations using the Cartesian coordinate plane, and make connections between transformations and the real
world.
“GSP” refers to The Geometer’s Sketchpad®, licensed for publicly-funded schools in Ontario and for students in these schools to take
home to install on their home machines; information may be found at: http://www.hpedsb.on.ca/sg/quinte/gsp.htm
Links:
► All “GSP Connection” files can be found at: http://www.hpedsb.on.ca/sg/quinte/grade_8.htm
► “Internet Connection” sites are linked from either:
o (A) http://www.hpedsb.on.ca/sg/quinte/geometry.htm or
o (B) http://www.hpedsb.on.ca/sg/quinte/interactive_math.htm#is
Additional Help: William Lundy, SETS-Mathematics, Hastings and Prince Edward DSB, 613-966-1170 ext 3326; [email protected]
#
Specific Expectation
Geometric Properties
sort and classify quadrilaterals by geometric
8m43
properties, including those based on
diagonals, through investigation using
a variety of tools (e.g., concrete materials,
dynamic geometry software)
8m44
GSP Connection
“Quadrilaterals and
Diagonals”
(2 activities)
Internet Connection
Remarks
If extensive review of
quadrilaterals is needed,
refer to the “Grade 4”
GSP page (modify URL
above to “…grade_4”
vice “…grade_8”): use
“The Story of
Quadrilaterals” (2 parts)
construct a circle, given its centre and
Use GSP help menu,
radius, or its centre and a point on the circle, index, and search for
or three points on the circle;
“Circles”: “Circle by
center + point”, “Circle
by center + radius”
Teacher Technology Companion for Grade 8
Page 1 of 3
investigate and describe applications of
geometric properties (e.g., properties of
triangles, quadrilaterals, and circles) in
the real world.
Geometric Relationships
determine, through investigation using a
8m46
variety of tools (e.g., dynamic geometry
software, concrete materials,
geoboard), relationships among area,
perimeter, corresponding side lengths, and
corresponding angles of similar shapes


determine, through investigation using a
variety of tools (e.g., dynamic geometry
software, concrete materials,
protractor) and strategies (e.g., paper
folding), the angle relationships for
intersecting lines and for parallel lines and
transversals, and the sum of the angles of a
triangle;

8m45
8m47
“Proportions with Area”






8m48
solve angle-relationship problems involving
triangles (e.g., finding interior angles or
complementary angles), intersecting
lines (e.g., finding supplementary angles or
opposite angles), and parallel lines and
transversals (e.g., finding alternate
angles or corresponding angles);
Teacher Technology Companion for Grade 8
“Dog Pens”
“Quadrilateral
Puzzle”
“Angle Properties of
Parallel Lines and
Transversals”
“Angle Relationships”
“Exploring Angles
Formed by Parallel
Lines and a
Transversal”
“Investigating the
Triangle Sum
Conjecture”
“Parallel Lines and
Triangles”
“Plane Geometry”
See remarks to right
Use GSP files for 8m47
to develop concepts and
big ideas before penciland-paper activities for
this expectation
Page 2 of 3
8m49
8m50
determine the Pythagorean relationship,
through investigation using a variety of
tools (e.g., dynamic geometry software;
paper and scissors; geoboard) and
strategies;
solve problems involving right triangles
geometrically, using the Pythagorean
relationship;
determine, through investigation using
concrete materials, the relationship between
the numbers of faces, edges, and
vertices of a polyhedron (i.e., number of
faces + number of vertices = number of
edges + 2)
Location and Movement
graph the image of a point, or set of points,
8m52
on the Cartesian coordinate plane after
applying a transformation to the
original point(s) (i.e., translation; reflection
in the x-axis, the y-axis, or the angle
bisector of the axes that passes through
the first and third quadrants; rotation of 90°,
180°, or 270° about the origin);
identify, through investigation, real-world
8m53
movements that are translations, reflections,
and rotations.
8m51
Teacher Technology Companion for Grade 8
“The Pythagorean
Relationship”
(A) “Pythagorean
Theorem”


(A) “How High? Making
and Using an
Inclinometer to
Measure the Heights
of Very Tall Objects”
(A) “Paper Models of
Polyhedra”
Internet activity uses
Pythagorean principles
but not the theorem
directly.
(B) “Transmographer”
“Plotting on the Cartesian
Plane” – use for review of
grade 7 topic
“Pythagorean Triples”
“The 30º-60º-Right
Triangle”
n/a
“Plotting on the Cartesian
Plane”
(A) “Pantograph”
Page 3 of 3
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