Today in class students began Unit 2 Ratios and Proportions. We know a ratio compares two things like 2 cups of red paint to 1 cup of white makes pink paint.
We will complete the review of, test on and corrections for, Unit 1 in Smart Block this week. Answers to HW: 1. C is different from A and B. The width:height ratio for A and B is 5:4. In figure C the width is 10 and the height is 6, so the ratio is 5:3. 2. Yes, because 3 times 1.5 is 4.5 and 2 times 1.5 is 3 3. a. 1 in: 1 ft b. 1: 1000 c. 1: 10,000,000 d. 1 cm: 1 m e. 1: 100,000 4. A
0 Comments
Today in class students figured out how to recognize scale factor relationships with or without units of measure.
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 went ahead and took the Unit 2 pre-diagnostic test (not for a grade). They then worked on some practice problems applying scale factors to various shapes. We had a sub today while I was a county mandated math training.
Sorry kiddos, I will have to post the HW to Lesson 9 on Thursday; left the book at school. One day soon, I hope to be able to post to this site at school.
Today in class students worked to use different scales to draw the same triangle shape. We divided up the original meter lengths into scaled centimeter pieces, and then saw how multiplying the scale as a fraction with the original lengths gets the same answer. 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 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 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. |
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
October 2018
Categories |