## The Plane! The Plane!

### Kristy RousseauBay District Schools

#### Description

Students draw, describe, and classify polygons built from points, lines, line segments, and rays within a two-dimensional plane. This lesson plan is the third in a series of five on geometry.

#### Objectives

The student creates ample development of supporting ideas by presenting facts and information that clearly relate to the focus.

The student uses appropriate geometric vocabulary to describe properties and attributes of two- and three-dimensional figures (for example, obtuse and acute angles; radius; equilateral, scalene, and isosceles triangles.).

The student draws and classifies two-dimensional figures having up to ten or more sides and three-dimensional figures (cubes, rectangular prisms, pyramids).

The student knows how to justify that two figures are similar or congruent.

#### Materials

-Overhead, chart paper, and/or white boards will be needed all week.

Day 1
-Drawing Plane Figures worksheet (See Associated File.)
-Classifying Plane Figures worksheet (See Associated File.)
-Sample Notes and Paragraph worksheet (See Associated File.)
-Short-Answer Question Rubric (See Associated File.)
-Classifying Polygons worksheet (See Associated File.)
-Student Web Lesson: Practice with Plane Figures from Beacon Learning Center (See Weblinks-optional)
-Presentation system (large screen TV/monitor) to display Student Web Lesson (optional)

Day 2
-Completed Classifying Polygons worksheets (See Day 1.)
-Short-Answer Question Rubric (See Associated File.)
-Geoboards and bands
-Building Polygons (See Associated File.)
-Textbooks and applicable work pages
-Student Web Lesson: Pete’s Polygon Picture from Beacon Learning Center (optional) (See Weblinks)
-Presentation system (large screen TV/monitor) to display Student Web Lesson (optional)

Day 3
-Short-Answer Question Rubric (See Associated File.)
-Completed Building Polygons worksheets (See Day 2.)
-Toothpicks (8 per group)
-Tape
-Highlighter or colored pen
-Waxed paper circles (from Week 2) or protractors
-Two-ring Venn Diagram (See sample in Associated File.)
-Building Polygons: Notes and Paragraph Page (See Associated File.)

Day 4
-Textbook
-Sorting All Sorts of Polygons worksheet (See Associated File.)
-Rulers
-Wax paper circles (or protractors)
-Picture sources: magazines, clip art, newspapers, etc.
-4x6 or 5x8 index cards (at least one per student)
-Glue sticks and scissors
-Pattern Blocks
-Enlarged copies of polygons A-F (See Associated File.)
-Computers and software with basic drawing capabilities
-Disks (one per student)(optional)
-Student Web Lessons: Carol’s Congruent Concentration and Sam’s Similar Shapes from Beacon Learning Center (optional) (See Weblinks)
-Paper

Day 5
-Building Code Check-Up # 3 (See Associated File.)
-Scoring Criteria (See Associated File.)

#### Preparations

Day 1:
1. Prepare student copies of Drawing Plane Figures,Classifying Plane Figures,Sample Notes and Paragraph,Short-Answer Question Rubric, and Classifying Polygons.
2. If using an overhead, prepare overhead transparencies of the handouts listed above to use during modeling and instruction.
3. Gather overhead grid paper and/or chart paper for recording students' responses to Drawing Plane Figures.
4. Preview and bookmark the Student Web Lesson: Practice with Plane Figures(optional).
5. Prepare presentation system to display Student Web Lesson (optional).

Day 2:
1. Prepare a copy of the Short-Answer Question Rubric found in Part A of the Scoring Criteria to guide students during the peer assessment review activity.
2. Prepare student copies of Building Polygons page 1 and 2. Optional: Print these pages back-to-back for easier management.
3. If using an overhead, prepare a transparency of Building Polygons, page 1 and 2, for modeling and instruction.
4. Gather geoboard and bands.
5. Review textbook for applicable work pages and exercises.
6. Preview and bookmark the Student Web Lesson: Pete's Polygon Picture and prepare presentation system for display purposes (optional).

Day 3:
1. Adapt* the Short-Answer Question Rubric found in Part C of the Scoring Criteria to guide students during the peer assessment review activity. (*Change the wording from similar to congruent.)
2. Prepare an instructional model (overhead transparency, chart paper, etc.) of Building Polygons, page 1, that contains examples of shapes created during
Day 2.
3. Gather toothpicks, tape, and rulers.
4. Gather wax paper circles (Week 2) or protractors.
5. Prepare an instructional model (overhead transparency, chart paper, etc.) of the two-ring Venn Diagram for Classifying Polygons.
6. Prepare student copies of Building Polygons: Notes and Paragraph Page.

