The content of these activities is appropriate to the Nova Scotia school curriculum for grades 6-9. Most of the material is review, although our experience is that it was all new to at least some students.
Activity 1 is a sequence of activities to get the students familiar with GSP and to review prior knowledge. Activity 1a introduces the GSP tools: Angle Bisector, Midpoint, Parallel Line, Perpendicular Line, Circle by Center and Point and Circle by Center and Radius. Activity 1b reviews the congruent angles formed by a transversal of two parallel lines.
Activity 2 is a sequence of activities concerning congruent triangles. Activity 2a explores whether two triangles with congruent corresponding sides (SSS) are congruent. Activity 2b explores whether two triangles with congruent corresponding angles (AAA) are congruent. In Activity 2c the students explore whether it is possible to construct many triangles, a unique triangle or no triangles at all given two angle measures and one side length. There are two cases: the given side can be between the two angles, or it can be one of the two sides not between the two angles. The abbreviations ASA and AAS stand for these two possibilities.In Activity 2d the students explore whether it is possible to construct many triangles, a unique triangle or no triangles at all given two side lengths and one angle measure. There are two cases: the given angle can be between the two sides, or it can be one of the two angles not between the two sides. The abbreviations SAS and SSA stand for these two possibilities.
Activity 3 is a sequence of activities concerned with quadrilaterals. Activity 3a focusses on the diagonal properties of squares. In Activity 3b the students explore what quadrilaterals result from subsets of the set of diagonal properties of the square.
Activity 4 involves the intersection of perpendicular bisectors of the sides of triangles, and angle bisectors of the angles of triangles.
Homework activities were also provided. HW1 and HW2 review parallel line properties introduced in Activity 1b.
|Activity||Topic||GSP tools introduced||Math concepts reviewed or introduced|
|1a||Exploring GSP||Angle Bisector, Midpoint, Parallel Line, Perpendicular Line, Circle by Center and Point and Circle by Center and Radius.||Angle Bisector, Midpoint, Parallel Line, Perpendicular Line, Circle|
|1b||Transversals of two parallel lines.||Angle measure.||Congruency of corresponding angles, alternate interior angles, vertical angles. Supplementary angles.|
|2a||SSS triangle congruency||Custom tool: Segment from Parameter (see file Six_parameters.gsp).||SSS triangle congruency.|
|2b||AAA triangle similarity||Custom tool: Angle from Parameter (see file Six_parameters.gsp).||AAA triangle similarity.|
|2c||AAS and ASA triangle congruency||None||AAS and ASA triangle congruency|
|2d||SAS triangle congruency and SSA situation||None||SAS triangle congruency and SSA situation|
|3a||Diagonals of a square||Drag test||Diagonals of a square, proof, converse.|
|3b||Diagonals of quadrilaterals||None|| Diagonals of rhombi,
rectangles, and parallelograms.
|4a|| Intersection of
perpendicular bisectors of a triangle.
|4b||Intersection of angle bisectors of a triangle.||None||Incentre|
|HW1||Parallel line exercises and problems||None||Congruency of corresponding angles, alternate interior angles, vertical angles. Supplementary angles.|
|HW2||Parallel line exercises and problems 2||None||Congruency of corresponding angles, alternate interior angles, vertical angles. Supplementary angles.|
|HW3|| Congruent triangle
exercises and problems 1
|HW4||Congruent triangle exercises and problems 2||None|
|HW5||Congruent triangle exercises and problems 3||None||None|
Supported by a research grant from the Social Sciences and Humanities Research Council of Canada
Page last updated July 2008 by David Reid