Complete Unit 6 Package

Transcription

1 Complete Unit 6 Package HighSchoolMathTeachers.com 2019

2 Table of Contents Unit 6 Pacing Chart Algebra 1 Unit 6 Skills List Unit 6 Lesson Plans Day 76 Bellringer Day 76 Activity Day 76 Practice Day 76 Exit Slip Day 77 Bellringer Day 77 Activity Day 77 Practice Day 77 Exit Slip Day 78 Bellringer Day 78 Activity Day 78 Practice Day 78 Exit Slip Day 79 Bellringer Day 79 Activity Day 79 Practice Day 79 Exit Slip Week 16 Assessment Day 81 Bellringer Day 81 Activity Day 81 Practice Day 82 Bellringer Day 82 Practice Day 83 Bellringer Day 83 Activity

3 Day 83 Practice Day 84 Bellringer Day 84 Activity Day 84 Practice Week 17 Assessment Unit 6 Test

4 CCSS Algebra 1 Pacing Chart Unit 6 Unit Week Day CCSS Standards Mathematical Practices Objective I Can Statements 6 Systems of Equations 6 Systems of Equations 6 Systems of Equations 16 Systems of Equations 16 Systems of Equations 16 Systems of Equations CCSS.MATH.CONTENT.HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. CCSS.MATH.CONTENT.HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* CCSS.MATH.PRACTIC E.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. CCSS.MATH.PRACTIC E.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTIC E.MP6 Attend to precision. The student will be able to approximate solutions to systems of two equations using graphing technology. The student will be able to graph the solution to systems of linear inequalities in two variables. The student will be able to explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). I can approximate solutions to systems of two equations using graphing technology. I can graph the solution to systems of linear inequalities in two variables. I can explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). HighSchoolMathTeachers 2019 Page 1

5 CCSS Algebra 1 Pacing Chart Unit 6 6 Systems of Equations 6 Systems of Equations 6 Systems of Equations 6 Systems of Equations 6 Systems of Equations 16 Systems of Equations 16 Systems of Equations 17 Elimination 17 Elimination 17 Elimination 79 CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. CCSS.MATH.PRACTIC E.MP1 Make sense of problems and persevere in solving them. The student will be able to identify the solutions as a region of the plane. I can identify the solutions as a region of the plane. 80 Assessment Assessment Assessment Assessment CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. CCSS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. CCSS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. CCSS.MATH.PRACTIC E.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. CCSS.MATH.PRACTIC E.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTIC E.MP7 Look for and make use of structure. The student will be able to graph the solution to systems of linear inequalities in two variables. The student will be able to solve a system of equations exactly (with algebra) and approximately (with graphs). The student will be able to solve a system of equations exactly (with algebra) and approximately (with graphs). I can graph the solution to systems of linear inequalities in two variables. I can solve a system of equations exactly (with algebra) and approximately (with graphs). I can solve a system of equations exactly (with algebra) and approximately (with graphs). HighSchoolMathTeachers 2019 Page 2

6 CCSS Algebra 1 Pacing Chart Unit 6 6 Systems of Equations 6 Systems of Equations 17 Elimination 17 Elimination 84 CCSS.MATH.CONTENT.HSA.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. CCSS.MATH.PRACTIC E.MP2 Reason abstractly and quantitatively. The student will be able to explain why the sum of two equations is justifiable in the solving of a system of equations (property of equality). I can explain why the sum of two equations is justifiable in the solving of a system of equations (property of equality). 85 Assessment Assessment Assessment Assessment HighSchoolMathTeachers 2019 Page 3

7 Algebra 1 Unit 6 Skills List Algebra 1 Unit 6 Skills List Number Unit Week CCSS Skill A.REI A.REI A.REI.5 Solve a system of equations by graphing Solve a system of equations by substitution Solve a system of equations by elimination HighSchoolMathTeachers 2019 Page 4

8 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 16 Systems of Equations Day: 76 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* Objective: The student will be able to approximate solutions to systems of two equations using graphing technology. Procedures: 1. Students will complete the Week 16 Bellringer (Day 76). 2. Students will work with partners and complete the Day-76-Activity. 3. The Day-76-Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-76-Exit-Slip before leaving for the day. 5. Use the Day-76-Practice as individual practice or homework. Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. I can statement: I can approximate solutions to systems of two equations using graphing technology. Materials: Week 16 Bellringer (Day 76) Day 76 Activity Day 76 Presentation Day 76 Exit Slip Day 76 Practice HighSchoolMathTeachers 2019 Page 5

9 Unit 6 Lesson Plan Name Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 6

10 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 16 Systems of Equations Day: 77 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Objective: The student will be able to graph the solution to systems of linear inequalities in two variables. Procedures: 1. Students will complete the Week 16 Bellringer (Day 77). 2. Students will work with partners and complete the Day-77-Activity. 3. The Day-77-Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-77-Exit-Slip before leaving for the day. 5. Use the Day-77-Practice as individual practice or homework. Accommodations/Special Circumstances: Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. I can statement: I can graph the solution to systems of linear inequalities in two variables. Materials: Week 16 Bellringer (Day 77) Day 77 Activity Day 77 Presentation Day 77 Exit Slip Day 77 Practice Technology: HighSchoolMathTeachers 2019 Page 7

11 Unit 6 Lesson Plan Reflection: Name Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 8

12 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 16 Systems of Equations Day: 78 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* Objective: The student will be able to explain why the x- coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Procedures: 1. Students will complete the Week 16 Bellringer (Day 78). 2. Students will work with partners and complete the Day-78-Activity. 3. The Day-78-Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-78-Exit-Slip before leaving for the day. Mathematical Practice: CCSS.MATH.PRACTICE.MP6 Attend to precision. I can statement: I can explain why the x- coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Materials: Week 16 Bellringer (Day 78) Day 78 Activity Day 78 Presentation Day 78 Exit Slip Day 78 Practice HighSchoolMathTeachers 2019 Page 9

13 Unit 6 Lesson Plan Name 5. Use the Day-78-Practice as individual practice or homework. Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 10

14 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 16 Systems of Equations Day: 79 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Objective: The student will be able to identify the solutions as a region of the plane. Procedures: 1. Students will complete the Week 16 Bellringer (Day 79). 2. Students will work with partners and complete the Day-79-Activity. 3. The Day-79-Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-79-Exit-Slip before leaving for the day. 5. Use the Day-79-Practice as individual practice or homework. Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. I can statement: I can identify the solutions as a region of the plane. Materials: Week 16 Bellringer (Day 79) Day 79 Activity Day 79 Presentation Day 79 Exit Slip Day 79 Practice HighSchoolMathTeachers 2019 Page 11

15 Unit 6 Lesson Plan Name Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 12

16 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 17 Elimination Day: 81 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Objective: The student will be able to graph the solution to systems of linear inequalities in two variables. Procedures: 1. Students will complete the Week 17 Bellringer (Day 81). 2. Students will work with partners and complete the Day-81-Activity. 3. The Day 81 Systems of Equations Applications will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-81-Exit slip- Maxmizing profit before leaving for the day. 5. Use the Day-81-Practice as individual practice or homework. Accommodations/Special Circumstances: Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. I can statement: I can graph the solution to systems of linear inequalities in two variables. Materials: Week 17 Bellringer (Day 81) Day 81 Activity Day 81 Systems of Equations Applications Day 81 Exit Slip Day 81 Practice Technology: HighSchoolMathTeachers 2019 Page 13

