Unit Overview

Content Area: Mathematics
Unit Title: Geometry Explorations
Name: Patti Ackerman
School: Lindenwold Middle
Date: July 22, 2010

Unit Summary
In this unit, students will examine properties of basic plane figures and will use tools of geometry; rulers, protractors and the geometry template, and students will explore tessellations. We will review names of polygons, line segments, rays and lines. The students in this classroom do not retain information from day to day, they extra practice and reinforcement to gain math skills.

Primary interdisciplinary connections
Literacy:

• Students read about different polygons in “The Greedy Triangle” by Marilyn Burns.
• Students read about shapes that tessellate in “A Cloak for the Dreamer” by Aileen Friedman.

Art:

• Students will draw pictures of polygons
• Students will create tessellations using pattern blocks

Music:

• Sum of angles song

Social Studies:
Polygon comes from Ancient Greece, poly = many and gon means knee or angle

21st century themes
Global Awareness
Polygons in nature: http://en.wikipedia.org/wiki/Polygon#History

Unit Rationale
I have chosen to focus on these concepts because angles and sums of angles are commonly used in geometric applications and reasoning. The instructional methods that I have chosen in this lesson will meet the needs of the students.
Many careers options will require students to be able to understand angle measurements: automotive careers, military careers, architecture and contractors, computer technology, and even some hobbies and crafts.

Learning Targets

Common Core Standards
5.G.3 and 5.G.4
New Jersey Core Curriculum Content Standards
4.2.5.A1, 4.2.5.A2, 4.2.5.A3, 4.2.5.A4, 4.2.5.B1, 4.2.5.E1

Content Statements
Students will classify two-dimensional figures into categories based on their properties.
5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
4.2.5.A1 Understand and apply concepts involving lines and angles.
4.2.5.A2 Identify, describe, compare, and classify polygons.
4.2.5.A3 Identify similar figures.
4.2.5.A4 Understand and apply the concepts of congruence and symmetry (line and rotational).
4.2.5.B1 Use a translation, a reflection, or a rotation to map one figure onto another congruent figure
4.2.5.E1 Use a protractor to measure angles.

Unit Essential Questions

• How are different polygons related to each other?
• How would you use measurements of polygons to solve problems?
• What situation can be analyzed using transformations and symmetries?

Unit Enduring Understandings

•  The angle sums of triangles, quadrangles, and polygons without measuring and basic plane figures that have distinct properties can be found with a formula or pattern.
• Everyday objects have a variety of attributes, each of which can be measured in different ways.
• Shapes and area can be conserved during math transformations.

Unit Learning Targets
Students will...

• Measure an angle to within 2 degrees.
• Identify types of angles, acute, obtuse or right.
• Identify types of triangles.
• List properties of polygons for identification.
• Create tessellations.
• Classify and sort geometric shapes by properties.

Evidence of Learning

Summative Assessment (2 days/160 minutes)
End of Unit Project Choices:

1. Create a Geometry Book that will include all concepts and skills taught in this unit and present to class.
2. Create a Power Point Presentation that includes all concepts and skills taught in this unit and present to the class.

Equipment needed
Paper booklets, directions, colored pencils or crayons, rulers, compass, Protractors, geometry templates, computers

Teacher Resources
Everyday Mathematics, IXL.com, Smart Board Notebook, Geometers Sketchpad

Formative Assessments

• Students will take quizzes to ensure mastery of concepts. Quiz 1 will cover lessons 1, 2 and 3. Quiz 2 will cover lessons 4, 5 and 6.
• Informal assessment through daily Math Messages or class work—white boards or oral.
• Everyday Math journal pages and Math Boxes
• Participation in using Smart board, dry erase boards, or pencil and paper tasks to solve problems

Lesson Plans
Lesson 1
Exploring Angle Measures
80 minutes/ 1 day

Lesson 2
Using a Protractor
160 minutes/ 2 days

Lesson 3
Congruent Triangles
80 minutes/ 1 day

Lesson 4
Properties of Polygons
160 minutes/ 2 days

Lesson 5
Regular Tessellations
80 minutes/ 1 day

Lesson 6
Angles of Polygons
80 minutes/ 1 day

Lesson 7
Solving Problems with the Geometry Template
80 minutes/ 1 day

Teacher Notes
Extra time will be given when necessary.

