Download 2012-2013 Enhanced Instructional Transition Guide Geometry Unit 01

Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Unit 01: Foundations of Geometry (10 days)
Possible Lesson 01 (4 days)
Possible Lesson 02 (6 days)
POSSIBLE LESSON 01 (4 days)
Lesson Synopsis:
Students develop an understanding of the structure of geometric systems from undefined terms including point, line, and plane to postulates and theorems.
Undefined terms are used to define foundational vocabulary for geometry. Undefined and defined terms are used to build postulates and theorems and applied to
problem situations.
TEKS:
G.1
Geometric structure. The student understands the structure of, and relationships within, an axiomatic system. The student is expected to:
G.1A
Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems.
G.1B
G.1C
Recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes. Supporting Standard
Compare and contrast the structures and implications of Euclidean and non-Euclidean geometries. Supporting Standard
G.2
G.2A
G.2B
G.7
G.7A
Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures. The student is expected to:
Use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships. Supporting Standard
Make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of
approaches such as coordinate, transformational, or axiomatic. Readiness Standard
Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures
and uses them accordingly. The student is expected to:
Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. Supporting Standard
Performance Indicator(s):
Study and analyze the map and number line provided below:
©2012, TESCCC
04/05/13
page 1 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
A
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
E
C
F
D
B
G
©2012, TESCCC
04/05/13
page 2 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
0
2
3
4
5
6
1
-5
-4
-3
-2
-1
A
E
C
G
B
D
F
Create a chart with a verbal description and specific examples that compare and contrast the concepts of points (location), lines, planes, distance (measure),
congruence, and “betweenness” (segment and angle addition postulates) among Euclidean and taxicab geometry. Summarize how formal constructions can be
used to create a number line and a protractor.
(G.1A, G.1B, G.1C; G.2A, G.2B; G.7A)
1C; 3D, 3H
Key Understanding(s):
• Euclidean geometry is an axiomatic system connecting undefined terms (point, line, and plane), definitions, postulates, theorems, and logical reasoning.
• Non-Euclidean systems of geometry have been developed for a variety of purposes and therefore, are built on a different structure of terms, definitions, and
postulates.
•
Underdeveloped Concept(s):
Although some students will have an extensive visual mathematical vocabulary and may be able to connect geometric terms to pictures or examples, the
students may have difficulty articulating formal verbal definitions of these terms.
©2012, TESCCC
04/05/13
page 3 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Geometry Unit 01
Vocabulary of Instruction:
• acute angle
•
•
•
•
•
•
•
•
•
•
•
•
•
•
adjacent angles
angle
“betweenness”
bisector of a segment
bisector of an angle
collinear
complementary angles
congruent angles
coplanar
defined terms
degree measure
distance
Euclidean geometry
•
•
•
•
•
•
•
•
•
•
•
•
•
•
grid
interior of an angle
intersection
length
line
line segment
linear pair of angles
non-collinear
non-coplanar
non-Euclidean geometry
obtuse angle
parallel lines
perpendicular lines
•
•
•
•
•
•
•
•
•
•
•
•
•
point
postulate
ray
right angle
skew lines
space
straight angle
supplementary angles
taxicab geometry
theorem
undefined term
vertex
vertical angles
plane
exterior of an angle
\
Suggeste
d
Day
1
Suggested Instructional Procedure
Topics:
• Euclidean geometry
Notes for Teacher
ATTACHMENTS
• Teacher Resource: Sample
Comparison Table for
Euclidean and Taxicab
Geometries KEY (1 per
teacher)
• Non-Euclidean (taxicab)
• Undefined terms (point, line, plane)
Engage 1
Students use taxicab geometry to introduce undefined terms in Euclidean geometry (e.g., map or grid map of
the area – plane; intersection – point; and street – line).
MATERIALS
• local map (1 per 4 students)
• local resource(s)
Instructional Procedures:
©2012, TESCCC
04/05/13
page 4 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
1. Display the terms point, line, and plane and facilitate a class discussion of these terms. Explain to
students that these are “undefined” terms that are the foundation of Euclidean geometry.
2. Place students in groups of 4. Distribute a copy of a local map to each group. Instruct students to identify
and discuss the characteristics of the map with group members. Facilitate a class discussion of student
responses, making sure that the map itself, streets, and intersections have been included as
characteristics.
Ask:
• What are the undefined terms in Euclidean geometry? (point, line, plane)
• What characteristics of the map correlate to the undefined terms in Euclidean geometry?
Although student answers may vary, students should be led to make the following connection: (map
or grid map of the area – plane; intersection – point; and street – line.)
Explain to students that a local map or city map with streets is a representation of taxicab geometry.
