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Mathematics

Grade 7: Geometry and Spatial Sense

Planning: Term #

Tracking: Ach. Level

Overall Expectations

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• 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 two-dimensional shapes, and apply transformations to create and analyse designs.

 

 

 

 

Specific Expectations

 

 

 

 

Geometric Properties

 

 

 

 

– construct related lines (i.e., parallel; perpendicular; intersecting at 30, 45, and 60), 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., side-side-side; side-angle-side; angle-side 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 two-dimensional 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 two-dimensional 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.