Today in class students worked again with positive and negative numbers, learning how to use them in the context of rewriting expressions and past/present events.
Answers to Lesson 13 Near and Far From Zero: 1. a b -a -4b −a+b a÷−b a squared b cubed -1/2 6 1/2 -24 6 1/2 1/12 1/4 216 1/2 -6 -1/2 24 -6 1/2 1/12 1/4 -216 -6 -1/2 6 2 5 1/2 -12 36 -1/8 2. a. b cubed = 216 b. -4b = −24 c. a ÷ (-b) = 1/12 3. a. -4b = 24 b. b cubed = -216 c. a ÷ (-b) = 1/12 4. a. a squared = 36 b. a ÷ (-b) = -12 c. b cubed = -1/8 Answers to Lesson 13 HW: 1.a. 11 tablespoons; from the information, one can determine that 1 tablespoon of coffee will be used for every 3 ounces of water, therefore for 33 ounces of water one would need 11 tablespoons of coffee. b. 70 minutes; from the information, one can determine that it would take the runner 7 minutes to run 1 km, therefore it would take the runner 70 minutes to run 10 km. 2. 8 %; Between 7.85 % and 8.15 % is close enough. 3. a. -17 b. -17 c. 110 d. -4.4 4. Agree with Lin. The soap in the old box represents 100% and the new box now holds 125% which is 2 kg. 5. x − 1, x, 1 − x, -1 ÷ x.The expressions’ values are -54, -14, 54, and 4. 6. -14 + (-12), 14 − 1, -3 ⋅ 14, -3 ÷ 4, 1 ÷ 4 − 1 Answers to Lesson 14 HW: 1. a. $2,400, because 1,200 ÷ 0.5 = 2,400. b. $1,600, because 2,400 ÷ 1.5 = 1,600. 2. a. January: 252.20; February: 88; March 1.70; April: -836.90 b. -123.75, because [252.20 + 88 + 1.70 + (-836.9)] ÷ 4 = -123.75 3. 12, because 85 ÷ 7.50 = 1113 which means it will take 12 months to have a negative balance in the account 4. a. 300 litres (225 + 15 ⋅ 5 = 300) b. 120 litres (225 + 15 ⋅ (-7) = 120) 5. a. $24.15 b. C, D, F
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Today in class students used negative numbers to indicate positive and negative water flow into an aquarium and calculated rates. Again, we used negative numbers to indicate elevation/depth.
Answers to HW: 1. a. 20 cookies; based on the information one can determine that 1 cup of flour makes 5 cookies, so 4 cups of flour will make 20 cookies. b. 40 centimeters; based on the information one can determine that 4 centimeters of tape will hang up 1 student project, so the teacher would need 40 centimeters of tape to hang 10 student projects. 2. a. 24 b. 28 c. -23 (or equivalent) d. -118 (or equivalent) 3. a. -2.55 miles; -3.4⋅0.75=-2.55 b. -5 miles per hour; -1.5÷0.3=-5 c. You had to choose one direction to be positive and the other to be negative. Positive distances could mean distances in one direction and negative distances mean distances in the other direction. Positive velocities could mean it was moving in the positive direction and negative velocities mean it was moving in the negative direction. 4. Your answers should be like maybe... a. Water leaking out of a tank b. An airplane descending c. Gravel being emptied out of a truck 5. a. i. -280 m; -340 + 60 = -280 ii. -220 m; -340 + 120 = -220 iii. -100m; -340 + 240 = -100 b. 6 stages of change. 340 ÷ 60 = 5.7 so the submarine would need 6 stages 6. a. not proportional b. proportional - the constant of proportionality is 0.8 sale dollars per original dollar 7. B, C, E Today in class students worked on multiplying and dividing with negative and positive numbers.
Answers to Lesson 10 HW: 1. a. -4 b. 4 c. -15 d. 15 2. a. -6 b. 6 c. -6 3. a. -6, -2, 0, 4, 8 b. -512, -5.2, -5, -52, 5.5 4. a. -589+589 b. -589+500+89 c. -589+500+90+(-1) 5. a. 255 m b. 172 m Answers to Lesson 11 HW: 1. -4, -50, 0.2 2. a. 815 b. -3 c. 157 d. -10 3. a. Positive b. Negative c. Negative d. Positive 4. a. a=-12 b. b=4 c. c=-1 d. d=-12 5. Blue: 37 1/2 cups, green: 12 1/2 cups, white: 50 cups. There are 4 cups in a quart so 112 quarts is 6 cups. There are 16 cups in a gallon so 12 gallons is 8 cups. So the ratio of cups of blue to cups of green to cups of white is 6 to 2 to 8 or, equivalently, 3 to 1 to 4. 3 + 1 + 4 = 8. 100 ÷ 8 = 12.5 So, the painter needs 37.5 cups of blue because 3 ⋅ (12.5) = 37.5. The painter needs 12.5 cups of green because 1 ⋅ (12.5) = 12.5. And the painter needs 50 cups of white because 4 ⋅ (12.5) = 50. Today in class students practiced multiplying negative numbers.