3. Instruct students to create a table to compare and contrast the “undefined” terms in Euclidean geometry
with the characteristics of taxicab geometry found on the map. Allow students time to complete their work,
and monitor students to check for understanding.
©2012, TESCCC
04/05/13
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
TEACHER NOTE
In this activity students compare
and contrast the foundational
terms for Euclidean and taxicab
geometries.
TEACHER NOTE
Use a map of the local area to
encourage student interest. A
local map may be printed from
online.
TEACHER NOTE
When comparing points and
intersections, students should
understand that a point actually
has no dimension as opposed to
an intersection of streets which
could be represented by a
square.
When comparing lines and
streets, students should
understand that a line actually
has only one dimension (length)
and goes on infinitely as opposed
to a street which has two
dimensions and has an end.
When comparing a plane and the
map, students should understand
that a plane and map both have
two dimensions (length and
width), but a plane goes on
infinitely as opposed to a map
which has an end. Comparisons
could also be made using the
curved surface of the earth, if a
page 5 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
map were to be extended.
Topics:
• Euclidean geometry
ATTACHMENTS
• Teacher Resource: Points,
Lines, and Planes KEY (1 per
teacher)
• Teacher Resource: Points,
Lines, and Planes (1 per
teacher)
• Handout: Points, Lines, and
Planes (1 per student)
• Undefined terms (point, line, plane)
• Defined terms
Explore/Explain 1
Students extend undefined terms to explore defined terms.
Instructional Procedures:
1. Distribute handout: Points, Lines, and Planes to each student. Refer students to the Background and
Geometric Vocabulary: Undefined terms. Instruct students to discuss Background and Undefined terms
with a partner. Display teacher resource: Points, Lines, and Planes, and facilitate a class discussion of
Naming and Symbolic Representation of Undefined terms.
2. Place students in pairs. Instruct students to answer problems 1 – 3, and discuss their responses with their
partner. Allow students time to complete their work, and monitor students to check for understanding.
Using teacher resource: Points, Lines, and Planes, facilitate a class discussion of student responses,
clarifying any misconceptions.
3. Refer students to Defined terms on handout: Points, Lines, and Planes. Using teacher resource: Points,
Lines, and Planes, facilitate a class discussion of Defined terms.
4. Refer students to Intersections of geometric terms on handout: Points, Lines, and Planes, and instruct
students to complete the blanks and compare responses with their partner. Allow students time to
complete their work, and monitor students to check for understanding. Using teacher resource: Points,
Lines, and Planes, facilitate a class discussion of student responses, clarifying any misconceptions.
Ask:
• What do you think coplanar means? Non-coplanar? Answers may vary. Coplanar means being in
the same plane. Non-coplanar means to not be in the same plane; etc.
• Is it possible for two lines to not intersect and not be parallel? (Yes, skew lines are non-coplanar
lines that do not intersect and are not parallel.)
• How important is the word coplanar to the definition of parallel? Explain. Answers may vary.
©2012, TESCCC
04/05/13
TEACHER NOTE
In this activity students investigate
the undefined terms in geometry
and use the undefined terms to
determine definitions for other
geometric vocabulary.
TEACHER NOTE
Most students have an intuitive
understanding of definitions (it
appears to be an angle), but are
not familiar with using critical
attributes to form definitions.
Transitioning students to reason
from what they think intuitively to
communicating and proving
critical attributes geometrically is
imperative in Geometry.
page 6 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
Skew lines also do not intersect, but they are in different planes. Parallel lines do not intersect, but
they are in the same plane; etc.
• What is a critical attribute for parallel lines? (They are in the same plane.)
• How many ways can two lines intersect? Describe. Answers may vary. If the lines just cross like
an “X”, they only intersect in 1 point. If the lines lay one on top of the other, they intersect in an infinite
amount of points; etc.
• How many ways can a plane and a line intersect? Describe. Answers may vary. If the line just
passes through the plane, they intersect in 1 point. If the line lies in the plane, they intersect in an
infinite amount of points; etc.
• How many ways can two planes intersect? Describe. Answers may vary. If the planes cross like
an “X”, they only intersect in a line. If the planes lay one on top of the other, they intersect in an
infinite amount of points; etc.
5. Instruct students to work with their partner to complete the Guided Practice problems on handout: Points,
Lines, and Planes. Allow students time to complete their work, and monitor students to check for
understanding. Using teacher resource: Points, Lines, and Planes, facilitate a class discussion of
student results, clarifying any misconceptions.
6. Instruct students to independently complete the Practice Problems on handout: Points, Lines, and
Planes. This may be assigned as homework, if necessary.
