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Instructional Plan Template

Mathematics Governor’s Institute 2006

(Download as Microsoft Word Document: Instructional Plan)

 

Names of group members:

 

·         Brenda Bare, Linda Carmichael, Deborah Koch, Danielle Retallack, Debra Wright

 

Topic/Theme:

 

·         Folded Eight-Point Pinwheel

 

Level:

 

·         6th Grade through Pre-Algebra

 

Time Element: 

 

·         2 class periods (40-50 minutes)

 

NCTM Standards Addressed:

 

·         Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

·         Precisely describe, classify, and understand relationships among types of two- and three- dimensional objects using their defining properties.

 

PA Math Standards Addressed: 

 

·         2.9.8.C Classify familiar polygons as regular or irregular up to decagon.

 

Math Assessment Anchors Addressed: 

 

·         M6.C.1.1.1 Analyze characteristics and properties of two- and three-dimensional geometric shapes and demonstrate understanding of geometric relationships.

·         M6.B.2.2 Solve problems involving length, perimeter, area and/or volume of geometric figures.

·         M7.B.2.1Develop, use and/or describe strategies to find the measure of length, perimeter, circumference, area or volume.

·         M8.B.2.2 Use, describe and/or develop procedures to determine measures of perimeter, circumference, area, surface area and/or volume.

 

 

 

Objectives: 

 

·         To recognize, name and use polygons

·         To classify polygons as regular or irregular

·         To follow oral and/or written directions

·         To calculate area of polygons

 

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

 

 

Previous learning:

 

·         Teacher will have read to the class A Greedy Triangle by Marilyn Burns.

·         Students are familiar with the names of polygons (from triangle to decagon).

·         Students are able to calculate the area of a square, triangle, rectangle, parallelogram and trapezoid.

 

Day 1: 

 

·         Each student must choose 8 squares of the 6” by 6” colored paper.

(Note: Any size square will work.  The 6” by 6” square is conducive to finding the area by subtraction.)

·         The students will construct the pinwheel following the oral and/or written directions found on the Folded 8-Point Pinwheel sheet.

·         The teacher will review the following vocabulary: diagonal, square, pentagon, trapezoid, parallel, parallelogram, octagon, perimeter, regular and irregular while guiding the students through the construction of the pinwheel.

·         See attachment for directions.

 

Day 2: 

 

·         Give each student a 6” x  6” square of white paper and a worksheet.

·         Students will work in pairs or groups.

·         Students will calculate the area of each shape that occurs following a fold as given on worksheet.

·         Students will then calculate each consecutive area using subtraction.

·         Students will then verify the answer for the area of the last polygon (parallelogram) by measuring height and base to calculate the area.

·         This lesson leads into determining sum of the angle measurements of various polygons.

·         See attachment for worksheet and answer key.

 

 

Materials/Resources:

 

·         Each student will need eight 6” x 6”squares; preferably Xerox quality assorted colored paper.

·         Each student will need one 6” x 6” square of Xerox quality white paper.

·         Worksheet

·         Ruler

·         Samples of pinwheel

·         Overhead and wax paper square for demonstration

·         Teacher copy of written directions with pictures

·         Sample Pinwheel

 

Interdisciplinary Connections:

 

·                    Reading

 

The Greedy Triangle by Marilyn Burns

 

·                    Technology

 

Geometer Sketchpad can be used for extension lessons, if desired.

 

·                     Other

 

                  Art

      Family and Consumer Science

                  Language Arts (for listening skills and following oral directions)

 

Assessment Strategies:

 

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

·         Day 1:  Ongoing assessment during proper folding and construction

·         Day 2:  Observation of students as they complete worksheet

 

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

·         Day 1: Construction of the pinwheel, manipulate pinwheel and identify various shapes which can be formed in the interior of the pinwheel.

·         Day 2: Completed worksheet

 

Correctives/Remediation:

 

·         Peer assistance

·         Flash cards of terms

 

Extensions/Enrichment:

 

·         Rosemary’s Circle Activity

·         See attachment for directions.

 

Special Accommodations (special needs students)

 

·          Description of the Special Needs student selected:

This female student is extremely withdrawn.  She appears to be depressed and has difficulty relating to peers and her teachers.  She lives with her father in a single parent household. The school record indicates that she has been physically abused. It has been reported that her father is an alcoholic and that he beats her when he is drunk. She has been doing poorly in school, but the school does not want to alert her father.

     

Accommodations to use with this student:   

·                     Create a safe classroom environment for the student.

·                     Build the student’s confidence.

·                     Build a relationship with the student outside of the classroom.

·                     Call on the student only when the student is correct and prepared.

·                     Alert the guidance counselor and/or school psychologist of potential problem.

·                     Refer her to Teen Al-Anon.

·                     Use alternate forms of assessment/projects (avoiding oral reports, etc. until the student is more comfortable and less withdrawn).

·                     Use nonverbal cues to reinforce times for conversation.

·                     Pair student with a peer.

·                     Praise efforts toward socialization.

 

Key Words:

 

  • Area
  • Polygon
    • Square
    • Pentagon
    • Trapezoid
    • Parallelogram
    • Octagon
    • Triangle
  • Pinwheel
  • Origami

 

FOLDED 8-POINT PINWHEEL

 

Folding of Paper for Pinwheel

 

 

This project works best by using Xerox quality colored

paper.

 

Start with 8, 6 by 6 inch squares (you can use a variety of

colors). When folding be sure to score each fold well.

