Download Grade 8 - HPEDSB

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/ec/services/cst/elementary/math/Sketchpad.html
Links:
All “GSP Connection” files can be found at: http://www.hpedsb.on.ca/ec/services/cst/elementary/math/Sketchpad.html#gsp8
Additional Help: William Lundy, SETS-Mathematics, Hastings and Prince Edward DSB, 613-966-1170 ext 3326; [email protected]
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Specific Expectation
Geometric Properties
sort and classify quadrilaterals by
8m43
geometric properties, including those
based on diagonals, through
investigation using
a variety of tools (e.g., concrete
materials, dynamic geometry software)
GSP Connection
8m44
construct a circle, given its centre and
radius, or its centre and a point on the
circle, or three points on the circle;
8m45
investigate and describe applications of ƒ
geometric properties (e.g., properties
ƒ
of triangles, quadrilaterals, and circles)
in “the real world.”
see note at right
“Dog Pens”**
“Quadrilateral
Puzzle”**
Teacher Technology Companion for Grade 8 – rev 05/10/2007
Internet Connection
Remarks
Use GSP help menu,
index, and search for
“Circles”: “Circle by
center + point”, “Circle
by center + radius”
**These activities
available in Key Press
Publication, “Shape
Makers.”
Page 1 of 3
Geometric Relationships
determine, through investigation using
8m46
a variety of tools (e.g., dynamic
geometry software, concrete materials,
geoboard), relationships among area,
perimeter, corresponding side lengths,
and corresponding angles of similar
shapes
8m47
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;
ƒ
ƒ
ƒ
ƒ
ƒ
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);
“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”
See remarks to right
Teacher Technology Companion for Grade 8 – rev 05/10/2007
Use GSP files for 8m47
to develop concepts
and big ideas before
pencil-and-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;
“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
8m52
points, 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, real8m53
world movements that are translations,
reflections, and rotations.
8m51
Teacher Technology Companion for Grade 8 – rev 05/10/2007
“Pythagorean Theorem” (19 Java
applets with different illustrations
of the theorem)
http://www.ies.co.jp/math
/java/geo/pythagoras.html
“How High? Making and Using an
Inclinometer to Measure the
Heights of Very Tall Objects”
http://www.exploratorium.edu
/math_explorer/
howHigh_makeInclino.html
“Paper Models of Polyhedra”
http://www.korthalsaltes.com
/index.html
Internet activity uses
Pythagorean principles
but not the theorem
directly.
ƒ
Links to using GSP as
well as on-line
activities for Cartesian
graphing
ƒ
“Plotting on the Cartesian
Plane”
http://www.hpedsb.on.ca/ec
/services/cst/elementary
/math/geometry.html#cartesian;
“Transmographer”
“Pantograph”
http://www.ies.co.jp/
math/java/geo/panta/
panta.html
Page 3 of 3