2
Topics:
• Lines and line segments
•
•
•
•
•
•
©2012, TESCCC
ATTACHMENTS
• Teacher Resource: Distance
and Length KEY (1 per
teacher)
• Teacher Resource: Distance
and Length (1 per teacher)
• Handout: Distance and
Length (1 per student)
Betweenness
Ruler postulate
Distance and length
Segment addition postulate
Definition of midpoint
Constructions (congruent line segments, perpendicular bisectors of line segments)
Explore/Explain 2
MATERIALS
• straight edge (1 per student)
• compass (1 per student)
Students continue to build an understanding of Euclidean geometry as a system by examining relationships in
lines and line segments, including the use of formal constructions.
TEACHER NOTE
In this activity students define and
04/05/13
page 7 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
Instructional Procedures:
1. Distribute handout: Distance and Length, a straight edge, and a compass to each student. Refer
students to the defined terms involving lines. Display teacher resource: Distance and Length, and
facilitate a class discussion of defined terms involving lines.
2. Place students in pairs. Instruct students to answer Example problems 1 – 4 on handout: Distance and
Length, and discuss their responses with a partner. Allow students time to complete their work, and
monitor students to check for understanding. Using teacher resource: Distance and Length, facilitate a
class discussion of student responses, clarifying any misconceptions.
Ask:
• What are parallel lines? (Coplanar lines that lie in the same plane and do not intersect.)
• Why does the definition of parallel lines include the word coplanar? Answers may vary. To
distinguish parallel lines from skew lines which also do not intersect, but are not in the same plane;
etc.
• What symbols indicate parallel lines in a drawing? In text? Answers may vary. Interior arrow
marks on paired lines in a diagram and
•
•
•
AB P CD
in text; etc.
What are perpendicular lines? Answers may vary. Lines that intersect to form right angles; etc.
How many right angles are formed by two intersecting perpendicular lines? (4)
What symbol indicates perpendicular lines in a drawing? In text? (A square at the intersection of
the two perpendicular lines; AB ⊥ CD .)
• What is a line segment? Answers may vary. A portion of a line marked by two endpoints; etc.
• How do you name segments? Is there more than one way? Answers may vary. With a bar over
the two endpoints which can be written starting with either endpoint AB or BA
; etc.
• How long is a segment (finite or infinite)? How many points does it contain? Answers may vary.
Its length is finite, but it contains an infinite number of points; etc.
• What is a ray? How do you name it? Is there more than one way? Answers may vary. Portion of
uuur
a line with 1 endpoint, can only be named beginning with the endpoint AB ; etc.
• What are some incorrect ways to name a ray? Answers may vary. You could not name the
uur
previous ray as BA because you must start with the endpoint; etc.
• How long is a ray? How many points are on a ray? Answers may vary. Both the length and
number of points in a ray are infinite; etc.
3. Refer students to Ruler Postulate on handout: Distance and Length, and instruct students to discuss the
©2012, TESCCC
04/05/13
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
investigate line segments. One
goal of the activity is for students
to discover 2 important
postulates: The Ruler Postulate
and the Segment Addition
Postulate. It is important for
students to understand that the
Ruler Postulate makes distance
and length measurement possible
by pairing numbers to a line just
as the mile marker system pairs
numbers to an interstate highway.
TEACHER NOTE
Some students may have been
introduced to the concept of
absolute value in middle school
and Algebra 1, but because it is
an Algebra 2 TEKS, most
students will probably not have an
understanding of this concept.
Therefore, when addressing the
Ruler Postulate and the
application of the distance
formula, be sure to develop the
concept of absolute value
geometrically (distance from
zero). For some classes you may
want to develop the concept
algebraically.
AB = a − b
12 = a − 5
, so
a − 5 = 12 or a − 5 = −12
a = 17 or a = −7
page 8 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
4.
5.
6.
7.
©2012, TESCCC
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
definition of the Ruler Postulate with their partner. Using teacher resource: Distance and Length,
facilitate a class discussion of the definition of the Ruler Postulate.
Instruct students to answer Example problems 5 – 14 on handout: Distance and Length, and discuss
their responses with a partner. Allow students time to complete their work, and monitor students to check
for understanding. Using teacher resource: Distance and Length, facilitate a class discussion of student
responses, clarifying any misconceptions.
Ask:
• Is distance or length ever negative? Answers may vary. Distance and length are always positive.
When a negative is attached, it relates to direction; etc.
• Is the distance from A to B always the same as B to A? (yes)
• How is betweeness illustrated on the number line? Answers may vary. The 2 is between the
number 1 and the number 3; etc.
