Download Geometry and Spatial Reasoning Activity: Two

Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Geometry and Spatial Reasoning
Activity:
Two-Dimensional Figures Important Book
TEKS:
(4.8) Geometry and spatial reasoning. The student identifies and
describes attributes of geometric figures using formal geometric language.
The student is expected to:
(A) identify and describe right, acute, and obtuse angles;
(B) identify and describe parallel and intersecting (including
perpendicular) lines using concrete objects and pictorial models;
and
(C) use essential attributes to define two- and three-dimensional
geometric figures.
Note: Portions of this lesson address TEKS at other grade levels as well;
however, the intent of the lesson fits most appropriately at the grade level
indicated.
Overview:
Students will investigate attributes of various two-dimensional figures. In
addition, students will examine and identify essential attributes for defining
two-dimensional figures as they explore relationships among various
types of quadrilaterals.
Materials:
The Greedy Triangle by Marilyn Burns (ISBN: 0-590-48991-7)
Construction paper (2 pieces per student)
Strips of heavy paper: cardstock or poster board
Brads
Hole punch
Scissors
Two-Dimensional Figures Recording Sheet – Handout/Transparency 1
The Important Book by Margaret Wise Brown (ISBN: 0-06-443227-0)
Glue or paste
Markers
3 "O" rings
Sample Quadrilaterals – Handouts/Transparencies 2a and 2b
Quadrilateral Definitions – Handout/Transparency 3
What’s In A Name? Explaining Quadrilaterals – Handout/Transparency 4a
What’s In A Name? Explaining Quadrilaterals Key –
Handout/Transparency 4b
Sample Word Map – Handout/Transparency 5
Words for a Word Map – Handout/Transparency 6
Sample Quadrilateral Word Map – Handout/Transparency 7
Assessment of Two-Dimensional Figures – Handout/Transparency 8
Geoboards
Geobands
Geoboard Recording Paper – Handout/Transparency 9
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 1
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Assessment of Two-Dimensional Figures (Key) – Sample Answers 10a,
10b, 10c, and 10d
Grouping:
Whole group and pairs
Time:
3 – 4 class periods
Lesson:
1.
2.
Procedures
Read The Greedy Triangle by Marilyn Burns
to the class. As you read the book, stop and
ask the students to predict the number of
sides they think will be on the next polygon
after the triangle visits the Shape Shifter.
Ask the students to provide the geometric
term for the figure, and ask if they have ever
seen anything made from that shape.
Notes
In this book, the Greedy Triangle
gets tired of having just three
sides, so the triangle goes to the
local shape shifter to have one
more side added. As the new
polygon continues to run into
troubles and continues to add one
more side he finally realizes that
his original three sides were just
enough, and he returns to his
original status.
After reading the book, review with students
various two-dimensional figures such as
triangles, quadrilaterals, pentagons,
hexagons, and so on.
Have each student take a piece of
construction paper and cut it on the diagonal.
Ask: What two-dimensional figure have you
made? How many sides does it have? How
many angles does it have?
A right triangle
3 sides
3 angles
This cut forms two right triangles.
Discuss with students which angle
is a right angle.
Distribute Two-Dimensional Figures
Recording Sheet – Handout/Transparency 1.
The first row is already completed on the
recording sheet for the triangle.
3.
Have students make an “angle maker” using
a hole punch, brads, and two strips of heavy
paper such as cardstock or poster board.
Using the angle maker, have the students
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 2
Mathematics TEKS Refinement 2006 – K-5
Procedures
show you an acute angle, obtuse angle, and
a right angle. As students model each type
of angle, ask the class for the definitions of
acute, obtuse, and right angles.
4.
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Notes
Ask the students to predict what shape they
will have if they cut off one vertex of the
triangle.
After making their predictions, have each
student cut only one vertex.
Ask: What two-dimensional figure have you
made? How many sides does it have? How
many angles does it have?
A quadrilateral
4 sides
4 angles
Students should again record the name of
this polygon, the number of sides and the
number of angles on Handout/Transparency
1.
Discuss with the class the attributes of each
of the different quadrilaterals that occur in
the class from cutting one vertex of the
triangle. Not all quadrilaterals will look the
same. Do they have zero, one, or two pairs
of parallel sides? Does the quadrilateral still
have a right angle?
5.
Continue this process, cutting just one vertex
at a time and naming the new polygon after
each cut. Each time, record the polygon’s
name, number of sides, and number of
angles on the recording sheet. Have
students discuss distinguishing properties of
each figure, including the number of sides
and the number of angles. Students should
identify any parallel and/or perpendicular
sides.
