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Geometry
2016-1017 ( 1 day is about 1 45 minutes of a class. A block period equals two days.)
First 6-weeks (Aug 23 - Sept 30)
Second 6-weeks (Oct 3 - Nov 10)
Third 6-weeks (Nov 14 - Jan 12)
Fourth 6-weeks (Jan 17 - Feb 24)
Fifth 6-weeks (Feb 27 - Apr 13)
Sixth 6-weeks (Apr 18 - June 2)
Unit 1: Geometry Basics (11 days)
Unit 3: Parallel/Perpendicular
Lines (15 days)
Unit 6: Triangle
Congruence/Proofs (13days)
Unit 9: Right Triangle
Relationships (15 days)
Unit 11: Area and Perimeter (10
days)
Unit 13: Circles (12 days)
G.1 A-G Mathematical Process
G.1 A-G Mathematical Process
G.1 A-G Mathematical Process
G.1 A-G Mathematical Process
Standards. The student uses
Standards. The student uses
Standards. The student uses
Standards. The student uses
mathematical process standards to
mathematical process standards to
mathematical process standards to
mathematical process standards to
acquire and demonstrate
acquire and demonstrate
acquire and demonstrate
acquire and demonstrate
mathematical understanding
mathematical understanding
mathematical understanding
mathematical understanding
[Process]
[Process]
[Process]
[Process]
G.2A determine the coordinates of a G.5A investigate patterns to make G.5A investigate patterns to make
G.8B identify and apply the
point that is a given fractional distance
conjectures about geometric
conjectures about geometric
relationships that exist when an
less than one from one end of a line
relation-ships, including angles
relation-ships, including angles
altitude is drawn to the hypotenuse of
segment to the other in one- and two- formed by parallel lines cut by a
formed by parallel lines cut by a a right triangle, including the geometric
dimensional coordinate systems,
transversal, criteria required for
transversal, criteria required for
mean, to solve problems [Supporting]
including finding the midpoint;
triangle congruence, special
triangle congruence, special
[Supporting]
segments of triangles, diagonals of segments of triangles, diagonals of
quadrilaterals, interior and exterior quadrilaterals, interior and exterior
angles of polygons, and special
angles of polygons, and special
segments and angles of circles
segments and angles of circles
choosing from a variety of tools;
choosing from a variety of tools;
[Readiness]
[Readiness]
G.2B derive and use the distance,
G.2C determine an equation of a
G.6B prove two triangles are
G.9A determine the lengths of
slope, and midpoint formulas to
line parallel or perpendicular to a
congruent by applying the Sidesides and measures of angles in a
verify geometric relationships,
given line that passes through a
Angle-Side, Angle-Side-Angle,
right triangle by applying the
including congruence of segments
given point. [Readiness]
Side-Side-Side, Angle-Angle-Side,
trigonometric ratios sine, cosine,
and parallelism or perpendicularity
and Hypotenuse-Leg congruence
and tangent to solve problems
of pairs of lines; [Readiness]
conditions; [Readiness]
[Readiness]
G.4A distinguish between undefined G.2B derive and use the distance,
G.6C apply the definition of
G.9B apply the relationships in
terms, definitions, postulates,
slope, and midpoint formulas to
congruence, in terms of rigid
special right triangles 30°-60°-90°
conjectures, and theorems
verify geometric relationships,
transformations, to identify congruent
and 45°-45°-90° and the
[Supporting]
including congruence of segments figures and their corresponding sides
Pythagorean theorem, including
and parallelism or perpendicularity
and angles[Supporting]
Pythagorean triples, to solve
of pairs of lines; [Readiness]
problems. [Readiness]
G.5B construct congruent segments,
congruent angles, a segment bisector,
an angle bisector, perpendicular lines,
the perpendicular bisector of a line
segment, and a line parallel to a given
line through a point not on a line using
a compass and a straightedge;
[Supporting]
G.5B construct congruent segments,
congruent angles, a segment bisector,
an angle bisector, perpendicular lines,
the perpendicular bisector of a line
segment, and a line parallel to a given
line through a point not on a line using
a compass and a straightedge;
[Supporting]
G.5C use the constructions of
congruent segments, congruent
angles, angle bisectors, and
perpendicular bisectors to make
conjectures about geometric