Day 4:
1. Prepare written directions for selected workstations.
2. Identify text pages that reinforce and extend instruction.
3. Prepare student copies of Sorting all Sorts of Polygons.
4. Gather bulletin board card materials.
5. If pattern blocks have not been used before, set aside orientation time for students to work and play with manipulatives.
6. Prepare copies of Enlarged Polygons (a-f) for hands-on symmetry activity.
7. Preview and bookmark the Student Web Lessons: Sam's Similar Shapes and Carol's Congruent Concentration.
8. Note: The one-minute papers are a formative assessment that are intended to help both the students and the teacher with learning issues. Although initial answers may be short and cryptic, students will gain confidence in sharing their thoughts about learning as they receive positive responses from the teacher.

Day 5:
1. Prepare student copies of Building Code Check-Up #3.
2. Review the Scoring Criteria for Building Code Check-Up #3.

#### Procedures

Day 1
1. Diagnostic Activity: Pass out student copies of Drawing Plane Figures. Review the directions and problem-solving steps with the students. Allow time for students to share ideas with one another before requiring them to complete the activity and paragraph. (Note: This activity should be used to assess students’ use of paragraph format-introduction, body, conclusion-and how well they develop supporting ideas by presenting facts and information that clearly relate to the focus. The writing needs identified in this activity will be addressed and developed during the week.)

2. Solicit students’ hypotheses to the problem and record on overhead grid paper or chart paper several of the plane figures students sketched on Drawing Plane Figures.

3. Present week’s goal: To draw and classify* two-dimensional plane figures. (*Written explanations will be used to explain classifications, and appropriate geometric vocabulary will be used to support students’ ideas and explanations.)

4. Introduce vocabulary terms —congruent and similar— to address the first part of the week’s goal (drawing). Refer to the students’ sketches, and identify whether the copies drawn on the overhead grid or chart paper are congruent or similar to the original version(s).

5. Approach the second part of goal (classifying). Ask: How can we organize, or classify these sketches using a 2-ring Venn Diagram? Solicit ideas from students and discuss the characteristics used for classification.

6. Using an overhead model of Classifying Plane Figures, sort similar versions of the sketches according to closed figures and open figures. Pass out student copies of the Classifying Plane Figures Venn Diagram and have them complete the same classification, labeling each group accordingly. Option: The Student Web Lesson: Practice with Plane Figures may also be used to provide examples and non-examples of plane figures.

7. As a class, complete the written descriptions for Group 1 and Group 2 on Classifying Plane Figures, using the definition format. (The definition format contains two parts, the general class the object(s) belongs to and the specific details that separate the object(s) from other members in the class.)

8. Redirect students’ attention to the question posed on Drawing Plane Figures: What happens when angles intersect with other lines, line segments, and rays within the plane? Tell the students that not only is it important to understand the building blocks of geometry, but they also need to be able to clearly and completely communicate their understandings to others.

9. Pass out the Sample Notes and Paragraph page. Use the Sample Notes section to record specific details about the figures constructed by the students. (Solicit descriptors from the students.) Direct students to list these descriptors on their page as well.

10. Ask how the students could use these notes to organize a paragraph that would explain what happens when angles intersect with other lines, line segments, and rays within the plane. Use the students’ ideas, and guide them in correct paragraph format (introduction, body, conclusion), as you model how to write an expository paragraph. Students should record the Sample Paragraph on their page as well.

11. Compare the paragraphs written in step A and L with the Explaining and Interpreting your Answer section of the Short-Answer Question Rubric. Discuss with the students what makes a clear and complete answer, and focus on the use of supporting facts and information that clearly relate to the main ideas of the paragraph. List improvements or revisions that could be made to both sets of paragraphs.

12. Explain that the closed plane figures on the Venn Diagram represent a specific class of plane figures known as polygons.

13. As a class, define polygons. Record the class definition on the board or chart paper. (Remember, the definition should include the general class polygons belong to plane figures and the specific details that separate them from the general class, closed figures made up of 3 or more line segments.)

14. Homework: Explain that there are a variety of ways to classify polygons and that you want to see their initial ideas. Provide copies of Classifying Polygons and the Short-Answer Question Rubric. Remind them that the Explaining and Interpreting your Answer section of the rubric will be used to help score their answers.

Day 2
1. Review: Solicit the classification schemes the students used on their homework, Classifying Polygons. Record the groupings students share on an overhead copy or chart paper. Discuss their use of appropriate geometric vocabulary in the selected titles.

