SIT Session Lesson Plan - Twu.edu

SIT Session Lesson PlanWeek/Chapter: Week 1Course Assistant:Course: College AlgebraInstructor:Objective: What are the one or two most difficult concepts that the students needto work on today? Parallel and Perpendicular LinesBeginning reminders:1.2.3.4.Arrange seats in a circleMake sure everyone has signed inReview lesson plan with groupRemember to relax and be flexible!Content to Cover:Processes to Use*:Time:Icebreaker: Have the students stand up and stretch.IntroductionReview the expectations of SIT sessions for thesemesterEncourage students to outline Chapter P from theirtextbooks and become familiar with the importantChapter P Reviewterms and procedures that will be covered inChapter 1.Textbook, Calculator and Explain to students how to use their calculators andHomeworkaccess their textbook and homework. (Make surethey know of the free 10-Day trial offered by WebAssign.)Parallel and Perpendicular Give the students two problems on the board. LetLinestwo students come up to the board and algebraicallyand graphically determine whether the lines areparallel or perpendicular.Check forGo around the room and have each student say oneunderstanding/Reviewor two things they learned or better understandfrom today's session.Tutoring Q & AAfter session comments/thoughts:Amended and used with permission from UMKC 12/201415 min10 min10-15min10-15min5 min5 – 10min

Equations used:1) y 8x 5; -x - 8y 33 (Perpendicular)132) 𝑦 3 𝑥 4; 𝑦 9 𝑥 15 (Parallel)Amended and used with permission from UMKC 12/20142

ReferencesLarson, Ron. (2011). Algebra and Trigonometry: Real Mathematics, Real People (6th Ed).Boston, MA: Cengage Learning.*Most activities are adaptations of the SI Strategy Cards from the International Center forSupplemental Instruction located at UMKC and may be found in:Leader Resource Manual for Supplemental Instruction (SI). (2004). Amanda McDaniel, ed.University of Missouri – Kansas City.Amended and used with permission from UMKC 12/20143

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Turn to your partner:1) f (x) (x22,x 0x 3,x0Graph the problem.(a) f ( 2)(b) f (3)(a) f ( 2) ( 2)22 2(b) f (3) (3) 3 62) f (x) (x2 5,x 03xx2,0Graph the problem.(a) f ( 1)(b) f (1)(a) f ( 1) ( 1)2 5 6(b) f (1) 3(1)2 1Amended and used with permission from UMKC 12/20142

Divide and conquer:(1) g(x) 2x4(2) p(x) x3xg( x) 2( x)444p( x) ( x)3( 4) 2x xneitherneitherAmended and used with permission from UMKC 12/201434 x34

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Parent Functions:y x )y x3 )y x2 )y x )y Example Equations for Board Work:(1) h(x) 2 x5 3vertical shrink(2) f (x) 3(x1)2 3vertical stretchshift downshift to the rightshift upshift to the rightAmended and used with permission from UMKC 12/20142px )

Tic-Tac-Toe:(1)f (x) 1x3(2)3f (x) f (x) x3g(x) (7)(5)f (x) 1xf (x) x2(3)x 1g(x) x3g(x) 3x 9(4)p31g(x) 14x2(6)f (x) g(x) 5x 2f (x) x2 2x(8)f (x) p1(x4(9)f (x) 563xg(x) 5x*The students will not know the functions until they choose the space.Answers to Tic-Tac-Toe:(1)(fg)(x) x(gf )(x) x(2)(fg)(x) x(gf )(x) x(3)(fg)(x) 2x2(4)(fg)(x) 1x3(5)(fg)(x) 425x2 20x 4(6)(fg)(x) x(7)(fg)(x) x2 10x 24(8)(fg)(x) (9)(fg)(x) p2x 1(gf )(x) 1(g(g(g(g5Amended and used with permission from UMKC 12/20143x21x320 2x2f )(x) xf )(x) x2 2x 4(g63xf )(x) f )(x) (gx2 11)g(x) 4x 1x 6g(x) x2g(x) x 4xf )(x) x 1f )(x) 63x5

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Important Terms and Formulas to Remember: Solution: Any (x, y) point that satisfies the equation in question.h)2 (y Equation of a Circle: (x Slope Formula: m point.y2x2 Undefined Slope: m Zero Slope: m k)2 r2 , where (h, k) center and r radius.y1, where m slope, (x1 , y1 ) represents initial point, and (x2 , y2 ) represents finalx1any number00any number Y-Intercept Form: y mx b, where b y-intercept. Vertical Line: x someconstant Horizontal Line: y someconstant Point-Slope Formula: yy1 m(xx1 ) X-Intercept: Set y 0 and solve for x. Y-intercept: Set x 0 and solve for y. Parallel: Two lines are considered parallel when their slopes are equal. Perpendicular: Two lines are considered perpendicular when their slopes opposite reciprocals of each other. Function: A relation from a set of inputs (x-values) to a set of possible outputs (y-values) where each input isrelated to exactly one output. A function can be determined using the Vertical Line Test. Domain: All x-values the graph of an equation pertains to. Range: All y-values the graph of an equation pertains to. Even Functions: Functions that are symmetric about the y-axis. To test if a function is even, set f ( x) f (x). Ifthe outcome produces a true statement, the function is even. Odd Functions: Functions that are symmetric about the x-axis. To test if a function is odd, set f ( x) f (x). Ifthe outcome produced is the original function with all opposite signs, the function is odd. Parent Functions: Functions that have not been transformed in any way. These functions are:y x2py xy xy x3y x y c Vertical Stretch: When a parent function is multiplied by a constant.Amended and used with permission from UMKC 12/20142

