Archdiocese of Newark Catholic Schools Curriculum Mapping
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Archdiocese of Newark Catholic Schools
Curriculum Mapping
Curriculum mapping is a process that helps schools and districts/dioceses determine the “agreed-upon” learning for all students. Curriculum
mapping was undertaken in the Archdiocese of Newark in order to ensure that a consistent, clearly articulated curriculum infused with Gospel values
is being provided to all students in our schools. The curriculum maps for the Catholic schools of the Archdiocese of Newark identify the content to be
taught and skills to be mastered at each grade level.
The expertise and experience of the educators within our schools is the main source for determining the content and skills students will be expected
to master. The Archdiocesan curriculum maps are developed through a collaborative process which involves individual teacher contributions, small
group sessions and larger group meetings. Relevant educational standards, including those proposed by content area experts, the New Jersey Core
Curriculum Content Standards, and the Common Core State Standards, are used as a resource in the curriculum mapping process. The resulting
consensus maps reflect the collective thinking of classroom teachers based on their observation of student learning and their knowledge of
educational practice and research. The Archdiocesan curriculum maps include teacher generated ideas for the infusion of Gospel values and faith
connection activities.
While the curriculum maps clearly articulate the expected learning for all students, individual teachers have the flexibility to teach the content and
skills in their own manner by:
utilizing their own particular strengths and teaching style
addressing the varying learning needs of their students
determining the order in which the content and skills are presented within a marking period
including additional content and skills once students have met the learning expectations identified in the curriculum map
Administrators at all levels will maintain the responsibility to ensure that teachers are following the curriculum maps and that appropriate teaching is
being conducted. This will be done through a combination of classroom observations, faculty meetings, professional development opportunities and
teacher evaluations, as well as by using various measurement tools, including but not limited to in-class and standardized testing. The Archdiocesan
curriculum maps will help ensure the academic excellence that is integral to the mission of our Catholic schools and will provide educators and
parents with a clear understanding of the learning expectations at each grade level.
High School Geometry
July 2014Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
This curriculum map reflects the general expectations of student learning in Geometry at the high school level. Each school will determine
the course-specific expectations based on the level of the course or courses offered. Schools will also determine the sequence in which the
various topics are taught within the specific course.
Basics of Geometry Basics of Geometry Student learning will be Gospel values should be
Inductive and Demonstrate assessed on a continual evident in the classroom
Deductive basis using various types environment and
understanding of the basic
reasoning of formal and informal referenced and reinforced
terms in geometry.
Conjecture assessments. A list of throughout the
Patterns Formulate conjectures possible assessment curriculum.
Counterexample based on inductive methods is provided
below: Gospel Values
reasoning.
Community
Tests
G.CO.1 Know precise definitions of o Points, Space, Compassion
Use patterns to determine Quizzes
angle, circle, perpendicular line, line, rays, planes the next number in a Faith in God
parallel line, and line segment, based o Collinear and Projects
sequence. Forgiveness
on the undefined notions of point, Non-collinear Homework
line, distance along a line, and points Hope
Sketch and label points, Classwork
distance around a circular arc. o Coplanar Justice
lines, and planes. Student presentations
o Intersecting lines Love
Observation of student
and planes Compare and contrast line, Peace
work
o Parallel, skew, ray, and segment.
Critical thinking Respect For Life
perpendicular
lines activities Service
Identify opposite rays,
o Line segment collinear, and non- Performance Tasks Simplicity
o Coordinate on a collinear points. Online Programs Truth
number line Class participation
o Vertex Classify lines as parallel, Teachers will also
o Acute, Right, Mid-term exams
perpendicular, or skew. highlight elements of
Obtuse, Straight Final exams
Catholic identity that can
angles Problem-solve using the be related to topics in the
Segment Addition Math curriculum.
Postulate.
High School Geometry July 2014
Page 1Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
G.CO.7: Use the definition of Analyze errors in various
congruence in terms of rigid motions to o Congruent sketches.
show that two triangles are congruent if segments
and only if corresponding pairs of sides o Midpoint and Calculate the length of a
and corresponding pairs of angles are distance formulas line segment by use of the
congruent.
o Angle distance formula or a
Congruence number line.
o Congruent angles
o Angle bisector Use absolute value of the
difference of coordinates
G.CO.9: Prove theorems about lines and of points to determine the
angles. Theorems include: vertical o Segment Addition length of a line segment.
angles are congruent; when a Postulate
transversal crosses parallel lines, o Segment addition Use the midpoint formula
alternate interior angles are congruent o Angle Addition to find the midpoint of a
and corresponding angles are Postulate line segment.
congruent; points on a perpendicular
bisector of a line segment are exactly Measure segments to
those equidistant from the segment's determine congruency.
endpoints.
o Perpendicular Analyze errors in the
bisector application of the distance
and midpoint formulas.
