Description

Students classify, flip, slide, and turn a quantity of quadrilaterals. Hands-on manipulatives and problem-solving steps are used to explore these four-sided polygons. This plan is the fifth in a series of lessons on geometry.

Materials

An overhead, chart paper, and/or white boards will be needed throughout the week.

Day 1:
-“The ‘Fun’ Polygon” (see Associated File)
-Scissors
-“A Quadrilateral Quagmire” (see Associated File)
-Additional white and/or notebook paper

Day 2:
-Completed homework “A Quadrilateral Quagmire—Parts 2 & 3” (see Day 1)
-Long-Answer Question Rubric (see Associated File)
-“A Quadrilateral Quandary” (see Associated File)
-“A Concept Map for Classifying Quadrilaterals” (see Associated File)
-Textbook

Day 3:
-Completed homework “A Concept Map…” (see Day 2)
-“A Quadrilateral Quagmire—Parts 2 & 3” (see Day 1)
-Paper
-Cardstock manipulatives of “A General Quadrilateral” (see Associated File) or other quadrilateral manipulatives such as pattern blocks and tangrams
-Scissors (if cardstock manipulatives are used)
-“Slides, Flips, and Turns” handout (see Associated File)
-Large teaching model of “Clockwise Rotations” (see Associated File)
-Large teaching model of “Counterclockwise Rotations” (see Associated File)
-Small practice models of “Clockwise and Counterclockwise Rotations” (see Associated File)
-“Turn, Turn, Turn” practice sheet (see Associated File)
-Textbook

Day 4
-Completed homework from Day 3 (written paragraphs and assigned textbook pages)
-Textbook
-Paper
-Picture sources (magazines, newspapers, catalogs, etc.)
-Scissors
-Gluesticks
-Construction paper
-Cardstock manipulatives of “A General Quadrilateral” (see Associated File)
-Colored pencils, crayons, and/or markers
-Long-Answer Question Rubric (see Associated File)
-Computers and software with basic drawing capabilities
-Disks (one per student)—optional
-Student web lesson, “The Quad Squad” (See Weblinks)

Day 5:
-Completed homework from Day 4
-“Building Code Check-Up #5” (see Associated File)
-“Building Code Check-Up #5—Manipulatives” (see Associated File)
-Scissors
-“Building Code Check-Up #5—Scoring Criteria” (see Associated File)
-Tessellation Coloring Page (see Extensions)
-Colored pencils, crayons, and/or markers
-Answers to “Quadrilateral Trivia Questions” (see Associated File)

Procedures

Day 1:

A. Pass out student copies of “The ‘Fun’ Polygon” and scissors. As students cut out each triangle, review why the triangle is the “fun”damental polygon. (The triangle is the basic unit from which all other polygons are constructed. A triangle is to polygons what an atom is to matter.)

B. Have students select one of the seven polygons and direct them to perform the following movements: slides, horizontal flips, and vertical flips. (Review as necessary, and do a quick visual check to make sure students are performing the movements correctly. The handout “Slide, Flips, and Turns” in the Associated File may be used as a reference if necessary.)

C. Present week’s goal: To classify,* flip, slide, and turn a quantity of quadrilaterals in order to explore and describe their properties and attributes. (*Paragraphs will be written to explain classifications.)

D. Tell the students that they will be using flips and the “fun” polygon today to create a “quantity of quadrilaterals.”

E. Pass out student copies of “A Quadrilateral Quagmire.” Define “quagmire” for the students using the definition on the bottom of the page.

F. Pose the question presented: “What quadrilaterals can be formed by flipping the following ‘fun’ polygons?” Solicit students’ hypotheses and explanations.

G. Use the following guided questions to help students review the first two problem-solving steps they will take. Step 1: Understand the Problem—What do you think this question is asking? Step 2: Decide on a Plan—How are you going to solve this problem?

H. Review the directions and example provided for Part 1 on the handout. Encourage students to “flip” each triangle 3 different ways (alternate the side that remains in place) and record the various quadrilaterals that are formed. (The backside of the page—and maybe even additional paper—will be needed to record the quadrilaterals.)

