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					                                             Instructional Unit Plan
                                           School: Sunrise Elementary




Teacher: Ms. Amato, Mr. DeJesus, & Mr. Kayser                  Grade Level: 5th

Unit Title: Patterns of Change                                 Implementation Dates:
(Tables & Graphs)



Unit Focus

 Students experiment with forms of geometric growth that express number patterns; show
growing patterns in number tables and on graphs; distinguish between growth, shrinkage,
oscillation; note differences between steady and accelerated growth



           New Mexico Content Standards, Benchmarks and Performances Addressed:

                                                 Strand 2: Algebra
Standard: Students will understand algebraic concepts and applications.

5-8 Benchmark 1: Understand patterns, relations, and functions
 Describe, represent, and analyze patterns and relationships.
 Identify, describe, and continue patterns presented in a variety of formats (e.g., numeric, visual, oral, written,
    kinesthetic, pictorial).
 Generate a pattern using a written description.

5-8 Benchmark 2: Represent and analyze mathematical situations and structures using algebraic symbols.
 Compute the value of the expression for specific numerical values of the variable.
 Use a letter to represent an unknown number.

5-8 Benchmark 3: Use mathematical models to represent and understand quantitative relationships
 Use mathematical models to represent and explain mathematical concepts and procedures.
 Understand and use mathematical models such as:
     Graphs, tables, and charts to describe data
 Demonstrate how a situation can be represented in more than one way.

5-8 Benchmark 4: Analyze changes in various contexts.
 Recognize and create patterns of change from everyday life using numerical or pictorial representations.
 Generalize patterns of change and recognize the same general patterns presented in different representations.


Strand 5: Data Analysis And Probability
Standard: Students will understand how to formulate questions, analyze data, and determine probabilities.



                                                           1
       5-8 Benchmark 1: Formulate questions that can be addressed with data and collect, organize, and display relevant
       data to answer them.
        Construct, read, analyze, and interpret tables, charts, graphs, and data plots.
        Construct, interpret, and analyze data from graphical representations and draw simple conclusions using bar
           graphs, line graphs, circle graphs, frequency tables, and Venn diagrams.
        Display, analyze, compare, and interpret different data sets, including data sets of different sizes.
        Organize and display single-variable data in appropriate graphs and representations.
        Organize, read, and display numerical (quantitative) and non-numerical (qualitative) data in a clear, organized,
           and accurate manner including correct titles, labels, and intervals or categories including:
           o Bar, line, and circle graphs
           o Pictorial displays
           o Charts and tables
        Formulate questions and identify data to be collected to correctly answer a question.

       5-8 Benchmark 3: Develop and evaluate inferences and predictions that are based on data.
        Make and justify valid inferences, predictions, and arguments based on statistical analysis.
        Compare a given prediction with the results of an investigation.
        Use counting strategies to determine all the possible outcomes of a particular familiar event.
        Find all possible outcome sets involving four or more sets of objects.
        Evaluate the reasonableness of inferences that are based on data in the context of the original solution.
        Identify the method used to make an inference and/or a prediction on a given data set and solve similar
           problems.
        Determine the accuracy of a prediction or an inference based on the accuracy of the data in a given data set.
        List all possible outcomes of simple events.

       5-8 Benchmark 4: Understand and apply basic concepts of probability.
        Use probability to generalize from a simple pattern or set            of examples and justify why the
           generalization is reasonable.



       Paraphrase knowledge and skills required by the Standards:

        INVESTIGATION 1: Number Patterns in Changing Shapes – students build designs that
       change in a regular way and according to number patterns; predict later steps of number patterns
       and designs; make tables and graphs to display number patterns; use language of speed and
       motion to describe number patterns


INVE INVESTIGATION 2: Motion Stories, Graphs, and Tables – students explore relationships
      among distance, time and speed; explore irregular increases; explore how distance, time and
      speed can be represented with tables, graphs, stories; an informal representations; interpret
      steepness in distance vs. time graphs as speed; make associations about tables, graphs, and
      stories of the same event




                                                               2
Description of the Assessments that will be used to provide evidence of student learning that
targets the standards:




Description of the rubrics or criteria that will be used to assess student performance:




                                                3
Learning Activities – Description of the learning activities that will develop the knowledge
and skills required by the performance standard:

              INVESTIGATION 1: Number Patterns in Changing Shapes p. 2-25

Materials:
   Square tiles in mixed colors: 1 bucket of 400 per 6-8 students (all sessions)
   Markers, colored pencils, or crayons in the colors of the tiles (all sessions)
   Overhead projector (all sessions)
   Blank transparency (Sessions 1-2, optional)
   Pens for overhead projector, in colors of tiles (Sessions 1, optional)
   Transparent tiles for overhead projector: 10 each of four colors (all sessions, optional)
   Large paper for posters: 1 sheet per group of 3-4 students (Sessions 3-4)
   Scissors and tape for each group (Sessions 3-4)

Session 1, 2: Analyzing Tile Patterns p. 4-13
Students build designs; predict later steps in tile patterns; make tables and graphs that describe
growth; find patterns in step numbers and totals

Preparation:
    Student Sheet 1, Tile Pattern Template (p. 109): 1 per pair and 2 transparencies
    Student Sheet 2, Growing Tile Patterns (p. 110): 1 per student (homework)
    Student Sheet 3, Growing and Graphing Tile Patterns (p. 111): 1 per student (homework)
    One-centimeter graph paper (p. 146): 1 sheet per pair
    Family letter (p. 108): 1 per student

Sessions 3, 4: Exploring Materials p. 14-25
Students extend patterns; make tables and graphs of step sizes and totals; investigate number
sequences; find the nth term of a series; make several growing designs that fit a table of numbers

Preparation:
    Student 4, Growing Tile Patterns (p. 112): 1 per student, and transparencies of first two
      patterns (Twos Tower and Squares)
    Student Sheet 5, Same Numbers, Different Patterns (p. 116): 1 per student (homework)
    One centimeter graph paper (p. 146): 2 sheets per 3-4 students


               INVESTIGATION 2: Motion Stories, Graphs, and Tables p. 26-53

Materials:
   Wide (2-inch) masking tape (see Other Preparation): about 50 meters (Session1)
   Unlined paper (Sessions 1, 3, and 5)
   Markers, crayons, or colored pencils (Session 1)
   Time pieces that show seconds: 1 per 4-6 students (Sessions 1-2)


                                                  4
      Beanbags : place about 12 of one color in a shallow container for each 4-6
       students(Session 2)
      Stick on notes: 1 pad (Sessions 3-4)
      Overhead projector (Sessions 3-4)
      Scissors and tape or glue sticks: 1 each per pair (Session 5)

Session 1: Describing Changing Speeds p. 28-32
Students make visual representations to describe trips; describe trips with changing speed


Preparation:
      Student Sheet 6, Describing a Straight Line Trip (p. 117): 1 per student (homework)


Session 2: From Beanbags to Tables p. 33-40
Students interpret spacing of dropped objects; collect
and record data in regular intervals; make and interpret a time/distance table;


Preparation:
      Student Sheet 7, Template for Tables (p. 118): 1 per pair
      Student Sheet 8, Height of a Girl (p. 119): 1 per student (homework), plus 1 transparency
       (for Session 3)

Session 3: Tables for Stories p. 41-47
Students make tables of total distances; analyze intervals in tables; compare tables of distances
that fit a story


Preparation:
      Student Sheet 9, Three Motion Stories (p. 120): 1 per student
      Student Sheet 10, Graph of a Trip (p. 121): 1 per student (homework), plus 1
       transparency (for Session 4)

Session 4: Graphs for Tables p. 48-51
Students make graphs of total distance for a table of points; compare graphs to stories


Preparation:
      Student Sheet 11, Graph Template (p. 122): 1 per student



                                                 5
      One-centimeter graph paper(p. 146) : 1 per student
       (homework, optional)
      Student Sheet 12, Planning and Graphing a trip (p. 123): 1 per student (homework)
      Student Sheet 13, Another Graph Template (p. 124): 1 per student (homework)


Session 5: Stories, Table sand Graphs p. 52-53
Students create a table of accumulated distances; write a motion story to fit a given
table and graph

Preparation:
Student Sheet 14, Matching Stories, Tables, and Graphs (p. 125): 1 per student




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