Problem-solve and
determine angle
measurements using the
Angle Addition Postulate.
Classify angles by
measure.
Identify parts of an angle.
High School Geometry July 2014
Page 2Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Use the definition of an
angle bisector to find the
measure of angles.
Problem-solve using
congruent angles.
Analyze errors in problems
dealing with angles.
Coordinate Coordinate Geometry
Geometry
N.RN.2: Rewrite expressions involving Perform basic function
radicals and rational exponents using o Radicals- adding, with radicals.
the properties of exponents. subtracting,
multiplying, Use the coordinate plane to
dividing represent points.
o Simplifying
radicals Name the quadrants or axis
G.GPE.4: Use coordinates to prove and be able to identify the
simple geometric theorems quadrant in which or axis
algebraically. For example, prove or on which a point lies.
disprove that a figure defined by four o Ordered pair
given points in the coordinate plane is a o Coordinate plane Find the distance between
rectangle; prove or disprove that the o Plotting points in two points on the
point (1, √3) lies on the circle centered the coordinate coordinate plane.
at the origin and containing the point plane
(0, 2).
o Quadrants Find the midpoint of a line
segment graphed on the
coordinate plane.
High School Geometry July 2014
Page 3Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Verify the midpoint is
o Graphing lines on equidistant from the
the coordinate endpoints.
G.GPE.5: Prove the slope criteria for plane
parallel and perpendicular lines and use o x and y intercepts Apply slope of lines to
them to solve geometric problems (e.g.,
o Slope determine if lines are
find the equation of a line parallel or
perpendicular to a given line that passes o Writing equations parallel, perpendicular, or
through a given point). of lines neither.
Use the slope intercept
form to write the equation
of a line.
Problem-solve using the
coordinate plane.
Analyze errors using
coordinate geometry.
Properties Properties
o Addition, Decide when a property is
Subtraction, used in solving a problem.
Multiplication,
A.REI.1 Explain each step in solving a
and Division Analyze errors in the
simple equation as following from the
Properties of application of properties.
equality of numbers asserted at the
previous step, starting from the Equality
assumption that the original equation o Reflexive,
has a solution. Construct a viable Symmetric, and
argument to justify a solution method. Transitive
Properties of
Equality
High School Geometry July 2014
Page 4Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
o Substitution
property of
equality
o Reflexive,
Symmetric, and
Transitive
Properties of
Congruence
Parallel and Parallel and
Perpendicular Lines Perpendicular Lines
G.CO.1: Know precise definitions of
angle, circle, perpendicular line, parallel o Angles and Compare and contrast
line, and line segment, based on the Intersecting lines vertical and adjacent
undefined notions of point, line, o Complementary angles.
distance along a line, and distance and
around a circular arc. Supplementary Compare and contrast
Angles complementary and
supplementary angles.
G.CO.9: Prove theorems about lines and
angles. Theorems include: vertical Sketch vertical, adjacent
angles are congruent; when a
o Right Angles complementary, and
transversal crosses parallel lines,
Congruence supplementary angles.
alternate interior angles are congruent
and corresponding angles are Theorem
congruent; points on a perpendicular o Proving lines Understand the
bisector of a line segment are exactly parallel relationship between a
those equidistant from the segment's o Proving lines transversal and 2 or more
endpoints. perpendicular lines.
High School Geometry July 2014
Page 5Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Compare and contrast
alternate interior angle,
same-side interior angles,
o Vertical and alternate exterior angles,
Adjacent angles and corresponding angles.
o Angle pairs
formed by two Apply the Corresponding
parallel lines cut Angles Postulate,
by a transversal Alternate Interior Angles
Theorem, Same Side
Interior Angles Theorem.
Problem-solve using
parallel lines cut by
transversal.
Analyze errors using
parallel and perpendicular
lines.
