LFP+Mathematical+Reflections,+p+26

October 15, 2008 AS Big Idea: Essential Question: How can I use square roots to find information about triangles? Notes: none

__Mathematical Reflections Investigation 2 Pg. 26__
To find areas, I divided the figure on the dot paper into squares and labeled each square with it's area, and added all of the pieces together. For example, for a triange with 3 regular squares and 1/2 of a square as it's area, I would add 3 + 0.5 = 3.5. I also surrounded the figure by another square or rectangle and subtracted the outside area from the total area of the square/rectangle to get the area of the figure. For example, a triangle surrounded by a box with 3 corners with areas of 1; with the total area being 9. So, the area of the triangle would be 6 because 9 - 3 = 6.
 * 1. Describe the strategies you used to find areas of figures drawn on dot paper.**

For an upright square, I could easily just count the number of squares inside (the area) and find the square root (which would be the side length) or just count the number of spaces across one side. For a tilted square though, I could draw an upright square around the tilted square and subtract the areas of the corners from the total area to get the area of the tilted square, then find the square root which equals the side length.
 * 2. Descibe how you would find the side length of a square drawn on dot paper without using a ruler.**

For a horizontal or vertical line segment, I could simply count the spaces across or down. For a tilted line segment, I formed a square with the line segment as one of the sides, found the area of the square, and found the square root of the line segment which is just the square root of the square's area.
 * 3. Describe how you would find the length of a line segment drawn on dot paper without using a ruler.**

In this investigation, I learned about square roots and how to find the square root of a figure from it's area. I also learned how to find a line segment's length. Also, I found out that square roots aren't always whole numbers; and that calculators aren't the most accurate way of finding a square root of a figure from it's area.
 * Summary:**