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MATERIALSExcursions student pages 87–90Household or classroom objects resembling

polyhedrons1 sheet of grid paper for each student1 or 2 sheets of construction paper for each

studentPattern blocksThe Greedy Triangle, Marilyn Burns (optional)

LESSON OVERVIEWStudents find everyday objects that have shapesresembling polygons and distinguish polygonsfrom other figures. They name polygons and dis-tinguish regular polygons from other polygons.Finally, they create new polygons by arranginggiven polygons (first, construction paper cut-outs;later, pattern blocks).

SETTING THE STAGEFind polygons in everyday objects.! Show the class one of the solid figures resem-bling a polyhedron (such as a box, a book, or apyramid). Ask volunteers to name the shapes of the

faces. You may wish to review with students thedefinition of a polygon: a closed figure made ofline segments that only meet at their endpoints.Ask volunteers to name objects in the classroom(or at home or in the neighborhood) that haveshapes resembling polygons. Make sure everyoneunderstands the differences among triangles,quadrilaterals, pentagons, hexagons, heptagons,and octagons. You may need to remind studentsthat polygons are named by the number of sidesthey have.

Draw polygons on grid paper.! Distribute a sheet of grid paper to each student.Have them use their rulers to draw polygons. Askvolunteers to describe the attributes of their poly-gons. Ask questions such as, Is your figure closed? Isyour figure made only with line segments? Where dothe line segments meet? How many sides does your fig-ure have? How many angles does your figure have?

! You may wish to read The Greedy Triangle withthe class. Have volunteers take turns reading sec-tions of the book. Afterward, lead a discussion byasking questions such as, What polygons did the tri-angle become? What objects did the polygons become?

BUILDING CONCEPTUALKNOWLEDGEDistinguish polygons from other figures.! Have students open their books to Polygonsand Other Figures, page 87. Make sure theyunderstand that a polygon must meet all three ofthe criteria at the top of the page. As an extension,you might want to ask students to write the nameof the polygons they circle. For example, theycould write square or quadrilateral for Figure A.

The Shape of Things to Come The Shape of Things to Come

MA.C.1.2.1.3.1, .2, and .3; MA.C.2.2.1.3.1LESSON FOCUS Using manipulatives to create polygons; discussing the attributes of polygons.COMPANION ANCHORS LESSONS Lines, Line Segments, Raysand Angles; Recognizing Polygons; Visualizing Polygons; Types ofAngles

LANGUAGE DEVELOPMENTanglecongruentendpointequilateral trianglefaceheptagonhexagonline segmentoctagonpentagon

polygonpolyhedronquadrilateralregular polygonrhombusright trianglesidesquaretriangle

87TOPIC 3 The Shape of Things to Come

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The Shape of Things to ComePOLYGONS AND OTHER FIGURES

A polygon is a closed figure. A polygon is made only of line segments.A polygon’s line segments meet only at their endpoints.

1. Circle the figures that are polygons.

Complete the sentence.

2. Figure F is not a polygon because

3. Figure H is not a polygon because

4. Figure I is not a polygon because

A B C D

E F G H

I J K L

one of its line segments meetsanother line segment in the middle, not at the endpoint.

it is not made of line segments.

it is not a closed figure.

Name

Page 87

88 TOPIC 3 The Shape of Things to Come

CREATE YOUR OWN POLYGONS

Choose three pattern blocks and arrange them to create your own polygon. Only align congruent sides of the blocks. Then answer the questions.

First Block

Number of Sides

Second Block

Number of Sides

Third Block

Number of Sides

New Polygon

Type of Polygon Number of Sides

1. What is the total number of sides of your three blocks?

2. How many sides does your new polygon have?

3. Does your new polygon have more sides or fewer sides than the total of thethree blocks?

4

7heptagon

Answers will vary.

Answers will vary.

fewer sides

4 3

Sample responses are shown.

Page 88

TOPIC 3 The Shape of Things to Come

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BUILDING SKILLS ANDSTRATEGIESMake polygons.! Distribute a sheet of construction paper to eachstudent. Model how to use a ruler to draw threesquares of equal dimensions (for example, 2 in. x 2 in.). Have students cut out their squares. Showhow to fold a square on a diagonal and then cut itin half along the fold. Tell students to cut two oftheir squares in half this way.

! On the overhead, model how to create differentpolygons with your four right triangles and onesquare. Trace the new polygons and remove theconstruction–paper figures so that students can seethe polygons clearly. Ask volunteers to name thepolygons you create. Point out the differencesbetween two polygons made with the same figureswhen congruent sides are aligned and when non-congruent sides are aligned.

! Have students use their triangles andsquares to create polygons by tracing the figures onblank sheets of paper. Encourage students to makeas many kinds of polygons as possible (a triangle, aquadrilateral, a parallelogram, a pentagon, and soon). Tell students to label their polygons.

Congruentsides aligned

Noncongruentsides aligned

quadrilateral (or trapezoid)

hexagon

! Tell students that polygons with all congruentsides and all congruent angles are called regularpolygons. A regular triangle has a special name—equilateral triangle. A regular quadrilateral also has a special name—square. Encourage students tomake as many regular polygons as possible and to label them.

PUTTING IT INTO ACTIONCreate a new polygon.! Distribute pattern blocks to each student. Havestudents open their books to CCreate Your OwnPolygon, page 88. You may want to model theexercise on the overhead, making sure studentsunderstand that they should only align congruentsides of blocks. If students have difficulty tracingthe shape of their new polygon, suggest that theyfirst tape the three blocks together.

HOME CONNECTIONDraw a picture using polgyons.! Have students take home Portrait withPolygons, pages 89 and 90. Challenge them to tryto draw a picture that includes at least one exampleof each listed polygon. Encourage students to bringtheir pictures to class to share with their classmates.

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TOPIC 3 The Shape of Things to Come

87TOPIC 3 The Shape of Things to Come

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The Shape of Things to ComePOLYGONS AND OTHER FIGURES

A polygon is a closed figure. A polygon is made only of line segments.A polygon’s line segments meet only at their endpoints.

1. Circle the figures that are polygons.

Complete the sentence.

2. Figure F is not a polygon because

3. Figure H is not a polygon because

4. Figure I is not a polygon because

A B C D

E F G H

I J K L

Name

88 TOPIC 3 The Shape of Things to Come

CREATE YOUR OWN POLYGONS

Choose three pattern blocks and arrange them to create your own polygon. Only align congruent sides of the blocks. Then answer the questions.

First Block

Number of Sides

Second Block

Number of Sides

Third Block

Number of Sides

New Polygon

Type of Polygon Number of Sides

1. What is the total number of sides of your three blocks?

2. How many sides does your new polygon have?

3. Does your new polygon have more sides or fewer sides than the total of thethree blocks?

4

7

Answers will vary.

Answers will vary.

fewer sides

4 3

Sample responses are shown.

HOME CONNECTION: PORTRAIT WITH POLYGONS

Dear Parent or Guardian:

Your child has been learning about polygons and their attributes. A polygon is aclosed figure made only of line segments that meet only at their endpoints. Squaresand triangles are polygons; lines and circles are not. With your help, your child willdraw a picture using as many polygons as possible. Encourage your child to be cre-ative. Ask your child to show you the polygons in his or her picture.

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89TOPIC 3 The Shape of Things to Come

Draw a picture using as many polygons as possible. Be creative!Your brother could be a triangle; a peanut-butter sandwich could be a rhombus.

triangle quadrilateral pentagonhexagon heptagon octagonsquare equilateral triangle right triangleregular polygon rhombus

90 TOPIC 3 The Shape of Things to Come