High School Geometry July 2014
Page 6Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
G.CO.10: Prove theorems about Triangles
triangles. Theorems include: measures Triangles
of interior angles of a triangle sum to Apply the Triangle Sum
180°; base angles of isosceles triangles o Triangle Theorem.
are congruent; the segment joining definition
midpoints of two sides of a triangle is
o Triangle Angle Classify triangles by sides
parallel to the third side and half the
length; the medians of a triangle meet at Sum Theorem and by angle measures.
a point. o Acute, Right,
Obtuse, Compare and contrast
Equiangular interior and exterior
triangles angles of a triangle.
o Equilateral,
Isosceles, Scalene Solve problems using
triangles triangles.
o Exterior Angle
Theorem Use Pythagorean Theorem
o Base Angle to find the missing side
Theorem lengths of a right triangle.
o Converse of Base
Angle Theorem Use the Converse of
o Bisector of vertex Pythagorean Theorem to
angle in isosceles determine if a triangle is a
triangles right, obtuse, or acute
o Equilateral and triangle.
Equiangular
Triangles Analyze errors in
problems using triangles.
G.CO.8: Explain how the criteria for
triangle congruence (ASA, SAS, and Sketch a triangle labeling
SSS) follow from the definition of o Proving triangles the altitude and
congruence in terms of rigid motions. congruent using corresponding base.
SSS, SAS, ASA,
AAS, HL
High School Geometry July 2014
Page 7Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Compare and contrast
included and non-included
sides and angles.
G.CO.7: Use the definition of Apply the properties of
congruence in terms of rigid motions to
Special Right Triangles.
show that two triangles are congruent if
and only if corresponding pairs of sides o CPCTC
(Corresponding parts Determine if two triangles
and corresponding pairs of angles are
of congruent triangles are congruent using SSS,
congruent. are congruent)
SAS, ASA, AAS, or HL.
G.SRT.4: Prove theorems about
triangles. Theorems include: a line Compare corresponding
parallel to one side of a triangle divides parts of congruent
the other two proportionally, and o 2-column proofs
triangles using CPCTC.
conversely; the Pythagorean Theorem
proved using triangle similarity. Apply the properties of
isosceles triangles.
G.SRT.6: Understand that by similarity,
side ratios in right triangles are o Special Right
properties of the angles in the triangle, Identify overlapping
Triangles
leading to definitions of trigonometric triangles and prove
ratios for acute angles. congruency.
G.SRT.8: Use trigonometric ratios and Analyze errors involving
o Hypotenuse
the Pythagorean Theorem to solve right proving triangles
triangles in applied problems. congruent.
Recognize that equilateral
o Pythagorean
triangles are isosceles
Theorem
triangles.
o Converse of
Pythagorean
Sketch concurrent lines
Theorem
and an altitude of a
o Pythagorean
triangle.
triples
High School Geometry July 2014
Page 8Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Predict if three line
segments can form a
triangle.
Problem-solve using
triangles.
Analyze errors in
problems using triangles
Relationships Within
G.GPE.4: Use coordinates to prove Relationships Within Triangles
simple geometric theorems Triangles
algebraically. For example, prove or Understand the
disprove that a figure defined by four
o Triangles in the relationship between the
given points in the coordinate plane is a
rectangle; prove or disprove that the coordinate plane mid-segment and the base
point (1, √3) lies on the circle centered of a triangle.
at the origin and containing the point
(0, 2). Distinguish between an
altitude, median, angle
G.CO.9: Prove theorems about lines and o Concurrent lines bisector, and
angles. Theorems include: vertical o Point of perpendicular bisector
angles are congruent; when a concurrency within a triangle.
transversal crosses parallel lines, Apply Triangle Inequality
alternate interior angles are congruent
to determine the largest
and corresponding angles are
and smallest angles of a
congruent; points on a perpendicular
bisector of a line segment are exactly o Altitude of a triangle.
those equidistant from the segment's triangle
endpoints. Problem-solve using
o Mid-segment relationships within
G.CO.10: Prove theorems about Theorem triangles.
triangles. Theorems include: measures
High School Geometry July 2014
Page 9Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
of interior angles of a triangle sum to
180°; base angles of isosceles triangles Analyze errors in
are congruent; the segment joining o Triangle problems using
midpoints of two sides of a triangle is inequalities relationships within
parallel to the third side and half the theorems triangles.
length; the medians of a triangle meet at
a point.
G.SRT.8: Use trigonometric ratios and
the Pythagorean Theorem to solve right
triangles in applied problems.
Polygons
Polygons
Classify polygons by
G.GMD.4: Identify the shapes of two- o Classification of sides.
dimensional cross-sections of three- polygons by sides
dimensional objects, and identify three-
o Naming polygons Compare and contrast
dimensional objects generated by
rotations of two-dimensional objects. by vertices convex and concave
o Convex and polygons.
