Today in math class, we started a new unit about comparing and scaling. It's all about comparing ratios, data, and the size of objects. The problem we worked on today was about comparing which soft drink people like better: Bolda Cola and Cola Nola. In this case, people preferred Bolda Cola over Cola Nola. It gave us soma data that a group of people found. The data included: 1.) In a taste test, people preferred Bolda Cola outnumbered those who preferred Cola Nola by a ratio of 17,139 to 11,426. 2.) In a taste test, 5,713 more people preferred Bolda Cola. 3.) In a taste test, 60% of the people preferred Bolda Cola. 4.) In a taste test, people who preferred Bolda Cola outnumbered those who preferred Cola Nola by a ratio of 3 to 2.
It asked which one could be used to best promote their business of Bolda Cola. In this case, I think it would be #2 because it shows how many more people preferred it over Cola Nola, and that option makes Bolda Cola look a lot more popular than Cola Nola.
Thursday, January 28, 2010
Monday, January 25, 2010
Saturday, January 23, 2010
Today in class we learned about how you can estimate heights and distances by using similar triangles. For instance, there is a telephone pole with a shadow of 5 ft. (length) There is a stick next to the telephone pole with a shadow of 1.25 ft. (length) The height of the stick is 2.5 ft. How tall is the telephone pole? the shadow next to the telephone pole makes a right triangle. The shadow next to the stick makes a right triangle. Because the sun is hitting the stick and the telephone pole at the same angle, the two triangles are similar. The telephone pole is 20 ft tall. I figured that out by finding the scale factor of the two triangles. Since I already have corresponding side measures and the height of the small triangle, I can figure it out. The corresponding side measures are 10 ft and 1.25 ft. To find the scale factor, I divided 10 by 1.25. That comes out to 8. Now I know that the scale factor from the smaller triangle to the larger
triangle is 8. To find the height of the telephone pole, I have to use the height of the smaller triangle. The height of the smaller triangle is 2.5 feet. I multiplied the height of the smaller triangle, (2.5 ft) by the scale factor (8). That equals 20 ft. That is the height of the telephone pole.
triangle is 8. To find the height of the telephone pole, I have to use the height of the smaller triangle. The height of the smaller triangle is 2.5 feet. I multiplied the height of the smaller triangle, (2.5 ft) by the scale factor (8). That equals 20 ft. That is the height of the telephone pole.
Thursday, January 21, 2010
Ratios
Today in class we learned about ratios. A ratio is a comparison between two quantities. You can compare numbers, side lengths, fruits to vegetables, you name it. Bottom line is that if it compares to quantities, its a ratio. An example of a ratio would be if you had five bananas and three apples, it would be a five to three ration or 5:3. You can also put ratios in fraction or decimal form. if you were comparing the numbers 7.3 and 9, you could write it as 7.3/9. Also, you can put that fraction into a decimal. 7.3/9 as a decimal is .81. sometimes you can't tell if a ratio is similar with another ratio unless you put it in decimal form. It's hard to tell if the ratios 11/13.5 and 18.3/22.5 are similar just by looking at them but if you put them into decimals they both equal .81.
by Quillen Bradlee
Thursday, January 14, 2010
Thursday, January 7, 2010
Similar polygons
Today we learned more about similar shapes. We reviewed the rules for telling weather two polygons are similar, which were equal angles, proportional sides, and the same basic shape. Finally, we learned how to find the angle measures and side lengths of 
one triangle, using it's similar shape. The picture to the left shows two similar triangles, UVY and XYZ. As you can see, all three of the corresponding angles are marked with the same number of arcs, which means that they are equal to eachother. The sides are also proplotinal to eachother. The scale factor of XYZ to UVW is two. This means that the are of XYZ is four times as large as the area of UVW. Finally, you can tell that they are similar because of their basic shape. This is one important rule used to find out if two shapes are similar.
one triangle, using it's similar shape. The picture to the left shows two similar triangles, UVY and XYZ. As you can see, all three of the corresponding angles are marked with the same number of arcs, which means that they are equal to eachother. The sides are also proplotinal to eachother. The scale factor of XYZ to UVW is two. This means that the are of XYZ is four times as large as the area of UVW. Finally, you can tell that they are similar because of their basic shape. This is one important rule used to find out if two shapes are similar. Wednesday, January 6, 2010
Tuesday, January 5, 2010
Lesson 3.2
Today in class we learned about how to use rep-tile triangles to construct larger similar triangles. A rep-tile in math is any shape that, in a group with identical shapes can fit to gather to make a larger version of the shape. For example, a square is a rep-tile because if you fit four squares together it creates a larger square. An example for a non-rep-tile is a hexagon because no matter how many hexagons you fit together you can't create a larger hexagon. So today we split up into groups and each group recieved a bag of pattern-block triangles. Each group received a bag of either, isosceles, scalene, or right tringles. Then, each group would have to figure out how to use the given triangles to create a larger version of their triangles. We would use the information we found to answer questions in the "Stretching and Shrinking" book section 3.2 Afterwards, as a class we reviewed our answers and learned that all triangles are rep-tiles.
Monday, January 4, 2010
Problem 3.1
In class today we learned about how larger shapes are similar to the original shape. For example If the original shape was a parallelogram the first lager similar shape would be 4 times larger than the original shape, 4 units would have been used and the scale factor would be 2. A good thing to remember is that in similar shapes the side lengths and perimeter change by the scale factor. Area of the original times the scale factor squared gives the area of the new shape. The definition of scale factor is the number used to multiply the lengths of a figure to stretch or shrink it to a similar image. For example if the scale factor was 3 all the lengths of the new image would be 3 times larger than the original image.
By Nicole Doherty
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