ACEI Standard 3c. Development of critical thinking,
problem solving, performance skills The following presentation is a geometry lesson for fifth to
sixth grade students. The slides show photographs of
different houses and an explanation or definition of
geometry terms. The students are also shown an example
of each term that has been highlighted within each picture.
The students are then to use their critical thinking skills to
search out more of the specified angle, shape, or line within
each picture.
Geometry
Around
Us
By Danielle LeoGrande
All pictures taken near Syracuse, NY
Directions
•This is your geometry workbook. Each page contains
definitions and illustrations of key geometry concepts
(ideas).
•After reading the definitions and looking at the
examples you are to go hunting for more of the same
geometric ideas that are hidden in the picture.
•Use a crayon or colored pencil to trace or highlight
each geometric idea that you find.
•Remember to be creative and think outside the box.
•Happy hunting!
Some of the important geometric
ideas that you will be searching for
are:
•Lines
•Angles
•Triangles
•Quadrilaterals
•Other polygons
•And much more…
Parallel Lines
Parallel lines are lines
that run in the same
direction and will never
meet. The distance
between the lines is
fixed, which means that
it never changes.
Here is an example of
parallel lines.
Can you find more
parallel lines?
Intersecting Lines
Intersecting lines are
lines that meet at a
single point. When the
lines intersect (meet)
angles are formed.
Here is an example of
intersecting lines.
Can you find more
intersecting lines?
Perpendicular
Lines
Perpendicular lines are
lines that intersect at a
point to form a 90° angle.
All perpendicular lines
are intersecting lines,
however not all
intersecting lines are
perpendicular.
Here is an example of
perpendicular lines.
Can you find more
perpendicular lines?
Angles
Acute angles measure less
than 90°.
Obtuse angles measure more
than 90°.
Right angles measure exactly
90°.
Here are some examples of
acute angles, obtuse angles
and right angles.
Can you find more acute
angles, obtuse angles, and
right angles?
Congruent Angles
Congruent angles are
angles that have the
same measurement.
Congruent angles do
not have to have the
same orientation (do
not have to be facing the
same way).
Here is an example of
congruent angles.
Can you find more
congruent angles?
Adjacent Angles
Adjacent angles are
angles that are right next
to each other. Adjacent
angles share one line
segment.
Here is an example of
adjacent angles.
Can you find more
adjacent angles?
Supplementary
Angles
Two angles are called
supplementary if the sum of
their angles is equal to 180°.
Supplementary angles can be
adjacent (next to each other), or
they may not be adjacent (not
next to each other).
Here is an example of adjacent
supplementary angles.
Here is an example of
supplementary angles that are
not adjacent.
Can you find more adjacent
supplementary angles.
Can you find more
supplementary angles that are
not adjacent?
Complementary
Angles
Two angles are called
complementary when the sum
of their angles is equal to 90°.
Complementary angles can also
be adjacent or not adjacent.
Here is an example of adjacent
complementary angles.
Here is an example of
complementary angles that are
not adjacent.
Can you find more adjacent
complementary angles?
Can you find more
complementary angles that are
not adjacent?
Triangles
Right triangles have one
angle that is equal to 90°.
A triangle is acute if all of it’s
angles are less than 90°.
Obtuse triangles have one
angle that is greater than 90°.
Here are some examples of
right triangles, acute
triangles, and obtuse
triangles.
Can you find more right
triangles, acute triangles, and
obtuse triangles?
Equilateral
Triangles
Equilateral triangles have
three sides of equal length
and three angles of equal
measure. All angles of
equilateral triangles
measure 60°.
Here is an example of an
equilateral triangle.
Can you find more
equilateral triangles?
Isosceles Triangles
An Isosceles triangle
has two sides of equal
length and two angles of
equal measure. The
equal angles are always
opposite the equal sides.
Here is an example of an
isosceles triangle.
Can you find more
isosceles triangles?
Scalene Triangles
A scalene triangle has
three sides of different
lengths and three angles
of different measure.
Here is an example of a
scalene triangle.
Can you find more
scalene triangles?
Polygons
Polygons are closed
figures that are made up
of several line segments
that are joined together.
The sides do not cross,
and exactly two lines
meet at every vertex.
Here are some examples
of polygons.
Can you find more
polygons?
Quadrilaterals
Quadrilaterals are two
dimensional, four sided
polygons.
Quadrilaterals have
four internal angles.
Here are some examples
of quadrilaterals.
Can you find more
quadrilaterals?
Parallelograms
A parallelogram is a
quadrilateral that has
opposite sides that are
parallel and of equal
length. The opposite
angles are also of equal
measure.
Here are some examples
of parallelograms.
Can you find more
parallelograms?
Rectangles
A rectangle is a special
parallelograms which
has equal and parallel
opposite sides. All of the
rectangle’s angles are
right angles.
Here are some examples
of rectangles.
Can you find more
rectangles?
Square
A square is a special
rectangle that has four
sides of equal lengths
and four right angles.
Here is an example of a
square.
Can you find more
squares?
Trapezoid
A trapezoid is a four
sided polygon that has
exactly two parallel
sides.
Here is an example of a
trapezoid.
Can you find more
trapezoids?
Other Polygons
A pentagon is a polygon with
five sides.
A hexagon is a polygon with
six sides.
Here is an example of a
pentagon.
Here is an example of a
hexagon.
Can you find more
pentagons?
Can you find more
hexagons?
Other Polygons
cont.
Octagons are polygons
that have eight sides.
Here is an example of an
octagon.
Can you find more
octagons?