Refer students to page 3 of handout: Distance and Length. Using teacher resource: Distance and
Length, facilitate a class discussion of the Betweenness Theorem, Segment Addition Postulate, and
Definition of Midpoint.
Instruct students to answer Guided Practice problems 15 – 20 on handout: Distance and Length, and
discuss their responses with a partner. Allow students time to complete their work, and monitor students
to check for understanding. Using teacher resource: Distance and Length, facilitate a class discussion of
student responses, clarifying any misconceptions.
Ask:
• How is betweenness illustrated by the Segment Addition Postulate? Answers may vary. On
given line segment AC, if point B is between points A and C, then AB + BC = AC; etc.
• What does the Segment Addition Postulate allow us to do with segment lengths? Answers may
vary. Add and subtract lengths to find distances; etc.
• What is a midpoint? Answers may vary. The middle point of a line segment in between the two
endpoints; etc.
• How is betweenness illustrated by the Definition of Midpoint? Answers may vary. Because the
midpoint is between the two endpoints, the distance from the midpoint to the one endpoint of the line
segment is equal to the distance from the midpoint to the other endpoint of the line segment;
betweenness is illustrated because the two distances from the midpoint to each of the endpoints of
the line segments is the same; twice the distance from the midpoint to one endpoint is equal to the
line of the entire line segment; etc.
Refer students to Constructions on handout: Distance and Length. Using teacher resource: Distance
and Length, model the construction of a congruent line segment and the construction of a perpendicular
bisector of a line segment.
04/05/13
page 9 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
8. Instruct students to use constructions to complete problems 21 – 24 on handout: Distance and Length,
and discuss their results with a partner. Allow students time to complete their work, and monitor students
to check for understanding. Using teacher resource: Distance and Length, facilitate a class discussion of
student results, clarifying any misconceptions.
9. Instruct students to independently complete Practice Problems on handout: Distance and Length. This
may be assigned as homework, if necessary.
3
Topics:
• Rays and angles
ATTACHMENTS
• Teacher Resource: All about
Angles KEY (1 per teacher)
• Teacher Resource: All about
Angles (1 per teacher)
• Handout: All about Angles
(1 per student)
• Protractor postulate
• Angle addition postulate
• Constructions (congruent angles, bisectors of angles)
Explore/Explain 3
Students continue to build an understanding of Euclidean geometry as a system by examining relationships in
rays and angles, including the use of formal constructions.
Instructional Procedures:
1. Facilitate a class discussion to debrief construction problems on handout: Distance and Length.
2. Distribute handout: All about Angles, a protractor, a straight edge, and a compass to each student. Refer
students to page 1. Display teacher resource: All about Angles, and facilitate a class discussion on
characteristics of angles.
3. Place students in pairs. Instruct students to complete problems 1 – 4 on handout: All about Angles, and
discuss their results with a partner. Allow students time to complete their work, and monitor students to
check for understanding. Using teacher resource: All about Angles, facilitate a class discussion of
student results, clarifying any misconceptions.
4. Refer students to Angle Classification on handout: All about Angles. Using teacher resource: All about
Angles, facilitate a class discussion on classifying angles.
5. Instruct students to complete problem 5 on handout: All about Angles, and discuss their results with a
partner. Allow students time to complete their work, and monitor students to check for understanding.
Using teacher resource: All about Angles, facilitate a class discussion of student results, clarifying any
misconceptions.
6. Refer students to Angle Postulates on handout: All about Angles. Using teacher resource: All about
©2012, TESCCC
04/05/13
MATERIALS
• protractor (1 per student)
• straight edge (1 per student)
• compass (1 per student)
TEACHER NOTE
In this activity students investigate
angles, their characteristics and
their relationships.
TEACHER NOTE
Vocabulary related to angles is
addressed in middle school, so
students should at least recognize
the vocabulary. Since this is a
review, the vocabulary portions of
the activity should move quickly
with more time focused on the
postulates, theorems, and
constructions.
page 10 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
7.
8.
9.
10.
11.
Notes for Teacher
Angles, facilitate a class discussion to review and name the Protractor Postulate and Angle Addition
Postulate.
Instruct students to complete problems 6 – 9 on handout: All about Angles, and discuss their results with
a partner. Allow students time to complete their work, and monitor students to check for understanding.
Using teacher resource: All about Angles, facilitate a class discussion of student results, clarifying any
misconceptions.
Refer students to Angle Relationships and Angle Theorems on handout: All about Angles. Using teacher
resource: All about Angles, facilitate a class discussion on angle relationships and angle theorems.
