Today in class students reviewed using scale, scale factors, and converting units. Test tomorrow
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Today in class students learned about using units in scaled drawings. I gave everyone a sheet of unit conversions to refer to, and these should now be in your math folder. We know that in order to scale a figure larger, we multiply by a number greater than 1. In order to revert back to the original size, we multiply by the reciprocal of that number.
Answers to HW: 1. E would work best. A, B, and D will not fit on the page, and C or F are a bit small 2. The scale is 1 inch = 9 feet 3. A and D 4. 36 square units. Use the scale factor squared times the original area. The scale factor is 2 and 2 x 2 = 4 and 4 x the original area of 9 = 36 5. a. $12.50 because $1.25 x 10 = $12.50 b. $25 because 1.25 x 20 = 25 c. $62.50 because 1.25 x 50 = 62.5 6. a. number of batches cups of water cups of detergent 1 6 1 2 12 2 3 18 3 4 24 4 b. 8 48 8 You could use the unit rate of 6 cups of water per batch x 8 batches, or you could double the amount used for 4 batches to find the answer. Today in class students learned about using one given scale to create another, and then used their scale drawing to find area, using 1/2 base x height, OR multiplying the scale factor squared times the original area. If you didn't try that in class, you absolutely should tonight! Oh, and if you haven't checked the google classroom lately, your classmates are posting helpful videos about scale and scale factors...
Answers to HW: 1a. Because the scale drawing is 10 cm long and 5 cm wide, the actual pool is 10 m long and 5 m wide. b. It will be smaller because it will take fewer cm to represent the actual width and length of the pool. c. Your pool should be about 1/2 the size of the given scale drawing; 5 cm long, and 2.5 cm wide. 2. The larger map has the scale of 1 inch to 500 feet. It takes twice the number of units on this map to represent the same distance as the other scaled map. Think about 1 inch = 1000 feet vs. 1 inch = only 500 feet, so 2 inches represents 1000 feet here. 3. Han is not correct. Every square inch represents a 12x12 square or 144 square feet in the restaurant. Actual area = 8,640 square feet. 4. 186 5. angle DEF angle EFD segment DF segment ED Today in class students learned how to create a scale, not just recognize a scale factor. A scale must have units, and often has two different units, e.g. centimeters and meters, so that you can convert the scale copy to the original, or vice versa.
Answers to HW: 1.a. 1 inch to 6 inches b. 18 inches 2.a. Your flag should be 3 cm long and 2 cm tall. The yellow rectangle is 1 cm tall and the red and blue rectangles are each 0.5 cm tall. b. Your flag should be 12 cm long and 8 cm tall. The yellow rectangle is 4 cm tall and the red and blue rectangles are each 2 cm tall. 3.a. 4 b. 1/4 c. 16 d. 1/9 e. 4/9 f. 9/16 4.a. C, D, E, and H have the same scale factor for both length and width, and the corresponding angles are the same. b. Check your rectangle with your classmates tomorrow, 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.
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 the size of scale factors. There are differences easily noticed when the scale factor is less than 1, equal to 1, or greater than 1.
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 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 scaled copies - what that means, what the copies have in common, and if they are actually to scale or not.
Answers to HW: (you can check out the answers to lesson 1 under the math 7 class tab) 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 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 :)
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October 2018
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