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Lenape Regional High School District – BOE Approved 2/15/12
Geometry
[Implement start year (2012-2013)]
Eileen Meyers, [email protected], ext. 8682, Stephanie Rieder-Ritter, [email protected], ext. 8768, Nikki Scott, [email protected], ext.
8808, Joanne Wagner, [email protected], ext. 8887
Unit 1 Spatial Relationships
Level 2: Approximately 35 days
Stage 1 – Desired Results
Established Goals
2009 NJCCC Standard(s), Strand(s)/CPI #
(http://www.nj.gov/education/cccs/2009/final.htm)
Common Core Curriculum Standards for Math and English
(http://www.corestandards.org/)
st
21 Century Themes
( www.21stcenturyskills.org )
Global Awareness
x Financial, Economic, Business and Entrepreneurial Literacy
Civic Literacy
Health Literacy
Environmental Literacy
Quantities N-Q: #1-3
st
Congruence G-CO: #1, 9, 12
Modeling with Geometry G-MG: #1, 3
Expressing Geometric Properties with Equations G-GPE: #4-6
21 Century Skills
Learning and Innovation Skills:
x Creativity and Innovation
x Critical Thinking and Problem Solving
x Communication and Collaboration
Information, Media and Technology Skills:
Information Literacy
Media Literacy
ICT (Information, Communications and Technology) Literacy
Life and Career Skills:
x Flexibility and Adaptability
x Initiative and Self-Direction
Social and Cross-Cultural Skills
x Productivity and Accountability
x Leadership and Responsibility
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Enduring Understandings:
Students will understand that . . .
Essential Questions:
EU 1
mathematical notation and language is necessary for a strong foundation
in Geometry.
EU 1
What is the significance of proper notation in the study of geometry?.
EU 2
geometric relationships and definitions can be used to construct geometric
figures and solve real world problems.
EU 2
Why do we measure?
EU 3
good decision making requires logical reasoning based on known facts.
EU 4
algebraic properties of equality are used in geometry to solve problems
and justify reasoning.
EU 2, EU 3
How does what we measure influence how we measure?
EU 3, EU 4
Why is it important to think logically?
EU 3, EU 4
What are the advantages and disadvantages to drawing conclusions from
given information?
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Knowledge:
Students will know . . .
EU 1, EU 2, EU 3, EU 4
special angle pairs can be used to identify geometric relationships and to
find angle measures.
EU 2
the special angle pairs formed by parallel lines and a transversal
are either congruent or supplementary.
formal geometric constructions can be created with a variety of
tools and methods to provide a visual representation of geometric
concepts.
Skills:
Students will be able to . . .
EU 1
identify and model points, lines, planes and their relationships.
identify and classify angles and their relationships.
utilize correct mathematical language and notation to
communicate ideas about geometric figures.
EU 2
make formal geometric constructions using various methods.
EU 3
make conjectures based on inductive reasoning.
EU 3
determine necessary and sufficient conditions for a statement to be true.
EU 2, EU 3
some mathematical relationships can be described using a variety of ifthen statements.
EU 3
by comparing the slopes of two lines it can be determined whether the
lines are parallel or perpendicular.
EU 2, EU 3, EU 4
utilize angle relationships to solve problems.
find the distance between a point and a line, and between two
parallel lines.
EU 3, EU 4
determine slopes of parallel and perpendicular lines.
EU 3, EU 4
formulas can be used to find the midpoint and length of any segment in the
coordinate plane.
EU 3, EU 4
write the equation of a line.
EU 3, EU 4
certain angle pairs can be used to determine whether two lines are
parallel.
EU 3, EU 4
formulate proofs involving segment and angle congruencies, parallel and
perpendicular lines.
EU 4
a line can be graphed and its equation written when certain facts about the
line, such as its slope and a point on the line, are known.
EU 3, EU 4
apply the midpoint formula and the distance formula to calculate length
and midpoint.
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Stage 2 – Assessment Evidence
Recommended Performance Tasks:.
You are seeking employment in the marketing field and will present your portfolio to a marketing director. Your portfolio will include a creative logo and
slogan. The logo is comprised of segments only. The segments are to be constructed to form a variety of geometric figures that are related to your
slogan and/or your product. The slogan, representing a product of your choosing that you will name, must be written as a conditional statement.
Include an explanation of why you chose your product and how your logo is related to your product. All written work must be typed.
Provide an oral/written/visual presentation of your finished product, including the geometric shapes contained in your logo.
All other specifications and requirements are to be determined by the classroom teacher.
Other Recommended Evidence:
Tests and quizzes to include: naming and identifying points, lines, planes, and angles; finding distance and midpoints on a number line and in
the coordinate plane; writing and solving algebraic equations about segment relationships and angle relationships; identifying the parts and
different forms of conditional statements; proofs on algebraic equations, segment relationships, angle relationships, parallel lines and the
angles formed by a transversal; writing linear equations; finding the distance between two parallel lines; constructions of/with segments,
parallel lines, angles, bisectors, and perpendicular lines
Assessed elements from the Performance Task
Other teacher–graded evaluations
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Stage 3 – Learning Plan
Suggested Learning Activities:
Before defining geometric figures, give examples and non-examples to have students discuss their observations. (A, M)
Give students a diagram (such as the one below) and have them discuss what can or cannot be assumed. (A, M)
A
B
1
E
F
2
C
D
TI-Nspire Activity: Points, Lines and Plane (M, T)
http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5024&t=5049&id=13167
* Students will identify parallel lines and planes.
* Students will identify perpendicular lines and planes.
* Students will recognize skew lines.
* Students will discuss the intersection of planes.
TI-Nspire Activity: Points. Lines and Distance (M. T)
http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5024&t=5049&id=13166
* Students will be able to recognize that the distance between two parallel lines is constant.
* Students will identify segments that represent the distance between two points, a point and a line, and parallel lines.
* Students will use appropriate tools strategically.
* Students will attend to precision.
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Complete proofs involving segment and angle congruence. (M, T)
Vocab Ladder based on past and current vocabulary – posted on District Geometry Wiki (A, M)
In-class journal to include 1.) definitions, diagrams, theorems, etc. 2.) real-life examples of the unit’s vocabulary (A)
The following is the suggested sequence of learning activities and number of days for the Geometry L2 class. Adjustments should be made
accordingly for other levels:
Approximate timeline for Level 2: 35 days
Identify and model points, lines and planes – day 1
Find segment lengths – day 2
Find distance and midpoint given two points – day 3
Find measures of and classify angles – day 4
Identify and use special angle pairs – day 5
Identify and name polygons – day 6
Construct congruent angles, congruent segments, and perpendicular lines – day 7, 8
Review and assessment – day 9, 10
Make conjectures based on inductive reasoning – day 11
Identify and use basic postulates about points, lines, and planes – day 12
Use algebra to write 2-column proofs – day 13
Write proofs involving segment addition and angle addition – day 14, 15, 16
Write proofs involving supplementary, complementary, congruent, and right angles – day 17, 18
Review and assessment – day 19, 20
Identify angle pairs formed by two lines and a transversal – day 21
Use theorems to determine relationships between angles formed by parallel lines and transversals – day 22
Find slope of lines and use it to identify parallel and perpendicular lines – day 23
Write and equation of a line using given information – day 24
Write proofs involving parallel lines – day 25, 26
Find the distance between two parallel lines – day 27, 28
Construct parallel lines – day 29, 30
Review and assessment – day 31, 32
Allow days for aforementioned activities
LRHSD (2011) Adapted from ASCD © 2004