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picture1_Quadratic Inequalities Pdf 178246 | Algebra Lesson Piecewise And Step Functions Teacher


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File: Quadratic Inequalities Pdf 178246 | Algebra Lesson Piecewise And Step Functions Teacher
algebra success t1 lesson 1 piecewise and step functions students will explore the process of graphing piecewise and step functions under specific conditions students will create piecewise function graphs and ...

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         Algebra Success                                            T1
         LESSON 1: Piecewise and Step Functions
         [Objective]
         Students will explore the process of graphing piecewise and step functions under 
         specific conditions. Students will create piecewise function graphs and will describe, 
         interpret, and evaluate these functions for particular values.
         [Prerequisite skills]
         Coordinate graphing, graphing functions: linear, absolute value, square root, quadratic, 
         and constant, graphing inequalities
         [Materials]
         Student pages S1 – S16
         Gridded index cards
         Ruler
         Scissors
         Tape/glue
         [essential que s t i O n s ]
         1.  What do the features of piecewise functions look like and how do we apply the 
           rules that define them? 
         2.  What do the features of step functions look like and how do we apply the rules 
           that define them?
         3.  What are some real life situations that can be modeled using piecewise functions?
         [WOrds FOr WOrd Wall]
         Piecewise function, stepwise function, function table, condition, parameters, 
         scatter plot
         [GrOuPinG]
         Cooperative Pairs (CP), Whole Group (WG), Individual (I)
         [levels O F  teacher suPPOrt]
         Modeling (M), Guided Practice (GP), Independent Practice (IP)
         [MultiPle rePresentatiOns]
         SOLVE, Graph, Algebraic Formula, Verbal Description, Graphic Organizer, Pictorial 
         Representation
         [WarM-uP] (IP, I, WG) S1 (Answers are on T9.)
         •  Have students turn to S1 in their books to begin the Warm-Up. Students will 
           graph inequalities in preparation for the lesson on piecewise and step functions. 
           Monitor students to see if they need help during the Warm-Up. Have students 
           complete the problems and then review the answers as a class. {Algebraic Formula, 
           Graphs}
         [hOMeWOrk]
         Take time to go over the homework from the previous night.
         [lessOn] [3 days (1 day = 80 minutes) (M, GP, IP, WG, CP, I)]
            T2                                                                                                                                 Algebra Success
            LESSON 1: Piecewise and Step Functions
              SOLVE Problem                                                                                            (WG, GP) S2 (Answers on T10.)
            Have students turn to S2 in their books. The first problem is a SOLVE problem. You 
            are only going to complete the S step with students at this point. Tell students that 
            during the lesson they will learn how to write and graph piecewise functions. They 
            will use this knowledge to complete this SOLVE problem at the end of the lesson. 
            {SOLVE, Verbal Description, Graphic Organizer}
              Introduction to Piecewise Functions – Discovery Activity                                                                                                             
                                                                                          (M, GP, CP, WG) S2, S3 (Answers on T10, T11.)
                  M, GP, CP, WG:                            Students will work in pairs, guided by the teacher, to 
                                                            explore the features of a piecewise function. Students will 
                                                            need gridded index cards (3 per pair), scissors and glue or 
                                                                        {Algebraic Formula, Verbal Description, Graph, Graphic 
                                                            tape. 
                                                            Organizer}
                                                                                    MODELING
                                 Introduction to Piecewise Functions - Discovery Activity
               Step 1: Have students work with a partner to complete the Function Table 1 on 
                                 S2 and plot the points on Card 1 for ƒ(x) = x + 2.
                                 •  Add the x and y axes and use a scale of 1.
                                 •  Put Card 1 aside for the next part of the activity.
                                                                                              y
                                                                                              5
                                                                                              4
                                                                                              3       y = x + 2
                                                                                              2
                                                                                              1
                                                                         -5  -4   -   -    -
                                                                                  3    2    1       12345
                                                                                             -                         x
                                                                                              1
                                                                                             -2
                                                                                             -3
                                                                                             -4
                                                                                             -5
                        Algebra Success                                                                                                                                                   T3
                        LESSON 1: Piecewise and Step Functions
                           Step 2: Students can work with a partner to complete the Function Table 2 on S2 
                                             and plot the points on Card 2 for g(x) = 1.
                                             •  Add the x and y axes and use a scale of 1.
                                                                                                         y
                                                                                                          5
                                                                                                          4
                                                                                                          3
                                                                                                          2            y = 1
                                                                                                          1
                                                                                    -   -    -   -    -
                                                                                     5   4    3   2    1        12345x
                                                                                                         -
                                                                                                          1
                                                                                                         -
                                                                                                          2
                                                                                                         -
                                                                                                          3
                                                                                                         -
                                                                                                          4
