SESSIONS #1- #3: ANGLES
GENERAL OUTCOMES
Students are expected to:
1. solve geometric problems using spatial reasoning (PS);
2. develop problem-solving skills (PS);
3. communicate mathematical ideas in speech, in writing, and graphically (C, TC);
4. develop skills in inquiry to investigate space and objects in the environment (PS);
5. Cooperate effectively with others (CIT).
6. use knowledge of characteristics and properties of shapes and solids to express mathematical ideas, and form and analyze
spatial and geometric relationships (AE, C);
7. Students will select and use a wide variety of tools and technology-supported methods to increase either the efficiency or
quality of results (TC);
8. use knowledge of characteristics and properties of angles to express mathematical ideas, and form and analyze spatial and
geometric relationships (AE, C);
*Essential Learning Outcomes:
Aesthetic Expression AE; Communication C; Citizenship CIT; Personal Development
PD; Problem Solving PS; Technological Competence TC)
Session #1 DEFINITION AND PROPERTIES OF A POINT, STRAIGHT LINE, LINE SEGMENT, RAY AND PLANE
SPECIFIC OBJECTIVES:
At the end of this unit
students will be able to
1. Construct and label
components of the
Cartesian plane,
including the x-axis,
y-axis, and origin
2. Plot points in the
form (x,y) on the
Cartesian Plane
3. Deduce the
coordinates of given
points plotted on the
Cartesian Plane
VOCABULARY
Cartesian plane: The
Cartesian plane, named after
the mathematician Rene
Descartes (1596 - 1650), is a
plane with a rectangular
coordinate system that
associates each point in the
plane with a pair of numbers.
Coordinates: A coordinate
is a number that determines
the location of a point along
some line or curve. A list of
two or three coordinates can
be used to determine the
location of a point on a
surface
x-axis: When referring to a
two and three-dimensional
plane, the x-axis refers to
the horizontal width of a two
or three-dimensional object
y-axis: a reference axis,
usually vertical, of a graph or
two- or three-dimensional
Cartesian coordinate system
PREVIOUS
SUGGESTED
SUGGESTED
KNOWLEDGE
RESOURCES
ASSESSMENT
Students are
familiar with the
concept of
Directed Numbers.
They also have
knowledge on the
definition and
orientation of right
angles and straight
line angles.
Writing utensils
Graph Paper
Long Ruler
Students construct and label
the components of the
Cartesian Plane and plot and
label given list of points in
the form (x,y)
Writing utensils
Graph Paper
Long Ruler
Writing utensils
Graph Paper
Long Ruler
Worksheet: Given a
Cartesian Plane with given
labeled plotted points,
students are required to
determine their coordinates,
writing them in the form
(x,y)
Worksheets containing at
least six(6) points in the
form ( x,y) and students
must represent these points
using a dot or X on graph
along which the y-coordinate
is measured
Origin: The origin has
coordinates (0,0). We can
think of the origin as the
center of the plane or the
starting point for finding all
other points.
Point: A point has no length
4. Explain what is
or width, it just specifies an
meant by the terms
exact location using
point, straight lines,
coordinates. The point A can
segments, rays, and
have the coordinates (5,4).
planes and show
Straight Line: Connects two
how these may be
points via the shortest path
represented on a
and continues indefinitely
Cartesian plane.
(forever) in both directions
Line Segment: Part of a line
between two points
Ray: A ray is a part of a line
5. Display how points,
that begins at a particular
straight lines,
point (called the endpoint)
segments, rays, and
planes relate in terms and extends endlessly in one
direction. A ray is also called
of their properties.
half-line.
Plane: A plane is a flat two
dimensional surface (similar
to a sheet of paper, but with
no thickness and no finite
length or width). A plane is
defined by three points, each
paper. Students are awarded
marks in accordance with a
Mark Scheme (Knowledge
& Comprehension: KC;
Algorithmic Thinking: AT;
Problem Solving: PS)
Geometrical
instruments
Graph paper
Writing utensils
Rubber band
Geoboard
Geometrical
instruments
Writing utensils
Students are required to
verbally explain the terms
point, straight line,
segments, rays and planes
and draw them on the
Cartesian plane using graph
paper.
