### Lesson Question:

How can students use the Visual Thesaurus to help them distinguish the key properties that define different types of polygons?### Applicable Grades:

3-8### Lesson Overview:

In this lesson, students deduce the unique properties of polygons and then use the Visual Thesaurus to help them identify a variety of polygon shapes that they have cut out from a worksheet. The class then further subcategorizes some of the polygons by assessing different properties of triangles and quadrilaterals.### Length of Lesson:

One hour to one hour and a half### Instructional Objectives:

Students will:- deduce the key properties of polygons
- use the Visual Thesaurus to identify a set of various polygons
- use the Visual Thesaurus to subcategorize triangles and quadrilaterals based on key attributes
- synthesize their knowledge of polygons by playing a "21 Questions" review game

### Materials:

- student notebooks
- white board
- computers with Internet access
- scissors (one pair per small group)
- markers (a few per small group)
- Polygon Worksheet, 2 pages (one per small group) [click here to download]

### Related links:

- Math League page on "Figures and Polygons"
- Math is Fun page on quadrilaterals
- "Using Semantic Maps to Develop Word Meanings," an excerpt from Gerald G. Duffy's
*Explaining Reading.*

### Warm-up:

**Deducing the properties of a polygon:**

- Organize the class in small groups and distribute a set of the two-page Polygon Worksheet to each group [click here to download].
- Instruct groups to study the twelve shapes on the worksheet and to make a short list of what traits or properties ALL of the shapes have in common.

### Instruction:

**Defining polygon with the Visual Thesaurus:**

- Elicit from groups those properties that they found in common among all the shapes, and list them on the board. [Students will most likely point out that all the shapes are closed, flat (two-dimensional), and made of straight lines.]
- Display the Visual Thesaurus word map for
*polygon*on the white board, pointing out the definition "a closed plane figure bounded by straight lines" and explain that the word*plane*refers to the shapes' two-dimensional quality.

**Identifying Different Types of polygons with the Visual Thesaurus:**

- Reveal the different types of polygons contained in the Visual Thesaurus database by clicking on the red meaning bubble attached to
*polygon*or by clicking on the definition of*polygon*listed in the meaning list on the right side of the word map display. [The word map should reconfigure to show the meaning "a closed plane figure bounded by straight lines" as the center of the map with fourteen other red meaning bubbles fanning out above the central meaning.] - Distribute a few markers and a pair of scissors to each group and have them cut out each of the twelve polygons along the dashed lines.
- Explain to groups that they will be using the different types of polygons listed in the Visual Thesaurus display to help them identify each of the twelve polygons (lettered "A" through "L") as one of the following:
**triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, or decagon.** - Instruct students that they will need to use the terms "triangle" and "quadrilateral" more than once and that they should use the markers to label the shapes once they identify them accurately.
- Circulate around the room as groups work, ensuring that students are clicking on each of the polygon terms in order to see how each of the shapes is defined. (Students may also need to be reminded that clicking on the "BACK" button in the upper left hand corner of the tool bar will return them to the previous display.)

**Discussing the properties that help distinguish among different types of polygon:**

- After groups have finished labeling each of their twelve polygons, call upon random students to correctly identify each lettered shape (i.e., A=nonagon; B=quadrilateral; C=triangle; D=heptagon; E=decagon; F=quadrilateral; G=quadrilateral; H=pentagon; I=octagon; J=quadrilateral; K=hexagon; L=triangle).
- Ask students how they correctly identified each polygon and establish that the number of sides of the polygon determined how they labeled it. [You may also want to point out that the names of the different polygons contain Greek or Latin roots that indicate the number of sides (e.g., the Latin
*tri*means three; the Greek*deka*means ten).] - Explain that the same polygon shape may have different names, depending upon the properties that shape possesses. Besides looking at number of sides, students should also look at the lengths of the sides as they investigate how to further classify polygons in subcategories. Click on the definition of triangle as a "three-sided polygon" to reveal all the types of triangles and then have students examine the two types of triangles from the polygon worksheet. Which one would be considered an
*isosceles triangle*and which one would be considered an*equilateral triangle*? How did the lengths of the sides help determine how they are named? [Students should use the Visual Thesaurus to learn that the equilateral triangle (C) is a "regular polygon" with three equal sides while the isosceles triangle (L) only has two equal sides.] - Visually reinforce this mini-lesson on triangles by clicking on the definition of
*triangle*and then right-clicking (control-clicking on the Mac) on the words*equilateral triangle*and*isosceles triangle*to search an image database (such as Google images) so students can see multiple examples of equilateral and isosceles triangles.