 

 

 

 

Step 1:  Fold each piece in half, open and then fold in half

the other way.

 

AB to CD

AC to BD

 

 

 

 

 

 

 

Step 2:  Fold two diagonals, opening between each fold.

 

A to D

B to C

 

 

 

 

 

 

 

 

Step 3:  Fold consecutive corners in to the center to create a

pentagon (do not reopen).

 

A to center

B to center

 

 

 

 

 

 

 

 

Step 4:  Fold in half on the center crease between the two triangles keeping the

triangles on the inside to create a trapezoid.

 

D to C

 

Step 5:  Hold “nose” in left hand, using your right index finger push midpoint fold on the DC line to the inside using the folds created from the original diagonals as your guide. Re-crease on the folds.                                             

 

 

This forms a parallelogram

Step 6:  Follow steps 1 through 5 with all eight pieces of paper.

 

Step 7:  When using a variety of colors, lay the parallelograms on the table in a row in the color sequence that you want to appear in the pinwheel.

 

Step 8:  Turn and flip the figure so that the open edges are on the bottom and the tail is on the right top.

 

 

.

 

 

 

 Construction of Pinwheel

 

Step 9:  Holding nose in left-hand, pick up second piece by the tail in right hand. Place nose of piece 2 into the tail of piece 1 keeping the open part down.

 

Step 10:  Fold tips of tail of piece 1 into tail of piece 2 between the two flaps so that they are flush with the top of piece 2.  The flaps will be able to be separated so that the next piece can be inserted.

 

 

 

Step 11:  Continue repeating steps 9 and 10 until all pieces are inserted in a circular pattern. The final parallelogram’s tail will hold the first parallelogram’s nose.  Be sure to fold the flaps in as your final folds.

 

 

 

The Pinwheel will slide open to form an octagon.  As you open your pinwheel many different polygons form in the center.

 

 

 

 

Picture taken from: 

http://oneweb.utc.edu/~deborah-mcallister/nctm06handout.html

Name________________________________

  Date_________________________________

 

 

 

Pinwheel Areas

 

 

 

             Fold #                    Shape                    Perimeter                     Area                             Regular/Irregular             

 

Beginning

 

 

 

 36 square in.

 

1

 

 

 

 

 

2

 

 

 

 

 

3

 

 

 

 

 

           

 

 

 

 

Now, calculate the area of the parallelogram by using the height and the base to check your work.

 

 

Base __________  X Height ______________ = ____________________square inches.

 

 

 

 

 

 

 

 

Teacher Key

 

 

Pinwheel Areas

 

 

 

     Fold #                Shape                  Perimeter                        Area              Regular/Irregular              

 

Beginning

 

square

24”

 36 square inches

regular

1

 

pentagon

20.5”

-2 triangles (-9 sq. in)

27 square inches

irregular

2

 

trapezoid

16.25”

- half (-13.5 sq. in.)

13.5 square inches

irregular

3

 

parallelogram

14.5”

- 1 triangle (4.5 sq. in.)

9 square inches

irregular

           

 

 

In addition, you can ask students to calculate the area of the square when folded in half and folded diagonally as an introduction to the above chart.

 

 

Note: For advanced students you may apply the Pythagorean Theorem.

 

Now, calculate the area of the parallelogram by using the height and the base to check your work.

 

 

Base ___3”_______  X Height ______3”________ = ___________9_________square inches.

 

 

 

 

 

 

 

 

 

 

ROSE MARY'S CIRCLE

 

1. Begin with a circle with a center point. Discuss plane figure, area, circumference, center of circle.

 

2. Make a mark on the edge of the circle with a pencil.

 

3. Fold the circular shape so that the mark on the circle touches the center dot.     The crease is a chord. Discuss diameter, radius, and segments of a circle.

 

4. Make another fold so that one end of the crease is at the end of the chord made in step 3, the edge of the circle touches the center dot, and the new segment is congruent to the smaller segment made in step 3. The folded figure now looks like an ice cream cone.

 

S. Make a third fold so that the edge of the arc (top of the ice cream cone) touches the center dot. You now have 3 congruent segments overlapping on an equivalent triangle. Discuss perimeter, sides, and angles.

 

6. Determine the midpoint of one side of the triangle by putting 2 endpoints together and pinching the midpoint.

 

7. Fold the opposite vertex to the midpoint. Discuss trapezoid, polygon, parallel and intersecting lines, acute and obtuse angles.

 

8. Hold the trapezoid so that the shorter of the 2 parallel sides is on the bottom. Pull the top right vertex to the opposite vertex and crease. (A rhombus is formed.) Pull the top left vertex to the opposite vertex and crease to form an equilateral triangle.

 

9. Now, no peeking! You have to guess the answer to the question without unfolding. "If you were to unfold the object to the original circular shape, how many congruent equilateral triangles would you see?" Guess. Then check.

 

10. Refold to the equilateral triangle in step 8. Put in the palm of your hand. Coax up the sides to form a pyramid with a special name of tetrahedron (4-sided pyramid). Discuss base, vertex, edge, face, volume.

 

II. Open the figure to the original large triangle.

 

12. Fold each vertex to the center and crease. Discuss hexagon.

 

13. Gently let the sides rise; coax the figure to become a truncated tetrahedron.

 

14. Open to the large triangle originally formed in step S. You will see two creases between each vertex and the center dot. Fold in on the longer crease and out on the shorter crease for all sides. You have a six-pointed star, the Star of David.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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