Complete Week 14 Package

Transcription

1 Complete Week 14 Package 2015

2 Table of Contents Unit 4 Pacing Chart Day 66 Bellringer Day 66 Activity Day 66 Practice Day 66 Exit Slip Day 67 Bellringer Day 67 Practice Day 67 Exit Slip Day 68 Bellringer Day 68 Activity Day 68 Practice Day 68 Exit Slip Day 69 Bellringer Day 69 Practice Day 69 Exit Slip Weekly Assessment

3 CCSS Algebra 1 Pacing Chart Unit 4 Unit Week Day CCSS Standards Mathematical Practices Objective I Can Statements 5 Linear Equations and Inequalities 5 Linear Equations and Inequalities 5 Linear Equations and Inequalities 5 Linear Equations and Inequalities 5 Linear Equations and Inequalities 14 Literal Equations 14 Literal Equations 14 Literal Equations 14 Literal Equations 14 Literal Equations CCSS.MATH.CONTENT.HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CCSS.MATH.CONTENT.HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CCSS.MATH.CONTENT.HSA.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. CCSS.MATH.PRACTIC E.MP8 Look for and express regularity in repeated reasoning. CCSS.MATH.PRACTIC E.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTIC E.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. The student will be able to solve and interpret the solution to multistep linear equations and inequalities in context. The student will be able to write equations in equivalent forms to solve problems. The student will be able to justify the steps in solving equations by applying and explaining the properties of equality. The student will be able to extend to concepts used in solving numerical equations to rearranging formulas for a particular variable. I can solve and interpret the solution to multistep linear equations and inequalities in context. I can write equations in equivalent forms to solve problems. I can justify the steps in solving equations by applying and explaining the properties of equality. I can extend to concepts used in solving numerical equations to rearranging formulas for a particular variable. 70 Assessment Assessment Assessment Assessment 2015 Page 1

4 Day 66 Bellringer Name Day 66 Solve the simple equations 1. x 7 = s 2 = y = b = Page 2

5 Day 66 Bellringer Name Answer Key Day x = y = 7 3. s = b = Page 3

6 Day 66 Activity Name Break-Even Point The pep squad at Barton High School is selling pennants to raise money for their activities. They must pay the manufacturer $65.25 for the design of the pennant and $2.15 for each pennant ordered. The pep squad plans to sell each pennant for $ Write a verbal expression to describe the total amount paid to the manufacturer for the pennants. 2. Revenue is the total amount received from the sales. Write a verbal expression to describe the revenue from selling the pennants. 3. Copy and complete the table with amounts for cost and revenue from the given numbers of pennant sales. Number of Pennants Total cost Total revenue 4. Write an algebraic equation for the total cost in terms of the number of pennants, p, ordered. 5. Write an algebraic equation for the total revenue in terms of the number of pennants, p, sold Page 4

7 Day 66 Activity Name 6. The point at which the total revenue equals the total cost is the break-even point. Write an equation that you could use to determine the number of pennants that must be sold to break even. 7. Solve the equation You Wrote in Step 6. How many pennants need to be sold to break even? Be sure that your answer is reasonable. 8. The profit from a sale is the total revenue minus the total cost. Write and solve an equation to determine the number of pennants the pep squad must sell to make a profit of $ Page 5

8 Day 66 Activity Name Answer Key plus $2.15 times the number of pennants purchased. 2. $4.50 times the number of pennants sold Number of Pennants Total cost $76 $86.75 $94.50 $ $119 $129.5 Total revenue $22.50 $45 $67.50 $90 $ $ C = p 5. R = 4.5p p pennants pennants 2015 Page 6

9 Day 66 Practice Name 1. Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water? 2. Tim is choosing between two cell phone plans that offer the same amount of free minutes. Cingular s plan charges $39.99 per month with additional minutes costing $0.45. Verizon s plan costs $44.99 with additional minutes at $0.40. How many additional minutes, a, will it take for the two plans to cost the same? 3. The cost to purchase a song from itunes is $0.99 per song. To purchase a song from Napster, you must be a member. The Napster membership fee is $10. In addition, each purchased song costs $0.89. How many downloaded songs, d, must be purchased for the monthly price of Napster to be the same as itunes? 4. Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water? 5. UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds, p, will it take for UPS and FedEx to cost the same? 6. A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours. 7. Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil? 2015 Page 7