Instruct students to complete problems 10 – 11 on handout: All about Angles, and discuss their results
with a partner. Allow students time to complete their work, and monitor students to check for
understanding. Using teacher resource: All about Angles, facilitate a class discussion of student results,
clarifying any misconceptions.
Refer students to Angle Constructions on handout: All about Angles. Using teacher resource: All about
Angles, model the construction of a congruent angle and the construction of a bisector of an angle.
Instruct students to independently complete problems 12 – 17 on handout: All about Angles. This may
be assigned as homework, if necessary.
Topics:
• Euclidean postulates
ATTACHMENTS
• Teacher Resource: A
Geometric Look at the World
KEY (1 per teacher)
• Handout: A Geometric Look
at the World (1 per student)
• Defined terms
• Applications to the real world
Elaborate 1
Students connect their understanding of definitions and postulates of lines, angles, and other geometric
vocabulary into the context of the real world.
Instructional Procedures:
1. Facilitate a class discussion to debrief construction problems on the handout: All about Angles.
2. Place students in pairs. Distribute handout: A Geometric Look at the World, a protractor, and a ruler to
each student. Distribute 1 sheet of chart paper and 1 set of chart markers to each pair of students.
3. Instruct students to work with their partner to complete problems 1 – 9 on handout: A Geometric Look at
the World. Allow students time to complete their work, and monitor students to check for understanding.
Facilitate a class discussion of student results on problems 1 – 9.
4. Instruct students to work with their partner to complete problems 10 – 13, and create a display of their
©2012, TESCCC
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
04/05/13
MATERIALS
• protractor (1 per student)
• ruler (1 per student)
• chart paper (1 sheet per 2
students)
• chart markers (1 set per 2
students)
TEACHER NOTE
In this activity students connect
their understanding of definitions
page 11 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
results on chart paper to post in the classroom. Allow students time to complete their work, and monitor
students to check for understanding.
5. Using a round robin setting moving in pairs around the room, instruct students to compare and contrast
results on the poster displays of problems 10 – 13. Facilitate a class discussion of student findings on the
poster comparisons, and instruct students to make any necessary corrections to their own handouts.
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
and postulates of lines, angles,
and other geometric vocabulary
into the context of the real world
situations.
TEACHER NOTE
For problem 10 on handout: All
about Angles, monitor students
carefully to determine if they need
instruction on drawing a sketch of
the drawbridge that spans
Descartes’ Bay.
STATE RESOURCES
TEXTEAMS: High School
Geometry: Supporting TEKS
and TAKS
I – Structure; 1.0 Bayou City
Geometry, 1.1, Act. 1 (Bayou City
Flyers), 1.2, Act. 2 (Assumptions),
1.3, Act. 3 (Assumptions about
Bayou City), 1.4, Act. 4
(Definitions), 1.5, Act. 5
(Definitions in Bayou City), 1.6,
Act. 6 (Lunch Anyone?), 1.7, Act.
7 (Which Supervisor?) 1.8, Act. 8
(Walk or Fly?), 1.9, Act. 9 (Getting
Around Bayou City) may be used
as alternate activities.
©2012, TESCCC
04/05/13
page 12 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
4
Notes for Teacher
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related
concepts and processes by using the
Performance Indicator(s) aligned to this lesson.
ATTACHMENTS
• Teacher Resource (optional): Evaluating
Foundations of Geometry KEY (1 per teacher)
• Handout (optional): Evaluating Foundations of
Geometry PI (1 per student)
MATERIALS
• protractor (1 per student)
• ruler (1 per student)
• compass (1 per student)
Performance Indicator(s):
Study and analyze the map and number line
provided below:
A
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
TEACHER NOTE
If time permits, in addition to the Performance
Indicator assessment, handout (optional):
Evaluating Foundations of Geometry PI maybe
used as an additional assessment tool.
E
C
F
D
B
G
©2012, TESCCC
04/05/13
page 13 of 14
Geometry/Mathematics
2012-2013 Enhanced Instructional Transition Guide
Geometry Unit 01
Suggeste
d
Day
Suggested Instructional Procedure
Unit 01: Possible Lesson 01
Suggested Duration: 4 days
Notes for Teacher
0
2
3
4
5
6
1
-5
-4
-3
-2
-1
A
E
C
G
B
D
F
Create a chart with a verbal description and specific
examples that compare and contrast the concepts of
points (location), lines, planes, distance (measure),
congruence, and “betweenness” (segment and
angle addition postulates) among Euclidean and
taxicab geometry. Summarize how formal
constructions can be used to create a number line
and a protractor.
(G.1A, G.1B, G.1C; G.2A, G.2B; G.7A)
1C; 3D, 3H
©2012, TESCCC
04/05/13
page 14 of 14