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Content Area: Math
Index: 4.2B Grade 12 CPI 1
Standard: 4.2 - Geometry and Measurement
Strand: B - Transforming Shapes
Cumulative Progress Indicator: 1 - The student will determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic object, and, conversely, determine whether and how one object can be transformed to another by a transformation or a sequence of transformations.
Grade: 12
Sample Activities:
· Students draw two congruent triangles anywhere in the plane and determine the minimum number of reflections needed to map one onto the other.
· Students draw a triangle on graph paper and then find the image of the triangle when the coordinates of each vertex are multiplied by various constants. They draw each resulting triangle and determine its area. They make a table of their results and look for relationships between the constants used for dilation and the ratios of the areas.
· Students use a Mira (Reflecta) to find the center of a circle, to draw the perpendicular bisectors of a line segment, or to draw the medians of a triangle.
· Students apply transformations to figures drawn on coordinate grids, record the coordinates of the original figure and its image, and look for patterns. They express these patterns verbally and symbolically. For example, flipping a point across the x-axis changes the sign of the y-coordinate so that the point (x,y) moves to (x, -y).
· Given the equation of a line, students plot the line on a coordinate grid and then shift the line according to a given translation. They then determine the equation of the resulting line. After doing several such problems, students identify patterns that they have found and write conjectures.
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