MS After School Intervention Unit: Simplifying Expressions Theme: Entertainment Day 3 Lesson Objective Students will write and evaluate algebraic expressions to represent unknown quantities. Common Core Standards: 6.NS.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.NS.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5y 6.NS.2b Identify parts of an expression, using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression 2(8 7) as a product of two factors; (8 7) as both a single entity and a sum of two terms. 6.NS.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formula V s 3 and A 6s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Materials Overhead projector or document camera Computer with speakers LCD projector Chart paper Tape Markers Moving with Math: Algebra (MH5) QuietShape algebra tiles “Wicked” resource sheet “Problem Solving Using Multiple Representations” resource sheets (one per student) “Expressions Cards” resource sheets (one per group – cut out prior to lesson) “Calendar Math” resource sheets (one per group) “Window Washing Student Sheet” resource sheets (one per student) “Raffle Ticket” resource sheets (one per student) “Wicked” Tickets (20 minutes) Post the “Wicked” scenario through the document camera and have a student read the scenario shown: “A local high school is selling tickets to their upcoming musical ‘Wicked.’ They have boxed the tickets in groups of 25 before they are routed to the middle schools in the county.” Distribute the “Problem Solving Using Multiple Representations” resource sheet to each student. Find a way to determine how many tickets have been distributed when various numbers of boxes have been routed to the middle schools using at least three of the representations. Post five pieces of large chart paper around the room, each one labeled with a representation. (Possible examples: Graph, Table, etc.) After students have represented their solutions on the “Problem Solving Using Multiple Representations” resource sheet, have them pick one of their representations and go to the chart paper. Along with the other students at the chart paper, work together to represent the expression on the chart paper. Next, have students walk around the room to view the multiple representations. Answers: Algebraic Expression Answer: Let n = the number of boxes 25n Other multiple representation answers may vary. Comparing Expressions (15 minutes) Arrange students in groups of three or four. Distribute a set of expression cards to each group. Have groups order these values from least to greatest. Students may need prompting to consider negative numbers or fractions. If they are struggling, encourage them to use a variety of strategies such as graphing or substitution to order their values. Once groups have arranged the cards, pose the following questions: Suppose n = 0. Would your ordering change? How do you know that 3n < 3n + 1 no matter what value n has? Representing Algebraic Expressions with Algebra Tiles (20 minutes) Complete the Introductory Activities on page 36 of Moving with Math: Algebra (MH5). Once completed, write two additional examples on the board and have students use the QuietShape algebra tiles to solve. Note: It may be helpful to create a large set of algebra tiles using colored paper to display on the board. Calendar Math (20 minutes) Show students the short video clip on the invention of the calendar, available on Discovery Education Streaming: http://player.discoveryeducation.com/index.cfm?guidAssetId=4C8792D2-57E4-4E4A8F68-2FE8AAE59275&blnFromSearch=1&productcode=US Calendar Magic Trick: Arrange students in groups of three or four. Distribute a “Calendar Math” resource sheet to each group. Ask one of the students in the classroom to pick out two days in a row (ex. the 14th and 15th) without telling the teacher. Have him or her secretly share the dates with a neighbor. Have them add up the dates together and give the teacher the sum. Note: You will be able to tell the students which dates the student picked out by completing the following equation: 1st Day + 2nd Day = Sum of Days n + (n + 1) = n + (n + 1) ex. Using the 14th and 15th 2n + 1 = 29; n = 14 So if the first day is the 14th, the next day must be the 15th. Reveal to students that you were able to know the dates by first writing an expression to represent the dates. Have them guide you through how they can designate the first date as n and then coming up with an expression to represent the second date (n + 1). As a class go through a second example by representing what any Monday and Wednesday could be. Ex. n + (n + 2). Working within their groups, have students write expressions for the following Calendar Problems: - Represent three days in a row Answer: n + (n + 1) + (n + 2) - Represent a block (2 by 2) of dates Answer: n + (n + 1) + (n + 7) + (n + 8) - Represent two consecutive Thursdays Answer: n + (n + 7) (Note: Encourage students to use Algebra Tiles to help them represent and combine like terms.) “Window Washing” High Five (10 minutes) Read the following to students: “Over the summer Nick is constantly complaining about being bored, so his father suggested he do some chores around the neighborhood. Nick decided to set up a window washing service within his neighborhood. He charges an $8 flat fee plus $2 per window to wash windows.” Distribute a “Window Washing” resource sheet to each student. Have students complete the following steps: 1. Answer question #1 and #2 on your paper. 2. Once completed, stand up and hold up your hand. Find someone else in the classroom with their hand up and high five. 3. Compare your answer to #1 and strategies used to solve the problem. 4. Repeat the high five process for question #2. Answers: 1. One possible solution strategy: 32 windows would cost 8 + 2(32) = 72 dollars 21 windows would cost 8 + 2(21) = 50 dollars Thus someone would pay 22 more dollars to have 32 windows washed rather than 21 windows. 2. There is not a possibility for someone to pay $41 since you are beginning at an even number (8) and then adding by increments of an even number (2). Closure: “Raffle Ticket” (5 minutes) Pass out a “Raffle Ticket” resource sheet to each student. Have students put their name on the resource sheet and answer the question. Collect all papers and draw desired amount of winners – students must attain the correct answer in order to receive a “prize.” (Prizes could consist of a pencil, choosing their own seat one day, etc.) Answers: Nick’s Fees: 8 + 2w # of Windows Cost to Customer ($) 1 10 Nick and Chris’ Fees: 5 + 4w # of Windows 1 2 12 2 3 14 3 4 16 4 5 18 5 Cost to Customer ($) 9 13 17 21 25 The better deal depends on how many windows the customer is having washed. If they are having more than one window washed, then it would be cheaper for the customer to have just Nick wash the windows. A local high school is selling tickets to their upcoming musical “Wicked.” They have boxed the tickets in groups of 25 before they are routed to the middle schools in the county. Find a way to determine how many tickets have been distributed when various numbers of boxes have been routed to the middle schools. http://www.brescia.edu/alumni/news/uploaded_images/wicked-logo-732362.jpg Expression Cards n 2 3n n•n 3n + 1 10 – n Calendar Math http://www.rocketcalendar.com/preview/2011-03.png Window Washing Student Sheet Nick decided to set up a window washing service within his neighborhood. He charges an $8 flat fee plus $2 per window to wash windows. 1. How much more would someone pay to have 32 windows washed than 21? Explain. 2. Is there a possibility for someone to pay $41 to have his/her windows washed? Explain. http://www.yesclean.com.au/images/window_cleaning.jpg Raffle Ticket Nick’s brother Chris has decided to join Nick in his window washing business. Together they charge a $5 flat fee and $4 per window. Is this a better deal than Nick’s original charge of an $8 flat fee plus $2 per window? Justify your answer. _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ http://www.raffle-drums.net/images/Tickets/Blank-Double-Raffle-Ticket-lg.gif