6.
Read The Important Book by Margaret Wise
Brown to the class.
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Students may use their “angle
makers” to determine if the
quadrilateral’s angles are acute,
obtuse, or right angles.
In The Important Book, the author
discusses the important attributes
Grade 4
Page 3
Mathematics TEKS Refinement 2006 – K-5
Procedures
7.
8.
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Discuss the pattern used in the book.
Notes
of familiar objects. She highlights
what each object looks like, what it
is used for, and what she believes
is its most important attribute.
Using Sample Quadrilaterals (see
Handouts/Transparencies 2a and 2b) and
Quadrilateral Definitions (see
Handout/Transparency 3), have students
discuss the attributes of quadrilaterals.
Many quadrilaterals share the
same attributes. This discussion
should lead students to identify
the most important attribute of a
quadrilateral.
Then, ask students to complete What’s In A
Name? Explaining Quadrilaterals (see
Handout/Transparency 4a). Students
should compare and contrast the differences
between these quadrilaterals.
A key for What’s in a Name?
Explaining Quadrilaterals is
provided on
Handout/Transparency 4b.
Divide the class into groups or pairs of
students.
For example, the group with the
Assign a different two-dimensional figure to
square might write something like
each group or pair and have them write a
page for a class book, The Important Book of the following:
Two-Dimensional Figures. They may glue
The important thing about a
their assigned two-dimensional figure at the
square is that it has 4
top of their paper or decorate their paper with
congruent sides and 4 right
the assigned figure. The class book should
angles.
follow the pattern found in The Important
It is true that it is a polygon and
Book. Before writing their page, the group
a quadrilateral.
must decide what the distinguishing attribute
It is a special kind of rectangle.
of their figure is. Then they may list other
It is also a special kind of
attributes, classifications, examples of where
rhombus.
their figure might be found in real life, lines of
It has 4 lines of symmetry.
symmetry, and other descriptive
You see squares on
characteristics.
checkerboards and
chessboards and lots of
When all of the groups have completed their
other places.
writing, collect the pages, add a front and
But the important thing about a
back cover, and assemble the pages into a
square is that it has 4
class book that can be placed in the library
congruent sides and 4 right
or the mathematics center. Allow students
angles.
time to present their page of the class book.
A class discussion of student’s reflections
should take place.
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 4
Mathematics TEKS Refinement 2006 – K-5
9.
Procedures
Model a word map for the students using the
Sample Word Map (Handout/Transparency
5). Explain that a word map is a visual way
to represent the relationships among various
two-dimensional figures.
Distribute Words for a Word Map (see
Handout/Transparency 6.) Each group of
students should have a set of words.
Tell the students that they are now going to
create a Quadrilateral Word Map to
represent the relationships among the
various two-dimensional figures and terms
that the students have investigated during
the lesson.
Have the groups cut out the words and make
a Quadrilateral Word Map with them. When
complete, have each group present its word
map to the class.
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Notes
Each column on Words for a Word
Map (Handout/Transparency 6)
contains a complete set of terms,
so each page will be enough for
two groups.
A Sample Quadrilateral Word Map
is provided at the end of this
lesson (Handout/Transparency 7).
Homework:
Have students cut out pictures from a magazine of examples of twodimensional figures.
Assessment:
Assign students Assessment of Two-Dimensional Figures (see
Handout/Transparency 8) to complete. Students should read the
description of the polygon, create the polygon on the geoboard and
record it on the Geoboard Recording Paper (Handout/Transparency 9).
Extensions:
Repeat the process using three-dimensional figures to create a new
class book, The Important Book of Three-Dimensional Figures.
Resources:
Burns, M. and Silveria, G. (1994). The greedy triangle. New York:
Scholastic.
Brown, M. W. and Weisgard, L. (1999). The Important Book. New
York: Haper Collins.
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 5
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Two-Dimensional Figures Recording Sheet
As you construct polygons, record the name of each polygon, its number of
sides, and its number of angles in the table below.
Name of Polygon
Number of Sides
Number of Angles
Triangle
3
3
Handout/Transparency 1
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 6
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Sample Quadrilaterals
Handout/Transparency 2a
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 7
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Sample Quadrilaterals
(continued)
Handout/Transparency 2b
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 8
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Quadrilateral Definitions
Quadrilateral – any closed, four-sided shape.
Parallelogram – a quadrilateral with two pairs of parallel sides.
