Subject Area: 7th grade Algebra
Supplemental Pre-Algebra Lesson
Lesson Design
Mathematics
Grade Level: 7
Benchmark Period: CST
Duration of Lesson: 2 hour
Standard(s): M.G. 3.1a: Identify basic elements of geometric figures (e.g., altitudes, mid-points,
diagonals, angle bisector & perpendicular bisectors, central angles, radii, diameters, & chords of circles).
Learning Objective: Students identify basic elements of geometric figures.
Big Ideas involved in the lesson:
Accurately naming, identifying and describing basic elements of geometric figures such as those listed
in the standard
As a result of this lesson students will:
Know:
 Vocabulary: altitude, midpoint, diagonal, central angle, angle bisector, perpendicular bisector,
radius, diameter, chord, bisector, perpendicular, center of a circle, straightedge, ruler, vertices,
segment, opposite, base, polygon
 The properties of a rectangle, sphere, parallelogram, rhombus, trapezoid, triangle, & circle
 Symbols of geometric attributes: Perpendicular  , Parallel ||, Ray  , Line  , Line Segment
 , Angle  Right angle  , Triangle
Understand:
 Altitude can either be in the interior, exterior or on a side of a triangle.
 A right angle is denoted with a box in the angle.
 Order makes a difference when reading polygons, angles and rays.
Be Able To Do:
 Identify geometric figures including altitudes, diagonals, angle bisector, perpendicular bisector &
midpoints.
 Identify the radii, diameter & chords of a circle.
Assessments:
Formative: Assessment By
CFU Questions:
What will be evidence Walking Around, Closure, quiz  Identify each part of a figure
of student knowledge,
 Draw the figure described.
understanding &
Summative: Unit Test, CST
ability?
Lesson Plan
Much of this standard is review, though there are a few new relatively new
Anticipatory Set:
terms like angle bisector and chord.
a. T. focuses students
b. T. states objectives
The review is housed in a PowerPoint called M&G 3.1a anticipatory set
c. T. establishes purpose of
the lesson
Definition review: In each case, give the definition, symbolic
d. T. activates prior
representation and a diagram. (See attachment M&G 3.1 a definition
knowledge
review which can be used as a handout or to project the shapes.)
 Line: A series of points thatsextends
in two directions without end.
uur
Line AB is represented as: AB
A
B


1
Line segment: Part of line between two fixed endpoints.
Line segment AB is represented as: AB
A
B
Ray: Part of a line that extends in one direction with a fixed end point.
uuur
Ray AB is represented as AB
A
B
Lesson Design
Mathematics







Angle: Two rays with a common end point.
Angle ABC is represented as: AB C or as B
A
B
Right Angle: An angle that measures exactly 90 degrees; or anCangle
whose rays are perpendicular.
B is a right angle
B
Acute Angle: An angle that measures less than 90 degrees
C is an acute angle
C
Obtuse Angle: An angle that measures more than 90 degree
A is an obtuse angle
C
Straight Angle: An angle that measures exactly 180 degrees
D is a straight angle
D
Radius (plural is radii): A segment that has one endpoint at the center
of a circle and another endpoint on the circle.
A
B
AB is a radius of circle O.
Diameter: A chord that passes through the center of the circle. A
BC is a diameter of circle O.
E

A
D
Chord: A segment whose endpoints are on the circle.
DE is a chord of circle O.
Explain how/model: Teacher gives students a definition and a pictorial
Instruction:
example. After each definition the teacher pauses to check for
a. Provide information
understanding as the students produce their own example and picture.
 Explain concepts
For some of the new words there are Frayer models which will be shared
 State definitions
 Provide exs.
with the students.
 Model
Altitude: Any segment from a vertex of a figure, perpendicular to the
b. Check for Understanding opposite side of the figure, or its extension.
 Pose key questions
Begin with Frayer model. Explain definition and model. Go over examples
E
 Ask students to explain and non-examples.
concepts, definitions,
Examples of Altitudes:
A
B
attributes in their own
words
G
 Have students
F
discriminate between
EG and FG are both altitudes of
EFG
examples and nonexamples
D
C
 Encourage students
E
generate their own
AE is an altitude to side DC of
ABCD
examples
2
B
A
Lesson Design
Mathematics

Use participation
Midpoint: The center of a line segment.
Examples of midpoints:
M
A
B
M is the midpoint of AB
X is the midpoint of PQ
Y is the midpoint of QR
Z is the midpoint of PR
Diagonal: A segment in a polygon that connect two nonconsecutive
vertices.
K
L
Examples of diagonals
F
G
J
M
N
O
JL , JM and JN are 3 of the
diagonals of hexagon JKLMNO
H
E
FH is one of the diagonals
of
EFGH
Perpendicular bisector: A line, segment, or ray that is perpendicular to a
segment at its midpoint.
A
GO over Frayer Model
Examples of perpendicular bisectors:
X
j
A
M
Line j is the perpendicular
bisector of AB
B
C
Y
B
suur
XY is the perpendicular bisector
of side BC in ABC
Angle bisector: A ray that divides a given angle into two congruent angles,
Q
each half the size of the given angle.
Go over Frayer model
Examples of an Angle Bisector:
A
P
R
S
B
D
uuur
BD is the angle bisector of
ABC
3
C
Lesson Design
Mathematics
QS is the angle bisector of PQR
Central angles: An angle
whose vertex is the center of a circle and whose rays contain radii of the
circle. (Go over Frayer model)
Examples of Central Angles:
C
A
O
B
P
D
CPD is a central
angle
of circle P.
AOB is a central angle of circle O.
CFU using white boards. Give students a geometric element such as
altitude and have them draw it. Have students draw non-examples of some
of the figures. Discuss why some of the examples work and why the nonexamples don’t.
Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step along
w/students at the same
time
b. Elicit overt responses from
students that demonstrate
behavior in objectives
c. T. slowly releases student
to do more work on their
own (semi-independent)
d. Check for understanding
that students were correct
at each step
e. Provide specific knowledge
of results
f. Provide close monitoring
What opportunities will
students have to read, write,
listen & speak about
mathematics?
Closure:
a. Students prove that they
know how to do the work
b. T. verifies that students
can describe the what and
why of the work
4
Teacher provides new examples and works with students to identify the
basic elements of the geometric figures. (See guided Practice ws)
Teacher demonstrates sketching diagrams given written descriptions.
Then, teacher provides examples for students to try drawing on their own.
Examples on Guided Practice Sheet:
a. Circle M with radius MN
b. Perpendicular Bisector YZ on line WX.
uuur
c. ABC with an angle bisector BD
d. Chord ST on circle U
e.
ABC with altitude AE
f. Mid-point K on HJ
CFU – For each of the examples, below, students first work with a partner,
then do examples alone, all on white boards.
Students will read the definitions off of the projection screen in pairs, write the
definitions in their notebooks, listen to instruction, speak and write closure prompt in
pairs.
Describe and draw a picture of a perpendicular bisector for segment AB.
Lesson Design
Mathematics
c. Have each student perform
behavior
Independent Practice:
Worksheet 3.1a
a. Have students continue to
practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
Resources: materials needed M&G 3.1a Independent Practice file
to complete the lesson
M&G 3.1a anticipatory set Powerpoint
M&G 3.1a Definitions Review
M&G 3.1a new terms file
M&G 3.1a guided practice
Frayer models for angle bisector, altitude, perpendicular bisector and central angle
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