2. Have students swap papers and use their copies of the Short-Answer Question Rubric to score the written explanation. (The adapted SAQ rubric found in Part A of the Scoring Criteria may also be used to help clarify any gray areas that students encounter as they peer assess.) Collect students’ work for further review. Note: Use this formative assessment to check students' usage of specific details and appropriate vocabulary. Based on students' written responses, plan the models and instruction that will be needed to help students clearly present facts and information that relate to the focus.

3. Review the vocabulary terms: congruent,similar, and polygons. Ask volunteers to explain how they know if a figure is congruent or similar to a given shape. Also have students orally review how polygons are related to the other geometric building blocks (points, lines, line segments, rays, and planes).

4. Present week’s goal: To draw and classify two-dimensional plane figures. Reiterate that yesterday’s lesson focused on drawing plane figures. Tell the students that the next two days will be used to classify one type of plane figures-polygons.

5. Explain that the number of sides, angles, and vertices on a polygon is one common way to classify, or organize, these plane figures. (If possible, use the Student Web Lesson: Pete’s Polygon Picture to further introduce the concept of classification according to sides, angles, and vertices.)

6. Use a geoboard and bands to model how various polygons can be built from three and four line segments. Record similar versions of these constructions under the Polygons Created column on an overhead copy of the Building Polygons worksheet. Name the polygons constructed (triangles and quadrilaterals) and identify the number of sides, angles, and vertices (3, 3, 3 and 4, 4, 4 respectively).

7. After modeling, pass out student copies of the Building Polygons and have them complete the first two sections as shown on the overhead transparency.

8. Provide students with geoboards and bands and instruct them to construct and record various polygons with 5, 6, 7, and 8 sides. If time permits, direct them to use their textbooks to find the name of the polygons created by 5, 6, 7, and 8 sides.

9. When most of the groups have finished, provide time for the students to show some of their more interesting or creative constructions with the class.

10. As a class, chart the general name of the polygons created (pentagons, hexagons, heptagons, and octagons). Share that the prefixes tri-, quad-,penta-, hexa-, and octa- are used in other words, as well, to identify 3, 4, 5, 6, or 8 of something. Brainstorm a list of such words with the students to help connect these mathematical terms with other familiar concepts (i.e., triangle, quadruplets, The Pentagon, octopus, etc.)

11. Pass out page 2 of Building Polygons and label the polygons created by 9 (nonagons), 10 (decagons), 11 (undecagons), 12 (dodecagons), 13 (13-gon), and 14 (14-gon) sides. Have students complete the number of angles and vertices that will be found in each of these polygons.

12. Homework: (a) Instruct students to draw at least 2 different polygons for each classification. Hint: Students may want to use a scrap piece of paper to experiment with various polygons before recording them. (b) When finished, have them circle the polygon that they think is the most interesting or creative. (c) Assign the students to write a paragraph (on a clean sheet of paper) explaining how to draw a figure that is congruent to the circled polygon. Remind the students that the Short-Answer Question rubric will be used to assess the content of their explanations. (Any applicable textbook pages may be assigned as well.)

Day 3
1. Review: Check assigned textbook pages and clarify any misconceptions as evidenced in students' answers. Have students swap homework paragraphs and use the Short-Answer Question Rubric to score the written explanations about drawing congruent figures. (The SAQ rubric found in Part C of the Scoring Criteria may be adapted to help clarify any gray areas students encounter as they peer assess. Simply change the wording from similar to congruent.) Collect students’ paragraphs for further review. Based on students' written responses, plan the models and instruction that will be needed to help students clearly present facts and information that relate to the focus.

2. As a class, write definitions of congruent and similar figures using the definition format (general class + specific details). Record definitions on the board or chart paper underneath the class definition for polygons that was written on Day 1.

3. Review week’s goal: To draw and classify two-dimensional plane figures. Ask a volunteer to summarize the classification scheme presented yesterday (organizing polygons according to the number of sides, angles, and vertices).

4. Redirect students’ attention to the polygons drawn on the Building Polygons worksheet. Ask: What other way could we classify these polygons?

5. Allow students to share and discuss ideas with the class. Explain that polygons can also be classified as regular or irregular.

6. Using the similar shapes recorded on an overhead copy of Building Polygons,(page 1) circle any examples of regular polygons that exist. Have students circle these examples on their papers as well.

7. Using toothpicks, model the regular polygons that can be built with 3 line segments (equilateral triangle) and four line segments (square).

8. Record similar versions of these regular polygons in the left-hand margin of page 1 of Building Polygons. Instruct students to do the same on their papers.

9. Ask: What do these regular polygons have in common? What characteristics do you see that are important to regular polygons?

