MS After School Intervention Theme: Summer Vacation Unit: Solving Equations and Inequalities Day 4 Lesson Objective Students will solve multi-step equations for the unknown. Common Core Standards: 8.EE.7 Solve linear equations in one variable. 8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Materials Folders Colored paper (optional) “Send a Problem” resource sheet “Day at the Races” resource sheet “3-2-1 Closure” resource sheets (one per student) Warm-Up Practice (10 minutes) Have students solve the following problems individually. When finished, have students compare answers with a partner and then go over as a class. 1. 8x 9 5x 6 2. 2 y 5 6 y 2 27 Solutions: 1. x = –3 2. y 6 Have students check their answer by substituting the solution into the original equation to get a true statement. Earning Money for Vacation – Part I (15 minutes) Read and display the problem for students: You have decided to go on vacation, but your parents aren’t willing to pay for it. This means you must get a summer job. You would like to be on vacation for as many days as you work. The vacation you have chosen is going to cost $40 per day for food and an additional $200 in overall travel expenses. You have been offered a job baby-sitting and will earn $60 per day. How many days must you work to receive an equal number of vacation days? Have students discuss how they would approach and solve the problem in small groups. A possible solution may be an algebraic or visual representation of the equation 40x 200 60x . Some groups may derive the equation 60x 40x 200 0 (Students may struggle with setting it equal to zero.) Another possibility may be that students guess and check. If you see students trying to guess and check, encourage them to set up a table of values. Have groups present their approach to the class. As a class, discuss the pros and cons to each approach. (Solution: x = 10 days.) Earning Money For Vacation -Part II (20 minutes) Give each group a copy of the following scenario after the groups have presented their solutions to Part I. “Your vacation plans have changed. In addition to the $40 per day for food and $200 for travel expenses, you have also decided to rent a beach umbrella for $10 each day in order to prevent sunburn. Your babysitting job still pays $60 per day and you still want to work the same number of days as your vacation. How does this change your vacation from Part I?” Have the groups rework their original approach to include the new information. Each group should present their solution. A possible equation is 40x 10x 200 60x . (Solution: x = 20 days.) Follow this scenario up by giving each group the following additional information. “On your birthday, your parents give you $100 for your vacation and your grandparents give you $50. Your vacation will still cost the same for food, the beach umbrella and travel expenses, and you will earn the same amount of money per day. How does this change the problem?” Have the class derive the problem together to include the new information. Solve the problem together. A possible equation may be 40x 10x 200 60x 100 50 . If students have combined some of the terms already from their previous work, be sure to discuss where the terms came from. For example, students may have 50x on the vacation side of the equation, so be sure to have them explain that $40 was for food and $10 was for the umbrella. (Solution x = 5 days.) Send-A-Problem (20 minutes) Attach each problem to the front of a folder, and place the folders around the room. Have each set of partners go to a folder and solve the problem together on a piece of paper. After solving the problem, students should place their solution into the folder. Partner sets should rotate at the same time and solve the problems at every folder. Once the students have returned to their original problem, they can open the folder and view all possible solutions. Students should be given a few minutes to review the solutions in their folder and decide which solution seems correct. They will then present their problem and solution to the class. You may want each partner set to have different colored paper so you can see which groups are getting the correct answers and which groups are struggling. If different colored paper is not available, have students write their names on their papers. This will allow you to determine groups for the differentiated activity. A Day at the Races (20 minutes) Assign students to small groups. Allow students access to QuietShape Algebra Tiles if necessary. Distribute a picture of a car to each group and have them decide on a team name. If time allows, have the groups decorate their cars. Draw vertical lines on the chalkboard to cut it into 7 equal segments. Write “START” at the top of the first chalkboard segment and “FINISH” at the top of the last segment. Students should tape their cars in the start segment of the board. Once all of the cars have been taped to the board, hand out the first problem to each group. Do not allow students to start the problem until you say “GO.” Once you say, “GO,” groups are to work through the problem they have. In order to get the next problem and move their car one segment closer to the finish line, groups must show you their correct solution. Continue the game until all cars make it to the finish line or until you run out of time. If a group finishes all problems early, separate them and send them to the remaining groups to help. 3-2-1 Closure (5 minutes) On the 3-2-1 resource sheet, have students identify three things they have learned so far in the course, two tools they can use to help them solve equations, and one question they have regarding the lesson. Send-A-Problem 18 6k 6 18k Solution: k = –1 8x 6 8 4 2 x Solution: x = 3 p 1 5 p 3p 8 Solution: p = 1 5 p 14 8 p 4 Solution: p = –6 8x 2 9 7 x Solution: x = –7 A Day at the Races Source: http://www.abcteach.com/free/b/basicshaperacecarbw.jpg A Day at the Races – Problems PROBLEM 1: 13 5 20m 2m Solution: m = –1 PROBLEM 2: 11 5a 30a 24 Solution: a = –1 PROBLEM 3: 20x 10 6 12x Solution: x = 2 PROBLEM 4: 10n 30 3n 20 8n Solution: n = 10 PROBLEM 5: 8 8x 6 4 2x Solution: x = 3 3-2-1 Closure In the space below, write: 3 things you have learned so far in this program. 1. 2. 3. 2 tools available to help solve equations. 1. 2. 1 question you have regarding the lesson. 1.