The Shape of
Things to Come
MA.C.1.2.1.3.1, .2, and .3; MA.C.2.2.1.3.1
LESSON FOCUS Using manipulatives to create polygons;
discussing the attributes of polygons.
COMPANION ANCHORS LESSONS Lines, Line Segments, Rays
and Angles; Recognizing Polygons; Visualizing Polygons; Types of
Angles
MATERIALS
faces. You may wish to review with students the
definition of a polygon: a closed figure made of
line segments that only meet at their endpoints.
Ask volunteers to name objects in the classroom
(or at home or in the neighborhood) that have
shapes resembling polygons. Make sure everyone
understands the differences among triangles,
quadrilaterals, pentagons, hexagons, heptagons,
and octagons. You may need to remind students
that polygons are named by the number of sides
they have.
Excursions student pages 87–90
Household or classroom objects resembling
polyhedrons
1 sheet of grid paper for each student
1 or 2 sheets of construction paper for each
student
Pattern blocks
The Greedy Triangle, Marilyn Burns (optional)
Draw polygons on grid paper.
◆ Distribute a sheet of grid paper to each student.
LANGUAGE DEVELOPMENT
angle
congruent
endpoint
equilateral triangle
face
heptagon
hexagon
line segment
octagon
pentagon
polygon
polyhedron
quadrilateral
regular polygon
rhombus
right triangle
side
square
triangle
Have them use their rulers to draw polygons. Ask
volunteers to describe the attributes of their polygons. Ask questions such as, Is your figure closed? Is
your figure made only with line segments? Where do
the line segments meet? How many sides does your figure have? How many angles does your figure have?
◆ You may wish to read The Greedy Triangle with
the class. Have volunteers take turns reading sections of the book. Afterward, lead a discussion by
asking questions such as, What polygons did the triangle become? What objects did the polygons become?
LESSON OVERVIEW
BUILDING CONCEPTUAL
KNOWLEDGE
Students find everyday objects that have shapes
resembling polygons and distinguish polygons
from other figures. They name polygons and distinguish regular polygons from other polygons.
Finally, they create new polygons by arranging
given polygons (first, construction paper cut-outs;
later, pattern blocks).
Distinguish polygons from other figures.
◆ Have students open their books to Polygons
and Other Figures, page 87. Make sure they
understand that a polygon must meet all three of
the criteria at the top of the page. As an extension,
you might want to ask students to write the name
of the polygons they circle. For example, they
could write square or quadrilateral for Figure A.
SETTING THE STAGE
Find polygons in everyday objects.
◆ Show the class one of the solid figures resembling a polyhedron (such as a box, a book, or a
pyramid). Ask volunteers to name the shapes of the
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TOPIC 3 The Shape of Things to Come
BUILDING SKILLS AND
STRATEGIES
Congruent
sides aligned
Make polygons.
◆ Distribute a sheet of construction paper to each
student. Model how to use a ruler to draw three
squares of equal dimensions (for example, 2 in. x
2 in.). Have students cut out their squares. Show
how to fold a square on a diagonal and then cut it
in half along the fold. Tell students to cut two of
their squares in half this way.
quadrilateral (or trapezoid)
◆ On the overhead, model how to create different
polygons with your four right triangles and one
square. Trace the new polygons and remove the
construction–paper figures so that students can see
the polygons clearly. Ask volunteers to name the
polygons you create. Point out the differences
between two polygons made with the same figures
when congruent sides are aligned and when noncongruent sides are aligned.
Noncongruent
sides aligned
hexagon
◆ Have students use their triangles and
squares to create polygons by tracing the figures on
blank sheets of paper. Encourage students to make
as many kinds of polygons as possible (a triangle, a
quadrilateral, a parallelogram, a pentagon, and so
on). Tell students to label their polygons.
CREATE YOUR OWN POLYGONS
Name
Choose three pattern blocks and arrange them to create your own polygon.
Only align congruent sides of the blocks. Then answer the questions.
The Shape of Things to Come
Sample responses are shown.
POLYGONS 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.
Second Block
First Block
Third Block
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1. Circle the figures that are polygons.
A
B
C
Number of Sides
D
4
Number of Sides
4
Number of Sides
3
New Polygon
E
F
G
H
I
J
K
L
Type of Polygon
heptagon
Number of Sides
7
1. What is the total number of sides of your three blocks?
Answers will vary.
Complete the sentence.
one of its line segments meets
another line segment in the middle, not at the endpoint.
3. Figure H is not a polygon because it is not made of line segments.
2. Figure F is not a polygon because
2. How many sides does your new polygon have?
Answers will vary.
3. Does your new polygon have more sides or fewer sides than the total of the
three blocks?
4. Figure I is not a polygon because
fewer sides
it is not a closed figure.
TOPIC 3 The Shape of Things to Come
87
88
Page 87
TOPIC 3 The Shape of Things to Come
Page 88
65
TOPIC 3 The Shape of Things to Come
HOME CONNECTION
◆ Tell students that polygons with all congruent
sides and all congruent angles are called regular
polygons. A regular triangle has a special name—
equilateral triangle. A regular quadrilateral also has
a special name—square. Encourage students to
make as many regular polygons as possible and
to label them.
Draw a picture using polgyons.
◆ Have students take home Portrait with
Polygons, pages 89 and 90. Challenge them to try
to draw a picture that includes at least one example
of each listed polygon. Encourage students to bring
their pictures to class to share with their classmates.
PUTTING IT INTO ACTION
Create a new polygon.
◆ Distribute pattern blocks to each student. Have
students open their books to Create Your Own
Polygon, page 88. You may want to model the
exercise on the overhead, making sure students
understand that they should only align congruent
sides of blocks. If students have difficulty tracing
the shape of their new polygon, suggest that they
first tape the three blocks together.
66
Name
The Shape of Things to Come
POLYGONS 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.
© School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal.
1. Circle the figures that are polygons.
A
B
C
D
E
F
G
H
I
J
K
L
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
TOPIC 3 The Shape of Things to Come
87
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.
Sample responses are shown.
First Block
Number of Sides
Second Block
4
Number of Sides
Third Block
4
Number of Sides
3
New Polygon
Type of Polygon
Number of Sides
7
1. What is the total number of sides of your three blocks?
Answers will vary.
2. How many sides does your new polygon have?
Answers will vary.
3. Does your new polygon have more sides or fewer sides than the total of the
three blocks?
fewer sides
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TOPIC 3 The Shape of Things to Come
Name
HOME CONNECTION: PORTRAIT WITH POLYGONS
Dear Parent or Guardian:
© School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal.
Your child has been learning about polygons and their attributes. A polygon is a
closed figure made only of line segments that meet only at their endpoints. Squares
and triangles are polygons; lines and circles are not. With your help, your child will
draw a picture using as many polygons as possible. Encourage your child to be creative. Ask your child to show you the polygons in his or her picture.
TOPIC 3 The Shape of Things to Come
89
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
hexagon
square
regular polygon
90
quadrilateral
heptagon
equilateral triangle
rhombus
pentagon
octagon
right triangle
TOPIC 3 The Shape of Things to Come