10 Day 66 Practice Name 8. A full 355 ml can of Coke is leaking at a rate of 5 ml per minute into an empty can. How long will it take for the two cans to have the same amount, a, of Coke? 9. On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game bowled is $3.50. On Sunday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. If you spent the same amount each day, how many games, g, were bowled? 10. At one store a trophy costs $ Engraving costs $0.40 per letter. At another store, the same trophy costs $ Engraving costs $0.25. How many letters, x x= x, must be engraved for the costs to be the same? 11. You are looking for an apartment. There are two final choices. Apartment A has a $1000 security deposit and costs $1200 each month. Apartment B has a $1500 and costs $1175 each month. How many months, m, will it take for the costs to be the same? 12. Lenny makes $55,000 and is getting annual raises of $2,500. Karl makes $62000, with annual raises of $2,000. How many years, y, will it take for Lenny and Karl to make the same salary? 13. In 1987, 34.7 million households owned a dog, and 27.7 million owned a cat. Since then, dog ownership has decreased by million households per year, and cat ownership has increased by million households per year. How many years, y, will it take for them to be equal? 14. In 2000, Ohio s population was 11.4 million and increasing by 0.5 million each year. Michigan s population was 9.9 million, increasing by 0.6 million each year. When will the two states have the same population? Let y represent the number of years Page 8

11 Day 66 Practice Name Answer Key minutes minutes songs minutes pounds 6. 4 hours 7. 5 months minutes games letters months years years 14. Year Page 9

12 Day 66 Exit Slip Name Container A has 500 L of water, and is being filled at a rate of 4 liters per minute. Container B has 1000 L of water, and is being drained at 5 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water? 2015 Page 10

13 Day 66 Exit Slip Name 16. Answer Key 17. x=100 minutes 2015 Page 11

14 Day 67 Bellringer Name Day 67 Solve the equations 1. y 5 = (b 3.7) = (x + 5) = = 7x Page 12

15 Day 67 Bellringer Name Day y = 2 2. x = 5 3. b = x = Page 13

16 Day 67 Practice Name Save each equation and justify each step. 1. 4g + 1 = 12 8g y = 5y x = 2x (2w + 5) = 12w Page 14

17 Day 67 Practice Name 5. 7m 2(m 3) = 3m r 8 = 5r f 3(f + 6) = 2f y = 12 8y 2015 Page 15

18 Day 67 Practice Name w = 7w (y 3) + 4y + 8 = 3(y + 6) 10. 5x 7 = 2x t 5 + 8t = 7(t + 6) 2015 Page 16

19 Day 67 Practice Name Answer Key Page 17

20 Day 67 Exit Slip Name Which of the following equations are equivalent? a.) 3x + 1 = 7x 5 b.) 6x + 1 = 4x 5 c.) 6x + 2 = 14x 10 d.) 12x + 2 = 8x 10 e.) 3x = 7x 6 f.) 3x + 4 = 7x 2 g.) 6x + 4 = 4x 2 h.) 6x = 4x 6 Explain your reasoning Page 18

21 Day 67 Exit Slip Name Answer Key A, F, C, E are equivalent B, D, G, H are equivalent Explain Answers will vary, but should include the addition and multiplication properties equality 2015 Page 19

22 Day 68 Bellringer Name Day 68 Solve the complex equations. 1. 4x + 7 6x = 5 4x (2z + 3) = 3(4z + 1) 2(3z + 2) 2. 2(3y 4) = 3x b b 4 = b Page 20

23 Day 68 Bellringer Name Answer Key Day x = 1 2. y = 3 3. z = 4 4. b = Page 21

24 Day 68 Activity Name Algebraic Properties and Proofs You have solved algebraic equations for a couple years now, but now it is time to justify the steps you have practiced. Remember taking action without thinking is a dangerous habit! The following is a list of the reasons one can give for each algebraic step one may take. ALGEBRAIC PROPERTIES OF EQUALITY ADDITION PROPERTY OF EQUALITY If a = b, then a + c = b + c SUBTRACTION PROPERTY OF EQUALITY If a = b, then a c = b c MULTIPLICATION PROPERTY OF EQUALITY DIVISION PROPERTY OF EQUALITY DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION or OVER SUBTRACTION SUBSTITUTION PROPERTY OF EQUALITY REFLEXIVE PROPERTY OF EQUALITY SYMMETRIC PROPERTY OF EQUALITY TRANSITIVE PROPERTY OF EQUALITY If a = b, then a c = b c If a = b, then a = b c c a(b + c) = ab + ac a(b c) = ab ac If a = b, then b can be substituted for a in any equation or expression For any real number a, a = a If a = b, then b = a If a = b and b = c, then a = c Complete the following algebraic proofs using the reasons above. If a step requires simplification by combining like terms, write simplify. Given: 3x + 12 = 8x 18 Prove: x = 6 Statement Reasons 1. 3x + 12 = 8x = 5x = 5x = x x = Page 22

