NJDOE MODEL CURRICULUM PROJECT
CONTENT AREA: Mathematics
#
STUDENT LEARNING
OBJECTIVES
1
UNIT #: 1
CORRE
SPOND
ING
CCSS
Use the undefined
notion of
a point, line,
distance along a line
and distance around
a circular arc
to develop
definitions for
angles, circles,
parallel lines,
perpendicular lines
and line segments.
Course: Geometry
Develop definitions: angles
Develop definitions: circles
G.CO.1
(supportin
g content)
Develop definitions: parallel lines
UNIT NAME: Congruence, Proof, and Construction
Develop definitions: perpendicular lines
Develop definitions: line segments
2
Apply the
definitions of
angles, circles,
parallel lines,
perpendicular lines
and line segments
to describe
rotations,
reflections, and
translations.
-Include graph shown
and student describes
translations
-describe translation
and student sketches
on grid
Apply definitions of angles, circles, parallel lines, perpendicular lines to describe translations
G.CO.1,
(supportin
g content)
G.CO.4
(supportin
g content)
Apply definitions of angles, circles, parallel lines, perpendic.lines to describe reflections
Apply definitions of angles, circles, parallel lines, perpendic.lines to describe rotations
3
Develop and
perform rigid
transformations
that include
reflections,
rotations,
translations and
dilations using
geometric software,
graph paper, tracing
paper, and
geometric tools and
compare them to
non-rigid
transformations.
G.CO.2
(supportin
g content)
G.CO.3
(supportin
g content)
G.CO.4
(supportin
g content)
G.CO.5
(supportin
g content)
Develop & perform transformation; w reflectns/rotations/translations/dilations: Use software
(Geometer’s Sketchpad or free-ware Geogebra)
Develop and perform transformation; include reflectns/rotations/translations/dilations: Use graph paper/tracing paper & geometric tools.
Use rigid
transformations to
determine, explain
and prove
congruence of
geometric figures.
Use transformations … determine/explain/prove congruency (consider a PartA PartB,PartC type ex.)
G.CO.6
(major
content)
G.CO.7(
4
major
content)
G.CO8
(major
content)
Create proofs of
theorems involving
lines, angles,
triangles, and
parallelograms.
Create proofs involving lines
* (Please note
G.CO.10 will be
addressed again in
unit2 and G.CO.11
will be addressed
again in unit 4)
G.CO.9(
major
content)
G.CO.10
5
(major
content)
G.CO.11
(major
content)
Create proofs involving angles
Create proofs
involving triangles
Generate formal
constructions with
paper folding,
geometric software
and geometric
tools to include,
but not limited to,
the construction of
regular polygons
inscribed in a
circle.
(see full standard,
PARCC Blueprints,
etc. for more
details)
6
(**On test
students may be
asked to recognize
a construction
process and not
actually perform
the constructions…
they see the tools
and construction
marks and must
tell what is being
constructed; such
as a compass
creating arc marks
to bisect a segment
or angle)
Formal constructions (paper folding) (e.g., create a square, an isosceles triangle, a trapezoid, …. Angle
bisector, …. **Recognize appropriate steps)
Formal constructions (software) (Geometer’s Sketchpad; free-ware Geogebra)
G.CO.12
(supporting
content)
,
G.CO.13
(supporting
content)
Formal constructions (geometric tools)
Use Theorem w/vertical angles:
*G.CO.9(Lines and Angles):
Theorems include: vertical angles are
congruent; when a transversal crosses
parallel lines, alternate interior angles
are congruent and corresponding
Use Theorems transversals w/parallel lines:
angles are congruent; (content new
(alt.inter.angles/ corresponding angles)
from grade-8 but not theorems.)
points on a perpendicular bisector of
a line segment are exactly those
equidistant from the segment’s
endpoints.
Use Theorems w/perpendicular bisector of line
segment
Use Theorems w/interior angle sum/triangle
Use Theorems w/base angles isosceles Triangles congruent
Use Theorems w/segment joining midpoints 2sides triangle // and half length 3rd side.
Use Theorems w/medians of a triangle meet at a point
*G.CO.10 (Triangles): Theorems
include: measures of interior angles of
a triangle sum to 180°; base angles of
isosceles triangles are
congruent;(content known from gr.8,
not formal theorems)
the segment joining midpoints of two
sides of a triangle is parallel to the
third side and half the length; the
medians of a triangle meet at a
point.(gr.8 learn about proportional
sides in similar triangles but not
necessarily this)
Use Theorems opposite sides congruent (parallelogram)
*G.C0.11: (Parallelograms) Theorems include: opposite sides are
congruent, opposite angles are
congruent, and the diagonals of a
parallelogram bisect each other and
conversely,
rectangles are parallelograms with
congruent diagonals. (Content
included in unit 2, repeated to assess
fluency.) (These “facts” introduced in
grade-8 or earlier)
Use Theorems opposite angles congruent (parallelogram)
Use Theorems diagonals bisect each other (parallelogram)
Major Content Supporting Content Additional Content (Identified by PARCC Model Content Frameworks).
Bold type indicates grade level fluency requirements. (Identified by PARCC Model Content Frameworks).
PARCC-LIKE FORMATTED QUESTIONS


Traditional short-constructed response (fill in the blank)
Traditional multiple-choice (A-D)

Part A: Part B: Part C: Shape(s) or 3D form given with range of questions Part A: Part B: Part C: from simple and computational, to
more complex and apply or compare/contrast and finally to explain (similar format as open-ended HSPA type questions)

More than one correct answer: One statement or graphic question where there is more than one correct answer. (“Which of the
following are equivalent ….?” … “Check all that apply.” “Which of the following are/are not ….” “Which are congruent to ….?” “Which
are similar to ….?”
Multiple questions about one polygon or types .… Check off ‘yes’ ‘no’ for each part
Include details in given that are essential (include which are not ….)
Compare and contrast data presented in different formats: graph, table, equation, scenario (i.e. compare rate-of-change; who running
faster?)
Compare and contrast different processes used (compare 2 different students’ work and solutions; who is correct and why?) … could be
appropriate for a construction example
In context: use to solve a “word problem.”
Draw, sketch, label, plot
Read scenario (from one paragraph to multiple) … find evidence in given information to support answer (important Language Arts
standard)
Explain process, Defend understanding/solution Vocabulary: rising/falling, positive/negative, increasing/decreasing, relationship
between x & y?, rate-of-change, …. adjacent, corresponding, (Many were used in grade-8 but are not ‘comfortable’ words; not used in
everyday language or readings.)
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RESOURCES:
PARCC: http://www.parcconline.org/search/node/?keys=PARCC+TYPES
PARCC content frameworks: http://www.parcconline.org/mcf/mathematics/parcc-model-content-frameworks-browser
PARCC high school tasks: http://www.ccsstoolbox.com/
Dana Center Toolbox : http://www.ccsstoolbox.com/ and http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdf
Achieve The Core: Annotated Tasks http://achievethecore.org/dashboard/300/search/1/2/9/10/11/12/page/786/annotated-tasks-list-pg8,
Achieve The Core: Annotated Lessons HS http://achievethecore.org/dashboard/300/search/1/2/9/10/11/12/page/855/annotated-lessonslist-pg
See Grade 8 math Common Core standards brief outline: http://achievethecore.org/content/upload/SAP_Focus_Math_8.pdf
Illustrative Math https://www.illustrativemathematics.org/standards/hs
NCTM: http://www.nctm.org/