Dilations with Scale Factors to Enlarge and Reduce Images

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We continued our exploration of coordinate points by learning about dilations. Dilation is a transformation that enlarges or reduces a figure to create a similar figure. For example, all circles are similar; all squares and regular polygons are similar. The scale factor of dilation is the ratio of a side length of the image to the corresponding side length of the original figure. Each coordinate point is multiplied by its scale factor. For example, if I have a square with side length of 2 and want to create an image of the square with a side length of 4, this dilation has a scale factor of 2. If I want to create an image of the original square to a square with a side length of 1, this dilation has a scale factor of 1/2.

During certain eye exams our doctor will put drops in your eye that will dilate your pupils to a scale factor of 2 in order to see inside your eye. I showed the students this video https://www.youtube.com/watch?v=R4kf6Z077eg.

We discussed map scales with dilation factors of 1/20,000 and up. The most relevant dilation for the children is the enlargement and reduction of digital images on phones and cameras. Each pixel has a numerical coordinate point location and when you put two fingers on the screen and slide outward, the image dilates to scale factors of greater than one. When you swipe in, the image dilates to scale factors between 0 and 1. 

The children were challenged to dilate multiple images on a coordinate graph. 1st-4th grade dilated with whole number scale factors only (such as 2, 3, 4, etc.). Grades 3 and 4 also experimented with scale factors of 1/2 and four quadrant dilations. 1st-2nd grade were only challenged to dilate in the first quadrant to avoid negative numbers. Since some of them want to explore negative numbers, I included the four quadrant challenges in their packet (they should not feel obligated to do those for fun work).

The 5th-6th graders were given different packets with scale factors of more difficult fractional scale factors. I taught them the standard algorithm of multiplying fractions. Essentially, they are to multiply numerators and then multiply denominators; then they are to divide the numerator by the denominator and write the coordinate as a mixed number such as 3 1/3 instead of 10/3. I will work with these groups over the next few weeks to learn how to cross simplify before multiplying across to avoid having to simplify the fractional product.

Dilations are so much fun when used to create models with scale factors between 0 and 1 and murals with scale factors of greater than one. Murals will be our quest next week; stay tuned.

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