10. Add to the students’ ideas and explain that a regular polygon is a polygon with all sides congruent and all angles congruent.

11. Use the equilateral triangle and square to help students understand that definition. Using tape, secure the toothpicks in place and trace around the perimeter of the polygons. Tell the students that we know the sides of the triangle are congruent (or the same length) because equal-length toothpicks were used to build the polygon. The same is true of the square. Ask: What could we use to measure the length of the sides to be certain that they are congruent?

12. Use a ruler to measure and record the length of each side of the triangle and square. Reiterate the first part of the definition of a regular polygon: a polygon with all sides congruent.

13. Next, highlight or color one interior angle of the traced equilateral triangle. Use the wax paper circles created in lesson 2 (or a protractor) to measure the angle. Record the angle measurement. Measure the other two interior angles to verify that the regular polygon also has congruent angles.

14. Pass out eight toothpicks to each group of students. Instruct the students to construct a regular quadrilateral (square) and use their waxed paper circles (or protractors) to verify that its interior angles are congruent.

15. Review the process of constructing, recording, and verifying regular polygons. Have the groups use toothpicks to construct and record regular polygons with 5, 6, 7 and 8 sides. (Note: A seven-sided regular polygon will not be possible.)

16. Have each student trace one of the regular polygons on a clean sheet of paper and use rulers and waxed paper circles (or protractors) to measure and record congruent line segment lengths and angles.

17. When most of the groups have finished, allow students to share which regular polygons were possible, as well as the length and angle measurements recorded. Help students define an irregular polygon based on their experiences with regular polygons.

18. For a visual review, use a 2-ring Venn Diagram and draw regular (equilateral triangle, square, pentagon, hexagon, and octagon) and irregular polygons in the respective rings.

19. Pass out the Building Polygons: Notes and Paragraph page to students. Have students list characteristics of each type of polygon in the Notes section.

20. Homework: Have students complete the Paragraph section explaining the differences between regular and irregular polygons. Discuss various introductory sentences that could be used to start the paragraph. Remind students to support their ideas using the facts and information presented in the Notes section. (Any applicable textbook pages may be assigned as well.)

Day 4
1. Review: Have students swap homework paragraphs and use the Short-Answer Question Rubric to score the written explanations about regular and irregular polygons. As a class, discuss the facts and information that were used to write a clear and complete explanation. (Homework paragraphs, and any completed textbook pages, will be further reviewed with the teacher during the workstations.)

2. Based on students’ input, write a class definition for regular and irregular polygons. Post the definitions on the board or chart paper that already contains the definitions for polygons and congruent and similar figures.

3. State the week’s goal: To draw and classify two-dimensional plane figures. Review the classification schemes explored during Day 2 and 3 (# of sides, angles, vertices and regular and irregular).

4. Tell the students that they will be practicing and applying what they have learned over the past few days about drawing and classifying polygons in today’s workstations.

5. Post written directions for the workstations (see Teacher Preparation) and review behavioral expectations. Note: If this is the first time stations have been used, allow time for both the students and yourself to become acclimated to the process. Take small steps and clearly model the outcomes you expect.
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WORKSTATIONS--Select and adapt these stations to fit the class’s needs:
1. Textbook: Assign text pages that require students to draw and classify polygons. The problems should reflect the types of problems that students have encountered during the week. The worksheet, Sorting All Sorts of Polygons, may also be assigned at this time.

2. Bulletin Board Cards: Students use picture sources, index cards and glue sticks to select, classify, and label polygons found in nature, architecture, and art. Encourage the groups to find similar and congruent polygons, as well as regular and irregular polygons.

3. Pattern Blocks: Students (a) draw and label congruent and similar* versions of each pattern block, (b) name the polygon represented, and (c) classify it as regular or irregular. When finished with the individual blocks, students may combine 2 or more blocks to form a new polygon. This polygon should be named and classified. (*Note: To form a true similar figure, careful calculations and measurements would have to occur to ensure that the angle measurements stayed the same and that the length measurements were proportional. The purpose of this activity is not precise measurements, but to assess whether or not the students understand that a similar figure has the same shape, but not necessarily the same size, of the original polygon.)

4. Teacher: Review the students’ paragraphs and the textbook pages that were assigned for homework. Based on the students’ work, provide instruction to strengthen the writing and classification skills of the students. If a clear understanding exists, use enlarged copies of polygons (a-f) to introduce a new property to classify by symmetry. Define symmetry and then model how to find lines of symmetry by folding the enlarged polygons. Work with the students to identify all lines of symmetry and then reclassify the polygons based on this characteristic.