17 Unit 6 Lesson Plan Reflection: Name Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 14

18 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 17 Elimination Day: 82 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Objective: The student will be able to solve a system of equations exactly (with algebra) and approximately (with graphs). Procedures: 1. Students will complete the Week 17 Bellringer (Day 81). 2. Students will work with partners and complete the Day-82-Activity-Elimination. 3. The Day 82 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-82-Exit slip- Elimination before leaving for the day. 5. Use the Day 82 Practice as individual practice or homework. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. I can statement: I can solve a system of equations exactly (with algebra) and approximately (with graphs). Materials: Week 17 Bellringer (Day 82) Day 82 Activity Elimination Day 82 Presentation Day 82 Exit Slip Elimination Day 82 Practice Accommodations/Special Circumstances: Technology: HighSchoolMathTeachers 2019 Page 15

19 Unit 6 Lesson Plan Reflection: Name Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 16

20 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 17 Elimination Day: 83 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Objective: The student will be able to solve a system of equations exactly (with algebra) and approximately (with graphs). Procedures: 1. Students will complete the Week 17 Bellringer (Day 83). 2. Students will work with partners and complete the Unit 6 application problems and Day 83 Activity. 3. The Day 83 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-83-Exit slip- Business project days 2 before leaving for the day. 5. Use the Day 83 Practice as individual practice or homework. Accommodations/Special Circumstances: Mathematical Practice: CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. I can statement: I can solve a system of equations exactly (with algebra) and approximately (with graphs). Materials: Week 17 Bellringer (Day 83) Unit 6 application problems and Day 83 Activity Day 83 Presentation Day-83-Exit slip-business project days 2 Day 83 Practice Technology: HighSchoolMathTeachers 2019 Page 17

21 Unit 6 Lesson Plan Reflection: Name Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 18

22 Unit 6 Lesson Plan Name Unit 6 Systems of Equations Course: Algebra 1 Topic: 17 Elimination Day: 84 Common Core State Standard: CCSS.MATH.CONTENT.HSA.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Objective: The student will be able to explain why the sum of two equations is justifiable in the solving of a system of equations (property of equality). Procedures: 1. Students will complete the Week 17 Bellringer (Day 84). 2. Students will work with partners and complete the Day 84 Activity. 3. The Day 84 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Day-84-Exit slip-proving elinimation before leaving for the day. 5. Use the Day 84 Practice as individual practice or homework. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. I can statement: I can explain why the sum of two equations is justifiable in the solving of a system of equations (property of equality). Materials: Week 17 Bellringer (Day 84) Day 84 Activity Day 84 Presentation Day-84-Exit slip-proving elinimation Day 84 Practice Accommodations/Special Circumstances: Technology: HighSchoolMathTeachers 2019 Page 19

23 Unit 6 Lesson Plan Reflection: Name Extra/Additional Resources: HighSchoolMathTeachers 2019 Page 20

24 Day 76 Bellringer Name Day 76 Find the inverse of each function. 1) f(x) = x 3 3) f(x) = 2x + 5 2) f(x) = 4x 4) f(x) = x HighSchoolMathTeachers 2019 Page 21

25 Day 76 Bellringer Name Answer Key Day f 1 (x) = x f 1 (x) = x 4 3. f 1 (x) = x f 1 3 (x) = x 2 HighSchoolMathTeachers 2019 Page 22

26 Day 76 Activity Name Work with partner. Use the graph to answer each question. 1. Approximate the y-coordinate of the point on the line with the given x - coordinate. a. 0 b. 10 c Approximate the x-coordinate of the point on the line with the given y coordinate. a. -7 b. -3 c What is the relationship between the x- and y- coordinates of a point on a line and the equation of the line? 4. What is an equation of the line in the graph? 5. Use a graphing utility to graph the line y = 2x Use DESMOS to make a table of about 8 ordered pairs (x, y) that are on the line y = 2x 0.8. HighSchoolMathTeachers 2019 Page 23

27 Day 76 Activity Name 7. Delete the graph of the equation y = 2x 0.8 and graph only the equation y = x Use DESMOS and make a table of about 8 ordered pairs (x, y)that are on the line y = x Examine your tables of ordered pairs. Write the coordinates of a point that is in both tables. If you cannot find such a point, write the coordinates of a point close to points on both tables. 10. Without graphing, how do you know that the graphs of y = 2x 0.8 and y = x will intersect? 11. Where do you think the lines will intersect? Check by graphing both lines on the same set of axes. Use DESMOS to find the point of intersection. 12. Clear the graph screen. On the same set of axes, graph the equations y = 0.4x and y = 1.2x 3.Use DESMOS to find the point of intersection. 13. Clear the graph screen. On the same set of axes, graph the equations y = 1.7x and = 1.7x 2.8. What happens when you try to find the point of intersection? Explain. 14. Write a pair of equations and have your partner find the point of intersection of the graphs of the equations. How can you be sure the pair of equations you write will intersect? HighSchoolMathTeachers 2019 Page 24

28 Day 76 Activity Name Answer Keys Positive, linear 4. y = x (2,3.2) 10. The lines have a negative and a positive slope x 2x x -x HighSchoolMathTeachers 2019 Page 25

29 Day 76 Practice Name Determine whether the point (2,10) is an exact solution for each system of equation y = 2x 4 1. { y = x + 8 y = x { y = 3x + 16 y = x { y = 3x + 16 x + 3y = 6 4. { 6y = 2x Find the point of intersection of y = x + 8 and y = 3x Use the graph to find the approximate point of intersection of y = x + 12 and y = 2x 4. Round your approximation to the nearest tenth. Check your approximation. 7. A plane at 3,800 feet is descending at a rate of 120 feet per minute, and a plane at 520 feet is climbing at a rate of 40 feet per minute. In how many minutes will they be at the same altitude? Write a system of equations. Then graph the system to determine the solution. Refer to points A(3, 5), B(4, 1) and C(9, 3). Lines AB and AC meet at point A. 8. Write an equation for line AB. 9. Write an equation for line AC. 10. Graph you equations from Exercises 8 and Use the coordinates of the point of intersection to check your equations. HighSchoolMathTeachers 2019 Page 26

30 Day 76 Practice Name HighSchoolMathTeachers 2019 Page 27

31 Day 76 Practice Name Answer Key 1. no 2. yes 3. yes 4. no 5. (4,4) 6. (5.3, 6.7) y = 120x { y = 40x y = 6x + 23 ; 20.5 minutes 9. y = 1 3 x (3,5) satisfies both equations. HighSchoolMathTeachers 2019 Page 28

32 Day 76 Exit Slip Name A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there? HighSchoolMathTeachers 2019 Page 29

33 Day 76 Exit Slip Name Answer Key 2 Ducks and 8 Pigs HighSchoolMathTeachers 2019 Page 30

34 Day 77 Bellringer Name Day 77 Graph the equation. 1. 2x + 3y = y = 6 3x 2. 2 = 4x 2y 4. 3x = 2y + 5 HighSchoolMathTeachers 2019 Page 31