Rectangle – a parallelogram with four right angles.
Rhombus – a parallelogram with four equal or congruent sides.
Square – a parallelogram with four right angles and four equal or
congruent sides.
Trapezoid – a quadrilateral with only one pair of parallel sides.
Handout/Transparency 3
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 9
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
What’s In A Name?
Explaining Quadrilaterals
Trapezoid
Square
Rhombus
Rectangle
Quadrilateral
Parallelogram
Instructions: Place a check mark in the box of each geometry term
that applies to each quadrilateral.
Handout/Transparency 4a
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 10
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
What’s In A Name?
Explaining Quadrilaterals
(Key)
Trapezoid
Square
Rhombus
Rectangle
Quadrilateral
Parallelogram
Instructions: Place a check mark in the box of each geometry term
that applies to each quadrilateral.
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
Handout/Transparency 4b
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 11
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Mathematics TEKS Refinement 2006 – K-5
Handout/Transparency 5
Sample Word Map
Grade 4
Page 12
Tarleton State University
Rectangle
Rhombus
Square
Trapezoid
Rectangle
Rhombus
Square
Trapezoid
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Quadrilateral
Quadrilateral
Handout/Transparency 6
Polygon
Parallelogram
Polygon
Parallelogram
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Grade 4
Page 13
Cut out the following words and use them to
create a word map:
Words for a Word Map
Cut out the following words and use them to
create a word map:
Mathematics TEKS Refinement 2006 – K-5
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Handout/Transparency 7
Sample Quadrilateral Word Map
Mathematics TEKS Refinement 2006 – K-5
Grade 4
Page 14
Tarleton State University
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Assessment of Two-Dimensional Figures
Make the following polygons on your geoboard and record on dot paper.
1.
Make a 3-sided polygon. What is this polygon called?
2.
Make a triangle with 1 right angle and no 2 sides the same length.
What is this triangle called?
3.
Make a 4-sided polygon with no parallel sides. What is this polygon
called?
4.
Make a 4-sided polygon with all sides different lengths. What is this
polygon called?
5.
Make a 4-sided polygon with no right angles but with 2 pairs of sides
parallel. What is this polygon called?
6.
Make a 4-sided polygon with right angles and two pairs of sides
parallel. What is this polygon called?
7.
Make a 4-sided polygon with 4 right angles and all sides congruent.
What is this polygon called?
8.
Make a 4-sided polygon with no right angles and all sides congruent.
What is this polygon called?
9.
Make a 5-sided polygon that has exactly one pair of parallel sides.
What is this polygon called?
10.
Make a 6-sided polygon with one pair of perpendicular sides. What is
this polygon called?
11.
Make a 7-sided polygon. What is this polygon called?
Handout/Transparency 8
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 15
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Geoboard Recording Paper
Handout/Transparency 9
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 16
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Assessment of Two-Dimensional Figures
(Key)
Make the following polygons on your geoboard and record on dot paper.
Note: Geoboard figures may vary on each question.
1.
Make a 3-sided polygon. What is this polygon called?
Triangle
2.
Make a triangle with 1 right angle and no 2 sides the same length.
What is this triangle called?
Right triangle
3.
Make a 4-sided polygon with no parallel sides. What is this polygon
called?
Quadrilateral
Sample Answers 10a
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 17
Mathematics TEKS Refinement 2006 – K-5
4.
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Make a 4-sided polygon with all sides different lengths. What is this
polygon called?
Quadrilateral
5.
Make a 4-sided polygon with no right angles but with 2 pairs of sides
parallel. What is this polygon called?
Parallelogram
6.
Make a 4-sided polygon with right angles and two pairs of sides
parallel. What is this polygon called?
Rectangle
Sample Answers 10b
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 18
Mathematics TEKS Refinement 2006 – K-5
7.
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Make a 4-sided polygon with 4 right angles and all sides congruent.
What is this polygon called?
Square
8.
Make a 4-sided polygon with no right angles and all sides congruent.
What is this polygon called?
Rhombus
9.
Make a 5-sided polygon that has exactly one pair of parallel sides.
What is this polygon called?
Pentagon
Sample Answers 10c
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 19
Mathematics TEKS Refinement 2006 – K-5
10.
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Make a 6-sided polygon with one pair of perpendicular sides. What is
this polygon called?
Hexagon
11.
Make a 7-sided polygon. What is this polygon called?
Heptagon
Sample Answers 10d
Geometry and Spatial Reasoning
Two-Dimensional Figures Important Book
Grade 4
Page 20