Today in class students reviewed the Unit 1 Test. Since we have been looking at graphs JUST like these in science, we will try the homework for Lesson 11 without the extra practice of the Lesson itself.
Answers to HW: 1.a. $7.99 b. The movie streaming service is $7.99 for one month of service. c. your points should lie on a straight line on the grid because there is a constant of proportionality d. C = 7.99m 2. The point (1,25) is on the line on the graph; it means that for each cup of oats there are 25 grams of almonds in the granola mix. 3. Yes, each row will have the same number of knots in it so the number of knots will always be a multiple of the number of rows. 4.You need to know the constant of proportionality and variables for the quantities
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Today in class students sorted graphs by whatever commonality they saw, then discussed what graphs of proportional relationships have in common, then sorted out data tables to match each graph.
Answers to HW: 1. A and C; lines on the graphs are both linear and run through the origin 2.a. x represents the cups of water, y represents the cups of lemon juice, and yes the relationship is proportional - therefore your graph for part b should be linear and run through the origin when you connect the points and draw the line. Graph paper can be tucked into your workbook. 3.a. The table does not show a proportional relationship because the ratio of width to height is not always the same. b. The table does not show a proportional relationship because the ratio of height to distance is not always the same. 4. A and D Today in class students had some fun with solving problems with requested data from a partner. We know there is certain information we need in order to solve proportional relationships.
Answers to HW: 1.a.Therre is a proportional relationship between weight and the number of sheets of paper because each sheet of paper has the same weight. Multiply the number of sheets in the stack by the weight of 1 sheet of paper (unit rate or constant of proportionality) to find the weight of any stack. b. There is not a proportional relationship between the number of books and the weight of the stack because each different size book has a different weight. You cannot determine the weight of a stack with the different books in it by multiplying the weight of 1 of the books times the total number of books. 2.a. Yes, the constants of proportionality are 2 and 1/2 b. b = 2t and t = 1/2b 3.a. Lin's age Her brother's age 5 2 6 3 15 12 28 25 b. There is no proportional relationship. The ratio of their ages changes each year because they each age 1 year. 4. Hope you disagreed with the student. Dividing by 9 is the same as multiplying by 1/9. We can write y = x/9 or y = 1/9x. Also - y/x = 1/9 is constant for all corresponding values of x and y. Today in class students determined that most had not completed enough of Lesson 8 yesterday to allow us to go on to Lesson 9 today, so those who had completed all of the activities split up to go and peer tutor those groups who had activities remaining for the lesson.
Answers to HW: 1.a. miles yards 1 1,760 5 8,800 2 3,520 10 17,600 b. Yes there is a constant of proportionality; 1,760 yards per mile. 2.a. no b. yes c. yes d. no 3.a. x | y 2 | 5 3 | 15/2 6 | 15 Yes it is proportional because y/x = 5/2 in each row. b. x | y 1 | 8.2 2 | 11.4 4 | 17.8 No, there is no proportional relationship between x and y because in the first row y/x = 8.2, but in the second row y/x = 5.7 4.a. 20 packets b. 45,000,000 bytes c. x = 12,000p Today in class students looked for proportions using tables of data. 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. Today in class students worked together to determine the relationship, an equation, between data given in a scenario (concert tickets and prices).
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 learned about two constants of proportionality - a coefficient and its reciprocal - that relate data in a table to each other. A unit rate is an example of a constant of proportionality.
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 students clarified some of our math vocabulary thus far, and worked out writing an equation to represent the proportions in a table of data.
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 took the Unit 2 Pre-diagnostic Test (not for a grade). They received their new Unit 2 workbooks, and determined some of the big ideas we will be learning about next. Hopefully those students who needed to finish the Unit 1 test did so today. We had a sub today while I was a county mandated math training.
Today in class students took the Unit 1 Unit Test. A few students will finish this tomorrow.
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October 2018
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