Today in class students learned that distance divided by time equals speed. When we have a given scale for a map, we can use that scale to measure distances on that map and then multiply it by the scale factor for the actual distance on the road. Divide this distance by the time it took to travel this distance and you have the speed at which you were traveling.
Answers to HW: 1.a. The road is not straight, so it's hard to be exact, but you can estimate that it's about 260 miles. b. No, it will take longer than 3 hours. 70 mph times 3 hours = only 210 miles. 2.a. Each side is 2,400 feet. 1 inch = 200 feet and there are 12 inches in 1 foot b. 4.5 inches
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Today in class students learned the differences between scale drawings and non scaled drawings. There are benefits and drawbacks to either. Scaled drawings include details inside the figure that are also drawn to scale, not just the perimeter.
Answers to HW: 1a. 46 feet b. 12 feet c. 9 meters 2. 30 feet long and 55 feet wide 3. a. about 800 ft by 500 ft b. 1 inch might represent 300 ft 4. a. 16 times larger (72/4.5 = 16) b. 4 c. 12 units Today in class students learned that while the scale factor is multiplied by all of the sides of a figure to create a scaled copy, to find the area of the new copy....you have to square the scale factor and multiply it with the original area.
Answers to HW: 1. The perimeter of Q is 20 units, and the area of Q is 16 units. The scaled copy perimeter is 40 units, and the area of the copy is 64 square units. The scale factor is 2 and the area is multiplied by the square of the scale factor. 2. The area of each scaled triangle is the area of the original times the square of the scale factor scale factor area (units squared) 1 36 2 144 3 324 5 900 1/2 9 2/3 16 3. Diego used the scale factor of 1/4. The area of Q is 4.5 square units. This area is 1/16 the area of P (1/4)(1/4). 4. a. 1/2 because the vertical side on the copy is 1/2 the length of the vertical side on the original b. 2 because the vertical side on the copy is twice the length of the vertical side of the original c. 3/2 because the vertical side on the copy is 3/2 the length of the vertical side on the original d. 1 because the original and the copy have the same size 5. a. x = 7 b. x = 11 c. x = 5 Today in class students learned about using the reciprocal of a scale factor to shrink a larger figure. The reciprocal of 16 = 1/16 if you have a figure that is 16x lager than the original, and the reciprocal of 5/2 = 2/5 if you have a figure that is 2 1/2 times larger than the original.
Answers to HW: 1.a. greater than 1 b. greater than 1 c. less than 1 d. greater than 1 e. equal to 1 f. less than 1 g. equal to 1 2.a. 2 b.1/2 c. 2/3; the two scale factors are reciprocals of each other 3. Yes; the scale factor is 1 4. No; the scale factor of the shortest corresponding sides is 2 and that is not the scale factor for each of the other sides. 5. C, D, and F are all equivalent ratios Today in class students worked to understand that the angles in scaled copies have the same measure as the original figure.
Answers to HW: 1. B, C, D, and F 2. Since the lengths of AC and BD are 6, and AC corresponds to PR.....the scale factor must be 1/2. Since QS corresponds to BD....QS must also be 3 units long. 3. a. 6 units b. 3 units c. 3 because distances between points in Figure 2 are 3 times the corresponding distances in Figure 1 d. 3 units because the scale factor is 3 4. You could use 12 cups of pink paint to 10 cups of blue paint to make 2 batches OR 18 cups of pink paint to 15 cups of blue paint to make three batches. Today in class students learned how to create scaled copies of given shapes.
Answers to HW: 1. When you get into class, check your drawings with your table partner. 2. The scale factor is 1/3. The side lengths of quadrilateral B must be 2,3,3, and 4. The perimeter is 2+3+3+4 = 12 3. Since the perimeter of the original polygon is 10, to achieve a perimeter of 30 the scale factor must be 3. Check your drawing with your table partner in class. 4. Ha, trick question. Actually only D is a scaled copy of A. Today in class students learned about scale factors, and how to tell if shapes that have corresponding parts are actually scaled copies.
Answers to HW: 1a. We can share the pair of corresponding points and pairs of lines we chose with our groups at the beginning of class tomorrow. b. Scale factor is how much the original is multiplied by to create the scaled copy. If you multiply the original by 1/4 or 0.25, you get the scaled copy. Count the square units and prove the math for yourself. 2. Statements B, D, and E MUST be true. 3. a. the scale factor is 2 because the top of A(2.5) corresponds to the top of B (5). b. Using a scale factor of 2 means you multiply each corresponding side on figure A to find out the sides of B...on the left side it measures 3, and on the right side is 5 c. The corresponding angles are also 53 degrees and 82 degrees because the figures are scaled copies of each other. 4. a. 5 b. 32 c. 3 d. 14 e. 1/3 Today in class students began learning about scale copies of shapes or pictures. We know that we can see if pictures are scale copies of each other by looking at the angles and shape. We know that shapes are scale copies of each other if they are multiplied ON EACH PART of the shape by the same number.
Answers to HW: 1. Figures 2 and 4 are scaled copies. Notice the same angle shapes, AND if you can draw a square around the letter like the original. Figure 1 fits inside a rectangle not a square, and figure 3 has different angles than the original. 2. Nope, sorry Tyler, but both the height AND the width have to be 1/2 the size of the original in order for it to be a scale copy. 3. Both A and D are scaled copies. B is flattened horizontally, and B is stretched vertically. Today in class students learned about their growth potential as students and people. We have our new math workbook for unit 1 and it should already have our name on it :)
Yesterday we began a geometric string art project and continued with it today. Everyone will complete at least one project for a class grade. They are starting to look very nice!
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October 2018
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