Download Geometry

Using Geoboards
Identify and describe shapes (squares, circles, triangles,
rectangles, hexagons, cubes, cones, cylinders, and
spheres).
This entire cluster asks students to understand that
certain attributes define what a shape is called (number
of sides, number of angles, etc.) and other attributes do
not (color, size, orientation). Using geometric attributes,
the student identifies and describes squares, circles,
triangles, rectangles, hexagons, cubes, cones, cylinders,
and spheres. Throughout the year, Kindergarten
students move from informal language to describe what
shapes look like (e.g.,
“That looks like an ice cream cone!”) to more formal
mathematical language (e.g., “That is a triangle. All of its
sides are the same length”).
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Create a rectangle. If I turn my geoboard, will
my rectangle look like your rectangle?
Create a square. If I turn my geoboard, will my
square look like your square?
Create a triangle. If I turn my geoboard, will my
triangle look like your triangle?
K.G.2 Correctly name shapes
regardless of their orientations
or overall size.
K.G.3 Identify shapes as two
dimensional (lying in a plane,
“flat”) or three dimensional
(“solid”).
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Draw a triangle, square, and a rectangle.
Now, look at your partner’s 3 flat shapes.
What do you notice? What looks the same?
What looks different?
K.G.4 Analyze and compare two- and
three-dimensional shapes, in different
sizes and orientations, using informal
language to describe their similarities,
differences, parts (e.g., number of
sides and vertices/“corners”) and
other attributes (e.g., having sides of
equal length).
Reason with shapes and their attributes.
Students describe and analyze shapes by examining their sides and angles.
Students investigate, describe, and reason about decomposing and
combining shapes to make other shapes. Through building, drawing, and
analyzing two- and three-dimensional shapes, students develop a
foundation for understanding area, volume, congruence, similarity, and
symmetry in later grades.
Mathematically proficient students communicate precisely by engaging in
discussion about their reasoning using appropriate mathematical
language. The terms students should learn to use with increasing precision
with this cluster are: attribute, feature angle, side, triangle, quadrilateral,
square, rectangle, trapezoid, pentagon, hexagon, cube, face, edge, vertex,
surface, figure, shape, closed, open, partition, equal size, equal shares,
half, halves, thirds, half of, a third of, whole, two halves, three thirds, four
fourths, partition, rows, columns.
Common Core Standard
Unpacking
2.G.1 Recognize and draw shapes
having specified attributes, such as
a given number of angles or a
given number of equal faces.
Identify triangles, quadrilaterals,
pentagons, hexagons, and cubes.
Second Grade students identify
(recognize and name) shapes and
draw shapes based on a given set
of attributes. These include
triangles, quadrilaterals (squares,
rectangles, and trapezoids),
pentagons, hexagons and cubes.
Example:
Teacher: Draw a closed shape that
has five sides. What is the name of
the shape?
Student: I drew a shape with 5
sides. It is called a pentagon.
Example:
Teacher: I have 3 sides and 3
angles. What am I?
Student: A triangle. See, 3 sides, 3
angles.
Common Core Standard
Unpacking
2.G.3 Partition circles and rectangles into two,
three, or four equal shares, describe the shares
using the words halves, thirds, half of, a third
of, etc., and describe the whole as two halves,
three thirds, four fourths. Recognize that equal
shares of identical wholes need not have the
same shape.
2nd grade students partition circles and
rectangles into 2, 3 or 4 equal shares
(regions). Students should be given ample
experiences to explore this concept with paper
strips and pictorial representations. Students
should also work with the vocabulary terms
halves, thirds, half of, third of, and fourth (or
quarter) of. While students are working on this
standard, teachers should help them to make
the connection that a “whole” is composed of
two halves, three thirds, or four fourths.
This standard also addresses the idea that
equal shares of identical wholes may not have
the same shape.
Example:
Teacher: Partition each rectangle into fourths a
different way.
Student A: I partitioned this rectangle 3
different ways. I folded or cut the paper to
make sure that all of the parts were the same
size.
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Teacher: In your 3 pictures, how do you know
that each part is a fourth?
Student: There are four equal parts.
Therefore, each part is one-fourth of the
whole piece of paper.
NOTE: It is important for students to
understand that fractional parts may not be
symmetrical. The only criteria for equivalent
fractions is that the area is equal, as
illustrated in the first example above.
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Example: How many different ways can you
partition this 4 by 4 geoboard into fourths?
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Student A: I partitioned the geoboard into four equal sized
squares.
Teacher: How do you know that each section is a fourth?
Student A: Because there are four equal sized squares.
That means that each piece is a fourth of the whole
geoboard.
Student B: I partitioned the geoboard in half down the
middle. The section on the left I divided into two equal
sized squares. The other section I partitioned into two
equal sized triangles.
Teacher: How do you know that each section is a fourth?
Student B: Each section is a half of a half, which is the
same as a fourth.
Common Core Standard
Unpacking
3.G.1 Understand that shapes in
different categories (e.g., rhombuses,
rectangles, and others) may share
attributes (e.g., having four sides), and
that the shared attributes can define a
larger category (e.g., quadrilaterals).
Recognize rhombuses, rectangles, and
squares as examples of quadrilaterals,
and draw examples of quadrilaterals
that do not belong to any of these
subcategories.
In second grade, students identify and draw
triangles, quadrilaterals, pentagons, and
hexagons.
Third graders build on this experience and
further investigate quadrilaterals (technology
may be used during this exploration). Students
recognize shapes that are and are not
quadrilaterals by examining the properties of
the geometric figures. They conceptualize that
a quadrilateral must be a closed figure with
four straight sides and begin to notice
characteristics of the angles and the
relationship between opposite sides. Students
should be encouraged to provide details and
use proper vocabulary when describing the
properties of quadrilaterals. They sort
geometric figures and identify squares,
rectangles, and rhombuses as quadrilaterals.
Parallelograms include: squares, rectangles, rhombi, or other
shapes that have two pairs of parallel sides. Also, the broad
category quadrilaterals include all types of parallelograms,
trapezoids and other four-sided figures.
Example:
Draw a picture of a quadrilateral. Draw a picture of a
rhombus.
How are they alike? How are they different?
Is a quadrilateral a rhombus? Is a rhombus a quadrilateral?
Justify your thinking.
A kite is a quadrilateral whose four sides can be grouped
into two pairs of equal-length sides that are beside each
other.