Concave polygons
G.MG.1: Use geometric shapes, their o Regular polygon Explore the relationship
measures, and their properties to between the number of
describe objects (e.g., modeling a tree sides of a polygon and
trunk or a human torso as a cylinder).
o Polygon Angle
how that relates to the
Sum Theorem
sum of the interior angles.
o Polygon Exterior
G.CO.6: Use geometric descriptions of Angle Sum
Explore how the number
rigid motions to transform figures and to Theorem
of sides of a polygon
predict the effect of a given rigid motion
o Congruent relates to the measure of
on a given figure; given two figures, use
the definition of congruence in terms of
polygons an exterior angle of a
rigid motions to decide if they are o Identifying regular polygon.
congruent. congruent parts of
polygons Identify congruent parts of
congruent polygons.
High School Geometry July 2014
Page 10Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
G.CO.13: Make formal geometric o Equilateral and Compare and contrast
constructions with a variety of tools and Equiangular perimeter and area.
methods (compass and straightedge, polygon
string, reflective devices, paper folding, Discover congruent
dynamic geometric software, figures have equal areas.
etc.).Copying a segment; copying an
angle; bisecting a segment; bisecting an
angle; constructing perpendicular lines, o Perimeter and area Decide the best way to
including the perpendicular bisector of of polygons analyze composite figures.
a line segment; and constructing a line
parallel to a given line through a point Problem-solve using
not on the line. perimeter and area.
o Areas of
G.SRT.8: Use trigonometric ratios and composite/irregula Analyze errors in the
the Pythagorean Theorem to solve right r polygons application of perimeter
triangles in applied problems. o Area of a region is and area.
the sum of the
G.GPE.7: Use coordinates to compute non-overlapping Problem-solve using
perimeters of polygons and areas of
parts polygons.
triangles and rectangles, e.g., using the
distance formula.
Analyze errors in
problems involving
polygons.
High School Geometry July 2014
Page 11Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Quadrilaterals Quadrilaterals
G.CO.11: Prove theorems about Classify quadrilaterals.
parallelograms. Theorems include: o Classification of
opposite sides are congruent, opposite Quadrilaterals Compare and contrast
angles are congruent, the diagonals of a o Definition/Propert properties of
parallelogram bisect each other, and
ies of quadrilaterals.
conversely, rectangles are
parallelograms with congruent parallelograms,
diagonals. rhombuses, Problem-solve using
rectangles, quadrilaterals.
squares, kites,
trapezoids, Recognize same side
isosceles interior angles as
G.GPE.4: Use coordinates to prove trapezoids consecutive angles.
simple geometric theorems o Proving a
algebraically. For example, prove or quadrilateral is a Use properties of isosceles
disprove that a figure defined by four parallelogram triangles and kites to
given points in the coordinate plane is a
illustrate the properties of
rectangle; prove or disprove that the
point (1, √3) lies on the circle centered o Classification of the diagonals within a
at the origin and containing the point quadrilaterals by kite.
(0, 2). coordinate
methods Use the properties of the
G.GPE.7: Use coordinates to compute special parallelograms to
perimeters of polygons and areas of determine the most
triangles and rectangles, e.g., using the specific name of a
distance formula. quadrilateral.
G.SRT.5: Use congruence and similarity
Use properties of right
criteria for triangles to solve problems
triangles in a rhombus and
and to prove relationships in geometric
figures. square.
Relate properties of
parallel lines cut by a
transversal with
parallelograms.
High School Geometry July 2014
Page 12Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Problem-solve using
quadrilaterals.
Analyzing errors in
problems involving
quadrilaterals.
Circles
G.CO.1: Know precise definitions of o Diameter, Radius, Circles
angle, circle, perpendicular line, parallel Pi, Chord, Secant
line, and line segment, based on the o Central Angle of a Apply knowledge of
undefined notions of point, line, circle diameter and radius to
distance along a line, and distance o Semicircle solve problems using area
around a circular arc.
o Arc and central and circumference.
angles
o Arc Addition Recognize minor arcs,
Postulate major arcs, adjacent arcs,
o Concentric circles and vertical angles.
G.C.2: Identify and describe
relationships among inscribed angles, Name arcs.
radii, and chords. Include the
relationship between central, inscribed, o Vertical Angles in Generalize the
and circumscribed angles; inscribed circles relationship between
angles on a diameter are right angles;
o Congruent arcs Angle Addition Postulate
the radius of a circle is perpendicular to
and chords and the Arc Addition
the tangent where the radius intersects
the circle. Postulate.
Apply measure of arcs
and central angles to draw
and interpret circle
graphs.
High School Geometry July 2014
Page 13Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
G.C.3: Construct the inscribed and o Inscribed or Calculate the area of the
circumscribed circles of a triangle, and circumscribed inscribed or circumscribed
prove properties of angles for a polygons polygon.
quadrilateral inscribed in a circle.