35 Day 77 Bellringer Name Answer Key Day HighSchoolMathTeachers 2019 Page 32

36 Day 77 Activity Name: Libby is making a window frame for etched glass. The frame will be for a window that is square on the bottom with an isosceles triangle on top. The perimeter of the window must be no more than 15 feet. What are some possible dimensions of the window? 1. Let x represent the length of each side of the square, and let y represent the length of one of the two congruent sides of the isosceles triangle. 2. The perimeter of the window must be no more than 15 feet. Write an inequality for the perimeter using the variables x and y. 3. The sum of two sides of a triangle is always greater than the third side. Use this fact to write the second inequality. HighSchoolMathTeachers 2019 Page 33

37 Day 77 Activity Name: 4. Write the system of inequalities. Solve each inequality for y. Recall that you can use a graph to find the solutions. All of the points that lie in the solution region of both inequalities are in the solution of the system. Remember that the dimensions of the windows must be positive, so the reasonable domain and range are contained in the first quadrant. 5. Graph the boundary lines. Is one or both of the boundary lines solid or dashed? Why? HighSchoolMathTeachers 2019 Page 34

38 Day 77 Activity Name: 6. Notice that the boundary lines divide the first quadrant into four regions. Points A, B, C and D are each placed in one of these four regions. In the following table the coordinates of each point in both inequalities, and complete the table. Point 3x + 2y 15 Is the inequality true? 2y > x Is the inequality true? Are both inequalities true? A (3, 1) 3(3) + 2(1) 15; Yes 2(1) > 3; No No B (2, 2) C (4, 4) D (6, 1) 7. On your graph, shade the region containing the point that makes both inequalities true. Do either of the boundary lines contain points that are solutions to this system of linear inequalities? Explain. HighSchoolMathTeachers 2019 Page 35

39 Day 77 Activity Name: Answer Key Day x + 2y y > x 3x + 2y { 2y > x Point 3x + 2y 15 Is the inequality true? 2y > x Is the inequality true? Are both inequalities true? A (3, 1) 3(3) + 2(1) 15; Yes 2(1) > 3; No No B (2, 2) 3(2) + 2(2) 15; Yes 2(2) > 2; yes Yes C (4, 4) 3(4) + 2(4) 15; No 2(4) > 4; yes No D (6, 1) 3(6) + 2(1) 15; No 2(1) > 6; No No 7. The line 3x + 2y 15 contains points that are solutions to the system because of the ( ) equal. Determine which of the given points are solutions to the system of inequalities. HighSchoolMathTeachers 2019 Page 36

40 Day 77 Activity Name: 2x 3y > { x + 4y < 6 a. (2, 1) b. (4, 7) c. ( 3, 5) x { x y > 5 a. (4, 1) b. (6, 5) c. ( 10, 6) 18x 12y > { 12x 11y > 12 a. (18, 20) b. (15, 10) c. ( 8, 30) 16x 24y > { 21x + 17y < 48 a. (17, 18) b. ( 14, 16) c. (22, 11) Determine each system of inequalities graphed HighSchoolMathTeachers 2019 Page 37

41 Day 77 Practice Name: Write a system of inequalities to describe the situation in each problem. Graph the system, and determine the reasonable domain and range for the situation. 9. Crafts Janice makes home decorations. It takes her 2 hours to make a wreath and 1 hour to make a basket. She can work no more than 40 hours per week. The cost to make a one wreath is $3 and the cost to make one basket is $2. She can afford to spend no more than $72 per week. How many wreath and baskets can she make each week? 10. Chemistry A salt solution is to be made with one solution that is 22% salt and another solution that is 30% salt. The solution must be at least ounces of each solution should be used? HighSchoolMathTeachers 2019 Page 38

42 Day 77 Practice Name: Answer Key 1. b. 2. b. 3. a,b 4. none y x { y x 6 x + y { 0.22x y { y < 1 2 x + 3 y > 2x + 3 y 4 7. { y > x 3 8. { y 3 5 x + 3 y > 2 3 x Let x represent the number of wreaths; let y represent the number of baskets. 2x + y 40 { 3x + 2y 72 Domain: x 0 Range: y 0 Baskets Wreaths Domain 0 x 20. Range: 0 y 36 HighSchoolMathTeachers 2019 Page 39

43 Day 77 Exit Slip Name: Graph 2y < 4x 6 y 1 2 x + 1 HighSchoolMathTeachers 2019 Page 40

44 Day 77 Exit Slip Name: Answer Key Day 77 2y < 4x 6 or y < 2x 3 y 1 2 x+1 Solutions to the system of inequalities (violet area) HighSchoolMathTeachers 2019 Page 41

45 Day 77 Exit Slip Name: Day 78 Graph the system of equation. 1. y = 1 2 x + 3 y = x x + y = 8 y = x x 4y = 7 2y + 4x = 3 4. y = 2x 1 2 x + 3y = 1 HighSchoolMathTeachers 2019 Page 42

46 Day 77 Exit Slip Name: Answer Key Day (2,4) 3. (7, 6) 2. (1, 0.5) 4. (0.125, 0.25) HighSchoolMathTeachers 2019 Page 43

47 Day 77 Exit Slip Name: Work with a partner to expand your understanding of solving systems with substitution. Explain: In the system of equations above, the first equation is y = x + 1. Explain what it means for two expressions to be equal. Observe and discover: y = x + 1 2x + y = 7 2x + x + 1 = 7 The system of equations is written on the left. The first step of the substitution method is on the right. Explain WHAT was done and WHY it would be OK to do that. HighSchoolMathTeachers 2019 Page 44

48 Day 77 Exit Slip Name: Using the equation from step 1 of the substitution method (also written below), solve for the variable. (Show your work!) 2x + x + 1 = 7 x= Finish solving: y = x + 1 2x + y = 7 Select either equation from the system and write it here: Using your answer from the Begin to Solve step above, how could you find the value of y? Explain in words. Now actually do the work you just described and find the value of y. (Remember to show your work.) Let s see if it would make a difference if we had chosen the other equation from the system to find y. Write down the equation you didn t pick follow the same process and find the value of y again. Was your answer the same? HighSchoolMathTeachers 2019 Page 45

49 Day 77 Exit Slip Name: Check: State the values you found for x and y as an ordered pair (x, y): Substitute those values for x and y into both equations and simplify. y = x + 1 2x + y = 7 If the result for both equations is a true statement (examples: 5=5 24=24-2=-2 etc.), that means our ordered pair IS a solution to the system because it satisfies (makes true) both equations. Sweet. Confirm: Let s graph the system of equations to confirm our solution from a graphical perspective. y = x + 1 Slope = y-intercept = 2x+y =7 Solve for y to get in slope-intercept form Slope = y-intercept = Graph the 2 equations on the graph above. State the intersection point: How does this compare to the solution you got using substitution? HighSchoolMathTeachers 2019 Page 46

