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Instructional Plan Template

Mathematics Governor’s Institute 2006

(Download as Microsoft Word Documents: Instructional Plan, Acute Triangle, Math Vocabulary, Obtuse Triangle, Right Triangle, Table)

Names of group members:

Melissa Stevens, Rich Blessing, Mollie McGeary, Marcia Curry, Cathy Tombasco

Topic/Theme: Sum of angles of a polygon

Level: 6 - 8

Time Element: – 1 class period

NCTM Standards Addressed:

Geometry Standard:

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

In grades 6-8, students should be able to:

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

· Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

· Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

· Use geometric models to represent and explain numerical and algebraic relationships.

· Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Measurement Standard:

Understand measurable attributes of objects and the units, systems, and processes of measurement.

· Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

Apply appropriate techniques, tools, and formulas to determine measurements

· Use common benchmarks to select appropriate tools to determine measurements.

Select and apply appropriate tools to accurately find length, volume, area, and angle measurements to appropriate levels of precision

PA Math Standards Addressed:

M6.C, M6.B, M7C, M8B, M8C (Sixth grade geometry and measurement, 7^th grade Geometry, 8^th grade geometry and measurement)

Math Assessment Anchors Addressed:

M6C1, M6B2, M7C1, M8C1, M8B2

Reading Assessment Anchors Addressed:

R6, 7, 8 A2 Understand nonfiction appropriate to grade level

R6, 7, 8 B3 Understand concepts and organization of non-fictional text

Objectives:

Find the sum of the angles in a triangle. Using the sum of angles of a triangle, find the sum of angles of other polygons. Develop and use a formula for the sum of angles of a polygon.

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

PROCEDURE:

Hand out the triangle worksheets. (Use 3 different types of triangles) Students will cut them out and place a dot inside each angle.
Rip the triangle into 3 pieces making sure that the angles stay in tact.
Have the students arrange the pieces so that the three pieces form a straight line. (Use the dots to help arrange the triangles appropriately)

Ask the student what relationship they can see in the arrangement. Making sure that they see a straight line as 180 degrees – Make the students aware that they all started with a different type of triangle. Thus it works for al types of triangles.
Hand out the sum of polygons worksheet (table)
Have the students fill out the table using their new knowledge of a triangle adding up to 180 degrees. They will need to form triangles within the polygons to discover the sum of angles of various polygons.

EXTENSION: Have the students try to devise a formula using n – gon for the sum of angles of a polygon.

Tactile – using hands on – Given one of the three different kinds of paper triangles, by ripping it apart, students can deduct that it is a straight line.

Auditory – Students are also listening to directions.

Visual – Students can see the sum of angles of a triangle add to 180 through the activity of producing a straight line.

Materials/Resources:

Paper and samples of different triangles, worksheets, overhead transparencies, quiz.

Interdisciplinary Connections:

· Reading – Math Vocabulary

· Technology – Do linear regression on the calculator

· Other – Going through the scientific method to form a hypothesis before using the worksheet (See procedure – step 6 – extension).

Assessment Strategies:

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

Teacher observation and peer observation

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

Collect the worksheets, present the project to the class. Take a quiz on the sum of angles in different polygons.

Correctives/Remediation:

Use a protractor to see that a straight line is 180 degrees. Let students look at the various geometric shapes as pictures instead of just reading them as words.

Extensions/Enrichment:

Find the diagonals and use linear regression on a graphing calculator.

Special Accommodations (special needs students)

· Description of the Special Needs student selected:

This male student has been sick very often. Because of this, his attendance at school has been erratic. He loves to experiment with things, however. At home, he is busy performing all kinds of experiments with household items. His school work has also been poor. It is unclear whether this is because of his attendance or a difficulty acquiring school related information.

· Accommodations to use with this student:

When the student is in attendance, the teachers will focus on such techniques as proximity, use of praise and rewards, possibly assign the student a responsible job within the group, assign a note-taking partner, recheck completed work, follow a lecture with a hands-on activity, and regularly use non-traditional teaching techniques including experiments, computer lab, graphing calculators, etc.

When the student is not present in the classroom, the teachers will engage the parents in the process by cooperatively making online resources available and providing a textbook on compact disk.

The teachers will also provide the parent/student a checklist of assignments missed and an outline of key concepts discussed in class. The teachers will also be in contact with the guidance counselor and school psychologist regarding the student’s frequent absences.

This plan will be constantly monitored, and altered if needed, if it becomes evident that the student is being enabled by having materials provided to him, and therefore, he does not effectively demonstrate effort in the process. The student will also be monitored to see his reaction toward students in his group, and to see his reaction toward the proximity of the teacher, specific students, and other adults with whom he has contact. Other accommodations will be made as needed to assist the student with receiving the best possible education based upon his need.

Key Words: Sum of Angles

Polygons

Sum of Angles in a Polygon

Math Vocabulary