# Acquisition Lesson Plan for the Concept, Topic or Skill---Not for the Day

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1 Acquisition Lesson Plan Concept: Linear Systems Author Name(s): High-School Delaware Math Cadre Committee Grade: Ninth Grade Time Frame: Two 45 minute periods Pre-requisite(s): Write algebraic expressions and equations to model real-world situations that represent the relationship between two variables; solve a literal equation for one of its variables; graph linear equations by hand and with technology using slope intercept form; simplify expressions; write equivalent expressions; and make tables of values from equations. Common Core Standard(s): A CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinates axes with labels and scales. A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Essential Question: (What question from your Student Learning Map and based on your standards/grade-level expectations will direct and focus this lesson?) How does understanding the solution(s) of a system of linear equations assist with decision making in a realworld situation? Assessment Prompts: (What do students need to learn to be able to respond to the Essential Question? What informal assessment prompts will you use to gather evidence of learning? You do not need to create the specific AP strategy here just list the topic/process/content of the chunk of the learning that each AP will assess.) Assessment Prompt (AP) #1: Construct equations using two variables to represent relationships between two quantities Assessment Prompt (AP) #2: Create graphs and tables representing a system of linear equations. Assessment Prompt (AP) #3: Use graphs and tables to estimate the solutions for a system of linear equations. Activating Strategy: (How will you hook students at the beginning of the lesson and activate and/or build the necessary prior knowledge?) Warm Up Activity: Going to the Movies Activity: Handout #1 / PowerPoint Slide 1 Hand to students as they enter the classroom. Let them work with a partner as a Think-Pair-Share. Have each pair solve the problem any way they chose. Have pairs share their solutions and strategies with the whole class to generate discussion. To facilitate the sharing out process and actively engage all students, have the audience write on an index card one thing they liked about the strategy and one suggestion to improve their delivery. After the first pair completes the presentation, ask the class if any other groups used the same strategy in solving the problem. If so, have each group share any variation(s) in their methodology. Repeat this process until all strategies have been presented. Collect the index cards and distribute to the presentation groups as feedback to improve both their mathematical process and presentation skills. The use of a document reader would enhance and expedite the process. Discuss with students that there is no right way to solve a problem. Key Vocabulary Words to Preview: (What content-specific vocabulary will students need to know in order to make meaning of the learning in the lesson?) System of equations Solution(s) of system of equations Variables

2 Explain the importance in utilizing foundational knowledge and approaching a mathematical problem from the angle most familiar to the student. The student will never know whether their idea will work, if they do not actively use their methodology. Differentiation: If students complete early, have them try to discover another way to solve the problem. Pairs or Small Groups Activity: Which Truck Should I Rent? Activity: Handout #2 / PowerPoint Slide 2 & 3 Introduce the Which Truck Should I Rent? Activity by asking students if their parents ever rented a car for vacation or a truck when they were moving. What did they need to consider? What were the variables? Help students by defining what the best choice i.e. spending the least, size needed, number of miles needed to drive, cost difference, etc. Tell students you need to help move your sister this weekend. She lives in a two bedroom apartment and you offered to rent the moving truck for her. Tell students that you have called two different companies and you trying to decide which company you should rent from. She lives the same distance from both rental companies and her new apartment is 50 miles away. It will take four trips from her old apartment to her new one to move all her belongings. Distribute the Which Truck Should I Rent? Activity (Handout #2 & #3) to the students. As a class, read the activity aloud. Ask students if any of the vocabulary is unfamiliar to them. Discuss the situation and any new terminology, as it relates to the real world, as a class. Use I Notice, I Wonder (Handout #3) to prompt students to articulate their unique questions, interests, and speculations that often lead to problem solving strategies. This enables students to begin to attack the problem without being given explicit questions to answer. Typically, they answer the questions that would be asked without guidance.