50 Day 77 Exit Slip Name: Substitution Explain each step in solving this system of equations using substitution. y = 4x + 2 3y 2x = 26 ORIGINAL SYSTEM OF EQUATIONS Explain in words what s been done in each step. 3(4x + 2) 2x = 26 12x + 6 2x = 26 10x + 6 = x = x = 2 y = 4x + 2 y = 4(2) + 2 y = 10 OR 3y 2x = 26 3y 2(2) = 26 3y 4 = y 3 = 30 3 Now your turn y = 10 Solve these systems of equations using substitution. 1) y = 4x 3y + 2y = 28 2) 3x 27 = 5 x = 15 y HighSchoolMathTeachers 2019 Page 47

51 Day 77 Exit Slip Name: Answer Key In the system of equations above, the first equation is y = x + 1. Explain what it means for two expressions to be equal. They are the same even though they may look different The system of equations is written on the left. The first step of the substitution method is on the right. Explain WHAT was done and WHY it would be OK to do that. They y was replaced with x + 1. This is OK because y = x + 1. y and x + 1 are equivalent. 2x + x + 1 = 7 3x + 1 = x 3 = 6 3 x = 2 Select either equation from the system and write it here: y = x + 1 Using your answer from the Begin to Solve step above, how could you find the value of y? Explain in words. I substituted the 2 in the place of the x and then calculated the result Now actually do the work you just described and find the value of y. (Remember to show your work.) y = y = 3 Let s see if it would make a difference if we had chosen the other equation from the system to find y. Write down the equation you didn t pick follow the same process and find the value of y again. 2(2) + y = y = 7 y = 3 Was your answer the same? Yes State the values you found for x and y as an ordered pair (x, y): (2,3) HighSchoolMathTeachers 2019 Page 48

52 Day 77 Exit Slip Name: Let s graph the system of equations to confirm our solution from a graphical perspective. y = x + 1 Slope = 1 y-intercept = 1 2x+y =7 Solve for y to get in slope-intercept form Slope = -2 y-intercept = 7 Graph the 2 equations on the grip above. State the intersection point: (2,3) Substitution Explain in words what s been done in each step. 3(4x + 2) 2x = 26 _substitute 4x + 2 in place of the y. 12x + 6 2x = 26 10x + 6 = x = x = 2 OR y = 4x + 2 y = 4(2) + 2 y = 10 3y 2x = 26 3y 2(2) = 26 3y 4 = y 3 = 30 3 y = 10 Distribute solve the equation for x. _Substitute the x into either of the original equations to solve for y HighSchoolMathTeachers 2019 Page 49

53 Day 77 Exit Slip Name: Now your turn Solve these systems of equations using substitution. 1) y = 4x 3y + 2y = 28 (2,8) 2) 3x 27 = 5 x = 15 y (7,8) HighSchoolMathTeachers 2019 Page 50

54 Day 77 Exit Slip Name: Solve and check by the substitution method. 2x + 8y = 1 1. { x = 2y 3x + y = 5 3. { 2x y = 10 x + y = 7 2. { 2x + y = 5 y = 5 x 4. { 1 = 4x + 3y HighSchoolMathTeachers 2019 Page 51

55 Day 77 Exit Slip Name: At the Boy Scout all you can eat spaghetti dinner the troop served 210 people and raised $ Write an equation for the total amount raised from adult and child dinners. Scout Troop 154 Invites you to Spaghetti Fest! all you can eat Spaghetti dinner 2. Write an equation for the total number of adult and child dinners served. Adults $6.00 Children $ Solve the system of equations from exercise 1 and 2. How many adult and child dinners were served? Westside Community Center Thursday 7:00pm 4. Name two methods for solving systems of equations that can be used to solve exercise 3. Why would you choose one method over another? 5. Geometry. The sum of the measures of angles A and B is 90. If the measure of angle A is 30 less than twice the measure of angle B, then find the measure of each angle. HighSchoolMathTeachers 2019 Page 52

56 Day 77 Exit Slip Name: Answer Key 1.( 1, 1 ) ( 2,9) 3.(3, 4) 4.( 14,19) 5.( 43, 6) 6.(1,3) 7.(0,3) 8.( 1, 1 ) 3 3 1) 6.00a c = 935 2) a + c = 210 3) 80; 130 4) Answers may Vary 5) 50, 40 HighSchoolMathTeachers 2019 Page 53

57 Day 77 Exit Slip Name: Margie is responsible for buying a week s supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is $4,240. How much can Margie spend on each dog for food and medication? HighSchoolMathTeachers 2019 Page 54

58 Day 77 Exit Slip Name: Answer Key She can spend $20 on each cat. She can spend $40 on each dog. HighSchoolMathTeachers 2019 Page 55

59 Day 77 Exit Slip Name: Day 79 Graph the system of inequalities 1. x + 2y 3 3x + y > 3 3. x 3y + 2 2y 5 + 4x 2. y 7 3 x 4 y y < 1 2 x 5 2x + y > 2 i. HighSchoolMathTeachers 2019 Page 56

60 Day 77 Exit Slip Name: Answer Key Day HighSchoolMathTeachers 2019 Page 57

61 Day 77 Exit Slip Name: In order for your team to find the hidden treasure, you must complete the following tasks. You will all have a map, and should all do the work first and then agree on an answer for the work done on the Large Map. 1. Your group will look at the first clue. Team Member #1 will read it aloud and everyone in the group will work on this clue on their small maps. When the group decides on the solution, Team Member #1 will duplicate the group s solution on the Large Map. ONLY when clue #1 is complete may your group look at clue #2. 2. Everyone in the group will work on clue #2 on their small maps. When the group decides on the solution, Team Member #2 will duplicate the group s solution on the Large Map. When all clues and tasks from the second report are completed, the group may then move on to the third clue. 3. All group members will work on clue #3 on their small maps. Team Member #3 in each group will be passed the map and respond to the clues found in the third report. When all the clues and task from the third report are completed, the team may look at the final clue. 4. Person #4 will be handed the map and will use it, with the help of the team, to write the inequalities of the graph. The team will determine the possible landing site for the balloon. 5. The team will agree on the possible landing site, circle the location on the Large Map, and sign your names to the map. 6. When your team finishes, fold your map and raise your hand to turn it in. HighSchoolMathTeachers 2019 Page 58

62 Day 77 Exit Slip Name: The Basic facts: The treasure was tied to a balloon that was blown far, far off course, and ended up going down somewhere in the South Pacific. Clue 1: Pilot s report from a nearby airplane: We were on our way from Australia, when we saw a hot-air balloon sinking rapidly. I am certain that it crashed south of our flight path. When we left Australia, we traveled 2000 km north of every 3000 km east that we flew. 1) Use a blue pencil to identify all of the places where the balloon could be. 2) Write an inequality to represent all the possible places the balloon could be. Clue 2: Report from the Secret Service According to a U.S. government plane flying from the northern tip of the Philippines to French Polynesia, the balloon s last known location was at (-1000, 1000) near the Solomon Islands. 1) Use a red pencil to identify all of the places where the balloon could be. 2) Write an inequality to represent all the possible places the balloon could be. Clue 3: Phone call received today: I was a passenger on a flight that flew directly from French Polynesia to Indonesia. I was looking out my window when I saw the balloon landing to the north of where we were flying. 1) Use a green pencil to identify all of the places where the balloon could be. 2) Write an inequality to represent all the possible places the balloon could be. Clue 4: Your Answer: On the map, write the following: 1) The three linear inequalities representing the information in the clues. 2) The location that is the most likely spot for the balloon to land? 3) What are the coordinates for this location? Once you have this information, every member of your group should verify its accuracy and sign it. Fold your map in half and hand it to the teacher. HighSchoolMathTeachers 2019 Page 59

