Subject: Algebra 1 Grade: 9 Unit: Multiplying And .
Lisa LammertEDT 517Unit AdaptationSubject: Algebra 1Grade: 9Unit: Multiplying and Factoring PolynomialsGoal of unit: Students will explain the connection between the processes of multiplyingbinomials and factoring trinomials.Lesson 1: Multiplying two binomialsObjective: Students will multiply two binomials.Common Core Standards:CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomialsKeystone Anchors:A.1.1.1.5.1 Add, subtract, and/or multiply polynomials.Materials: Chromebooks, guided notes, online tutorials and videos, Big Ideas Math textbook, BigIdea Math e-book, algebra tiles, graphing calculatorsNote: This lesson takes into account previously taught vocabulary terms including polynomials,binomials, and trinomials. Students were also previously taught how to multiply monomials andhow to apply the distributive property to multiply a monomial by a binomial.Opening (Anticipatory Set):We begin with a class discussion: “Two friends (Alice and Betty) challenge two other friends(Charles and David) to individual tennis matches. How many matches does that make?”Alice plays against Charles, and then Alice plays against David.Betty plays against Charles, and then Betty plays against David.Use letters to represent each person, ! # % ! !% # #%.Thus there are 4 tennis matches.Ask the students to explain how this applies the concept of the distributive property.! % ! !%Work Period (Procedures):The teacher will demonstrate on the SMARTboard several methods for multiplying binomials.One of the methods is called the window method or area method. Another method is known bythe acronym FOIL which stands for first, outer, inner, and last. There is a third method forteaching multiplication of polynomials, which involves using algebra tiles. Students can usephysical algebra tiles or virtual algebra tiles.1
Variety of methods:Method with Algebra TilesMethod with FOILMethod with algebra tiles when an integer is negative.Window Method2
Here is a brief video of me demonstrating the window method and the FOIL method.https://youtu.be/t94LdnUreq4Together the teacher and students do several examples. The problems will begin in the form(( )(( ), but then progress to the other forms: ( ( and( ( .The students should try each of the methods and record their work in their guided notes packet ornotebook. (If a student has a writing barrier or a digital preference, the teacher can adapt thelesson so that students can complete this assignment on their Chromebooks as a Googledocument). After practicing multiple examples, the teacher will ask some of the students to sharetheir method preference.After the demonstration lesson, students can choose to work individually, in pairs, or in smallgroups to complete practice problems. They may choose to complete practice problems in theirguided notes packet or on Khan Academy.The teacher will circulate the room, observe, and answer questions as needed. The problemsincrease in difficulty. For students who master the basics quickly, they will be asked to multiplybinomials in the form (2( 1)(3( 3) where the coefficients of the variables are not 1. Ifstudents need a scaffold, the teacher will offer one. Here is one example of a scaffold.Closing: The teacher will gather the attention of the whole class and put some problems on theboard. The students will volunteer to come up to the board to display their answers.At the end of class, students need to complete an exit ticket. The exit ticket will be posted inSchoology (our online classwork/homework management system). The exit ticket providesstudents with immediate feedback. The teacher will also post the exit ticket question on the boardin case students forgot to charge their Chromebooks or if a student prefers paper and pencil.Assessment: After class, the teacher will review the exit tickets to determine who needs morepractice. For those who need more practice, the teacher will meet with these students in smallgroups during core extension time.3
Lesson 2: Factoring trinomials in the form /01 20 3, when / 4Objective: Students will factor trinomials in the form !( 5 #( , when ! 1Materials: Chromebooks, guided notes, online tutorials and videos, Big Ideas Math textbook, BigIdea Math e-book, algebra tiles, graphing calculatorsCommon Core Standards:CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomialsKeystone Anchors:A.1.1.1.5.2 Factor algebraic expressionsNote: This lesson builds upon the previous lesson, multiplying binomials. If students are stillstruggling with that lesson, additional supports will be provided during core extension time.Opening (Anticipatory Set):The teacher will display some warm up problems on the board in regards to previous lesson.Multiply:1)2)3)( 6 ( 1( 2 ( 3( 2 ( 7Give the students time to write these down. This is to be done independently. During this time,the teacher will circulate the room to see who understood the previous lesson of multiplyingbinomials and can suggest scaffolding to those who need help. (If the teacher is aware of astudent who has writing difficulties, the teacher can ask the student to explain one of the aboveproblems orally).The teacher will say, “today we will be factoring polynomials. Factoring polynomials is theprocess of breaking a larger polynomial into the product of two (or more) monomials orpolynomials.”Work Period (Procedures):For today’s lesson, we will start by viewing the You Tube video “The X Factor” athttps://youtu.be/vVWm2gyROQQ.The teacher will demonstrate on the SMARTboard two additional methods for factoringtrinomials in the form !( 5 #( , when ! 1. One of the methods involves the windowmethod from the previous lesson. The other method is the reverse of FOIL.For the example, to factor ( 5 5( 6 you need to identify two numbers that multiply to 6 andadd to 5. Represent this in the form (( )(( ).4
