Read a Book about Shapes. Read
aloud a book about shapes. After reading, revisit the pictures
and ask students to trace (with their fingers), identify, and
describe the shapes they see on the pages. Conduct a discussion
about the shapes encouraging students to use geometric properties
(number of sides, length of sides, number of corners) to describe
the shapes. See Sample Dialog 1.
If the read-aloud book of shapes is small in size, include
a large shape on each Shape Chart you prepared to help students
trace the shapes they see on the pages. This will facilitate
ease with tracing while making the shapes more visible to the
class.
Sample Dialog 1 helps students identify and describe
shapes from a book using geometric properties.
Teacher: Can you name a shape that you see in the
picture?
Lin: The sail on the boat is a triangle.
Teacher: Please come and outline the triangle with your
finger. Show the rest of the class.
[Lin comes to the front to the class and outlines the
shape.]
Teacher: Tell me about this shape. Describe it.
Lin: It is white with writing on it.
Teacher: Do you agree with Lin? Is this a triangle? How
do you know?
Jessie: Yes, it's a triangle because it has three sides.
Teacher: Excellent. Let's count the sides. [Teacher
outlines the sides of the triangle as the class counts.]
Teacher: Can we count any other parts of the triangle?
Frank: The corners! It has three corners.
Teacher: Let's count the corners together.
Identify and Describe Shapes. Tell students they are going
on a secret shape hunt. Ask them to walk around the classroom to
find examples of geometric shapes on objects such as a clock, a
chalkboard eraser, or a desktop. Direct them to keep the object a
secret, remember where they found it, and then return to their
place. Tell them they will discuss the objects later in the
lesson.
Display the class collection of shapes. See Materials
Preparation. Lead a discussion in which students name and
describe the two-dimensional faces they see on each object. For
purposes of this lesson these will be called flat shapes.
Introduce the term face. Be careful to paraphrase the term
as a flat shape to make the concept accessible. See Content Note.
As students identify a shape, ask them to trace the shape with
their fingers. Draw the two-dimensional shape so it is visible to
all and label it with the name of the shape. As you draw each
shape, have the class trace the shape in the air.
Within the discussion, students will likely use everyday
language to name shapes and describe shapes using attributes such
as color. See Content Note.
Geometry, Vocabulary, and Young Children. In
teaching geometric concepts to young children, it is important
to focus on those ideas that are accessible to them and to use
appropriate vocabulary. With young children, the teacher can
model the mathematical terms during class discussion, while
accepting students' everyday vocabulary when appropriate. The
teacher may first use the student's word and then use the
correct mathematical term. For instance, the teacher might say,
"Yes, the corner or vertex (angle)." It is equally important to
carefully introduce concepts and terminology so that early
learning does not interfere with acquiring important concepts
and vocabulary that will be taught in later grades. For example,
a tennis ball may be called a ball, but it is definitely not a
circle. Below are examples of ideas that may surface in class
discussion and result in interesting conversations about
mathematics.
Is a square a rectangle? Is a square a rhombus?
Students often think that a square is not a rectangle. They
believe that all rectangles have one side longer than another.
This may result from the fact that every shape they have seen
labeled as a rectangle has one side longer than another.
However, mathematicians define a rectangle to be a four-sided
polygon having four right angles (square corners). This makes a
square part of the "rectangle family" of shapes. Similarly,
since a rhombus is defined as a polygon with four sides of equal
length, then squares are also part of the "rhombus family" of
shapes. A square is a rhombus with four right angles. Since
understanding definitions and ideas of class inclusion are
sophisticated topics, mastery of these concepts will come in
later grades. However, it is important that teachers understand
the distinctions in case they come up in class discussion. For
example, a student who draws a square oriented so that it looks
like a kite may choose to categorize it with the students who
drew rhombuses. A short discussion can take place that brings
students to the idea that a drawing of a square can correctly go
on a chart with rhombuses as well as on charts with squares and
rectangles.