63 Day 77 Exit Slip Name: Additional Group Members Clue 1 (Blue): Clue 2 (Red): Clue 3 (Green): The location that is the most likely spot for the ballon to land is. What are the coordinates for this location? HighSchoolMathTeachers 2019 Page 60

64 Day 77 Exit Slip Name: Answers: Clue 1 (Blue): y < 2 3x 2000 Clue 2 (Red): y 2 3x Clue 3 (Green): y > 1/5x The location that is the most likely spot for the ballon to land is Somoa. What are the coordinates for this location? (4000, -1000) HighSchoolMathTeachers 2019 Page 61

65 Day 77 Exit Slip Name: Given the system of inequalities shown below, select all the point that are solutions (if any) to the following systems of inequalities. (if any) 2x + y > 8 1. { y < 2 o A o B o C o D o E o F o G o H o I o J y 4x 1 2. { y > 2x + 1 o A o B o C o D o E o F o G o H o I o J y < x 3. { y 3 x o A o B o C o D o E o F o G o H o I o J HighSchoolMathTeachers 2019 Page 62

66 Day 77 Exit Slip Name: 3x y 6 4. { x 4y 8 o A o B o C o D o E o F o G o H o I o J y x 5. { y < 3 x > 0 o A o B o C o D o E o F o G o H o I o J y < x { y 2x > 1 y 1 o A o B o C o D o E o F o G o H o I o J HighSchoolMathTeachers 2019 Page 63

67 Day 77 Exit Slip Name: Answer Key 1. C. F. I. 2. A. 3. H. J. 4. D. I. 5. E. 6. NONE HighSchoolMathTeachers 2019 Page 64

68 Day 77 Exit Slip Name: Sarah is selling bracelets and earrings to make for summer vacation. The bracelets cost $2 and earrings cost $3. She needs to make at least $500. Write an inequality to represent the income from the jewelry sold. Sarah knows that she will sell more than 50 bracelets. Write an inequality to represent this situation. Graph the two inequalities and shade the intersection. Identify a solution. How many bracelets and earrings could Sarah sell? HighSchoolMathTeachers 2019 Page 65

69 Day 77 Exit Slip Name: Answer Key (200, 200) Sarah could sell 200 bracelets and 200 pairs of earrings. HighSchoolMathTeachers 2019 Page 66

70 High School Math Teachers Algebra 1 Weekly Assessment Package Week 16 HighSchoolMathTeachers

71 Week 16 Weekly Assessments 68

72 Week #16 1. Solve the system of equations by graphing. 2. Solve the system using substitution. y = 2x 6 { y = 1 x x + 2y = 12 { y = 1 2 x 3 3. Solve the system using substitution. 4. Solve and graph the inequality. 2x 3y = 7 { y = 6x 11 5x + 4 < 3x 6 69

73 5. Which number is the most precise? How do you know? 6. Solve for x. 5 (x + 4) = 11x 3 a inches b inches 70

74 Week 16 - KEYS Weekly Assessments 71

75 Week #16 KEY 1. Solve the system of equations by graphing. y = 2x 6 { y = 1 x Solve the system using substitution. x + 2y = 12 { y = 1 2 x 3 x + 2 ( 1 x 3) = 12 2 x = y = 12 y = 4. 5 (3, 4. 5) 3. Solve the system using substitution. 2x 3y = 7 { y = 6x 11 2x 3(6x 11) = 7 x = 2 y = 6(2) Solve and graph the inequality. 5x + 4 < 3x 6 8x < 10 x > 5 4 y = 1 (2, 1) 5. Which number is the most precise? How do you know? a inches b inches A 6. Solve for x. 5 (x + 4) = 11x 3 5 x 4 = 11x 3 1 x = 11x 3 x =

76 Day 81 Bellringer Name Day 81 Graph for the system of inequalities. 1. y 2x + 1 y < x < 3x + y x y > x 5 > y 2y < 2x z < 2x + 6 y < HighSchoolMathTeachers 2019 Page 73

77 Day 81 Bellringer Name Answer Keys Day HighSchoolMathTeachers 2019 Page 74

78 Day 81 Activity Name Work with a partner. Let X represent the number of lawn seats and y represent the number of reserve seats. 1. Tickets for the dark Knight concert are $15 for lawn seats and $25 for reserve seats. Each person waiting in line for tickets buy at least one ticket. Some will buy both types of tickets. Write an inequality that represents the amount of money each person will spend. 2. Make a list of five ordered pairs that are solutions of the inequality you wrote. 3. Cross out any ordered pairs you wrote that could not represent a company shouldn't of lawn seat and reserve seat tickets. 4. Because the concert is expected to be a sellout, each person is limited to buying six tickets. Write an inequality that represents the number of tickets each person will buy. 5. Cross out any ordered pairs that remain on your list that are not solutions of the inequality you wrote in question For an ordered pair to remain on your list, what must be true about it? HighSchoolMathTeachers 2019 Page 75

79 Day 81 Activity Name Answer Key 1. 15x + 25y Vary = all positive numbers 3. Answers may Vary 4. x + y < 6 5. Answers may vary 6. The ordered pair must be true for both inequalities. HighSchoolMathTeachers 2019 Page 76

80 Day 81 Practice Name Given the system of inequalities shown below, select all the point that are solutions (if any) to the following systems of inequalities. (if any) 2x + y > 8 7. { y < 2 o A o B o C o D o E o F o G o H o I o J y 4x 1 8. { y > 2x + 1 o A o B o C o D o E o F o G o H o I o J y < x 9. { y 3 x o A o B o C o D o E o F o G o H o I o J HighSchoolMathTeachers 2019 Page 77

81 Day 81 Practice Name 3x y { x 4y 8 o A o B o C o D o E o F o G o H o I o J y x 11. { y < 3 x > 0 o A o B o C o D o E o F o G o H o I o J y < x { y 2x > 1 y 1 o A o B o C o D o E o F o G o H o I o J HighSchoolMathTeachers 2019 Page 78

82 Day 81 Practice Name Answer Key 7. C. F. I. 8. A. 9. H. J. 10. D. I. 11. E. 12. NONE HighSchoolMathTeachers 2019 Page 79

83 Day 82 Bellringer Name Day 82 Solve the system of equations using substitution 1. x + y = 25 5x + 3y = x + 3y = 2 2 = x 5y 4. x + 2y = 2x 5 x y = x 5y = 10 x 3y = 4 HighSchoolMathTeachers 2019 Page 80

84 Day 82 Bellringer Name Answer Key Day y = 62 x = y = 2 3 x = y = 39 x = y = 2 x = 1 HighSchoolMathTeachers 2019 Page 81

85 Day 82 Practice Name Solve each system of equation using elimination by addition. Check your solutions. x + 2y = 3 1.{ 3x 2y = 5 x + 4y = { x + 3y = 13 x y = 3 2. { 2x y = 2 4. { 7a + 5c = 37 2a 5c = 8 HighSchoolMathTeachers 2019 Page 82

