Content Area: Math

 

Index: 4.2B Grade 8 CPI 1

 

Standard: 4.2 - Geometry and Measurement

 

Strand: B - Transforming Shapes

 

Cumulative Progress Indicator: 1 - The student will understand and apply transformations.

·        Finding the image, given the pre-image, and vice-versa

·        Sequence of transformations needed to map one figure onto another

·        Reflections, rotations, and translations result in images congruent to the pre-image

·        Dilations (stretching/shrinking) result in images similar to the pre-image

 

Grade: 8

 

Sample Activities:

 

·        Students analyze the patterns found in Arabic designs such as tiled floors and walls in Spain, identifying figures that represent translations, reflections, and rotations. Then they generate their own tile designs using basic geometric shapes. They can create their own tile patterns using Tesselmania! software.

 

·        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).

 

·        Students practice doing geometric transformations mentally by using the Geometric Golfer or similar computer software. These programs present a series of puzzles in which there is an object shape and a target shape. The task is to use the fewest transformations possible to change the object shape so that it is congruent to the target shape. In the golf game, the object is a ball and the target is a hole.