Stories from the Classroom

Three days bridging from slopes to medians with Grade 9 students

Contributed by: Shirley Baird, KCVI;
Nathalie Sinclair, Queen's

The Setting: October 24th at the Computer Lab at KCVI in Kingston, Ontario. There are 24 PCs (one per student, but not all in working condition...). Shirley had just completed a unit with her students on slopes and was about to start with the product rule for perpendicular lines. But all of a sudden the computer lab became available and it was 'now or never' for Sketchpad. We had planned on starting with some triangle properties but Shirley didn't want the students to experience such a big disconnect between their work in class and the Sketchpad activities. So this is what we did...

Principles of Mathematics, Grade 9, Academic (MPM1D)
  • Analytic Geometry
    • identify the properties of the slopes of line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity) through investigations facilitated by graphing technology, where appropriate.
  • Investigating Geometric Relationships
    • illustrate and explain the properties of the interior and the exterior angles of triangles and quadrilaterals, and of angles related to parallel lines;
    • determine the properties of the sides and the diagonals of polygons (e.g., the diagonals in quadrilaterals, the diagonals of regular pentagons, the figure that results from joining the midpoints of sides of quadrilaterals) through investigation;
    • determine the properties of angle bisectors, medians, and altitudes in various types of triangles through investigation;
    • pose questions about geometric relationships, test them, and communicate the findings, using appropriate language and mathematical forms (e.g., written explanations, diagrams, formulas, tables);
    • confirm a statement about the relationships between geometric properties by illustrating the statement with examples, or deny the statement on the basis of a counter-example (e.g., confirm or deny the following statement: If a quadrilateral has perpendicular diagonals, then it is a square).

Day 1:

Day 2, October 25th, 2000

Day 3: October 26th