Accurately make
representation of a point,
straight line, line segment,
ray and plane on a geoboard
and by drawing. Students
will be evaluated based on a
formulated rubric.
of which forms a line with
the other two points within
the plane.
Session #2: DEFINITON OF AN ANGLE AND THE TYPES OF ANGLES
SPECIFIC OBJECTIVES
At the end of this unit
students will be able to
1. Use geometrical
instruments to
measure and draw
angles in the range
0º – 360º (limit to
protractor and ruler).
VOCABULARY
PREVIOUS
KNOWLEDGE
Angle: an angle is
- Students have previous
the figure formed by
knowledge on the
two rays sharing a
definition and
common endpoint,
orientation of right
called the vertex of
angles and straight
the angle. The
line angles. They also
magnitude of the
know the definition
angle is the "amount
and the properties of a
of rotation" that
point, straight line,
separates the two
line segment, ray and
rays.
plane
Right Angle: An
angle that measures
90°
Acute Angle: An
angle that measures
less than 90°.
SUGGESTED
RESOURCES
Geometrical instruments
(ruler, compass,
protractor)
Writing utensils
SUGGESTED
ASSESSMENT
Activity Sheet- In
groups of three or four,
students will measure
and draw given angles
between 0º – 360º.
Results are checked for
accuracy.
Marks will be awarded
for accurate use of
geometrical instruments
as well as accuracy in
the size of angle drawn
and measured.
2. classify angles
according to type
(acute, right, obtuse,
straight, and reflex)
Obtuse Angle: An
angle that measures
more than 90°
Straight Line
Angle: An angle that
measures 180°
Reflex Angle: An
angle that measures
more than 180° but
less than 360°.
Intersection: a
single point where
two lines meet or
cross each other.
Vertex: Point at
which two line
segments intersect
(forming an angle)
Writing utensils
Geometrical instruments
Worksheets- drawing
and defining each type
of angle. Marks will be
awarded based on
understanding of the
types of angles and
accuracy of drawing.
Session #3: CALCULATING MISSING ANGLES
SPECIFIC OBJECTIVES
At the end of this unit
students will be able to
VOCABULARY
Adjacent angles:
two angles with a
common vertex and
1. investigate and state
a common side, but
the properties of
no
angles when two lines common interior
intersect;
points
Vertical angles:
two non-adjacent
angles formed by
two intersecting
lines.
Complementary
Angles: Two
Angles are
Complementary if
they add up to 90
2. Use angle properties
of intersecting lines to degrees (a Right
Angle). They don't
calculate missing
have to be next to
angles
each other.
Supplementary
Angles: Two
Angles are
Supplementary if
they add up to 180
degrees. But the
PREVIOUS
KNOWLEDGE
Students have previous
knowledge on the
definition and
orientation of right
angles and straight line
angles. They can also
identify and define an
angle and the types of
angles.
SUGGESTED
RESOURCES
Writing utensils
Geometrical instruments
(protractor, divider,
compass)
Calculator
Writing utensils
SUGGESTED
ASSESSMENT
Students are asked to
verbally explain the type
of angles formed when
two lines intersect.
Activity Sheet- Students
are required to draw two
intersecting lines and
measure the angles
formed. Marks will be
awarded based on a
formulated rubric.
Worksheet- Students are
asked to use angle
properties of intersecting
lines to solve various
problems based on
missing angles. Students
are awarded marks in
accordance with a Mark
Scheme (Knowledge &
Comprehension: KC;
Algorithmic Thinking:
angles don't have to
be together.
Vertically
Opposite Angles:
vertically opposite
angles are the
angles opposite
each other when
two lines cross
AT; Problem Solving:
PS)