This week in math we are going to continue with our study of expressions and equations (our mid unit exam tested our knowledge of these today) by adding inequalities to the mix. We have used visual representations with balanced hangars and tape diagrams, and have also solved written equations. We will be including both positive and negative integers as we go along.
0 Comments
This week in math we are learning about solving equations using balanced hanger diagrams and simple equations. We can solve these even if negative numbers are involved. This reviews Unit 5 where we learned how to apply all four operations ( + , - , x , / ) to integers, including negative ones.
This week students will be working with using tape diagrams to illustrate, recognize, and create equations.
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 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. |
## AuthorWrite something about yourself. No need to be fancy, just an overview. ## Archives
October 2018
## Categories |