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New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative
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Slide 2 / 97
5th Grade
Geometry
2011-11-02
www.njctl.org
Slide 3 / 97
Geometry Unit Topics
Click on the topic to go to that section
· Polygons
· Classifying Triangles & Quadrilaterals
· Coordinate Plane
· First Quadrant
Slide 4 / 97
Polygons
Click to return to the
table of contents
Slide 5 / 97
Examples of polygons and figures that are not polygons
These are polygons
These are not polygons
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Why these figures are not polygons
This is not a polygon.
to reveal
It is click
open,
not closed.
This is not a polygon.
The click
sides
cross over.
to reveal
This is not a polygon
click toare
reveal
Not all sides
straight.
Slide 7 / 97
A polygon is a simple, closed plane figure made up of 3
or more line segments.
Simple - line segments do not intersect
Closed - When you trace the figure, it ends at the
starting point.
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Slide 9 / 97
1 Is this figure a polygon?
Yes
No
Pull
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2 Is this figure a polygon?
Yes
No
Pull
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3 Is this figure a polygon?
Yes
No
Pull
Slide 12 / 97
4 Is this figure a polygon?
Yes
No
Pull
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5 Is this figure a polygon?
Yes
No
Pull
Slide 14 / 97
Polygons are named by
their number of sides.
Name
Number
of Sides
Triangle
3
Quadrilateral 4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
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6 How many sides does a heptagon have?
Pull
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7 How many sides does a nonagon have?
Pull
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8 Name the figure.
A Quadrilateral
B Hexagon
C Decagon
D Octagon
Pull
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9 Name the figure.
A Decagon
B Hexagon
C Nonagon
D Octagon
Pull
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Regular vs. Irregular Polygons
If the figure's sides and angles are congruent, it is called
a regular polygon.
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Regular vs. Irregular Polygons
If both the figure's sides and angles are not congruent, it
is called an irregular polygon.
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Slide 22 / 97
10
What kind of polygon is this?
A
regular
B
irregular
C
not a polygon
Pull
Slide 23 / 97
11
What kind of polygon is this?
A
regular
B
irregular
C
not a polygon
Pull
Slide 24 / 97
12
What kind of polygon is this?
A
regular
B
irregular
C
not a polygon
Pull
Slide 25 / 97
13
What kind of polygon is this?
A
regular
B
irregular
C
not a polygon
Pull
Slide 26 / 97
14
What kind of polygon is this?
A
regular
B
irregular
C
not a polygon
Pull
Slide 27 / 97
15
What kind of polygon is this?
A
regular
B
irregular
C
not a polygon
Pull
Slide 28 / 97
Classifying
Triangles &
Quadrilaterals
Click to return to the
table of contents
Slide 29 / 97
Classifying Triangles- Triangles can be classified
by their angles or their sides.
By Sides
Equilateral Triangle
All sides are congruent.
Isosceles Triangle
At least two sides are
congruent.
Scalene Triangle
No sides are congruent.
Match the picture to the definition
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16
Classify the triangle by its sides
A
equilateral
B
scalene
C
isosceles
Pull
Slide 31 / 97
17
Classify the triangle by its sides
A
equilateral
B
scalene
C
isosceles
Pull
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By Angles
Acute Triangle
All three angles are less
than 90 degrees.
Right Triangle
One angle is 90 degrees.
Obtuse Triangle
One angle is more than 90
degrees.
Match the picture to the definition
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18
Classify the triangle by its angles
A
acute
B
obtuse
C
right
Pull
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19
Classify the triangle by its angles
A
acute
B
obtuse
C
right
Pull
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20
Classify the triangle by its angles
A acute
B obtuse
C right
Pull
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Click to go to web site then
choose Triangle Sort.
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21
Classify the triangle.
A equilateral
B isosceles
C scalene
D acute
E
right
F obtuse
Remember: Classify by sides and
angles (put in two answers)
Pull
Slide 38 / 97
22
Classify the triangle.
A equilateral
B isosceles
C scalene
D acute
E
right
F
obtuse
Remember: Classify by sides and
angles (put in two answers)
Pull
Slide 39 / 97
23
If each of the angles in a triangle measures
60 , what is the triangle?
A equilateral
B isosceles
C scalene
D acute
E
right
F
obtuse
Remember: Classify by sides and
angles (put in two answers)
Pull
Slide 40 / 97
24
Classify the triangle.
A equilateral
B isosceles
C scalene
D acute
E
right
F
obtuse
Remember: Classify by sides and
angles (put in two answers)
Pull
Slide 41 / 97
25
Classify the triangle in the yield sign.
A equilateral
B isosceles
C scalene
D acute
E
right
F
obtuse
Remember: Classify by sides and
angles (put in two answers)
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26
Classify the triangle this bridge makes.
A equilateral
B isosceles
C scalene
D acute
E
right
F
obtuse
Remember: Classify by sides and
angles (put in two answers)
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Classifying Quadrilaterals
You must use the properties of quadrilaterals
to identify and classify them.
Trapezoids - Exactly one pair of parallel sides
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Classifying Quadrilaterals
You must use the properties of quadrilaterals
to identify and classify them.
Parallelogram - Opposite sides are congruent & parallel.
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Classifying Quadrilaterals
You must use the properties of quadrilaterals
to identify and classify them.
Rectangle - Special parallelogram with four right angles
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Classifying Quadrilaterals
You must use the properties of quadrilaterals
to identify and classify them.
Rhombus - Parallelogram with four congruent sides
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Classifying Quadrilaterals
You must use the properties of quadrilaterals
to identify and classify them.
Square - Rhombus with four right angles or a Rectangle with
four congruent sides.
