Today in class students worked on filling in a data table given one relationship to get started.
Answers to HW: 1.a. $0.45 per ounce b. about 2.2 ounces c. c = 0.45h and h = 2.2c d. Either data gives you a linear graph going through the origin. If you used c = 0.45h then your y axis should be labeled cost in dollars and your x axis labeled ounces of honey. If you used h = 2.2c then your y axis should be labeled ounces of honey and your x axis labeled cost in dollars. 2. A, B, E 3.a. p = 6/4 r. Your graph should have cups of raisins on the x axis and cups of peanuts on the y axis. Data points should be linear and go through the origin. b. r = 4/6 p. Your graph should have cups of raisins on the y axis and cups of peanuts on the x axis. Data points should be linear and go through the origin. 4.a. For every 2 gallons of gray paint, 1 gallon of black paint is used. b. The x axis is labeled gray paint in gallons, y axis is labeled black paint in gallons. c. Title: The Amount of Black Paint Needed to Create Gray Paint d. The point (60, 30) means that making 60 gallons of gray paint requires 30 gallons of black paint
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Today in class students learned about how to use the same graph to plot multiple proportions. You can compare data easily with this graphic display.
Answers to HW: 1.a. 5 b. 1 c. 4 d. 2 e. 3 f. 6 2.a. The first graph is cost vs. volume and the second graph is calories vs. volume. Notice that the y values on the first graph are most likely dollars, and the second is a better fit for calories. b. Calories and volume are proportional - every ounce has the same number of calories. The line is straight (linear) and goes through the origin. There is more involved in the expense of making the coffee so it is not proportional. c. The constant of proportionality is 15 calories per ounce. You can determine this from either 150/10 or 360/24. Coffee has 15 calories per ounce. 3.a. Include your graph paper in your work book. b. For Lin, k = 0.3 and for Andre, k = 2/8 or 0.25 c. Lin is moving faster at 0.3 km per minute since Andre is moving at 0.25 km/min. Today in class students worked out that they can find the constant of proportionality from a graph, unit rates can be calculated from the graph or found at (x, k), and that all proportion graphs have lines that go through the origin.
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 Today in class we discovered that proportional data on a graph creates a line that is straight and goes through the origin of the 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 worked out the unit rate, or constant of proportionality, from word problems. Once we have a relationship given between two data points, we can use the ratio to figure out the constant that helps us find more data points. For any value x...y = kx and k is the constant, we can solve for y.
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 used given equations to substitute in given values, find the outcome, plot the data, and determine if the relationships were proportional or not.
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 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. 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 | y2 | 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 = 4 sb. constant of proportionality is 3.14 and C = 3.14 d4. 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. |
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