Today in class students found that not all data in a table is proportionate. Proportionate data has a constant of proportionality or unit rate that you use to multiply.
Answers to HW: 1.a. Not proportional since the ratio of distance to listener to sound level is not always the same. b. Not proportional since the ratio of volume to cost is not always the same. 2. distance traveled price 9/10 1.80 2 2.90 3 1/10 4.00 10 10.90 This is not proportional; the ratio of distance to price is not always the same 3. The turtle data may be proportional. d = 54 x t where d is distance traveled and t is time in minutes. 4.a. 7 (or 1/7) b. 120 (or 1/120) c. 1/25 (or 25) d. 2 1/2 (or 5/2) 5. Kiran is correct. If the figure length and width are scaled by 2, the diagonal will be scaled by 2 as well.
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Today in class students worked out the parts of an equation that describes a proportional relationship. y = kx where y is the output result of multiplying the constant of proportionality, or unit rate, times any input x.
Answers to HW: 1.a. The car travels 65 miles in 1 hour; the car is traveling 65 miles per hour; 65 miles per hour is the constant of proportionality. b. The car travels 97.5 miles in 1.5 hours. c. It take the car 2/5 of an hour, or 0.4 hours, or 24 minutes to travel 26 miles. 2.a. w = 17b or b = 1/17 w b. 867 fluid ounces because 17 times 51 = 867 c. 3 bottles because 51/17 = 3 3. x = 1.61y and y = 1/1.61 x OR y = 0.62x 4.a. number of quarters number of toonies 1 1/8 16 2 20 2.5 24 3 b. 1/8 means that one eighth of a toonie equals one quarter 5. The scale factor down the first table is times 3/2, down the second table is times 2, and down the third table is times 3. The unit rate, or constant of proportionality, is 1:5 for the first table, 1:1/4 for the second table, and 1:3/5 for the third table x | y x | y x | y 2 | 10 12 | 3 5 | 3 3 | 15 20 | 5 10 | 6 7 | 35 40 | 10 30 | 18 1 | 5 1 | 1/4 1 | 3/5 Today in class students looked at proportions, constant of proportionality, the reciprocal of proportionality, and how to write an equation using the constant of proportionality. For example y = 100x
Answers to HW: 1.a. meters kilometers 1,000 1 3,500 3.5 500 0.5 75 0.075 1 0.001 x 0.001x b. y = 0.001x 2.w = 28b and b = 1/28w 3.a. $0.80 per meter b. 1.25 meters or 5/4 meters or 1 1/4 meters Today in class we determined that most students had completed Lesson 3 well enough yesterday to allow us to move on to Lesson 4 today. We learned about recognizing the constant of proportionality and writing equations that describe how we are filling in proportion data tables.
Answers to HW: 1. square meters of ceiling number of tiles 1 10.75 10 107.5 9 100 a 10.75a 2. 1.6 hours because 1/500(800) = 1.6 3.a. constant of proportionality is 4 and P = 4s b. constant of proportionality is 3.14 and C = 3.14d 4. Yes; 12 inches per foot and 5,280 feet per mile, so there's 63,360 inches per mile and 1,267,200 inches in 20 miles. Today in class students completed tables of data to show proportionality. The unit rate is the constant of proportionality.
Answers to HW: 1.a. cups of milk, tablespoons of chocolate syrup b. 4 c. 3/2 d. tablespoons of chocolate syrup, cup of milk 2.a. 3/7 cups of red paint b. 3/7 or 0.43 3.a. 21,600 square miles. The area on the map is 24 square inches. Each square inch represents 900 square miles since 30 times 30 = 900. The actual area is 24 times 900 = 21,600 square miles. b. 1 inch to 60 miles. If 21,600 square miles has to be represented by only 6 square inches, then each square inch has to be 21,600/6 = 3,600 square miles. Each side of the inch is 60 because 60 times 60 = 3600. OR you may have thought about 6 square inches is 1/4 of 24 square inches, so each square inch has to represent 4 times as much land area as the first scale.900 times 4 = 3,600, and each side of the square inch is 60. 4. The area of polygon Q is 45 square units, so the area has been scaled by a factor of 9. 9 times 5 = 45. So the scale factor of the original figure had a scale factor of 3 since 3 times 3 = 9 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 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 |
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October 2018
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