How many sides does a circle have? This is an
interesting but tricky question with answers that depend on
mathematical definitions. If a side is a line between two
corners of a shape, then the question is too ambiguous to have a
definite answer. One way to talk about this with students is to
ask how circles are different from the other shapes that are
discussed in the lesson. Appropriate responses to this question
include, "circles don't have corners and all the other shapes
do" and "the circle is round (curved) and the other shapes have
straight sides." If the class can agree that counting sides
means finding the number of straight sides between corners, then
they may decide that a circle has no sides. Or, they may decide
that it does not makes sense to try to count the sides of a
circle.
Help refine notions that they already have and introduce
useful vocabulary as appropriate. Guide the discussion so that
students focus on geometric properties such as number of sides,
length of sides, and number of corners. See Sample Dialog 2.
Sample Dialog 2 guides students to focus on geometric
properties of shapes.
Teacher: What flat shapes do you see?
Luis: I see squares and rectangles on the cracker box.
Teacher: Outline the square with your finger. [Luis
outlines the square with his finger.] Trace a square in
the air with your finger as I draw it on the board. [The
teacher draws the square on the board and labels it. Students
trace the shape in the air.] What can you tell me about
the square?
Luis: It has four sides.
Teacher: Right. Can someone tell me anything else about
the square? Can you count any other parts of the square?
John: The corners. There are four corners.
Teacher: Let's count them together.
Class: One, two, three, four.
Teacher: Luis said he saw a rectangle when he looked at
this box. Do you see it, too? Can you draw around it with your
finger?
Ana: I see it. [She outlines it with her finger.] It has
four sides, too.
Teacher: Draw a rectangle in the air with your finger.
[Draws the rectangle and labels it.]
Can you tell me anything else about the rectangle?
Nick: It has four corners.
Teacher: Good thinking. Anything else?
Irma: All the sides are not the same.
Teacher: Right. All the sides are not the same length.
Let's look back at Luis's square. What do you notice about the
sides?
Roberto: They are the same.
Teacher: Right. All four sides of the square are the
same length.
Discuss the shapes students found in the secret shape hunt.
Have several students name their object and identify and describe
the geometric shapes they found on it. If possible, hold the
objects up or direct attention to them and ask questions similar
to those in Sample Dialog 2. During the class discussion, point
out some critical distinctions and properties if the students do
not. For example, use prompts to help students distinguish
between the three-dimensional objects (ball, box, cone) and the
two-dimensional shapes (faces) that form the sides.
You might introduce the terms side and corner
discuss the size or shape of angles.Contrast shape
and size by pointing out that all squares have the same
shape but come in different sizes.
Discussions such as these should be brief so that the focus
remains on the key ideas of the lesson: identifying and
describing shapes. See Mathematics in this Unit for more
information on young children's understanding of geometric ideas.
Draw Shapes. Begin this part of the lesson by pointing out
the seven Shape Charts on display in various parts of the room.
See Materials Preparation. Name the shape represented on each.
Students will look around the room to find and draw a shape on
one of the charts. For example, they may see a rectangle in the
window or a circle on the clock.
- Look around the room for a flat shape. Find one of
these shapes: rectangle, square, rhombus, triangle, hexagon,
circle, or trapezoid. Examples of these shapes are on the
charts around the room. For example, the cover of this book is
in the shape of a rectangle. Draw the shape you find.
Assure students that the shape they will draw will not look
exactly like the shapes they see. It is okay if the shapes are
not perfectly straight or if each side of the square is not
exactly the same length. Ask students to take their pictures and
stand under the chart that matches the shape they drew.
Pose the following questions and ask students to
discuss them in their small groups:
As groups talk together, probe further with questions.
- Where did you see your shape in the room? (Possible
responses: I saw a triangle on the front of the book we read.
The top of the teacher's desk is a rectangle.)
-
What makes your shape a [triangle]?
-
How are the shapes in your group alike?
-
How are they different?
- How are the triangles alike? (They all have
three sides and three corners.)
-
How are the triangles different? (Possible responses:
They are different sizes. Some have short sides and some have
long sides.)
