Today in class we did a Math Reflection Gallery Walk which is like a rough draft for the Math Reflection final. It consisted of 3 questions:
1. How can you tell if two polygons are similar?
Answer: You can tell if two polygons are similar by whether or not they have a scale factor. For example, if one polygon had dimensions of 4 and 6 and another polygon had dimensions of 8 and 12, the 2nd polygon is 2x bigger (length wise) than the 1st polygon so the scale factor would be 2.
2. If two polygons are similar, how can you find the scale factor from one polygon to the other? Describe how you find the scale factor from the smaller figure to the enlarged figure. Then, describe how you find the scale factor from the larger figure to the smaller figure.
Answer: You find the scale factor from the smaller figure to the enlarged figure by figuring how many side lengths of the smaller figure go into the enlarged figure. Like, 4 and 6 with 8 and 12, 4 goes into 8 twice and 6 goes into 12 twice so the scale factor is 2. You can find the scale factor from the enlarged figure to the small figure because it's the reciprocal of the scale factor from small to large, so the scale factor is 1/2.
3. For parts (a)-(c), what does the scale factor between two similar figures tell you about the given measurements?
a. side lengths
b. perimeters
c. areas
Answer:
a. You can use the scale factor to find the similar side lengths because the side lengths would be the scale factor times the original side lengths to get the side lengths of the bigger polygon. For example, if one side is 4, you can do 4*2 to get 8 and 8 would be the length of the similar line.
b. You can use the scale factor to find the perimeter because the perimeter would be the scale factor times the perimeter to get the bigger polygon's perimeter. If the dimensions of the smaller polygon are 4 and 6, the perimeter is 20. And the dimensions of the larger polygon are 8 and 12, so the perimeter is 40. So that means the perimeter is 2x bigger than the smaller polygon, which is the same as the scale factor.
c. You can use the scale factor to find the area because the area of the larger polygon would be the scale factor squared times the area of the smaller area. So if the area of the smaller polygon (4 by 6) was 24, the area of the larger polygon (8 by 12) would be 96 because the scale factor is 2 and the 2 squared is 4 and 4*24 is 96. The way you can check is because 8*12 also equals 96 and its the same number so it is correct.
☺That is what we did in math today!☻
Friday, January 8, 2010
Thursday, January 7, 2010
Wednesday, January 6, 2010
Daily Scribe
Today in class we worked on scale factors and similar shapes. We made similar rectangles and triangles for problems A and B for problem 3.3. We had to make new rectangles with the information that they gave us. One of the problems was to make rectangle A to a new rectangle with the scale factor of 2.5. To do this, you would have to first multiplied to base by 2.5, and then the height by 2.5. The new rectangle should be 2.5 times larger and still be similar to the original rectangle.
Another problem on 3.3 was to to make a new rectangle have and area 9 times larger than triangle B and still be similar. To figure this out, you would have to multiply the dimensions by 3. You would do this because to find out the area of a new shape, you would have to multiply the scale factor by itself, then multiply the area from the original shape by that.
This is what we worked on in class!!!
Another problem on 3.3 was to to make a new rectangle have and area 9 times larger than triangle B and still be similar. To figure this out, you would have to multiply the dimensions by 3. You would do this because to find out the area of a new shape, you would have to multiply the scale factor by itself, then multiply the area from the original shape by that.
This is what we worked on in class!!!
Tuesday, January 5, 2010
Today in class, we learned about the scale factor inside bigger shapes like triangles. We figured out a strategy to make perfect smaller shapes. First look at each side of the shape. Find the halfway point and make a dot. Do this for every side of the shape. Now connect the dots from each point so your lines make a smaller version of the original shape. The scale factor would be a fraction, because you are dividing the shape large to small. This would've been dividing the number too, but since the scale factor doesn't work in division, the factor would be less than 1. The area of the new perimeter is the scale factor times the original area squared. Example: the original area=2 and the scale factor from the original to the new is 3. 3 squared is 9, so the new area of the shape is 18. 2•(3^2)= 18.
Monday, January 4, 2010
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