I. Once students have a clear handle on the “plan,” allow them to “Carry Out the Plan” (step 3). Monitor their flips and recordings. Provide immediate and corrective feedback as needed to guide their exploration.

J. When students are finished, have them count the quadrilaterals formed from flipping the “fun” polygons. (Note: I found 13 quadrilaterals: #1 formed a rhombus; #2 formed a general quadrilateral; #3 formed three general quadrilaterals; #4 formed a square; #5 formed a rhombus and a general quadrilateral; #6 formed a rhombus and a general quadrilateral; and #7 formed three general quadrilaterals. Some students may have flipped #1 twice, and formed a trapezoid as well. The labels used to identify these quadrilaterals—general, rhombus, etc.—are for the teacher’s information right now. Students will be introduced to these classifications in the days to come.)

K. Review the week’s goal: To classify,* flip, slide, and turn a quantity of quadrilaterals in order to explore and describe their properties and attributes. Tell the students now that they have a “quantity of quadrilaterals,” they have something to classify, explore, and describe.

L. Direct their attention to Parts 2 and 3 of “A Quadrilateral Quagmire.” Read the directions together and clarify any questions students may have about them.

M. Review the characteristics* of a strong paragraph: 1) Its explanation is so “clear and complete” someone else can use the facts and information presented in the paragraph to classify a new quadrilateral; 2) Its ideas are presented in an organized fashion—there is an effective beginning (introduction), a substantial middle (supportive facts and information), and an ending (conclusion). *These characteristics were taught and practiced in previous lessons. If writing in math is a new area for your students—and if you have not been working through this series of lessons—adjust this writing exercise to meet your students’ needs.

N. Allow students time to complete Parts 2 and 3. Collect students’ work and review their written paragraphs to diagnose their strengths and weaknesses—see Assessment.

O. Homework: If class time is short, assign Part 2 and/or Part 3 for homework. If students are able to complete both parts in class, assign applicable work pages that review “flips” and/or require students to construct other polygons (pentagons, hexagons, etc.) by flipping the “fun” polygons more than once.

P. Option: The handout “Quadrilateral Trivia Questions” may be introduced as a mini-research project. See “Extensions” (#2) for further details.

Day 2:
A. Review week’s goal: To classify, flip, slide, and turn a quantity of quadrilaterals in order to explore and describe their properties and attributes. Discuss the properties and attributes students identified in the quadrilaterals they formed while flipping the “fun” polygons on Day 1.

B. Present students with a copy of the Long-Answer Question Rubric. Review the criteria presented under the section, “Explaining and Interpreting your Answer.” (If this is the first time students have seen this rubric, take time to orient them to the criteria and scores. Explain to them that this rubric will be used to score their written explanations.)

C. Direct students to reread their paragraph from “A Quadrilateral Quagmire—Part 3” and then score their written response using the criteria provided on the rubric. Clarify any questions students have as they compare their work with the rubric. If necessary, define even further that a clear answer has a “clear, central focus” with “little or no repetitious information.” A complete answer addresses all areas of the question and includes an effective beginning (introduction), middle, and end (conclusion).

D. Have students swap papers and peer assess the explanations. (A score may be written on the bottom right-hand corner if desired.) After the explanations have been scored, draw a rectangle on the overhead or whiteboard. Instruct students to draw the rectangle into the classification scheme (Part 2) based on the descriptions provided in Part 3.

E. After students have attempted to classify the new figure, explain that our writing goal this week is to construct a clear and complete explanation so others can use the specific details and vocabulary to classify or draw a related quadrilateral.

F. Have students return the papers to their owners, and allow them a chance to review their “score” and ask any related questions about the rubric. Collect the students’ papers for further review (see Assessment).

G. For review, ask a student to define “quagmire” (a difficult situation or predicament). Tell the students that today they will experience “A Quadrilateral Quandary.”

