Today in class students worked to clarify the different ways one can express a proportional relationship. The classwork was collected today.
Answers to HW: 1.a. Given the equation c = 2.95g ... here's an example table gallons of gas | cost in dollars 1 | 2.952 | 5.90 10 | 29.50 20 | 59.00 b. graph your data from answer a. c. The unit rate is $2.95 per 1 gallon of gas, $2.95 is the cost for 1 gallon of gas, 2.95 is the constant of proportionality d. Because 2.95 is close to 3, Jada's mom reasons that $3/ 1 gallon means that the reciprocal rate is 1/3 gallon is $1. 2.a. and b. graphs should be tucked into your workbook c. 16 d. 16 tablespoons per cup e. t = 16c
0 Comments
Today in class students worked on calculating data given a relationship, labeling a graph appropriately, and plotting that data correctly.
Answers to HW: 1.a. y = 3/2 x b grams of fish | number of calories1000 | 1500 1334 | 2001 1 | 3/2 2.a. M = 12/5 R ( or something like that, decimal or mixed fraction equivalent is fine) b. Put R on the x axis and M on the y axis with a ray through the origin and (10, 24) or another proportional point. Today in class students worked to write equations for graphs given a data point. Good practice recognizing the unit rate, constant of proportion, and scale factor from Unit 1.
Answers to HW: 1. A ray through (0,0) and (2,8) 2.a. distance (cm) | weight (N)20 | 28 55 | 77 100 | 140 1 | 7/5 b. Maybe from 0 - 100 on the x axis and 0 - 140 on the y axis Today in class students discovered that a time/distance graph is a reciprocal of a distance/time graph and the pace that a time/distance graph shows is the opposite of speed on a distance/time graph. Twice as fast means half the pace.
Answers to HW: 1. Diego's distance and time line should be straight through the origin and steeper than Prya's. 2. Your line should be straight through the origin (0,0) and the point (6, 16.5). Today in class students worked out the rest of a table of data, the constant of proportionality, and the graph, from a given coordinate pair. They noticed the
equation that gave them the constant of proportionality and which coordinate pair showed them the unit rate, or constant of proportionality.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. Today in class students graphed multiple sets of data on the same graph and compared the steepness of the lines with their proportions.
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 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 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 |
## AuthorWrite something about yourself. No need to be fancy, just an overview. ## Archives
August 2018
## Categories |