Today in math class we reviewed the scale factor,and similar figures. The scale factor is the number used to multiply the x and y cordinates. For example if the scale factor was two then the x and y cordinates would be multiplied by two times the original cordinates. Similar figures are any shapes that have corresponding angles of equal measurements. For example b is similar to a and the scale factor for a to b is 2.
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[__] a ____
[ ]
[____ ] b
Monday, December 14, 2009
Thursday, December 10, 2009
Today we Learned
Today in math we learned about how similar shapes are scaled, and we used a program on the computer to show us how you change the side lengths and the position of a similar figure on a grid. Using the scale factor we learned if you multiply a number by both the x and y axis you will get a corresponding figure. The example Ms. Favazza gave us was that if you multiply a rectangle with dementions of 3cm width and 2cm height by 3 you will get a figure that is corresponding that has a 9cm width and a 6cm height, that is exactly 3 times larger than the original image. On the computer program geometric sketchpad where you could change the scale of the image, you could make it both corresponding and not, you could also change it so the image would be parralel or above the original image.
Moving a shape on a grid
Today in class we were reviewing formulas and the effect on the x and y axis. When you add to the x coordinate the object moves to the right. When you subtract from the x coordinate the coordinate moves to the left. When you add to the y coordinate the shape moves up and when you subtract the shape moves down. An example would be hat 1, 2 and 4 are similar because hat 1 and 2 are moved to a different place. Their formulas only include adding and subtracting so the size or shape never changes. Hat 4 is reduced by two or times by 1 half. Since it was that on both axes, they were both reduced by the both amount leaving them the same shape but a different size. When you multiply the coordinates by a fraction or a decimal the shape or object gets smaller. If you multiply it by a whole number the object will get bigger and is similar. If both coordinates are multiplied by the same number the image is similar. If they are multiplied by different numbers the image is an “imposter” or not similar.
Example: What rule would make a hat with a line segments twice as long as Hats 1 and moved 8 units to the right?
(x+2, 2y+3)=Hats 1 formula
(2x+10, 2y+3) would be one answer because 2x and 2y would be the twice as long part. X+2+8 would be the 8 units to the right but you have to take notice that this is for Hat 1 and so you must add two to x because that was in the Hat 1 formula. So 8+2 is to. Same thing with y.
Wednesday, December 9, 2009
Tuesday, December 8, 2009
Tuesday December 8, 2009
Today we compared the Wumps. Glug and Lug are impostors because their formulas do not multiply x and y by the same number. This makes them not similar to Mug Wump because Glug and Lug are either long and skinny or short and fat. If the Wump is not an impostor (like Bug, Zug, and Mug) they are similar figures to Mug. Also, the area of the Wumps do not go up at a steady rate. The area changes differently. For example, the area of Mug's mouth equals 4, Zug = 16, and Bug= 36. When our group compared the Wumps, our notes were:
- all of Zug's features are twice as long as Mug's
- Glug is 3 times taller than Mug
- Lug is 3 times as wide as Mug
- Lug is 24 units wide and 7 units high
- Mug is 8 units wide and 7 units high
- Zug is 16 units wide and 14 units high
- Bug is 24 units wide and 21 units high
Monday, December 7, 2009
Pixels, and Similarity
Today in class we learned about pixels. In old video games things are more square and unrealistic. The more pixels you have the more expensive cameras are. Things are rounder the more pixels they have. We also learned that when the image is distorted it isn't similar to the basic image.
Friday, December 4, 2009
area, perimeter, and corresponding
Today while we were correcting homework we talked about how hight and base meet at a 90 degree angle. When finding an area always do ase times hight. If it's a triangle then you would do the base times the hight times one half. In order to compare the parts of these triangles we use the terms corresponding sides. and corresponding angles. The rectangles angles are all 90 degrees. Corresponding can be sides or angles. It is also the same position on both sides. we learned today that corresponding means to be similar in many ways.
Scaling Up & Down
Our notes from Stretching & Shrinking Problem 1.3.
Stretching & Shrinking Problem 1.3 Rr
View more documents from Kathy Favazza.
Thursday, December 3, 2009
Similarities In Real Life Compared to Pictures
Today in class we learned the similarities between an image and what actually happened.
In real life, things are balanced when it comes to size. In an image, everything is out of proportion. When we used computers in class today, we used a document called "rubber band", which was used to show the different sizes of proportion. There was a line with three points. The first point could be moved around and would decide the size of the image, the point in the middle was used to draw around the already existing figure, and the last dot on the right would draw the image as you traced over the figure. The image of something that happened may look like the situation, but really it's all out of proportion.
Stretching & Shrinking Problem 1.2
When enlarging a figure, what changes and what stays the same? See our notes from today's class.
Stretching & Shrinking 1.2 Rr
View more presentations from Kathy Favazza.
Tuesday, December 1, 2009
Multiplying and Dividing Fractions, GCM, and LCM
Today in math we reviewed multiplying and dividing fractions. To multiply fractions; you reduce them and then multiply the numerators and then the denominators. Then you simplify. If you want to multiply mixed numbers you have to change them to mixed numbers. To divide fractions, you multiply the first fraction by the second fraction's recipricle. Also, we reviewed Gcf and LCM. To find two numbers' GCF you find the prime factorization of each number and the largest number they both have in common is the GCF. To find the LCM you put the factors of each number in a venn diagram (the numbers that they have in common go in the center) and then multiply all of the numbers together.
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