![]() Some are suprised to see that the product = -1. Values of the slopes in your sketch-they will appear in the window on the calculator). Lines using the Sketchpad calculator (Select Calculate under the Measure menu and click on the So i tell them that i have a trick: I ask them to find the product of the slopes of the I ask those who have perpendicular lines whether the slope measures provide any clues. ![]() I then ask them how they could figure out whether they were perpendicular if they weren't able to measure the angles. Some of the students have perfect (!) perpendicular lines, others are a few decimals places off. So we do this by selecting the three points that define the angle and choosingĪngle under the Measure menu and although One (or all) of the angles and check whether they meaure 90 degrees. The students do this by eye-balling, so I challenge them toįigure out how they could prove that their lines were really perpendicular. IĪsk them to drag their line segments so that they are perpendicular to each other. We discuss how many angles have now been formed and how they are related. I then ask the students to draw another line segment that intersects with their first line segment and to measure its slope as well. We try toĮxplain why the slope becomes undefined when it is a vertical line by watching it grow largerĪnd larger as it approaches the vertical. We then discuss positionings that give rise to negative, positive, zero, and undefined slopes while they manoeuvre theĮndpoints of their line segments around to watch the changing value of the slope. IĪsk each student to draw a (long) line segment on their sketches and to measure its slope by first selecting the line then chossing Slope With some ideas that they are already familiar with from their work on slopes in the classroom. The students have never worked with The Geometer's Sketchpad before so we decided to start quite simply. 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).pose questions about geometric relationships, test them, and communicate the findings, using appropriate language and mathematical forms (e.g., written explanations, diagrams, formulas, tables).determine the properties of angle bisectors, medians, and altitudes in various types.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.illustrate and explain the properties of the interior and the exterior angles of triangles and quadrilaterals, and of angles related to parallel lines.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,.Principles of Mathematics, Grade 9, Academic (MPM1D) Some triangle properties but Shirley didn't want the students to experience such aīig disconnect between their work in class and the Sketchpad activities. But all of a sudden the computer lab becameĪvailable and it was 'now or never' for Sketchpad. The product rule for perpendicular lines. Shirley had just completed a unit with her students on slopes and was about to start with There areĢ4 PCs (one per student, but not all in working condition.). The Setting: October 24th at the Computer Lab at KCVI in Kingston, Ontario. Three days bridging from slopes to medians with Grade 9 students Stories from the classroom Stories from the Classroom
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