H. Pass out “A Quadrilateral Quandary” and have students silently read the definition presented on the bottom of the first page. Ask, “What perplexing situation do you think we’ll experience with these quadrilaterals?” Have students brainstorm some possible quandaries.

I. Review the directions for Part 1 and the sample provided for Shape A. As a class, generate a list of appropriate geometric vocabulary that may be used in the descriptions (congruent, parallel, sides, acute, right, obtuse, angles).

J. Model Shape B and Shape C as needed. (At the teacher’s discretion, students may use abbreviations and mathematical symbols in their notes, and/or work with a partner to complete the descriptions.)

K. Rotate among the students as they work to monitor their progress. As students begin to notice patterns among their descriptions, talk with them about the emerging patterns that they see.

L. When most of the students have finished, direct their attention to Part 2. Review the directions for classifications. Emphasize that the quadrilaterals MAY be used more than once, and that not all six ovals have to be used. (Option: Have students work in partners on Part 2.)

M. As the students work and discuss the reasoning behind their classifications, rotate among them to observe their progress.

N. Reconvene as a whole class to discuss the various classifications students used. Record the students’ ideas as they are presented, emphasizing the similarities and patterns that exist between the students’ answers.

O. Pass out “A Concept Map for Classifying Quadrilaterals” and present a copy on the overhead or whiteboard. Explain that this map can be used to help identify and classify a quantity of quadrilaterals.

P. Have the students review the titles of the quadrilaterals: special, general, trapezoid, parallelogram, rectangle, rhombus, and square. Ask, “What patterns do you see on this map?” For example, students may recognize that rectangles, rhombi, and squares are all special types of parallelograms.

Q. Have students review the criteria for each quadrilateral. Ask, “What characteristics are used to classify the quadrilaterals?” (Parallel sides, congruent sides, and right angles)

R. Review the directions presented on the top of the page. Draw students’ attention to the numbers presented in parentheses in six of the ovals. Explain that these numbers represent the number of quadrilaterals that fit the criteria shown. For example, two (2) of the shapes from A-L are “General Quadrilaterals.” With the students, review the criteria for a general quadrilateral and identify the two shapes that match that description (Shapes K and L). Sketch similar figures of Shapes K and L in or near the “General Quadrilateral” oval.

S. Continue modeling, as necessary, with “Trapezoid.” Once students have a clear understanding about how to use the descriptions to identify the quadrilaterals, allow them time to work (or assign for homework if time is limited.)

T. Review that it is the quadrilaterals’ unique properties and attributes that make it possible to classify a “quantity of quadrilaterals.”

U. Homework: Have students complete the sketches on the Concept Map, and/or assign related textbook pages that further explore the various classifications of quadrilaterals.

Day 3:
A. Review the homework from Day 2. Pose the following question for discussion, “Why can a square also be called a rectangle, a rhombus, and a parallelogram?” As students share their ideas, refer back to the Concept Map to show how the square is related to each classification because of its unique properties and attributes. Have students identify other quadrilaterals (such as the rectangle and rhombus) that can be classified in more than one way.

B. Hand back Parts 2 and 3 of “A Quadrilateral Quagmire” from Day 1. Discuss any similarities that exist between the students’ original classifications and the Concept Map presented on Day 2. How close were their classifications? How would they reclassify the shapes using what they now know about quadrilaterals?

C. Have students take out a clean sheet of paper and fold it in half. They should label the top half “Classification” and the bottom half “Explanation.”

D. Explain to the students that for homework they are to reclassify the shapes from Part 2 of “A Quadrilateral Quagmire,” using the Concept Map as a guide. A written explanation should accompany their classification diagram. Review the qualities of a clear and complete paragraph as needed (see Day 2, step C ). Instruct them to set these papers aside for now and/or store them in their homework folders.

E. Review the week’s goal: To classify, flip, slide, and turn a quantity of quadrilaterals in order to explore and describe their properties and attributes.

F. Pass out quadrilateral manipulatives (pattern blocks, tangrams, and/or cardstock manipulatives of the general quadrilateral attached in the Associated File) and “Slides, Flips, and Turns” handout. Tell the students that today they will be working with some of the movements (or transformations) that quadrilaterals can perform.