3 Teaching Strategies: (What specific teaching strategies, will you use to engage students in their learning? e.g. distributed guided practice, numbered heads, collaborative pairs, think-pair-share, jigsaw, exit tickets, note to absent student, writing-to-learn strategies, etc.) Pairs or Small Groups I Notice, I Wonder Summarizing Strategies Think Pair Share Probing Questions I Notice, I Wonder Coordinate Graph It is important to allow students enough time to process and complete all activities. Provide extensions, if needed, to differentiate the lesson. The majority of the instruction revolves around discussion and presentation with the entire class Instructional Plan: (How will you provide instruction and/or specific learning experiences which lead students to the understanding necessary to respond to each assessment prompt? What will be the sequence of these learning experiences?) Instruction: 1. After the students have completed the I Notice/I Wonder activity, share out student ideas. Focus discussion towards identifying the variables to consider when renting from the two companies. After the discussion, split the class in half. Students should work collaboratively in pairs. Have half of the class focus on the Yellow Truck Rental Company and the other half on the Orange Truck Rental Company. 2. Ask students to construct a linear equation using two variables to represent the relationship between the number of miles driven and total rental cost for their respective Truck Rental Company. 3. Discuss the difference between the independent variable (number of miles, N) and dependent variable (total rental cost, C). 4. Provide each pair of students with a sheet of graph paper and ask them to create a graph and a table representing the total rental cost, as related to the cost per mile to rent the truck from their assigned company? Have one pair from the Yellow Truck Rental Company and one pair from the Orange Truck Rental Company share their graph and table, with the class. The use of a document reader would enhance and expedite the process. Differentiation: If students complete early, have them write the equations for the other truck rental company and/or predict which rental company is a better buy. Instruction: Create a graph and a table to represent a linear equation: PowerPoint Slides #4 & #5 5. Ask students to identify what questions could be asked and answered using either the equation, table or graph of either the Yellow Truck Rental Company or the Orange Truck Rental Company. 6. Have students answer the following questions: a. How much will it cost to rent a truck from your company if you will be traveling 120 miles? b. How much will it cost to rent a truck from your company if you will be traveling 300 miles? 7. Discuss with students how the cost of renting a truck varies due to the number of miles traveled. Ask students if they can think of a way to analyze both graphs at the same time.

4 8. Introduce a system of equations by displaying a graph with both equations graphed together (PowerPoint Slide #6). Explain to the students how this process is available when the independent and dependent variables of two different equations represent the same quantity within the same context. Ask students to analyze the significance of the point at which both graphs cross (intersect) each other. Explain that this is referred to as the intersection point and also the solution to the two equations. Have students collaborate with a partner to verbally create a question that matches this context and the intersection point of the two graphs. Have partners share their answers with another pair of partners. Explain that they need to help each other be successful, so if one group does not have a correct question, the other group needs to teach the group the significance of the intersection point. 9. Using a visual graphic display of the system of equations (PowerPoint Slide #7 & # 8), show students how to determine the intersection point of the graphs both graphically and using a table. Complete the instruction by discussing with students the information that can be gleaned from a system of equations and the importance in determining the location of each graph on both sides of the intersection point (PowerPoint Slide #9 & # 10). Instruction: Present similar problem with a change in the variables i.e. weight restrictions, ratios, etc. 10. To have students demonstrate their ability to construct equations using two variables to represent relationships between two quantities, have them respond to the following Assessment Prompt: Assessment Prompt #1: Write two equations representing the number of student and adult tickets sold for the following scenario. Tickets for a school play sell for \$3 for a student and \$5 for an adult. One night 595 people bought tickets. The school took in \$1951. How many adult tickets and how many student tickets were sold? 11. To have students demonstrate their understanding of how to create graphs and tables representing a system of linear equations, have them respond to the following Assessment Prompt: Assessment Prompt #2: Five gallons of regular unleaded gas and eight gallons of premium gas cost \$ Five gallons of regular unleaded and two gallons of premium gas cost \$8.75. Create a graph and a table representing the following system of equations representing this context. 5R + 9P = \$ R + 2P = \$ To have students demonstrate their understanding of how to estimate the solution for a system of linear equations, have them respond to the following Assessment Prompt: Assessment Prompt #3: Veronica is considering two job offers in car sales. The first job pays \$400 per week plus 15% sales commission. The second job pays \$350 per week plus 20% sales commission. What amount would Veronica have to sell for her weekly salary to be the same at either job? First, write two equations, one for each job, representing the amount of weekly sales, x, and total weekly salary, y.

5 Second, graph the functions. Find the point of intersection of the two lines. What is the ordered pair? At what amount of sales will the two jobs have the same salary? What will that salary be? Summarizing Strategy: On chart paper or in a Smart file record advice and solutions to the problem. List various processes and solutions. Post on teacher website. Respond to the lesson essential question in paragraph form, basing your response on a situation in your life today. How does understanding the solution(s) of a system of linear equations assist with decision making in a real-world situation? Attachments: All attachments need to be included within the Acquisition Lesson, in sequence, as acknowledged throughout the lesson.

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