Mathematics
Grade 7: Geometry and Spatial Sense 
Planning: Term # Tracking: Ach. Level 

Overall Expectations 
1 
2 
3 
4 
•
construct related lines, and classify triangles, quadrilaterals, and prisms; 




•
develop an understanding of similarity, and distinguish similarity and
congruence; 




•
describe location in the four quadrants of a coordinate system, dilatate
twodimensional shapes, and apply transformations to create and analyse
designs. 




Specific Expectations 




Geometric Properties 




–
construct related lines (i.e., 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 quadrilaterals by geometric properties
related to symmetry, angles, and sides, through investigation using a variety
of tools (e.g., geoboard, dynamic geometry software) and strategies (e.g.,
using charts, using Venn diagrams) (Sample problem: Investigate whether
dilatations change the geometric properties of triangles and
quadrilaterals.); 




–
construct angle bisectors and perpendicular bisectors, using a variety of
tools (e.g., Mira, dynamic geometry software, compass) and strategies (e.g.,
paper folding), and represent equal angles and equal lengths using
mathematical notation; 




–
investigate, using concrete materials, the angles between the faces of a
prism, and identify right prisms (Sample problem: Identify the perpendicular
faces in a set of right prisms.). 




Geometric Relationships 




–
identify, through investigation, the minimum side and angle information
(i.e., sidesideside; sideangleside; angleside angle) needed to describe
a unique triangle (e.g., “I can draw many triangles if I’m only told the
length of one side, but there’s only one triangle I can draw if you tell me
the lengths of all three sides.”); 




–
determine, through investigation using a variety of tools (e.g., dynamic
geometry software, concrete materials, geoboard), relationships among area,
perimeter, corresponding side lengths, and corresponding angles of congruent
shapes (Sample problem: Do you agree with the conjecture that triangles with
the same area must be congruent? Justify your reasoning.); 




–
demonstrate an understanding that enlarging or reducing twodimensional
shapes creates similar shapes; 




–
distinguish between and compare similar shapes and congruent shapes, using a
variety of tools (e.g., pattern blocks, grid paper, dynamic geometry
software) and strategies (e.g., by showing that dilatations create similar
shapes and that translations, rotations, and reflections generate congruent shapes)
(Sample problem: A larger square
can be composed from four congruent square pattern blocks. Identify another
pattern block you can use to compose a larger shape that is similar to the
shape of the block.). 




Location
and Movement 




–
plot points using all four quadrants of the Cartesian coordinate plane; 




–
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); – create and
analyse designs involving translations, reflections, dilatations, and/or
simple rotations of twodimensional shapes, using a variety of tools (e.g., concrete
materials, Mira, drawings, dynamic geometry software) and strategies (e.g.,
paper folding) (Sample problem: Identify transformations that may be observed
in architecture or in artwork [e.g., in the art of M.C. Escher].); 





determine, through investigation 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. 




Student Name: 




Expectations: Copyright The Queen's Printer for Ontario, 2005. Format: Copyright B.Phillips, 1998.