Horizontal Stretch: When a parent function is divided by a constant. Vertical Reflection: A reflection of a function over the x-axis. Horizontal Reflection: A reflection of a function over the y-axis. Shifts: Shifts occur when a constant is either added to or subtracted from a function.Example:Vertical Shift Upward : (")Vertical Shit Downward : (#)f (x) x2 c)f (x) (x c )2Horizontal Shift Right : (!)f (x) (x - c )2Horizontal Shift Left : (f (x) x2 - c Finding Inverse: Switch the x and y of a function, then solve for y. One-to-One: A function is considered one-to-one if the function and its inverse are both functions. Horizontal Line Test: Tests whether the inverse of a function is a function itself. (No “y” can have more than one“x”.) Piecewise Functions: A function containing restrictions on“x”. (Note: and are open circles , while andare closed circles ) Composite Functions: Combined functions where the output from one function becomes the input for anotherfunction.Example:(fg)(x) ) Substitute g(x) wherever there is an x in f (x).(gf )(x) ) Substitute f (x) wherever there is an x in g(x).Amended and used with permission from UMKC 12/20143

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Solve the equation (if possible).(1)2(z4)(2)12 0xx 5(3)3x1 (x245 5 10z2) 10.(1)2(z4)5 5 10zStep 1Step 42(z4)5 5 10z2 z 52z 2552(z4)5 10z2 5 2z 2 58 50z17 48z5Step 5Step 2(5)2(z52(z4) 10z4) 50z174 8z 484 8 525z 1748Step 32(z4) 50z2z8 50zStep 625Plug your solution into the originalequation to check your answer.25Amended and used with permission from UMKC 12/20142

(2)12 0xx 5(3)3x1 (x24Step 1Step 1: Finding the LCD(x)(x5)Step 21(xx(x2) 103x1 (x242) 103xx 245)2(x) 05)(x 5)(x)1 102Step 2: Finding the LCDx 5 2x 0(x)(x 5)4Step 33x (2)x 2 (2)4Step 33x 5 0(x)(x 5)1 (2) 102 (2)6xx 442 1046x x4Step 43x 5 (x)(x 5) 0(x)(x (x)(x 5) 3x5)5 0Step 4(4) Step 53x5 0 52 105x425x425x2 40 10 10(4) 5Step 55x3x5 33x 2 40 2 25x42 5553x Step 6425Step 6Plug your solution into the originalequation to check your answer.Plug your solution into the originalequation to check your answer.Amended and used with permission from UMKC 12/20143

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Finding Intersections and Zeros(1)f (x) x3(2)6x2 5xf (x) xzeros : 0, 5, 1zeros :(0, 0) (5, 0) (1, 0)10x32, 5( 2, 0) (5, 0)Using Conjugates to Simplify Complex NumbersFind the conjugate and simplify to a bi form.(1)81(2)7i2i24Conjugate : 4 5iConjugate : 1 2i817i 1 2i8 7i 16i 2i 1 2i1 2i 2i214i24i248 9i 14( 1)22 9i 1 4( 1)5 5i5i 4 5i 4 5i1616229 i558 10i8 10i 25( 1)41 Amended and used with permission from UMKC 12/201428 10i20i 20i810 i414125i2

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SIT Session Lesson PlanWeek/Chapter: Week 7Course Assistant:Course: College AlgebraInstructor:Objective: What are the one or two most difficult concepts that the students needto work on today? Solving Quadratic Equations (focus on radicals); SolvingInequalitiesBeginning reminders:1.2.3.4.Arrange seats in a circleMake sure everyone has signed inReview lesson plan with groupRemember to relax and be flexible!Content to Cover:Introduction/Warm-upSolving Quadratic, Radicals,and Absolute ValueEquationsSolving InequalitiesChecking forUnderstandingProcesses to Use*:Time:Order of Operations Discussion: What are they? Why arethey important? Special Acronym? (PEMDAS – PleaseExcuse My Dear Aunt Sally)Think Pair Share – Encourage students to show every stepinvolved to ensure accuracy of their answer. Make surestudents understand how to obtain both the positive andthe negative answer.Go around the circle and ask students to recall the stepsinvolved with solving an inequality. Practice properutilization of the steps with an example (send scribe to theboard). Make sure to review the properties of inequalities.Without looking at the notes, have students write downthe quadratic equation, and discuss where to find a, b, cvariables.Tutoring Q & A5 min20 min10 min5 min5-10 minAfter session comments/thoughts:Think Pair Share Problems:Amended and used with permission from UMKC 12/20141

1. Solve by factoring:2x - 16x 64 0Check:(x - 8)(x - 8) 028 16(8) 64x–8 0x–8 064 – 128 64 0x 8x 80 0 True2. Solve using the Quadratic Formula (no radical):22x – 9x 9 0x x x x a 2, b -9, c 9 𝑏 𝑏2 4𝑎𝑐*Recognize the variables before moving forward2𝑎 ( 9) ( 9)2 4(2)(9)2(2)2*Remember: ax bx c 09 81 7249 94,x x 3, x 9 94343. Solve Equation Involving Radical:3 2𝑥 5 3 0Check:33 2𝑥 5 -3 *Remem

Course: College Algebra Instructor: _ Objective: What are the one or two most difficult concepts that the students need to work on today? Parallel and Perpendicular Lines Beginning reminders: 1. Arrange seats in a circle 2. Make sure everyone has signed in 3. Review les