25 Day 68 Activity Name Given: 3k + 5 = 17 Prove: k = 4 Statement 1. 3k + 5 = k = k = 4 3. Given: 6a 5 = 95 Prove: a = 15 Statement Reasons Reasons Given: 3(5x + 1) = 13x + 5 Prove: x = 1 Statement Reasons 2015 Page 23

26 Day 68 Activity Name Given: 7y 84 = 2y + 61 Prove: y = 29 Statement Reasons Given: 4(5n + 7) 3n = 3(4n 9) Prove: n = 11 Statement Reasons 2015 Page 24

27 Day 68 Activity Name Answer Key Statement Reasons 1. 3x + 12 = 8x Given = 5x Subtraction property of equality = 5x 3. Addition property of equality 4. 6 = x 4. Division property of equality 5. x = 6 5. Symmetric property of equality Given: 3k + 5 = 17 Prove: k = 4 Statement Reasons 1. 3k + 5 = Given 2. 3k = Subtraction property of equality 3. k = 4 3. Division property of equality Given: 6a 5 = 95 Prove: a = 15 Statement 1. 6a 5 = a = a = 15 Reasons 1. Given 2. Addition property of equality 3. Division property of equality 2015 Page 25

28 Day 68 Activity Name Given: 3(5x + 1) = 13x + 5 Prove: x = 1 Statement 1. 6(5x + 1) = 13x x + 3 = 13x x = 13x x = 2 5. x = 1 Given: 7y 84 = 2y + 61 Prove: y = 29 Statement 1. 7y 84 = 2y y 84 = y = y = 29 Reasons 1. Given 2. Distributive property of multiplication over addition 3. Subtraction property of equality 4. Subtraction property of equality 5. Division property of equality Reasons 1. Given 2.Subtraction property of equality 3. Addition property of equality 4. Division property of equality Given: 4(5n + 7) 3n = 3(4n 9) Prove: n = 11 Statement Reasons 1. 4(5n + 7) 3n = 3(4n 9) 1. Given 2. 20n n = 12n Distributive property of 3. 17n 39 = 12n 27 multiplication 4. 5n + 28 = Subtraction 5. 5y = Subtraction property of equality 6. y = Subtraction property of equality 6. Division property of equality 2015 Page 26

29 Day 68 Practice Name Put the correct letter on the corresponding line below. A. Area Model for Multiplication B. Associative Property of Multiplication C. Commutative Property of Multiplication D. Property of Reciprocals Area Model for Multiplication E. Multiplicative Identity Property of 1 F. Multiplication Property of Zero G. Reciprocal of a Fraction Property 1. For any real number a, a 0 = 0 a = 0 2. Suppose a = 0 and b = 0. The reciprocal of a b is b a. 3. For any real number a, a 1 = 1 a = a. 4. Suppose a = 0. The reciprocal of a is 1 a. 5. For any real numbers a, b, and c, (ab)c = a(bc). 6. For any real numbers a and b, ab = ba. 7. The area A of a rectangle with length l and width w is lw Page 27

30 Day 68 Practice Name Answer Key 1. F 2. D 3. E 4. G 5. B 6. C 7. A 2015 Page 28

31 Day 68 Exit Slip Name Identify the Properties of Mathematics 1) The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example a x(b + c) = a x b + a x c 2) The sum of any number and zero is the original number. For example a + 0 = a. 3) When three or more numbers are multiplied, the product is the same regardless of the order of the multiplicands. For examples (a x b)x c = a x (b x c) 4) Adding 0 to and number leaves it unchanged. For example a + 0 = a. 5) When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example a x b = b x a 2015 Page 29

32 Day 68 Exit Slip Name Answer Key 1. Distributive Property 2. Identity Property of Addition 3. Associative Property of Multiplication 4. Addition Property of Zero 5. Commutative Property of Multiplication 2015 Page 30

33 Day 69 Bellringer Name Day 69 Solving problems involving unit conversions 1. Drew has a 1.2 meter long steel bar. He wants to cut it into 3 equal lengths. In millimeters, how long is should be? 2. Grace walks her dog 2 kilometers a day. In two days, how many meters does she and her dog walked? 3. A bag contains 4 boxes of chalk. A box of chalk is 2 kg in mass. How many grams are there in the bag? 4. Maya's weight is 75 kilograms, while Charlene's weight is 15 kilograms less than Selma. What is Charlene's weight in pounds? 2015 Page 31

