Download Teacher Technology Companion for Grade 7 Geometry

Teacher Technology Companion for Grade 7 Geometry
Overall Expectations: (Ontario Mathematics Curriculum, rev. 2005)
► 7m43: construct related lines, and classify triangles, quadrilaterals, and prisms;;
► 7m44: develop an understanding of similarity, and distinguish similarity and congruence;
► 7m45: describe location in the four quadrants of a coordinate system, dilatate two-dimensional shapes, and apply transformations to
create and analyze designs.
“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#gsp7
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
construct related lines (i.e.,
7m46
parallel; perpendicular;
intersecting at 30º, 45º, and 60º),
using angle properties and a
variety of tools (e.g., compass
and straight edge, protractor,
dynamic geometry software) and
strategies (e.g., paper folding);
sort and classify triangles and
7m47
quadrilaterals by geometric
properties related to symmetry,
angles, and sides, through
investigation using a variety of
tools (e.g., dynamic geometry
software) and strategies (e.g.,
charts, Venn diagrams);
GSP Connection
“Constructions” –
Intersecting Lines,
Perpendicular Bisector
Internet Connection
Remarks
Construction directions
found in BLMs for
version 3 manual still
available
“Angle Properties of
Triangles and
Quadrilaterals”
Teacher Technology Companion for Grade 7 – rev 05/10/2007
Page 1 of 4
7m48
construct angle bisectors and
perpendicular bisectors, using a
variety of tools (e.g., …,dynamic
geometry software,…) and
strategies (e.g., paper folding),
and represent equal angles and
equal lengths using mathematical
notation;
7m49
investigate, using concrete
materials, the angles between the
faces of a prism, and identify
right prisms
“Constructions” –Angle
Bisector, Perpendicular
Bisector, Perpendicular
Bisectors in a Triangle,
Trisecting an Angle
Geometric Relationships
identify, through investigation,
“Triangle Congruence”
7m50
the minimum side and angle
information (i.e., side-side-side;
side-angle-side;
angle-side-angle) needed to
describe a unique triangle ;
determine, through investigation
7m51
using a variety of tools (e.g.,
dynamic geometry software),
relationships among area,
perimeter, corresponding side
lengths, and corresponding angles
of congruent
shapes;
demonstrate an understanding
7m52
that enlarging or reducing twodimensional shapes creates
similar shapes;
Teacher Technology Companion for Grade 7 – rev 05/10/2007
“MathsNet Geometry” > “Interactive
Construction” http://mathsnet.net/
geometry/index.html
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Construction directions
found in BLMs for
version 3 manual still
available;
Angle Trisection and
Perpendicular Bisectors
in Triangles may be
more appropriate
activities for
extension/enrichment
“Paper Models of Polyhedra”
http://www.korthalsaltes.com
/index.html
“Studying Polyhredra”
http://mathforum.org/
alejandre/applet.polyhedra.html
Unit 3: “Surface Area & Volume”
http://www.shodor.org/
interactivate/activities/
SurfaceAreaAndVolume/
“Pantograph”
http://www.ies.co.jp/
math/java/geo/panta/
panta.html
Page 2 of 4
7m53
distinguish between and compare
similar shapes and congruent
shapes, using a variety of tools
(e.g., dynamic geometry
software) and strategies (e.g., by
showing that dilatations create
similar shapes and that
translations, rotations, and
reflections generate congruent
shapes)
“Similarity and
Congruency”
Location and Movement
plot points using all four
7m54
quadrants of the Cartesian
coordinate plane;
7m55
identify, perform, and describe
dilatations (i.e., enlargements and
reductions), through investigation
using a variety of
tools (e.g., dynamic geometry
software, geoboard, pattern
blocks, grid paper);
7m56
create and analyse designs
involving translations, reflections,
dilatations, and/or simple
rotations of two-dimensional
shapes, using a variety of tools
(e.g., concrete materials, Mira,
drawings, dynamic geometry
software) and strategies (e.g.,
paper folding)
http://www.hpedsb.on.ca/ec
/services/cst/elementary
/math/geometry.html#cartesian
Links to using GSP as
well as on-line activities
for Cartesian graphing
“Pantograph”
http://www.ies.co.jp/
math/java/geo/panta/
panta.html
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“Ferris Wheel”
“Glide Reflections”
“Hexatessellations”
“Kaleidoscope”
“Properties of
Reflections”
“Semicephalus”
“Tessellations”
Teacher Technology Companion for Grade 7 – rev 05/10/2007
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“MathsNet Geometry” >
“Interactive Transformations”
http://mathsnet.net/transform/index.
html
“Virtual Manipulatives”
http://nlvm.usu.edu/en
/nav/category_g_2_t_3.html
“What is a Tiling?
http://mathforum.org/sum95
/suzanne/whattile.html
Page 3 of 4
7m57
determine, through investigation “Transformations”
using a variety of tools (e.g.,
pattern blocks, Polydrons, grid
paper, tiling software,
dynamic geometry software,
concrete materials), polygons or
combinations of polygons that tile
a plane, and describe the
transformation(s) involved.
Teacher Technology Companion for Grade 7 – rev 05/10/2007
Page 4 of 4