Convex Polygons
A polygon is a convex
polygon if a straight
line drawn through it at
any point crosses at
most two sides. Every
interior angle in a
convex polygon is less
than 180°.
Here are some examples
of convex polygons.
Can you find more
convex polygons?
Concave Polygons
A polygon is a concave
polygon if you can draw at
least one straight line
through it that crosses
more than two sides.
Concave polygons have at
least one interior angle
that is greater than 180°.
Here are some examples of
concave polygons.
Can you find more
concave polygons?
Symmetric
Polygons
Symmetric polygons have
the quality that when they
are bisected into two
congruent parts, each point
on one side of the line of
symmetry (bisection line)
will have a reflective point
on the other side of the
bisection line.
Here are some examples of
symmetric polygons.
Can you find more
symmetric polygons?
Non-Symmetric
Polygons
When bisected, a non –
symmetric polygon
does not have a
reflective point for every
point across the line of
symmetry (bisection
line).
Here are some examples
of non-symmetric
polygons.
Can you find more nonsymmetric polygons?
Translation
When an object is
translated, all of the points
in the object are moved in a
straight line in the same
direction. Size, shape, and
orientation (direction the
object faces) all stay the same.
The object “slides” from one
place to another.
Here is an example of a
translated object.
Can you find more
translated objects?
Reflection
When an object is
reflected, all points of
the object are reflected or
“flipped” over a line called
the axis of reflection. The
reflected object looks
backwards or reversed
from the original.
Here is an example of a
reflected object.
Can you find more
reflected objects?
The next time you are walking down your
street, sitting in your classroom, or playing on
the playground take a look around you.
Shapes are everywhere and in everything.
They are not always obvious, sometimes you
have to take a good look. After a little
practice, finding the geometry in your day to
day life will be a breeze…
Differentiation
It is the teacher’s responsibility to ensure that every child’s learning challenges are
accommodated for. Teachers can accommodate for learning challenges by
changing any number of things such as lesson content, lesson process, student’s
expected output, or the learning environment.
Children that have difficulty with fine motor skillsTeachers can show these students the photographs and then the students can
illustrate the geometric concept that they see by using the geoboards from the
http://www.nlvm.usu.edu/ web page or from
http://www.mathclub.com/download/download.html.
Children that are visually impairedThese students can be given shapes traced with glue on construction paper and be
asked to color in the shapes. They can the pick the corresponding shape out of a
basket full of blocks that correlate to the geometric concepts in the lesson.
Lines
I would like the students to be able to differentiate between
parallel, perpendicular, and intersecting lines. The students
should also understand that all perpendicular lines are
intersecting, but all intersecting lines are not perpendicular.
Angles
I would like the students to be able to differentiate between
acute, right, obtuse, and straight angles. The students should
also be able to identify what it means for angles to be
congruent, adjacent, complementary, and/or supplementary.
Triangles
I would like the students to be able to compare and contrast
triangles. The students should understand that triangles, like
angles, can be acute, right, or obtuse. The children should also
be able to compare and contrast isosceles triangles, equilateral
triangles, and scalene triangles. Students should understand
that the measure of all of the angles of a triangle add up to 180°.
Quadrilaterals
I would like the students to be able to compare and contrast
quadrilaterals so that they will know and understand the
individual properties of the most common quadrilaterals. The
students should be able to identify squares, rectangles,
rhombuses, parallelograms, and trapezoids.
Other Polygons
I would like the students to understand the difference between
convex and concave polygons. The students should also be
able to identify polygons that are symmetric or non-symmetric.
The students should be able to identify and name other
polygons, recognizing that their names are related to the
number of sides and angles that are present.
Rigid Transformations
I would like for the students to be able to understand and
illustrate the properties of translation, rotation, and reflection.
The students should be able to speak to each transformation
and be able to compare and contrast the way each object looks
after it has been transformed in some way. The students should
realize that transforming the object does not change the
perimeter, length, or area of the object.
Relationships
The final thing that I would like for the students to develop is
a relationship between all of the concepts that we have
discussed in the lesson. I would like for the students to see a
connection between all of these geometric concepts and to
also be able to connect geometry with their every day lives.
Standards
3.PS.5 Formulate problems and solutions from everyday situations
3.PS.12 Use physical objects to model problems
3.G.1 Define and use correct terminology when referring to shapes (circle, triangle,
square, rectangle, rhombus, trapezoid, and hexagon)
3.G.2 Identify congruent and similar figures
3.G.5 Identify and construct lines of symmetry
4.PS.11 Make pictures/diagrams of problems
4.CM.5 Share organized mathematical ideas through the manipulation of objects,
drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions
in written and verbal form
4.CM.10 Describe objects, relationships, solutions, and rationale using appropriate
terminology
4.CN.6 Recognize the presence of mathematics in their daily lives
4.R.4 use standard and non-standard representation with accuracy and detail
4.R.5 Understand similarities and differences in representations
Standards (cont.)
4.G.1 Identify and name polygons, recognizing that their names are related to the
number of sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon)
4.G.2 Identify points and line segments when drawing a plane figure
4.G.6 Draw and identify intersecting, parallel and perpendicular lines
4.G.8 Classify angles as acute, right, obtuse, or straight
5.CM.9 Increase their use of mathematical vocabulary and language when
communicating with others
5.G.2 Identify pairs of similar triangles
5.G.4 Classify quadrilaterals by properties of their angles and sides
5.G.6 Classify triangles by properties of their angles and sides
5.G.9 Identify pairs of congruent triangles
5.G.11 Identify and draw lines of symmetry of basic geometric shapes