Calculate the measure of
the intercepted arc.
G.C.4: Construct a tangent line from a
point outside a given circle to the circle. o Point of tangency Utilize the relationship
between tangent and
radius at the point of
tangency.
o Relationship
G.C.5: Derive using similarity the fact between the Problem-solve using
that the length of the arc intercepted by measures of an arc circles.
an angle is proportional to the radius, and the
and define the radian measure of the corresponding Analyze errors in
angle as the constant of proportionality;
central angle problems using circles.
derive the formula for the area of a
sector. o Arc length
o Sector of a circle
o Area of a sector of
a circle
o Percent in terms
of a circle
G.GMD.1: Give an informal argument
o Circumference
for the formulas for the circumference
and Area
of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use
dissection arguments, Cavalieri's
principle, and informal limit arguments.
High School Geometry July 2014
Page 14Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
7.RPA.1: – Compute unit rates Similarity Similarity
associated with ratios of fractions,
including ratios of lengths, areas and o Ratio, proportion, Write and simplify ratios.
other quantities measured in like or extended
different units. proportion Use Cross Product
o Properties of Properties to solve
proportions proportions.
o Cross Product
Property Apply proportions when
dealing with similar
polygons.
G.SRT.3: Use the properties of o Proving triangles
similarity transformations to establish similar by using Prove triangle similar
the AA criterion for two triangles to be AA~ using AA~, SAS~, SSS~.
similar.
o Parallel
G.SRT.4: Prove theorems about Proportionality Determine the relationship
triangles. Theorems include: a line (Side-Splitter between perimeter and
parallel to one side of a triangle divides Theorem) areas of similar figures.
the other two proportionally, and o Triangle-Angle-
conversely; the Pythagorean Theorem Bisector Theorem Apply proportions when
proved using triangle similarity. o Prove triangles dealing with parallel lines
similar by SAS~, and transversals.
SSS~
Problem-solve using
similarity in polygons.
G.SRT.5: Use congruence and similarity
criteria for triangles to solve problems o Scale drawing Analyze errors involving
and to prove relationships in geometric o Similarity ratios similarity in polygons
figures. o Perimeters and
areas of similar
figures
High School Geometry July 2014
Page 15Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
o Similarity/perimet
er ratios of similar
figures
o Indirect
measurement
o Similar polygons
Trigonometry Trigonometry
G.SRT.6: Understand that by similarity,
o Tangent, Sine, and Identify the adjacent and
side ratios in right triangles are
properties of the angles in the triangle, Cosine Ratios opposite legs to the named
leading to definitions of trigonometric angle.
ratios for acute angles.
o Inverse Tangent, Apply the correct.
Sine, and Cosine trigonometric ratio to a
G.SRT.7: Explain and use the Ratios given problem.
relationship between the sine and cosine
of complementary angles. Solve problems using
angles of elevations and
o Angles of depression.
G.SRT.8: Use trigonometric ratios and
elevation and
the Pythagorean Theorem to solve right
triangles in applied problems. depression Analyze errors involving
trigonometry.
High School Geometry July 2014
Page 16Archdiocese of Newark Catholic Schools
Curriculum Map for High School Geometry
Standards Content Skills Assessment Gospel Values
Solid Geometry Solid Geometry
G.GMD.1: Give an informal argument o Nets of solids Recognize and name the
for the formulas for the circumference parts of a solid.
of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use
Correlate the net of a solid
dissection arguments, Cavalieri's o Volume
with the formula for
principle, and informal limit arguments. o Volume of Prisms
lateral area and surface
and Cylinders
G.GMD.3: Use volume formulas for area.
cylinders, pyramids, cones, and spheres
to solve problems. Determine the relationship
o Definition of a between lateral area and
G.GMD.4: Identify the shapes of two- solid surface area.
dimensional cross-sections of three- o Polyhedron
dimensional objects, and identify three- o Face, Edge, and Determine the relationship
dimensional objects generated by Vertex between perimeter, area,
rotations of two-dimensional objects. o Right Prisms and volume of a solid.
o Bases, Lateral
Faces
Solve problems using
o Altitude, Height,
lateral area and surface
Perimeter
o Lateral and
area.
Surface Area of
Prisms Analyze errors involving
o Cylinder solids.
o Lateral and
Surface Area of
Cylinders
o Composite figures
o Lateral Area,
Surface area, and
Volume of
Composite Figures
High School Geometry July 2014
Page 17You can also read