34 Day 69 Bellringer Name Day mm meters grams lbs 2015 Page 32

35 Day 69 Practice Name Solve for the indicated variable in the parenthesis. 1) P = IRT (T) 2) A = 2(L + W) (W) 3) y = 5x 6 (x) 4) 2x 3y = 8 (y) 5) x+y 3 = 5 (x) 6) y = mx + b (b) 7) ax + by = c (y) 8) A = 1 2 h(b + c) (b) 9) V = LWH (L) 10) A = 4πr 2 (r 2 ) 11) V = πr 2 h (h) 12) 7x y = 14 (x) 13) A = x + y 2 (y) 14) R = E I (I) 15) x = yz 6 (z) 16) A = r 2L (L) 17) A = a + b + c 3 (b) 18) 12x 4y = 20 (y) 19) x = 2y z 4 (z) 20) P = R C N (R) 2015 Page 33

36 Day 69 Practice Name Answer Key 1) T P IR 2) W A 2L 3) 2 6 x y 5 4) 8 2x y 3 5) x = 15 y 6) b = y mx 7) c ax A y 8) b 2 c b h 9) L V WH 10) r 2 A 4 11) V h r 2 12) 14 y x 7 13) y = 2A x 14) E I 15) R 6x z 16) y L r 2A 17) b = 3A a c 18) y = 3x 5 19) z = 2y 4x 20) R = PN + C 2015 Page 34

37 Day 69 Exit Slip Name Show your work: Brandon knows that his truck route from Illinois to Tennessee is 430 miles long. He also knows that Distance = rate time (D = rt) How long will his route take if he averages a speed of 50 mi/hr.? Start by first solving the formula for time. How long will his route take if he averages a speed of 50 mi/hr.? Start by first solving the formula for time Page 35

38 Day 69 Exit Slip Name Answer Key Solutions: Steps: D = rt D r = rt r D r = t substitute 430 in for D and 50 in for r solve = 8.6 It will take Brandon 8.6 hours. solve for t(time) 2015 Page 36

39 Complete Week 14 Algebra 1 Teachers Weekly Assessment Package Unit 5 Created by: Jeanette Stein 2015 Algebra 1 Teachers 37 Semester 1 Skills

40 Complete Week 14 Algebra 1 Common Core Semester 1 Skills Number Unit CCSS Skill 25 5 A.REI.3 Solve advanced linear equations 26 5 A.REI.1 A.CED.4 Solve literal equations and justify the steps 27 5 A.REI.3 Solve inequalities 28 5 A.REI.12 Graph inequalities 38 Semester 1 Skills

41 Complete Week 14 Unit 5 Weekly Assessments 39 Unit 5

42 Complete Week 14 Week #14 1. Solve for x. 2. Solve for x. 3x + (3x 12) = x 4 3x = ax a 3. What is the greatest possible error for a measurement of 5 inches? 4. The mean of the following data is 17. Find the value of x. 14, 22, 8, 17, 15, x 5. Given the box and whisker graph, find the following. Minimum: Maximum: Upper Quartile: Lower Quartile: Median: 6. There are 640 acres in a square mile and 5280 feet in one mile. How many square feet are there in 3 acres? 40 Unit 5

43 Complete Week 14 Unit 5 - KEYS Weekly Assessments 41 Unit 5 - KEYS

44 Complete Week 14 Week #14 KEY 1. Solve for x. 2. Solve for x. 3x + (3x 12) = x 4 3x = ax a 3x ax = 5 + a 6x 12 = x 4 x = 2 x(3 a) (3 a) = 5 + a 3 a x = 5 + a 3 a 3. What is the greatest possible error for a measurement of 5 inches? 0.5 feet (The greatest possible error is half of the unit of measure to which a measure is rounded.) 4. The mean of the following data is 17. Find the value of x. 14, 22, 8, 17, 15, x 76 + x 6 = 17 x = Given the box and whisker graph, find the following. Minimum: 2 Maximum: 16 Upper Quartile: 11 Lower Quartile: 4 Median: 6 6. There are 640 acres in a square mile and 5280 feet in one mile. How many square feet are there in 3 acres? 1 mi 3 acres 640 acres 5280 ft 5280 ft = 130, 680 ft 2 1 mi 1 mi 42 Unit 5 - KEYS