                                                                                                         -
                                                                                                          5
                                             •  Put Card 2 aside for the next part of the activity.
                           Step 3: Students can work with a partner to complete Function Table 3 on S2 and 
                                                                                                                        2
                                             plot the points on Card 3 for h(x) = x .
                                             •  Add the x and y axes and use a scale of 1.
                                                                                                               y
                                                                                                                5
                                                                                                                4
                                                                                                                3
                                                                                                                2         y = x2
                                                                                                                1
                                                                                           -5  -4  -3   -2  -1       12345x
                                                                                                               -1
                                                                                                               -2
                                                                                                               -3
                                                                                                               -4
                                                                                                               -5
                                             •  Put Card 3 aside for the next part of the activity.
            T4                                                                                                                          Algebra Success
            LESSON 1: Piecewise and Step Functions
              Step 4: Have students look at Card 1 and Function Table 1.
                               •  What is the function of the line? f(x) = x + 2
                                                                                                          -
                               •  Given: f(x) is restricted to when x ≤  1
                               •  Have students draw a vertical line at negative one.
                               •  What are the coordinate pairs that will fit the parameters of the 
                                                                                                                                                          -
                                     situation  described  by  the  condition  of  the  restriction?  ( 1,  1),  
                                      -             -     -        -     -
                                     ( 2, 0), ( 3,  1), ( 4,  2) Have students circle the points on the table on S2.
                               •  Have students determine which side of the graph they will need. 
                                     (The left side)
                               •  Have the students mark the left side with a 1 and cut the graph on 
                                     the vertical line. Have the students tape or glue Graph 1 in place on 
                                     S3.
                                                                                             y
                                                                            1              5
                                                                                           4
                                                                                           3
                                                                                           2
                                                                                           1
                                                                             -  -  -  -  -
                                                                              5 4  3  2   1    12345
                                                                                           -                x
                                                                                           1
                                                                                           -2
                                                                                           -3
                                                                                           -4    y=x+ 2
                                                                                           -5
              Step 5: Have students look at Card 2 and Function Table 2.
                               •  What is the function of the line? g(x) = 1
                                                                                                    -
                               •  Given: g(x) is restricted to when  1 < x < 1
                               •  Have students draw a vertical line at negative one and positive one.
                               •  What are the coordinate pairs that will fit the parameters of the 
                                     situation described by the condition of the restriction? (0, 1) Have 
                                     students circle the points on the table on S2.
                               •  Have students determine part of the graph they will need. (The 
                                     middle section.) 
                               •  Have students cut the graph on the vertical lines. Have students 
                                     tape or glue Graph 2 in place on S3.
                                                                                         y 2
                                                                                         5
                                                                                         4        y = 1
                                                                                         3
                                                                                         2
                                                                                         1
                                                                          -  -  -  -   -
                                                                           5  4  3  2   1     12345
                                                                                         -                  x
                                                                                         1
                                                                                         -2
                                                                                         -3
                                                                                         -4
                                                                                         -5
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...Algebra success t lesson piecewise and step functions students will explore the process of graphing under specific conditions create function graphs describe interpret evaluate these for particular values coordinate linear absolute value square root quadratic constant inequalities student pages s gridded index cards ruler scissors tape glue what do features look like how we apply rules that define them are some real life situations can be modeled using stepwise table condition parameters scatter plot cooperative pairs cp whole group wg individual i modeling m guided practice gp independent ip solve graph algebraic formula verbal description graphic organizer pictorial representation answers on have turn to in their books begin warm up preparation monitor see if they need help during complete problems then review as a class take time go over homework from previous night problem first is you only going with at this point tell learn write use knowledge end introduction discovery activity ...

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