86 Day 82 Practice Name 4w 2z = { 3w + 2z = 13 2m 3n = { 5m 3n = 13 4w + 5c = { 4w + 6c = { 4p 5q = 11 2p 5q = 17 HighSchoolMathTeachers 2019 Page 83

87 Day 82 Practice Name 3x y = { y = 3x { x + 2y = 6 x + 5y = 21 4m + 3n = { 4m = 2n { x + 3y = 4 5 x 3y = 1 5 HighSchoolMathTeachers 2019 Page 84

88 Day 82 Practice Name 13. { 5x y = 3 5 2x y = x = 2.5y { y = 1.3x + 3 5y = 2x { y = 2x { 0.2m 0.3n = m 1.5n = 6.2 HighSchoolMathTeachers 2019 Page 85

89 Day 82 Practice Name Use a system of equations to solve each problem. 1. Drama club members sold tickets to an afternoon children's program. They charged $1 for each child's ticket and $2 for each adult ticket. They sold $656 worth of tickets. If they sold a total of 400 tickets, home many tickets of each kind did they sell? 2. The Crockett High School Band Boosters plan to sell buttons and programs at the homecoming game to raise money for new equipment. They plan to sell a total of 150 items, and they need to make $285 to have enough money for the equipment. How many buttons and how many programs do they need to sell? 3. Morris can invest a certain amount of his savings in a secured fund at 4% interest and the rest of his savings in a secured fund at 6% interest. He will earn $216. If he instead chooses to invest the rest of his savings in an unsecured fund at 8% interest rather than in the secured fund at 6% interest, his total interest income will be $272. How much is Morris planning to invest in each fund? HighSchoolMathTeachers 2019 Page 86

90 Day 82 Practice Name Answer Key 1. (2, 1 ) 2 2. ( 1, 4) 3. (22, 3) 4. a = 5, c = w = 4, z = w = 2, c = 4 7. m = 1, n = 6 8. p = 3, q = (2 5, 3 1 ) m = 0, n = ( 5,5) 12. ( 3, 1 ) ( 2, 7 ) ( 4, 1 ) ( 10, 8 ) m = 1, n = 4 Use a system of equations to solve each problem child, 256 adult buttons, 135 programs 3. $1200 at 4%; $2800 at 6% or 8% HighSchoolMathTeachers 2019 Page 87

91 Day 83 Bellringer Name Day 83 Solve the system of equations using elimination. 1. 5x = y + 1 y = 2x y = 2x 6-3y 7 = x 2. x = 4y + 6 y 3 = 2x 4. 2x 3y = 6 4x + 9y = 2 HighSchoolMathTeachers 2019 Page 88

92 Day 83 Bellringer Name Answer Key Day y = 16 x = 3 2. y = 1 x = 2 3. y = 5 2 x = y = 2 3 x = 2 HighSchoolMathTeachers 2019 Page 89

93 Day 83 Activity Name Mrs. Smith decided to purchase candy for her whole class as a treat. She bought Smarties and Dum-Dum lollipops as brain food for their next exam. Each bag of Smarties cost $7.00 (including tax). The bag of Dum-Dum lollipops cost $8.50 (including tax). She ended up spending $60.50 on her purchase of 8 items. 1. Using the information above, complete the following table: Number of Smarties Bags Number of Dum-Dum lollipops Bags Total Cost for 8 Items ($) Circle the row that has a total cost of $ How many bags of Smarties did Mrs. Smith buy? 4. How many bags of Dum-Dum lollipops did Mrs. Smith buy? HighSchoolMathTeachers 2019 Page 90

94 Day 83 Activity Name 5. Define your variables. 6. Write a system of equations to model the situation. 7. How many bags of Smarties did Mrs. Smith buy? 8. How many bags of Dum-Dum lollipops did Mrs. Smith buy? HighSchoolMathTeachers 2019 Page 91

95 Day 83 Activity Name Answer Key Mrs. Smith decided to purchase candy for her whole class as a treat. She bought Smarties and Dum-Dum lollipops as brain food for their next exam. Each bag of Smarties cost $7.00 (including tax). The bag of Dum-Dum lollipops cost $8.50 (including tax). She ended up spending $60.50 on her purchase of 8 items. 1. Using the information above, complete the following table: Number of Smarties Bags Number of Dum-Dum lollipops Bags Total Cost for 8 Items ($) 0 8 $ $ $ $ $ $ $ $ $ Circle the row that has a total cost of $ How many bags of Smarties did Mrs. Smith buy? 5 4. How many bags of Dum-Dum lollipops did Mrs. Smith buy? 3 5. Define your variables. x = number of Smarties bags y = number of Dum-Dum lollipop bags 6. Write a system of equations to model the situation. Items: x + y = 8 Cost: 7.00x y = How many bags of Smarties did Mrs. Smith buy? Finding the number of Smarties bags means I should eliminate y since that is the variable that defines Dum-Dum lollipop bags. x + y = 8 (multiply this equation by to eliminate y) 8.50x 8.50y = x y = (nothing needs to change here) x y = x = x = 5 HighSchoolMathTeachers 2019 Page 92

96 Day 83 Activity Name 8. How many bags of Dum-Dum lollipops did Mrs. Smith buy? Finding the number of Dum-Dum lollipop bags means I should eliminate x since that is the variable that defines Smarties bags. x + y = 8 (multiply this equation by to eliminate x) 7.00x 7.00y = x y = (nothing needs to change here) x y = y = y = 3 HighSchoolMathTeachers 2019 Page 93

97 Day 83 Practice Name Solve each system. 3x + y = 9 1.{ 2x + y = 1 3x + 2y = 7 3. { 5x 2y = 1 5r s = { 3r s = 15 2t + 3v = 6 4. { 2t 5v = 22 HighSchoolMathTeachers 2019 Page 94

98 Day 83 Practice Name 2x + y = 3 5. { 7x 4y = 18 4a + 3b = 2 7. { 8a 2b = 12 7r 5r = 2 6. { 8r t = 9 2a + 5b = { 5a + b = 18 HighSchoolMathTeachers 2019 Page 95

99 Day 83 Practice Name 9c + 7d = { 6c d = 2 11.{ 6n 2k + 3 = 0 3n + 4k 5 = 0 4x 3y 5 = { 2x + 9y + 1 = 1 HighSchoolMathTeachers 2019 Page 96

100 Day 83 Practice Name Answer Key 1. (8, 15) 2. ( 4,3) 3. ( 1, 2) 4. (6, 2) 5. (2, 1) 6. ( 1, 1) 7. (4,2) 8. (1, 2) 9. (0,2) 10. (1 2 5, 1 5 ) 11. (1 2 7, 1 14 ) HighSchoolMathTeachers 2019 Page 97

101 Day 84 Bellringer Name Day 84 Solve the system of equations by your choice of method x 5y = 3 6x + 4y = x + 25 = 5y 6x + 4y = 6 HighSchoolMathTeachers 2019 Page 98