G. Use the handout to review the slides and flips that can occur with polygons. (If previous lessons have been completed, this will be a review.) Discuss that slides can occur in any direction (up, down, right, left, diagonal) and allow students to practice these movements. Review that flips can occur both horizontally and vertically. Model these movements using a manipulative and have students practice them as well.

H. As each movement is practiced, review the appropriate symbols (straight arrows and dotted lines) to record whether the figure was slid or flipped.

I. Model for the students how manipulatives are also turned. Start in an “original position” and then turn the manipulative 90 degrees to the right and 90 degrees to the left. Tell the students that they will be exploring turns with their quadrilaterals today.

J. Pass out a copy of “Clockwise Rotations” and/or present an overhead model for the students to follow as you instruct. Tell the students that turns are measured in degrees, and that the measures of 90, 180, 270, and 360 degrees are most often used. Use an overhead manipulative to model each type of turn. Be sure to emphasize the complete circle that is made with a 360-degree turn. (The “Counterclockwise Rotation” handout may also be used when the students are ready to explore the other direction turns may take.)

K. Pass out student copies of the “Clockwise Rotation and Counterclockwise Rotation” sheet. Have students place their manipulative with one corner touching the center of the clockwise model and one side lined up with either the vertical or horizontal axis. (If the general quadrilateral is being used, have students line up its 90 degree angle with the center point; one side of the angle will then align with the vertical axis and the other side the horizontal axis.) Instruct students to trace their manipulative and label this position as “Home, 0 degrees.”

L. Have students practice 90, 180, 270, and 360 degree turns by turning the manipulative around the center point in the required direction (clockwise). Have students trace the manipulative after each turn and label it according to the number of degrees rotated. If necessary, model this procedure on the overhead before having students practice this activity independently.

M.Repeat step L, but use the counterclockwise direction this time.

N. For additional practice, use the “Turn, Turn, Turn” handout and a new manipulative with one of the following activities: a) Pair students and allow them to challenge one another to perform specific turns. For example, one student places the manipulative, and challenges his partner to rotate it 270 degrees counterclockwise (degrees and directions may vary). The student performs the movement and if correct, offers a counter challenge. b) Use an overhead transparency of “Turn, Turn, Turn” and place a manipulative in a “Home” position. Perform a movement on the overhead and ask students to identify the direction and degrees turned. (Adapt these options as necessary to fit the students’ needs for additional practice.)

O. Review the progress students made today towards accomplishing the week’s goal: To classify, flip, slide, and turn a quantity of quadrilaterals in order to explore and describe their properties and attributes.

P. Remind students of the paragraphs they are to rewrite for homework (see step D). Encourage them to use the criteria presented in the Long-Answer Question rubric to guide their writing.

Q. Assign any related textbook pages that reinforce the students’ work with turns.

Day 4
A. Check the homework pages assigned in Day 3 and collect students’ written paragraphs. (The paragraphs will be reviewed during the Teacher workstation today.) During the homework check, review the different turns quadrilaterals can make (90, 180, 270, and 360 degrees) in both clockwise and counterclockwise directions.

B. Review the week’s goal: To classify, flip, slide, and turn a quantity of quadrilaterals in order to explore and describe their properties and attributes.

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

D. 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.

WORKSTATIONS—Select and adapt these stations to fit the class’ needs.
1. Textbook: Assign practice pages and activities that will help students hone their skills at classifying quadrilaterals and performing various transformations (flips, slides, and turns). Sample testing problems (such as FCAT practice problems) that relate to quadrilaterals and transformations may also be used during this time.

2. A Quadrilateral Quest: Have students search the room for different examples of quadrilaterals and sketch similar versions of them on their paper. The quadrilaterals should then be classified and labeled using the criteria specified on the Concept Map. (Students may also search various picture sources such as magazines for quadrilaterals. The shapes may be cut out and arranged to create a pictorial Concept Map of Quadrilaterals.)

