Scale (or Grid) Drawings
and Dilations

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A simple activity to reinforce the concept of dilation is that of the scale (or grid) drawing.  While scale drawings are generally introduced to the student at an early age, they can be revisited here as applications of the concept of dilation.  In addition, this activity will allow students to clarify the concept of the scalar factor.

Directions:

  • Give each student a drawing.  Keep the drawing fairly simple.  The more complex the drawing, the longer it will take the students to complete the task.  Good sources of drawings are clipart cartoons, coloring book pages (avoid juvenile pictures), and student doodlings (this is a good opportunity to highlight student drawings).

  • Tell the students that the task has two parts: (a) to dilate the drawing by a scalar factor of 2; and (b) to dilate the drawing by a scalar factor of 1/2.  They will have two separate drawings when they are finished.

  • Discuss with the students that a scale (or grid) drawing method will be used.  Many students will be familiar with this technique.

 

Scale (or grid) drawing method:

1.  Using a ruler, draw a grid (horizontal and vertical lines) covering the entire drawing.  At this age level, allow the students to determine an appropriate size (and units) for the side of each square in the grid (or if you prefer, establish an acceptable range).  Remind them to record the size they are using for the length of each square.

2.  On another sheet of paper, reproduce the original grid using a scalar factor of 2.  With the enlarged grid complete, reproduce the portion of the original drawing that appears in each square.  Most likely, freehand drawing will be used at this point.

3.  On another sheet of paper, reproduce the original grid using a scalar factor of 1/2.  Proceed as in step 2.