5. Computers:
Option 1 (for Internet-accessible computers): Students complete the Student Web Lessons: Sam’s Similar Shapes and Carol’s Congruent Concentration available from the Beacon Learning Center. (See Weblinks.)
Option 2 (for software with basic drawing capabilities): Students use the drawing tools to construct an interesting or creative polygon. The polygon should be labeled and classified as regular or irregular. If time permits, have students complete congruent and similar versions of this polygon as well. The students’ work should be saved either on the hard drive or on a personal disk.
Note: If students are unable to complete the computer work, a rotation schedule can be developed to provide additional computer time during the upcoming week.
************************************************************************************
6. Reconvene to review the workstation activities. Check the textbook problems and collect the bulletin board cards and pattern block constructions to display.

7. Allow students to share any breakthroughs they encountered while working on the computers. (Often students will find new and novel ways to accomplish tasks on the computer because they are willing to take risks with the technology.)

8. Review the week’s goal (to draw and classify two-dimensional plane figures) and have students complete the following one-minute paper. On a clean sheet of paper, answer the following two questions: What do you know about drawing and classifying polygons? What do you still need to know about drawing and classifying polygons? Let the students know that this paper will not be graded; you simply want a peek of their thoughts and thinking.

9. Assign homework (textbook pages, Sorting All Sorts of Polygons worksheet, written paragraphs, etc.) as needed to reinforce and strengthen students’ understandings of drawing and classifying polygons.

Day 5
1. Review: Check assigned homework. Provide feedback to the students based on the concepts and understandings reflected in their one-minute papers from Day 4. Use this initial review time to clarify any misunderstandings that were represented and further solidify the connections they are building about drawing and classifying polygons.

2. Ask a student to state the week’s goal: To draw and classify two-dimensional plane figures.

3. Explain that what the students have learned this week about drawing and classifying polygons builds upon the foundation they have developed about the geometric building blocks (points, lines, line segments, rays, and planes) and angles. With each new step in the building process, however, a check-up must be completed to ensure that the building is being developed according to code.

4. Pass out Building Code Check-Up #3. Review the directions for each section of the assessment and remind students that this check-up will identify both the strengths and weaknesses of their foundations. Any weaknesses will be strengthened in future lessons to ensure that all students are building strong understandings of geometry.

5. Use the Scoring Criteria provided in the Associated File to grade the students’ work. Based on the extent of mastery shown on the assessment, provide feedback to the students that will help them reflect on where they are in the learning process.

6. Plan any steps and/or activities needed to address deficiencies identified by the assessment before continuing with the next lesson.

#### Assessments

Building Code Check-Up # 3

Part A
Total Points: 40
Students classify and draw polygons, use appropriate geometric vocabulary to identify common properties and/or attributes, and write a paragraph to explain their individual classification schemes.

Part B
Total Points: 20
Students draw and label regular and irregular polygons.

Part C
Total Points: 40
Students draw and label similar and congruent figures and then write a paragraph to explain their understanding of similar figures.

Extra Credit--optional
Students draw line(s) of symmetry on the polygons (a-f) shown in Part A. (One point per correct line.)

See the Scoring Criteria attachment for specific criteria and individual point values (Associated File).

#### Extensions

1. This lesson plan represents the third lesson of instruction in a series of lessons on geometry.
2. Extra Credit option for Day 3: Have students identify the regular polygons that can be constructed from 9, 10, 11, 12, 13 and 14 sides.
3. Marilyn Burns’ book, [The Greedy Triangle] (published by Scholastic Trade, 1995), serves as a great review of polygons. It would also serve as a great introduction for the next week of instruction that focuses on the triangle, The Fun Polygon.

Web supplement for The Plane! The Plane!
Practice with Plane Figures

Web supplement for The Plane! The Plane!
Pete's Polygon Picture

Web supplement for The Plane! The Plane!
Sam's Similar Shapes

Web supplement for The Plane! The Plane!
Carol's Congruent Concentration

The first lesson in a series of geometry lessons.
The Building Blocks of Geometry

The second lesson in the series of lessons on geometry.
Classifying and Constructing Corners

The third lesson in the series of lessons on geometry and where you are now.
The Plane! The Plane!

The fourth lesson in the series of lessons on geometry.
The Fun Polygon

This is the fifth lesson in the series of lessons on geometry.

This is an Internet research lesson (a supplemental lesson in the series of lessons on geometry.)

The online Student Web Lesson can be used as a supplement for this series of lessons on geometry.
Anglemania

This online Student Web Lesson can be used as a supplement for the series of lessons on geometry.
Triangles Side by Side

This online Student Web Lesson can be used as a supplement for this series of lessons o geometry.