102 Day 84 Bellringer Name 3. x 8y = 2 4x + 2y = x 7y = 2 8y = 5x 2 HighSchoolMathTeachers 2019 Page 99

103 Day 84 Bellringer Name Answer Key Day y = 0, x = 2 1. y = 97 31, x = y = 6, x = 5 4. y = , x = HighSchoolMathTeachers 2019 Page 100

104 Day 84 Activity Name Writing a System of Linear Equations Work with a partner. 1. Your cousin is 3 years older than you. Your ages can be represented by two linear equations. y = t y = t + 3 Your age Your cousin s age a. Graph both equations in the same coordinate plane. b. What is the vertical distance between the two graphs? What does this distance represent? c. Do the two graphs intersect? If not, what does this mean in terms of your age and your cousin s age? Using A Table To Solve A System Work with a partner. 1. You invest $500 for equipment to make dog backpacks. Each backpack costs you $15 for materials. You sell each backpack for $15. a. Copy and complete the table for your cost C and your revenue R. x C R b. When will your company break even? What is wrong? HighSchoolMathTeachers 2019 Page 101

105 Day 84 Activity Name Using A Graph To Solve A Puzzle Work with partner. 1. Let x and y be two numbers. Here are two clues about the values of x and y. WORDS EQUATION Clue 1: y is 4 more than twice the value y = 2x + 4 of x. Clue 2: The difference of 3y and 6x is 12. 3y 6x = 12 a. Graph both equations in the same coordinate plane. b. Do the two lines intersect? Explain. c. What is the solution of the puzzle? d. Use the equation y = 2x + 4 to complete the table. HighSchoolMathTeachers 2019 Page 102

106 Day 84 Activity Name X Y e. Does each solution in the table satisfy both clues? f. What can you conclude? How many solutions does the puzzle have? How can you describe them? HighSchoolMathTeachers 2019 Page 103

107 Day 84 Activity Name Answer Key Writing a System of Linear Equations a. Graph both equations in the same coordinate plane. b. 3 units. 3 years y = t + 3 c. No, my cousin will always be 3 years older than me. y = t Using A Table To Solve A System 1. a. x C R b. Never. Both numbers are growing up (slope) by $15. The revenue will never catch up to the cost. Using A Graph To Solve A Puzzle 1. Clue 1: WORDS y is 4 more than twice the value of x. EQUATION y = 2x + 4 Clue 2: The difference of 3y and 6x is 12. 3y 3 6x 3 = 12 3 y = 2x + 4 HighSchoolMathTeachers 2019 Page 104

108 Day 84 Activity Name a. Graph both equations in the same coordinate plane. y = 2x + 4 b. yes at every point c. all the solutions on the line y = 2x + 4 3y 6x = 12 d. Use the equation y = 2x + 4 to complete the table. X Y e. yes f. infinite solutions on the line y = 2x + 4 HighSchoolMathTeachers 2019 Page 105

109 Day 84 Practice Name If the system has a unique solution, find it. If it does not, state whether the system is inconsistent on dependent. 1.{ y = 2 3 x + 5 y = 2 3 x 2 x 2y = 4 2. { 3y x = y 8 3. { 2(6x + 10y) + 8 = 0 2 = 3x + 5y HighSchoolMathTeachers 2019 Page 106

110 Day 84 Practice Name 4. State whether the system shown is independent, inconsistent, or dependent. HighSchoolMathTeachers 2019 Page 107

111 Day 84 Practice Name 5. NAVIGATION The map shows a section of the Indian Ocean. The system of equations 2x + 3y = 96 and x + 2y = 42 gives the courses of two freighters headed in a southeasterly direction where x represents latitude and y represents longitude. Will the freighters meet? If so, where? If not, why not? 6. WRITING MATHEMATICS Write a real world problem that involves a system of inconsistent linear equations. Interpret what the inconsistency means in the situation. 7. The equations 12x + 10y = 20 and ax + 2y = b form a dependent system. Find a and b. 8. The equations y = 3x 5 and 5y = ax + b form an inconsistent system. Find a. Find a value that b cannot have. Why? 9. Write a system of equations based on the tables of values shown at the right. Then solve the system. x y x y The equations 5x 4y = 7 and ax + 4y = 1 form an independent system with the solution (3, 2). Find a. HighSchoolMathTeachers 2019 Page 108

112 Day 84 Practice Name Describe each linear system in terms of the slopes and y-intercepts of the graphs of the equations in the system. 11. independent 12. Inconsistent 13. Dependent 14. INDUSTRY Sawmills A, B, and C can turn out 11,900 board feet of lumber per day. Mills A and B together produce 7,700 board feet daily, while mills B and C together produce 8,300 board feet daily. Find the production capacity of each mill. HighSchoolMathTeachers 2019 Page 109

113 Day 84 Practice Name Answer Key 1. Inconsistent 2. Inconsistent 3. Dependent 4. Inconsistent 5. (66, 12) 6. My sister is 2 years older than me. When will we be the same age? We will never be the same age x + 10y = 20 a = 2.4 ax + 2y = b b = 4 8. y = 3x 5 a = 15 5y = ax + b b 5 9. y = 2x 2 2x 2 = 3x 6 y = 3x 6 +3x 3x + 2 y = x 4y = 7 3(5 + a) = 6 ax + 4y = a = 6 (5 + a)x = 6 3a = 9 a = Slopes are different usually y = intercepts are different 12. Slope is equal, y=intercept is different 13. Slope is equal, y=intercept is equal 14. A+B+C = 11,900 A+B =7,700 A=7,700 B B+C = 8,300 C=8,300 B (7700 B) + B +(8300 B) = B = 11,900 B = 4100 A = 3600 C = 4200 x = 4 HighSchoolMathTeachers 2019 Page 110

114 High School Math Teachers Algebra 1 Weekly Assessment Package Week 17 HighSchoolMathTeachers

115 Week 17 Weekly Assessments 112

116 Week #17 1. Solve the system of equations by elimination. 2x + 5y = 7 { 3x 5y = 8 2. Solve the system of equations by graphing. 3. Solve the system using substitution. x + 2y = 10 { y = 3 x { 12x + 6y = 10 y = 2 3 x 1 113

117 4. Solve and graph the inequality. 5. Solve the system of equations by elimination. 5x + 6 < 3x { 12x + 6y = 6 3x 5y = 8 114

118 Week 17 - KEYS Weekly Assessments 115

119 Week #17 KEY 1. Solve the system of equations by elimination. 2x + 5y = 7 { 3x 5y = 8 5x = 15 x = 3 2(3) + 5y = 7 y = 1 5 (3, 1 5 ) 2. Solve the system of equations by graphing. 3. Solve the system using substitution. x + 2y = 10 { y = 3 x x + 6y = 10 { y = 2 3 x 1 12x + 6 ( 2 x 1) = x + 4x 6 = 10 x = y = 10 y = 1 3 (1, 1 3 ) 116

120 4. Solve and graph the inequality. 5. Solve the system of equations by elimination. 5x + 6 < 3x x + 6y = 6 { 3x 5y = 8 25x + 30 < 3x x < 22 x < 1 12x + 6y = 6 12x + 20y = 32 26y = 26 y = 1 12x + 6( 1) = 6 x = 1 (1, 1) 117

