3.2+Building+with+Re-tiles

November 5, 2008 OC Big Idea: Many things in our world are mathematically similar and we can use this to understand and describe the world around us. Essential Question: How can I use math to check if two figures are similar? Notes: The change in area between similar figure is the scale times 2. The change in area between similar figures is the scale factor.


 * Question A: Start with four copies of one of the shapes. Try to find a way to put the four copies together-with no overlap and no holes-to make a larger, similar shape. If you are successful, make a sketch showing how the four shapes (rep-tiles) fit together, and give the scale factor from the original shape to the new shape. Repeat this process with each shape.**

Answer A:
 * Question B: For each rep-tile you found in part A, try to find a different way to arrange the copies to get a similar shape. Sketch each new arrangement. How does the scale factor for each new arrangement compare to the scale factor for the first arrangement?**

Answer B:
 * Question C: Start with one of the rep-tiles you found in part A. Try to add copies of the rep-tile to this shape to make the next-largest similar shape. If you are successful, make a sketch showing how the copies fit together. Repeat this process with each rep-tile you found in part A.**

Answer C:

=Follow Up=


 * Question 1: Examine your work from Problem 3.2 carefully. What is the relationship between the scale factor and the number of copies of an original shape needed to make a larger, similar shape?**

Answer 1: The scale factor squared it self is the area of the shape.


 * Question 2: Is the number of copies of an original shape used to make a new shape related to the side lengths or the area of the new shape?**

Answer 2: The number of copies of an original is related to the area because it is squared.