Today in class students learned about representing subtraction in different ways using negative numbers and a number line.
Answers to HW: 1. a=6+9 (or a=9+6) p=-30+20 (or p=20+-30) z=15+(-12) (or z=(-12)+15) x=-10+(-7) (or x=-7+(-10)) 2. 5 -5 13 -5 -13 13 5 -13 3. 22%, because 13 ÷ 59 is about 0.22 4. a=10 b=-300 c=-1 d=-3,567 5. pounds kilograms 2.2 1 11 5 5.5 2.5 1 0.450.45 kilogram per pound kilograms pounds 1 2.2 7 15.4 30 66 0.5 1.1 2.2 pounds per kilogram
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Today in class students learned about using rational numbers to represent money deposits, withdrawals, and debts.
Answers to HW: 1. yes no yes no 2. $64 because 54+10=64 $25 because -60+85=25 -$110 because -180+70=-110 -$50 because 37−87=-50 3. B, C, E 4. transaction amount account balance 200 200 -147 53 90 143 -229 -86 86 0 5. 512 -36 or -12 -4720 6. Diagram A:
Today in class students worked on understanding integers applied to changes in temperature and elevation.
Answers to HW: Lesson 2 1. 13 degrees Celsius 15 degrees Celsius 2. You may have different numbers for these... 5 degrees C -8 degrees C -0.7 degrees C 4 degrees C 3. Your number line diagram should have an arrow that starts at 80, is 20 units long, and points to the left. 80+(-20) Your number line diagram should have an arrow that starts at -13, is 9 units long, and points to the right. -13+9 Your number line diagram should have an arrow that starts at -5, is 8 units long, and points to the left. -5+(-8) 4. a. Proportional with 6 wheels per bus b. Not proportional; different trains have different number of cars 5. 8 cookies were left; he made 80 cookies, because (1.25)⋅64 = 80. 72 were sold, because (0.9)⋅80 = 72 and then 80−72 =8. Lesson 3 1. First table is Not proportional. Second table is Proportional. The constant of proportionality is 0.8 sale dollars per original dollar. 2. 36 m because 20+16=36 4 m because 20+(-16)=4 -11 m because 5+(-16)=-11 2 m because -9+11=2 -20 m because -9+(-11)=-20 3. Carbon: -6+6=0 Neon: -10+10=0 Oxide: -10+8=-2 Copper: -27+29=+2 Tin: -50+50=0 4. B, C, E 5. 43.6 -4.8 -93.4 51 Today in class students took the Unit 5 Pre-Diagnostic Assessment, for a classwork grade. We moved on to mostly complete Lesson 1 with our groups.
Answers to HW: 1. It was colder in Oslo because -12 is less than -5. 2.a. -12 meters b. 28 meters c. 40 meters 3.a. > b. < c. > d. = e. > f. < g. = h. > i. = j. < 4. $90. If a 100% increase would be an additional $30, a 200% increase would be an additional $60. 5.a. 1 cup of yellow and 1.75 cups of blue b. 4 cups of yellow and 7 cups of blue c. 2 cups of yellow and 4 cups of blue d. 2 cups of yellow and 2 cups of blue 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 | 2.95 2 | 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 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 calories 1000 | 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. |
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October 2018
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