Problem Set and Answer Key Blueface is going to open up for Kodak Black’s next concert on the Gulf Coast! Amar is trying to make some money by selling Blueface and Kodak Black T-shirts outside the Coliseum. Each Kodak T-shirt sells for 20 dollars, and each Blueface T-shirt sells for 15 dollars. Amar made 235 dollars and sold 14 T-shirts. How many Kodak Black shirts did he sell, and how many Blueface T-shirts did he sell? 20 ( K ) + 15 ( B ) = 235 K + B = 14 K=5 B=9 KK and Caleb want to make the high school basketball gym, so they are going to join a gym over the summer. KK decided to go to Planet Fitness, which costs $30 to join, and $5 per visit. Caleb decided to go to Club4Fitness, which just charges $8 per visit. After how many visits have KK and Caleb spent the same amount of money, and how much money did they spend? KK: d = 5 v + 30 Caleb: d = 8 v V = 10 Ariana Grande is coming to North Gulfport Middle School for a fundraising benefit concert! Nevaeh is selling tickets. This week, she sold 3 kids tickets and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 5 adult tickets for $67. How much was each adult ticket, and how much was each kids ticket? 3 k + 9 a = 75 8 k + 5 a = 67 K=4 A=7 Solve this system of equations using the graphing method and the substitution method: 5x − 3y = −12 2x + 3y = −9 (-3,-1) System Of Equations Project You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain your findings. Rubric A: Exemplary B: Proficient C: Developing D: Beginning Equations Student defined the variables and correctly created both equations. Student correctly created both the variables. Student made a couple mistakes when creating their equations. Equations are random and not relevant to the problem. Graphing Student rewrote both equations in y=mx+b and graphed correctly. Student graphed both lines correctly. Student made one or two errors when graphing the equations. Student did not graph equations correctly at all. Substitution Student solve the system using substitution correctly and wrote solution as a coordinate point. Student solve the system using substitution correctly Student messed up or forgot one step in solving the system of equations using substitution. Student did not substitute correctly. Explanations Student responses were complete, make sense, and are grammatically correct. Student responses were complete and make sense. Student responses are not fully developed and have grammatical errors. Student responses are not relevant, mathematically correct, or grammatically correct. Poster Poster includes all relevant information and it neat, organized, and aesthetically pleasing. Poster includes all relevant information. Poster is missing one aspect of the project. Poster is missing more than one aspect of the project. Problem Blueface is going to open up for Kodak Black’s next concert on the Gulf Coast! Amar is trying to make some money by selling Blueface and Kodak Black T-shirts outside the Coliseum. Each Kodak T-shirt sells for 20 dollars, and each Blueface T-shirt sells for 15 dollars. Amar made 235 dollars and sold 14 T-shirts. How many Kodak Black shirts did he sell, and how many Blueface T-shirts did he sell? Project Components ● ● ● ● ● ● ● Title, Name, Word Problem Variables Defined and Two (2) Equations Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be identified as a coordinate point. Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable. All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable, then the second substitution to find the second variable). Explanations for both the graphing and substitution method, stating what steps mathematically were taken. Explanation of solution with regard to the context of the problem. A paragraph explaining which method the student prefers when solving a system of equation. Example Poster System Of Equations Project You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain your findings. Rubric A: Exemplary B: Proficient C: Developing D: Beginning Equations Student defined the variables and correctly created both equations. Student correctly created both the variables. Student made a couple mistakes when creating their equations. Equations are random and not relevant to the problem. Graphing Student rewrote both equations in y=mx+b and graphed correctly. Student graphed both lines correctly. Student made one or two errors when graphing the equations. Student did not graph equations correctly at all. Substitution Student solve the system using substitution correctly and wrote solution as a coordinate point. Student solve the system using substitution correctly Student messed up or forgot one step in solving the system of equations using substitution. Student did not substitute correctly. Explanations Student responses were complete, make sense, and are grammatically correct. Student responses were complete and make sense. Student responses are not fully developed and have grammatical errors. Student responses are not relevant, mathematically correct, or grammatically correct. Poster Poster includes all relevant information and it neat, organized, and aesthetically pleasing. Poster includes all relevant information. Poster is missing one aspect of the project. Poster is missing more than one aspect of the project. Problem KK and Caleb want to make the high school basketball gym, so they are going to join a gym over the summer. KK decided to go to Planet Fitness, which costs $30 to join, and $5 per visit. Caleb decided to go to Club4Fitness, which just charges $8 per visit. After how many visits have KK and Caleb spent the same amount of money, and how much money did they spend? Project Components ● ● ● ● ● ● ● Title, Name, Word Problem Variables Defined and Two (2) Equations Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be identified as a coordinate point. Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable. All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable, then the second substitution to find the second variable). Explanations for both the graphing and substitution method, stating what steps mathematically were taken. Explanation of solution with regard to the context of the problem. A paragraph explaining which method the student prefers when solving a system of equation. Example Poster System Of Equations Project You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain your findings. Rubric A: Exemplary B: Proficient C: Developing D: Beginning Equations Student defined the variables and correctly created both equations. Student correctly created both the variables. Student made a couple mistakes when creating their equations. Equations are random and not relevant to the problem. Graphing Student rewrote both equations in y=mx+b and graphed correctly. Student graphed both lines correctly. Student made one or two errors when graphing the equations. Student did not graph equations correctly at all. Substitution Student solve the system using substitution correctly and wrote solution as a coordinate point. Student solve the system using substitution correctly Student messed up or forgot one step in solving the system of equations using substitution. Student did not substitute correctly. Explanations Student responses were complete, make sense, and are grammatically correct. Student responses were complete and make sense. Student responses are not fully developed and have grammatical errors. Student responses are not relevant, mathematically correct, or grammatically correct. Poster Poster includes all relevant information and it neat, organized, and aesthetically pleasing. Poster includes all relevant information. Poster is missing one aspect of the project. Poster is missing more than one aspect of the project. Problem Ariana Grande is coming to North Gulfport Middle School for a fundraising benefit concert! Nevaeh is selling tickets. This week, she sold 3 kids tickets and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 5 adult tickets for $67. How much was each adult ticket, and how much was each kids ticket? Project Components ● ● ● ● ● ● ● Title, Name, Word Problem Variables Defined and Two (2) Equations Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be identified as a coordinate point. Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable. All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable, then the second substitution to find the second variable). Explanations for both the graphing and substitution method, stating what steps mathematically were taken. Explanation of solution with regard to the context of the problem. A paragraph explaining which method the student prefers when solving a system of equation. Example Poster System Of Equations Project You are going to create a poster demonstrating your skills in solving systems of equations. You will be given a word problem, create two equations based on the real-world problem, solve the system of equations using graphing AND substitution, and then explain your findings. Rubric A: Exemplary B: Proficient C: Developing D: Beginning Equations Student defined the variables and correctly created both equations. Student correctly created both the variables. Student made a couple mistakes when creating their equations. Equations are random and not relevant to the problem. Graphing Student rewrote both equations in y=mx+b and graphed correctly. Student graphed both lines correctly. Student made one or two errors when graphing the equations. Student did not graph equations correctly at all. Substitution Student solve the system using substitution correctly and wrote solution as a coordinate point. Student solve the system using substitution correctly Student messed up or forgot one step in solving the system of equations using substitution. Student did not substitute correctly. Explanations Student responses were complete, make sense, and are grammatically correct. Student responses were complete and make sense. Student responses are not fully developed and have grammatical errors. Student responses are not relevant, mathematically correct, or grammatically correct. Poster Poster includes all relevant information and it neat, organized, and aesthetically pleasing. Poster includes all relevant information. Poster is missing one aspect of the project. Poster is missing more than one aspect of the project. Problem Solve this system of equations using the graphing method and the substitution method: 5x − 3y = −12 2x + 3y = −9 Project Components ● ● ● ● ● ● ● Title, Name, Word Problem Variables Defined and Two (2) Equations Graphing Method Solution: Graph must be labeled and numbered. If original equations are in standard form, they must be re-written in slope-intercept form. (work must be shown). Both lines must be graphed correctly and the solution should be identified as a coordinate point. Substitution Method Solution: If both equations are in standard form, one must be rewritten so it has an isolated variable. All steps of substitution must be shown in a neat and organized fashion (The original substitution to find the first variable, then the second substitution to find the second variable). Explanations for both the graphing and substitution method, stating what steps mathematically were taken. Explanation of solution with regard to the context of the problem. A paragraph explaining which method the student prefers when solving a system of equation. Example Poster