LFP+Mathematical+Reflections,+p+26+0910

9.10.09 SM Big Idea:The dimensions of a right triangle can be determined with limited information. Essential Question:How can I use square roots to find information about triangles. Notes- How to find a square root- e.g.- √2= 1.41421356237309504880168872420969807856967187537694807317667973799. But we don't write the all the numbers after the decimal point and we round it to the nearest thousand so √2 is 1.414.

Finding the areas for upright squares was very simple. I counted the distance between intercepts on the the grid, vertically and horizontally and multiplied it and I found the area. To find the areas for the tilted squares; first I drew a upright square joining the points and find the area of the that. After finding the area of the upright square I count the triangles I added and subtract it from the area of the upright square and find the area of the tilted square.
 * 1. Describe the strategies you used to find the areas of figures drawn on dot paper. Give examples if it helps you to explain your thinking.

2. Describe how you would find the side length of a square drawn on dot paper without using a ruler. Consider both upright and tilted**

To find the side length of the upright square I counted how many lines between the intercepts the square is touching on the grid paper. For finding the side length of a tilted square first I found the area of the tilted square then for the side length I wrote the area of the square square rooted. e.g. area of a titled square= 25 square units the side length will be √25=5 square units. So the side length of the tilted square that has 25 square units is 5. We square root the are because sometimes the area because sometimes the area does not turn out to be a whole number's square.
 * 3. Describe how you would find the length if a line segment drawn on dot paper without using a ruler. Be sure to consider horizontal, vertical, and tilted segments.

To find the measurement of a horizontal line segment I counted the lines between the intercepts. I also did the same thing for vertical lines, I counted the lines between the intercepts on the dot paper. To find of the length of a tilted line segment I first made a whole square with the side length and then found the area of the square. The line segment's length would be **√area = length of line segment.


 * Summary

In this investigation I learned how to find the area and side length of a tilted square. To find the area first draw a upright square around the tilted square then subtracted the triangles I added to form the upright square and found the area of the tilted square. To find the length of any side of the square you just have to write √area because most of the areas don't have a whole number as their square root. Finding the area and the side lengths for and upright square was easy because I just had to count the number of lines between the intercepts on grid paper to find the length of the side length. To find the area I just squared one of the side lengths. **