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Quadrilateral
Parallelogram
Trapezoid
Rhombus
Rectangle
Square
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Polygon
Quadilateral
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Polygon
Quadilateral
Trapezoid
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Polygon
Quadilateral
Parallelogram
Trapezoid
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Polygon
Quadilateral
Parallelogram
Trapezoid
Rectangle
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Polygon
Quadilateral
Parallelogram
Trapezoid
Rectangle
Rhombus
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Polygon
Quadilateral
Parallelogram
Trapezoid
Rectangle
Square
Rhombus
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Click for web site and then choose polygon sort.
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27
Which of the following shapes is a
trapezoid?
A
C
B
D
Pull
Slide 57 / 97
28
Which of statement(s) do NOT describe the
figure?
A trapezoid
B parallelogram
C rectangle
D rhombus
E
square
Pull
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29
Which of the statements does NOT describe the
figure?
A trapezoid
B parallelogram
C rectangle
D rhombus
E
square
Pull
Slide 59 / 97
30
Which of the statement(s) does NOT describe
the figure?
A trapezoid
B parallelogram
C rectangle
D rhombus
E
square
Pull
Slide 60 / 97
31
Which of the following statements is true?
A
A square is not a rectangle.
B
A rectangle is a square.
C
A square is not a parallelogram.
D
A square is a rectangle.
Pull
Slide 61 / 97
32
Describe the figure. Choose all
answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
Pull
Slide 62 / 97
33
Describe the figure. Choose all
answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
Pull
Slide 63 / 97
34
Describe the figure. Choose all
answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
Pull
Slide 64 / 97
35
Describe the figure. Choose all
answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
Pull
Slide 65 / 97
36
Describe the shape of the top of the desk.
Choose all answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
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37
Describe the shape for the face of the clock.
Choose all answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
Slide 67 / 97
38
Describe the shape of the mouth of the shark.
Choose all answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
Slide 68 / 97
39
Describe the shape of this marker.
Choose all answers that apply.
A Quadrilateral
B Trapezoid
C Parallelogram
D Rectangle
E
Rhombus
F
Square
G
None of the Above
Slide 69 / 97
40
Which of the following shapes could never have
perpendicular sides?
A rectangle
B triangle
C circle
D square
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41
Which of these shapes could never have
parallel oppopsite sides?
A trapezoid
B triangle
C rectangle
D rhombus
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Coordinate Plane
Click to return to the
table of contents
Slide 72 / 97
The coordinate plane is formed by two
intersecting number lines called axes.
The horizontal line is the x-axis.
The vertical line is the y-axis.
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Origin
(0, 0)
The point at which the x and y axes intersect is called the origin.
The coordinates of the origin are (0, 0).
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y
x
Points can be plotted on the plane using one
coordinate from each of the axes.
These sets are called ordered pairs. The
x coordinate always appears first in these pairs. The
y coordinate appears second.
(x,y)
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To graph an ordered pair, such as (4,3):
· start at the origin (0,0)
· move right on the x-axis since the first
number is positive
· then move up since the second number is
positive
· plot the point
(4,3)
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y
x
(x,y)
This point is (3,2)
To plot the point, go over 3, then up 2
Slide 77 / 97
y
x
(x,y)
This point is (1,4)
To plot the point, go over 1, then up 4
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y
x
(x,y)
This point is (5,0)
To plot the point, go over 5, then up 0
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42
Which point is at the origin?
y
A
B
C
D
x
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43
Which point is at (1,3)?
y
A
B
C
D
x
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44
Which point is at (3,3)?
y
A
B
C
D
x
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45
Which point is at (0,5)?
A
y
B
D
C
x
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46
Which ordered pair is the origin?
A (4,0)
B (0,0)
C (0,4)
D (4,4)
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47
Which number in the ordered pair (7,3) is
the x-coordinate?
A 7
B 3
C 0
D x
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48
Which number in the ordered pair (5,9) is
the y-coordinate?
A 0
B 5
C 9
D y
Slide 86 / 97
49
Which number in the ordered pair (7,12)
is the y-coordinate?
A 7
B 12
C 0
D y
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50
Which number in the ordered pair (7,12) is
the x-coordinate?
A 7
B 12
C 0
D x
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First Quadrant
Click to return to the
table of contents
Slide 89 / 97
First Quadrant
When the x and y coordinates are both
positive, points are plotted in the first
quadrant.
Slide 90 / 97
Play Billy Bug and His Quest for Grub Game
Pull
for teacher instructions
Click for web site.
http://resources.oswego.org/games/BillyBug/bugcoord.html
Slide 91 / 97
Sometimes we are asked to create a shape in
the first Quadrant by finding the missing
point....
Try these examples.
Slide 92 / 97
51
Which point will create a square?
A (3,2)
B (5,1)
C (2,1)
D (1,2)
Slide 93 / 97
52
Which point will create a
right triangle?
A (1,4)
B (4,1)
C (3,4)
D (2,1)
Slide 94 / 97
53
Which point will create a
parallelogram?
A (4, 8)
B (8, 4)
C (9, 5)
D (7, 4)
Slide 95 / 97
54
Which point will create a
trapezoid?
A (1, 3)
B (1, 1)
C (3, 3)
D (3, 1)
Slide 96 / 97
55
Emily drew a figure on a coordinate grid.
The figure has one pair of opposite sides
that are parallel, but not equal. Which of
the following figures could Emily have
drawn?
A
C
B
D
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Coordinate Grid Geoboards Activity
· Work in partners.
· One partner creates a polygon on the
geoboard and writes down the vertices.
· Other partner plots the points, and
connects them with line segments.
· Compare the polygons, then switch roles.
This example, the
vertices are:
(1,3)
(4,1)
(4,3)
Click above to practice using the
National Library of Virtual
Manipulatives web site.