Variety of methods:Together the teacher and students should do several examples. The problems will begin in theform (( )(( ), but then progress to the other forms: ( ( , and then( ( .The students should practice each of the methods and record their work in their guided notespacket or notebook. (If a student has a writing barrier or a digital preference, the teacher canadapt the lesson so that students can complete this assignment on their Chromebooks as a Googledocument). After presenting multiple examples, the teacher will ask some of the students to sharetheir method preference.After the demonstration lesson, students can choose to work individually, in pairs, or in smallgroups to complete practice problems. They may choose to complete practice problems in theirguided notes packet or on Khan Academy.The teacher will circulate the room, observe, and answer questions as needed. The problemsincrease in difficulty. The teacher will assist students who need help working through them.Students who need a scaffold will be advised to use the “X factor.” For students who master thislesson quickly, they can complete an extension activity called finding the “zeros” in factoredform.If multiple students need assistance, the teacher can work with small groups at the front table.The teacher can also change the number of required problems (differentiate the product).5
Closing: The teacher will gather the attention of the whole class and put some problems on theboard such as ( 5 15( 36 and ( 5 12( 36. The class can discuss the similarities anddifferences of the two trinomials.At the end of class, students will need to complete an exit ticket. The exit ticket will be posted inSchoology (our online classwork/homework management system). The exit ticket providesimmediate feedback. The teacher will also post the exit ticket question on the board in casestudents forgot to charge their Chromebooks or if a student prefers paper and pencil.Assessment: After class, the teacher will review the exit tickets to determine who needs morepractice. For those who need more practice, the teacher will meet with these students in smallgroups during core extension time.Lesson 3: Students will explain the connection between the processes of multiplyingbinomials and factoring trinomials.Objective: Students will connect the processes of multiplying and factoring trinomials in theform !( 5 #( , when ! 1.Common Core Standards:CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomialsKeystone Anchors:A.1.1.1.5.1 Add, subtract, and/or multiply polynomialsA.1.1.1.5.2 Factor algebraic expressionsMaterials: Chromebooks, Rally Coach, guided notes, online tutorials and videos, Big Ideas Mathtextbook, Big Idea Math e-book, algebra tiles, graphing calculatorsOpening (Anticipatory Set): Students will listen to this catchy tune on factoring trinomials.https://youtu.be/s0R5hHZQvaEWork Period (Procedures):For today’s lesson, students will be working in partners to complete a lesson called “RallyCoach.” It will be offered in paper format as well as a Google document. For Rally Coach, thereare two columns, and each partner is responsible for his/her column. The students take turnscompleting one row at a time, guiding each other. This lesson encourages the students to becomethe “teacher.” Throughout this activity, the teacher will circulate the room, observe, and answerquestions as needed. The Rally Coach assignment will be collected and checked by the teacher.6
Rally CoachPerson A Person BDirections: Complete one row at a time, alternating between the first and second columns.Person A completes column APerson B completes column BMultiply1) (( 4)(( 3)2) (( 4)(( 3)3) (( 5)(( 3)4) (( 5)(( 3)5) (( 5)(( 3)6) (( 5)(( 3)FactorFactor7) ( 5 14( 498) ( 5 14( 499) ( 5 3( 1010) ( 5 3( 1011) ( 5 9( 2012) ( 5 12( 20Closing:After completing the Rally Coach activity, the students will need to do an individual reflectionpiece answering the question, “How is the process of multiplying binomials connected tofactoring trinomials? Demonstrate your understanding in either short answer form (written ortyped), with a drawing or diagram, by taking pictures of algebra tiles, or a digital presentationsuch as Power Point, Google slides. In this reflection, you must provide one example for each ofthe forms (( )(( ), ( ( , and ( ( .”7