Answers to HW: 1. a. (-2)⋅(-4.5)=9 b. (-8.7)⋅(-10)=87 c. (-7)⋅(-2)=14 d. (-9)⋅(-10)=90 2. The temperature will be: a. -6∘C, because -3 ⋅ 2 = -6 b. -15∘C, because -3 ⋅ 5 = -15 c. -1.5∘C, because -3 ⋅ 0.5 = -1.5 The temperature was: d. 3∘C, because -3 ⋅ (-1) = 3 e. 9∘C, because -3 ⋅ (-3) = 9 f. 13.5∘C, because -3 ⋅ (-4.5) = 13.5 3. a. -3 b. -13 c. 60 d. 310 e. -112 4. a. 9 oz red, 6 oz gray, and 5 oz brown. The given amounts of dye make 212 oz so each quantity needs to be multiplied by 8 to get 20 oz. b. 45 oz red, 30 oz gray, and 25 oz brown. 100 oz is 5 batches of 20 oz. 5. a. Yes, it could be proportional. The constant of proportionality is 6 wheels per bus. b. No, it would not be proportional because the train cars have a different number of wheels. 6. There were 8 cookies left. Noah made (1.25)(64) = 80 cookies. (0.90)(80) = 72 cookies sold. 80 - 72 = 8 Today in class students learned a little bit about percentages. This was really fast and everyone should take a few minutes to look over the notes in the back of their workbook and let this sink in. We moved on to Lesson 7 with more practice adding and subtracting negative numbers. The main idea is to really think about what the negative numbers represent (like debt) so that it gets easier to add and subtract them.
Answers to HW: 1. a. $0.99 because 15⋅0.066=0.99 [Remember the answer should be less than $1.50] b. Answers vary. Sample response: I think Tyler should pay $19 in all, because that would cover his meal, the sales tax, and a 20% tip for the server. 2. seconds in circle health gained 4 100 10 250 3 75 40 1,000 3. a. 100 m, because 400+100=500 b. 900 m, because -400+900=500 c. -5,100 m, because 8,500+(-5,100)=3,400 d. -8,800 m, because 8,500+(-8,800)=-300 e. -650 m, because 450+(-650)=-200 [This one was worded very oddly, just find the difference] 4. transaction amount account balance 360 360 -22.50 337.50 -155.15 182.35 -223.75 -41.40 5. a. 1. 0.5 inches. 0.67 − 0.17 = 0.50 b. 1.14 inches. The departure from average was negative, the actual rainfall needed to be 0.36 inches less than the average rainfall. c. 2.43 inches; 0.86 inches. The departure from the average in June was -0.5 and for July was -0.36, so for those two months it was -0.5 + (-0.36) = -0.86. So it will have to rain 0.86 more inches in August than usual to make that up and the departure from the average will be 0.86. 0.86 + 1.57 = 2.43. Today in class students took some time to look back over the cool down activities from Unit 5 Lessons 1 - 6. We looked again at many ways to wrap our minds around how we add and subtract integers correctly! We also experienced a code red drill during this class period, and aside from a couple of children that wanted to play during the drill, your students did a great job! We did not move on to Lesson 7, but should be ready to do so tomorrow. There are a couple of virtual nerd videos added to the google classroom too.
Today in class students used a climber's elevation to think about subtracting rational numbers. It helps to think about elevation like a thermometer - a sideways number line; so how many units does it take to get to the new elevation...
Answers to HW: 1. 82 is 42 degrees warmer than 40. 82 is 122 degrees warmer than -40. 2. It is a proportional relationship which can be represented as p=5,184⋅a where p represents the number of pixels and a is the area of the screen in square inches. (Same format as y = kx) 3. The difference in height is -57 m, because 30 − 87 = -57. The distance is 57 m, because |-57| = 57. The difference in height is 130 m, because 100 −(-30) = 130. The distance is 130 m, because |130| = 130. 4. -11 43 -15 -318 5. The bill was close to $32.60. We can't tell the exact amount because the suggested dollar amounts have been rounded to the hundredths place. 4.89 ÷ 0.15 = 32.60, 5.87 ÷ 0.18 = 32.61, and 6.52 ÷ 0.2 = 32.60. The first and third quotients are exact while the middle quotient is rounded to the nearest hundredth. 6. Polygon D is a scaled copy of Polygon A. This is true because all of the side lengths are doubled. The area of Polygon D is 4 times the area of Polygon A. 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 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 |
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