3. Problem-Solving Investigation: Provide several sheets of the general quadrilateral cardstock manipulative and have students construct small and large squares by piecing four or more of the quadrilaterals together. Final constructions should be glued on construction paper and will be shared with the other groups at the end of class. If time permits, students should create a color pattern in their finished squares.

4. Teacher: Have students self- and peer-assess the paragraphs written for homework using the Long-Answer Question Rubric. Discuss how paragraphs can be strengthened so that they provide a clear, central focus with little or no irrelevant or repetitious information. Focus on the qualities of a complete paragraph (an effective beginning, middle, and end) as the group reviews the properties and attributes of quadrilaterals that are used for classification (i.e., parallel sides, congruent sides, right angles).

5. Computers:

Option 1 (for Internet-accessible computers): Students complete the student Web lesson “The Quad Squad” available from the Beacon Learning Center (See weblinks.) Also have students check out the “Quadrilateral Problem” (see weblinks.)

Option 2 (for software with basic drawing capabilities): Students use the drawing tools to create congruent copies of a quadrilateral that has been flipped, slid, and rotated (turned). The specific name of quadrilateral and the movements it has undergone should be clearly labeled. All completed work is saved to students’ disks. Note: Computer time may also be used for research if students are working on the “Quadrilateral Trivia Questions.”

F. Reconvene to review the workstation activities. (If more time is needed to complete the textbook problems or finish classifying the quadrilaterals gathered during “A Quadrilateral Quest,” assign these tasks as homework). If not, check the textbook problems and allow the groups to share the small and large squares they constructed from the general quadrilaterals. Discuss how the small square was formed by turning the general quadrilateral each time. Explore the larger squares for specific color and movement patterns.

Day 5:
A. Check any assigned homework. Take time to review and clarify any misunderstandings that were presented in the students’ work and writings collected from Day 4’s workstations.

B. Ask a student to state the week’s goal: To classify, flip, slide, and turn a quantity of quadrilaterals in order to explore and describe their properties and attributes.

C. Explain that what the students have learned this week about quadrilaterals builds upon the foundation they laid during the previous weeks as they studied about the geometric building blocks (points, lines, line segments, rays, planes), angles, polygons, and triangles.

D. Reiterate that with each new step in the building process, a check-up is completed to ensure that the building is being developed according to “code.”

E. Pass out “Building Code Check-Up #5,” the accompanying manipulative sheet, and a pair of scissors to each student. Review each section of the assessment (Part A deals with classification, Part B reviews symmetry, and Part C focuses on flips, slides, and turns). Tell the students that they may cut out and use any of the manipulatives that they need during the check-up. Remind students that this check-up will help to identify both the strengths and the weaknesses of their “foundations.”

F. Optional: As students finish, provide them with a quadrilateral tessellation coloring page to reinforce the concepts covered during the week (see Extensions).

G. Optional: When all students have completed the assessment, discuss the answers to the mini-research project, “Quadrilateral Trivia Questions.”

H. 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 to know where they are in the learning process and what they need to do next.

I. Plan any steps and/or activities needed to address deficiencies identified by the assessment before continuing with any additional instruction on geometry.

Extensions

1. This lesson plan represents the fifth lesson in a series on geometry.
2. Quadrilateral Trivia Questions: Have students search the Internet, electronic encyclopedias, and other references for real-world information (not pictures) about quadrilaterals in nature, architecture, and art. Use the questions on the “Quadrilateral Trivia Questions” handout as a starting point for this mini-research project. (An Answer Key is attached.)
3. Sample coloring pages of quadrilateral tessellations may be used to reinforce the concepts covered during the week (congruency, flips, slides, turns). [Tesstellations: The Geometry of Patterns]by Stanley Bezuska (published by Creative Publications, 1977) and [Introduction to Tessellations] by Dale Seymour and Jill Britton (published by Dale Seymour, 1986) contain several appropriate designs and investigations.

Attached Files

The worksheets identified in the Materials Required section. 19-pages     File Extension: pdf

Answer Key     File Extension: pdf