ReflectionWhat are the potential barriers to the lesson and how you will work around the barriers?There are several barriers in this lesson, and I’ve tried to address each of them. First of all, this isa complex math lesson and since math builds upon prior knowledge, sometimes students don’thave a solid understanding of the prerequisite topics. Some of the ways that I address thesebarriers are by allowing calculators and building in a variety of supports and scaffolds (which arementioned throughout the lesson plan). Another potential barrier is the confusion about thesymbolic representation of the variables. To address this issue, I provide students with theopportunity to work with algebra tiles.I recognize that an instructional barrier includes teacher lecture while students take notes. Toalleviate this barrier, I use guided notes that allow students to fill in the examples. I could alsoprovide my students with an already completed copy of the notes, so they can just watch as Idemonstrate. In addition to printed notes, for the students who may have a writing barrier (or justa preference for digital), I am going to create Google documents and create a copy for eachstudent in Schoology. Students can use text to speech if necessary.In addition to our physical textbook, our textbook comes in an e-book form. The dynamic e-bookhas built in tutorials, which can be played in English/Spanish and with or without closedcaptioning. The e-book allows for zooming and has a built-in screen reader. It also gives studentsthe option of posting notes and highlighting.To get students excited about learning mathematics, I started each lesson with an engagingopener. I also try to keep the students engaged throughout the lesson by giving students thechoice of working alone, with partners, or in small groups.How does this unit (instructional activities, materials, and assessment) align with the principlesof UDL?When we redesign our curriculum to align to the principles of Universal design for learning, weneed to consider the goals, assessments, methods, and materials. In designing this lesson, the firstthing I considered was my overall goal for the unit. This guided my decision making for theassessments, methods, and materials. In regards to assessment, I selected a variety of formativeassessments (observation, whole group discussions, exit tickets, rally coach), and for mysummative assessment, I offered a choice of expression in how students could compose theirreflection piece. The UDL framework emphasizes the need to employ many kinds of teachingmethods and materials. In order to meet the diverse needs of my students, I incorporated acombination of video, audio, and hands-on opportunities, as well as provided students withchoice on whether to complete practice problems in their guided notes packet or through KhanAcademy. The materials also were designed to provide a variety of challenge.8
Universal Design for Learning is based on three principles: provide multiple means ofrepresentation; provide multiple means of action and expression; and provide multiple means ofengagement. I believe that my lesson addresses all three principles.For the first principle, provide multiple means of representation, I presented at least threerepresentations of the concepts for both multiplying binomials and factoring trinomials. I alsopresented the same information through different sensory modalities. There are visual diagrams,physical manipulatives (algebra tiles), and online tutorials (audio/visual). I also create my ownguided notes, which serve as concept organizers. I have uploaded digital formats of my notes toGoogle. This allows for students to adapt the notes using a variety of fonts, text size, and color. Ican also insert links to web pages or narrated tutorials within a Google document.For the second principle, provide multiple means of action and expression, I recognize thatlearners differ in the ways they express what they know. Some will prefer to answer thequestions orally, some will love demonstrating their work on the board, and others will be happyto work on the computer (Khan Academy). Since no one means is optimal for everyone,providing options is essential. As a math teacher, it is important for me to encourage my studentsto solve problems using a variety of strategies. Throughout the first two lessons, I gave mystudents options to choose their preferred strategy for solving the problems. I also gave a varietyof formative assessments, so I could tell if students were learning the material and if they neededextra support or additional challenges. In regards to the reflection piece, I provided a variety ofoptions for expression including written summaries, drawings, and digital presentations.For the third principle, provide multiple means of engagement, teachers can optimize choice andautonomy. This includes the opportunity to work alone or with others, to complete writtenpractice problems or computer problems (Khan Academy), and to determine one’s preference inthe presentation of the final reflection piece. The problems were also offered at various levels ofdifficulty. Most importantly, I believe that the classroom environment must be positive andsupportive, and students must have opportunities for collaboration as well as independentpractice. Another way teachers can foster an engaging environment is by giving the students arole in teaching itself. That is one of the benefits of rally coach.ResourcesLammert, L. (2017). FOIL Tutorial. Retrieved from https://youtu.be/t94LdnUreq4Math is Fun. (2015). Multiplying polynomials. Retrieved s-multiplying.html)Spicer, R. (2017). Factoring Trinomials Song (a 1) “Math Song Guy.” Retrieved fromhttps://youtu.be/s0R5hHZQvaETutor Zone. (2010). Factoring Trinomials-Algebra. Retrieved fromhttps://youtu.be/vVWm2gyROQQ9
Lesson 3: Students will explain the connection between the processes of multiplying binomials and factoring trinomials. Objective: Students will connect the processes of multiplying and factoring trinomials in the form !(5 #( , when ! 1. Common Core Standards: CC.2.2.HS.D.3 Extend the knowledge of arithm
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