121 Unit 6 Test Name: Work with partner. Use the graph to answer each question. 15. Approximate the y-coordinate of the point on the line with the given x - coordinate. a. 0 b. 10 c Approximate the x-coordinate of the point on the line with the given y coordinate. a. -7 b. -3 c What is the relationship between the x- and y- coordinates of a point on a line and the equation of the line? 18. What is an equation of the line in the graph? Determine whether the point (2, 10) is an exact solution for each system of equation 5. { y = 2x 4 y = x + 8 HighSchoolMathTeachers 2019 Page 118

122 Unit 6 Test Name: y = x { y = 3x + 16 y = x { y = 3x + 16 x + 3y = 6 8. { 6y = 2x + 12 Determine each system of inequalities graphed HighSchoolMathTeachers 2019 Page 119

123 Unit 6 Test Name: Solve and check by the substitution method. 2x + 8y = { x = 2y 3x + y = { 2x y = 10 x + y = { 2x + y = 5 y = 5 x 16. { 1 = 4x + 3y HighSchoolMathTeachers 2019 Page 120

124 Unit 6 Test Name: Given the system of inequalities shown below, select all the point that are solutions (if any) to the following systems of inequalities. (if any) 2x + y > { y < 2 o A o B o C o D o E o F o G o H o I o J y 4x { y > 2x + 1 o A o B o C o D o E o F o G o H o I o J y < x 19. { y 3 x o A o B o C o D o E o F o G o H o I o J 3x y { x 4y 8 o A o B o C o D o E o F o G o H o I o J HighSchoolMathTeachers 2019 Page 121

125 Unit 6 Test Name: Work with a partner. Let X represent the number of lawn seats and y represent the number of reserve seats. 21. Tickets for the Dark Knight concert are $15 for lawn seats and $25 for reserve seats. Each person waiting in line for tickets buy at least one ticket. Some will buy both types of tickets. Write an inequality that represents the amount of money each person will spend. 22. Make a list of five ordered pairs that are solutions of the inequality you wrote. 23. Cross out any ordered pairs you wrote that could not represent a company shouldn't of lawn seat and reserve seat tickets. 24. Because the concert is expected to be a sellout, each person is limited to buying six tickets. Write an inequality that represents the number of tickets each person will buy. HighSchoolMathTeachers 2019 Page 122

126 Unit 6 Test Name: 25. Let x represent the number of correct answers. Let y represent the incorrect answers. Write a system of equations. Janet s scoring system 2 spaces forward for a correct answer Matthew s scoring system 3 spaces forward for a correct answer 1 space forward for + an incorrect answer 10 spaces forward 1 space backward for + an incorrect answer 10 spaces forward? +? = 10? +? = Rewrite the equation representing Matthew's scoring system using a minus sign. Model this system of equations using the x-tiles and y-tiles. 2x + y = 10 3x y = 10 HighSchoolMathTeachers 2019 Page 123

127 Unit 6 Test Name: 27. Combine the two models. Remove neutral pairs, and write the new equation. (2x + y) + (3x y) = Which variable was eliminated? Why? Solve the resulting equation for the remaining variable. HighSchoolMathTeachers 2019 Page 124

128 Unit 6 Test Name: Solve each system of equation using elimination by addition. Check your solutions. x + 2y = 3 29.{ 3x 2y = 5 x y = { 2x y = 2 HighSchoolMathTeachers 2019 Page 125

129 Unit 6 Test Name: x + 4y = { x + 3y = { 7a + 5c = 37 2a 5c = 8 HighSchoolMathTeachers 2019 Page 126

130 Unit 6 Test Name: Mrs. Smith decided to purchase candy for her whole class as a treat. She bought Smarties and Dum-Dum lollipops as brain food for their next exam. Each bag of Smarties cost $7.00 (including tax). The bag of Dum-Dum lollipops cost $8.50 (including tax). She ended up spending $60.50 on her purchase of 8 items. 33. Using the information above, complete the following table: Number of Smarties Bags Number of Dum-Dum lollipops Bags Total Cost for 8 Items ($) Circle the row that has a total cost of $ How many bags of Smarties did Mrs. Smith buy? 36. How many bags of Dum-Dum lollipops did Mrs. Smith buy? HighSchoolMathTeachers 2019 Page 127

131 Unit 6 Test Name: 37. NAVIGATION The map shows a section of the Indian Ocean. The system of equations 2x + 3y = 96 and x + 2y = 42 gives the courses of two freighters headed in a southeasterly direction where x represents latitude and y represents longitude. Will the freighters meet? If so, where? If not, why not? 38. WRITING MATHEMATICS Write a real world problem that involves a system of inconsistent linear equations. Interpret what the inconsistency means in the situation. 39. The equations 12x + 10y = 20 and ax + 2y = b form a dependent system. Find a and b. 40. The equations y = 3x 5 and 5y = ax + b form an inconsistent system. Find a. Find a value that b cannot have. Why? HighSchoolMathTeachers 2019 Page 128

132 Unit 6 Test Name: Answer Key 1. a) x = 0; y = 4 b) x = 10; y = 14 c) x = 2; y = 6 2. a) y = 7; x = 11 b) y = 3; x = 7 c) y = 4; x = y x y x Each point on the line has x and y coordinates. If we know x coordinate of any point, we can easily find y coordinate of the same point. Also, if we know y coordinate of any point, we can find x coordinate of the point. 13. x = 1 6 y = y = x no 6. yes 14. x = 2 y = x = 3 y = x = 14 y = yes 8. no y x 4 y x 6 y 2x 3 1 y x 3 2 y 4 2 y x I, F, C 18. A. 19. I, F, C 20. I x + 25y Vary=All Positive numbers 23. Answers may Vary 24. x + y < Let x represent the number of correct answers. Let y represent the incorrect answers. Write a system of equations. Janet s scoring system: 2x + y = 10 Matthew s scoring system: 3x y = Rewrite the equation representing Matthew's scoring system using a minus sign. Model this system of equations using the x-tiles and y-tiles. 3x y = 10 HighSchoolMathTeachers 2019 Page 129

133 Unit 6 Test Name: 27. Combine the two models. Remove neutral pairs, and write the new equation. 28. y was eliminated. Because we had 2x + y + 3x y = Combining like terms, we get (2x + 3x) + (y y) = And we know y y equals 0, so we eliminated y. Solving this equation, we have: (2x + 3x) + (y y) = x = 20 x = (2, 1 2 ) 30. ( 1, 4) 31. (22, 3) 32. a = 5, c = Yes, the freighters will meet. The point of their meeting is (66, 12). To get it, we just need to solve the system of two equations. 38. Two cars are driving on different roads. The system of equations y = 3x + 5 and y = 2 + 3x represents the courses of their directions. Will the cars meet? In this case inconsistency means they are driving in parallel roads and they will never meet. 39. a = 12 b = a = 15 b cannot be 5, because in that case we would have two the same equations and that wouldn t be a system, that would be a one line. 33. & 34. Number of Smarties Bags Number of Dum-Dum lollipops Bags Total Cost for 8 Items ($) 0 8 $ $ $ $ $ $ $ $ $ Mrs. Smith bought 5 Smarties bags 36. Mrs. Smith bought 3 DumDum lollipops bags. HighSchoolMathTeachers 2019 Page 130