Curriculum Development Resources

Teacher’s Manual for Everyday Mathematics, IXL.com

Sum of angles song

Internet Math Games:
Finding angle measurements:
http://www.mathplayground.com/alienangles.html
What type of angle, acute, obtuse or right?
http://www.toonuniversity.com/6m_angle_d.html

Lesson Plan 1
Content Area: Mathematics
Lesson Title: Angles of Polygons
Timeframe: 160 minutes/ 2 days

Lesson Components

21st Century Themes
X Global Awareness
Financial, Economic, Business, and Entrepreneurial Literacy
Civic Literacy
Health Literacy

21st Century Skills
x  Creativity and Innovation- Drawing polygons, create a geometry book
x  Media Literacy- read literature on polygons and angles
x  Critical Thinking and Problem Solving- Solve for sum of angles independently
ICT Literacy
x  Communication and Collaboration- work in small groups and discuss strategies
Life and Career Skills
Information Literacy
Interdisciplinary Connections: Art, Literacy, Social Studies, Music
Integration of Technology: Computer with Smart Board technology and Internet access and Document      Camera, Geometers Sketchpad, Internet games and songs
Equipment & materials needed: Paper, rulers, geoboards with rubber bands, Geo templates, computers, Smart Board notebook activities, document camera

Goals/Objectives/CPIs
Students:

• Students will draw polygons to find the angle sum measurements with an 80% accuracy.

Learning Activities/Instructional Strategies

• Engagement
• Math Message: matching polygons with names of polygons on the Smart Board.
• Draw a measure angles of a triangle; on SB create line graph to show data. After students draw triangles, and measure their angles, we will create a line plot to display their findings and discuss.
• Exploration
• Draw triangles and quadrilaterals to demonstrate why their angles sums are 180 and 360 degrees.
• Students use geoboards or draw polygons to determine the sum of the angles.
• Students manipulate shapes of the Smart Board to determine the sum of the angles.
• Explanation
• Complete journal page 86: students will draw polygons and complete table with angle sums.
• Display completed work on document camera and explain answers
• Elaboration
• Geometers sketchpad will be used for explanation and demonstration examples.
• Start with creating a triangle and measuring the 3 angles. What is the sum of the angles?
• Create a square, pentagon and hexagon and follow the same steps. Students can make a table on the geometers sketchpad.
• Evaluation
• Observation of drawing or making polygons
• Questioning on why and how students solved the problems of finding sums of angles

• Creating polygons with drawing or geoboards
• Math Message on matching polygons
• Journal page 86:  students will draw polygons and complete table with angle sums.
• Exit Card: What is the sum of the angles in a triangle?

What is the sum of the angles in a quadrilateral?

Universal Design for Learning Options

 Multiple Means of Representation Perception: Students will see polygons with drawing, building on geoboards and creating on the sketchpad. See exploration Language & symbols: Use American Sign Language to help students recall names for shapes. Comprehension : students will work in pairs or small groups for discussion of strategies,
 Multiple Means of Action and Expression Physical activity: Fine motor with creating polygons on geoboard, walking to Smart Board to solve problems. See Exploration. Expressive skills and fluency: Cooperative learning groups, and discussion of strategies for solving journal page. Executive functions: recall of facts in Math Message, the song to help memory, poster to display key information, group discussions, and technology through games and Smart Board activities.
 Multiple Means of Engagement Recruiting interest: Students will be interested in drawing, using the geoboards and Smart Board, they also will enjoy singing the angle song. see Elaboration Sustaining effort and persistence see Elaboration Self-regulation: Journal pages and Sketchpad activities will need to be completed.

Resources