**Distinguishing among quadrilaterals:**

- Inform students that they should also consider sets of parallel lines as they try to further classify quadrilaterals into subcategories. Out of the four quadrilaterals from today's exercise, which ones would be considered parallelograms, or "quadrilaterals whose opposite sides are both parallel and equal in length"? (Answer: B, F, and G)
- Challenge groups to use the Visual Thesaurus to help them further identify and label the four quadrilaterals as either a
*square*, a*rectangle*, a*trapezoid*or a*rhombus*. (Answers: B=rectangle; F=rhombus; G=square; J=trapezoid) - Visually reinforce this mini-lesson on quadrilaterals by right-clicking (control-clicking on the Mac) on the terms
*rectangle, rhombus, square,*and*trapezoid*and displaying images of these shapes.

### Wrap-up:

**Playing 21 questions with polygons:**

- As a review of all the polygon types discussed in class, you could have each student write the name of a particular polygon on a slip of paper and not reveal it to anyone else. Then, other students in the class could play "21 questions" to try to figure out what polygon that student is "playing." For example, students could begin by asking about number of sides and then narrow their questions to address other properties (e.g., "Do you have four sides?" "Are you a parallelogram?" "Are you regular?" etc.). The student answering the class's questions should only respond with "yes" or "no" until his or her specific polygon shape is revealed.

### Extending the Lesson:

- For a homework assignment or in a subsequent class lesson, you could have students use semantic mapping to graphically display what they have learned about polygons and the key attributes or properties that distinguish one polygon from another. A semantic map of polygons would have the word
*polygons*on top and then various branches of polygons drawn below it. For example, there would be a line connecting the word*polygons*down to the word*quadrilaterals*and then*quadrilaterals*would be connected to lower subcategories such as*parallelograms*and*trapezoids*, and so on. To see a model of semantic mapping and to read more about how it helps students learn to categorize more complex vocabulary, see "Using Semantic Maps to Develop Word Meanings," an excerpt from Gerald G. Duffy's*Explaining Reading*

### Assessment:

- Check whether or not groups accurately identified the twelve polygons (lettered "A" through "L") by using the Visual Thesaurus.
- Assess students' comprehension of the various subcategories of polygons by seeing if they can correctly distinguish among the different types of triangles and quadrilaterals. (This could be assessed by giving students a traditional quiz where they have to label polygons or by challenging students to create a semantic map of a certain set of polygons.)

### Educational Standards:

**Mathematics**

**Standard 5.** Understands and applies basic and advanced properties of the concepts of geometry

Level II (Grade 3-5)

Benchmark 1.Knows basic geometric language for describing and naming shapes (e.g., trapezoid, parallelogram, cube, sphere)

Knowledge/skill statements

1. Understands the concept of a trapezoid

2. Understands the concept of a parallelogram

Benchmark 2.Understands basic properties of figures (e.g., two- or three-dimensionality, symmetry, number of faces, type of angle)

Knowledge/skill statements

1. Understands the concept of two-dimensionality

2. Understands the concept of three-dimensionality

3. Understands the concept of symmetry

4. Understand the defining number of faces for a three-dimensional object

5. Understands that objects have a defining number and types of angles

Benchmark 3.Predicts and verifies the effects of combining, subdividing, and changing basic shapes

Knowledge/skill statements

1. Predicts the effects of subdividing shapes

2. Predicts the effects of changing shapes

3. Predicts the effects of combining shapes

4. Verifies the effects of subdividing shapes

5. Verifies the effects of changing shapes

6. Verifies the effects of combining shapes

Benchmark 4.Understands that shapes can be congruent or similar

Knowledge/skill statements

1. Understands the concept of similar shapes

2. Understands the concept of congruent shapes

**Language Arts**

**Standard 8. **Uses listening and speaking strategies for different purposes

Level II (Grades 3-5)

- Contributes to group discussions
- Asks questions in class (e.g., when he or she is confused, to seek others' opinions and comments)
- Responds to questions and comments (e.g., gives reasons in support of opinions, responds to others' ideas)
- Listens to classmates and adults (e.g., does not interrupt, faces the speaker, asks questions, summarizes or paraphrases to confirm understanding, gives feedback, eliminates barriers to effective listening)
- Uses strategies to convey a clear main point when speaking (e.g., expresses ideas in a logical manner, uses specific vocabulary to establish tone and present information)
- Uses level-appropriate vocabulary in speech (e.g., familiar idioms, similes, word play)
- Makes basic oral presentations to class (e.g., uses subject-related information and vocabulary; includes content appropriate to the audience; relates ideas and observations; incorporates visual aids or props; incorporates several sources of information)

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