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Instructional Plan Template

Mathematics Governor’s Institute 2004

(Download: Instructional Plan Temp1.doc, The Paper Folding Activity1.doc, Paper Folding Solution.doc, PostT1.doc, PreT1.doc, PreT2.doc, TI-83.doc)

 

Names of group members: Jerry Yoder, Cindi Varcoe, Johnson Mathew, Gerald Burkepile

 

Topic/Theme:  Exponential Decay or Growth

 

Level: Algebra I or II

 

Time Element:  1 period or ˝ block

 

NCTM Standards Addressed:  Measurement, Data Processing, Algebra

 

PA Math Standards Addressed:  2.3    2.6    2.8

 

Math Assessment Anchors Addressed:  M8.B.2.3,  M11.D.1.1,  M11.D.4.1,  M11.E.1.1

 

Reading Assessment Anchors Addressed:  R11.A.2

 

Objectives: Students will explore the patterns of exponential models in tables, graphs, and symbolic forms.

 

Instructional Strategies and Plan (include strategies used to help different types of learners, i.e. auditory, visual, etc):

1.      Review concepts and teach vocabulary

2.      Model the procedure for the experiment

3.      Conduct the experiment and record results

4.      Analyze the results

5.      Generalize the results

 

Materials/Resources:

            Worksheets

            Rectangular sheets of paper

Rulers

            Graphing calculator

 

Interdisciplinary Connections:

·         Reading:  Identification of vocabulary, main idea, and relevant details in a story problem. 

·         Technology:  Create scatterplots on a TI 83+ calculator and find the regressive equation.

Assessment Strategies:

·         Formative Evaluation (checking student understanding during the lesson):

Teacher will observe and question students as they fold their papers, calculate the areas, enter data into calculators,and analyze their findings.

 

·         Summative Evaluation (How will it be determined that the objectives were achieved?):

Teacher will conduct a post experiment discussion.

Students will complete the Frayer Model for concept reinforcement.

Teacher will evaluate the student’s lab worksheets.

 

Correctives/Remediation: 

            Students will conduct a second exponential experiment (Growth) counting regions formed by each fold of a sheet of paper.

 

Extensions/Enrichment:

Students will conduct an exponential decay experiment with M&M’s: “Rhinos and M&M’s”. (http://www.pbs.org/teachersource/mathline/lessonplans/hsmp/rhinos/rhinos_procedure.shtm)

 

Special Accommodations (special needs students)

·          Description of the Special Needs student selected:

  1. Functioning three years below grade level.
  2. Directions need to be broken down into single units and modeled.
  3. Able to answer literal comprehension questions.
  4. Unable to answer inferential questions.
  5. Needs to be paired with another individual.
  6. Needs to do math computations with calculator.

 

·          Accommodations to use with this student:

  1. Pre-teach vocabulary and review mathematical concepts involved.
  2. Read the problem to the class as students follow along.
  3. Model the procedure for the experiment for the class.
  4. Provide a guided experiment record sheet with tables to complete, graphs to plot, and graphing calculator to use.

5..Special rectangular paper (6 x 8).

6. Assign partner to assist.

 

 

Area of Note Cards

 

Jon is interested in making some different size note cards by folding rectangular sheets of paper in half repeatedly and cutting the paper on the folds.  He is interested in finding the amount of writing area on the different note cards obtained by cutting on the different folds. Jon is wondering if it is possible to find the area of the note cards if he just knows the size of the original sheet and how many ˝ folds he makes.

 

The Paper Folding Activity

 

1.      Fold a sheet of paper in half and determine the area of the smallest section after you have made the fold.

 

2.     Record this data in the table and continue in the same manner until it becomes too hard to fold.

 

3.     Make a scatter plot of your data.

 

4.     Determine a mathematical model that represents this data by examining the patterns in the table.

 

 

 

Area of Smallest Section

Number of Folds

Area of Smallest Section

0

 

1

 

2

 

3

 

4

 

5

 

6

 

7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

Area of Note Cards

 

Jon is interested in making some different size note cards by folding rectangular sheets of paper in half repeatedly and cutting the paper on the folds.  He is interested in finding the amount of writing area on the different note cards obtained by cutting on the different folds. Jon is wondering if it is possible to find the area of the note cards if he just knows the size of the original sheet and how many ˝ folds he makes.

 

The Paper Folding Activity(Solutions)

 

5.      Fold a sheet of paper in half and determine the area of the smallest section after you have made the fold.

 

6.     Record this data in the table and continue in the same manner until it becomes too hard to fold.

 

7.     Make a scatter plot of your data.

 

8.     Determine a mathematical model that represents this data by examining the patterns in the table.

 

 

 

Area of Smallest Section

Number of Folds

Area of Smallest Section

0

93.5

1

46.75

2

23.375

3

11.6875

4

5.84375

5

2.921875

6

1.4609375

7

.73046875

 

 

 

 

 

 

 

 

4. Mathematical Model: 93.5 x (˝)n

 

 

Vocabulary and Formula Review

Pre-Teach

 

1.      Scatter Plot – To show where data points fall in relation to     

   two variables.

 

2.    Coordinate Grid - A grid used to locate a point by the distance from two intersecting lines.

 

 

3.    X Axis – A horizontal number line on the coordinate grid.

 

4.    Y Axis – A vertical number line on a coordinate grid.

 

5.     Quadrants – X and Y axis divides the coordinate grid into 4 regions called quadrants.

 

 

Formula for Area of a Rectangle:     Base x Height (b x h)

 

 

 


Height

  (h)

 

 

                                Base (b)

 

 

 

Directions For Using the TI-83+ to: Graph a Scatter Plot,

Determine an Exponential Model, and Graph the Model

 

 

 

To enter the data:

            STAT   1:EDIT   ENTER

(Clear any data in the lists by using the up arrow button to go to the top and push CLEAR then ENTER.

            Enter the data with the independent data in L1 and the dependent data in L2.

 

 

To plot the scatter graph:

            2nd Y=(STAT PLOTS)   1:PLOT 1   ENTER

Highlight ON, push ENTER, highlight the first type, push ENTER, make sure X list has L1 in it and Y list has L2 in it.  Highlight the first choice after Mark and push ENTER

 

 

To set the window and show the graph:

    ZOOM    9:ZoomStat    ENTER

YOU SHOULD SEE A SCATTER PLOT

 

 

 

To find the exponential regression equation and store the it in Y1;

STAT   CALC    A:ExpReg    ENTER   2nd  1(L1)   ,    2nd 2(L2)   ,    VARS    Y-VARS    1:FUNCTION     1:Y1    ENTER    GRAPH

 

YOU SHOULD GET A CURVE THROUGH THE SCATTER PLOT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

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