relationships [Supporting]
G.6A verify theorems about angles
formed by the intersection of lines
and line segments, including
vertical angles, and angles formed
by parallel lines cut by a
transversal and prove
equidistance between the
endpoints of a segment and points
on its perpendicular bisector and
apply these relationships to solve
problems; [Readiness]
Unit 7: Special Segments in
Triangles (9 days)
G.1 A-G Mathematical Process
Standards. The student uses
mathematical process standards to
acquire and demonstrate
mathematical understanding
[Process]
G.1 A-G Mathematical Process
G.1 A-G Mathematical Process
Standards. The student uses
Standards. The student uses
mathematical process standards to
mathematical process standards to
acquire and demonstrate
acquire and demonstrate
mathematical understanding
mathematical understanding
[Process]
[Process]
G.10B determine and describe how G.5A investigate patterns to make
changes in the linear dimensions
conjectures about geometric
of a shape affect its perimeter,
relation-ships, including angles
area, surface area, or volume,
formed by parallel lines cut by a
including proportional and nontransversal, criteria required for
proportional dimensional change.
triangle congruence, special
[Readiness]
segments of triangles, diagonals of
quadrilaterals, interior and exterior
angles of polygons, and special
segments and angles of circles
choosing from a variety of tools;
[Readiness]
G.11A apply the formula for the area of G.12A apply theorems about circles,
regular polygons to solve problems including relationships among angles,
using appropriate units of measure;
radii, chords, tangents, and secants,
[Supporting]
to solve non-contextual problems
[Supporting]
G.11B determine the area of
composite two-dimensional figures
comprised of a combination of
triangles, parallelograms,
trapezoids, kites, regular polygons,
or sectors of circles to solve
problems using appropriate units
of measure [Readiness]
G.12B apply the proportional
relationship between the measure of
an arc length of a circle and the
circumference of the circle to solve
problems [Supporting]
G.6 D verify theorems about the
relationships in triangles, including
proof of the Pythagorean Theorem, the
sum of interior angles, base angles of
isosceles triangles, midsegments, and
medians, and apply these
relationships to solve problems;
[Supporting]
Unit 12: Solid Figures (12 days)
G.12C apply the proportional
relationship between the measure of
the area of a sector of a circle and the
area of the circle to solve problems;
[Supporting]
Unit 10: Polygons/Quadrilaterals (15
days)
G.1 A-G Mathematical Process
Standards. The student uses
mathematical process standards to
acquire and demonstrate
mathematical understanding
[Process]
G.12D describe radian measure of an
angle as the ratio of the length of an
arc intercepted by a central angle and
the radius of the circle [Supporting]
G.6A verify theorems about angles
formed by the intersection of lines
and line segments, including
vertical angles, and angles formed
by parallel lines cut by a
transversal and prove
equidistance between the
endpoints of a segment and points
on its perpendicular bisector and
apply these relationships to solve
problems; [Readiness]
Unit 2: Logic and Reasoning (9
days)
G.1 A-G Mathematical Process
Standards. The student uses
mathematical process standards to
acquire and demonstrate
mathematical understanding
[Process]
Unit 4: Transformations (8 days)
G.5A investigate patterns to make
conjectures about geometric
relation-ships, including angles
formed by parallel lines cut by a
transversal, criteria required for
triangle congruence, special
segments of triangles, diagonals of
quadrilaterals, interior and exterior
angles of polygons, and special
segments and angles of circles
choosing from a variety of tools;
[Readiness]
G.1 A-G Mathematical Process
G.5C use the constructions of
Standards. The student uses
congruent segments, congruent
mathematical process standards to
angles, angle bisectors, and
acquire and demonstrate
perpendicular bisectors to make
mathematical understanding
conjectures about geometric
[Process]
relationships [Supporting]
G.3A describe and perform
G.6D verify theorems about the
transformations of figures in a plane
relationships in triangles, including
using coordinate notation; [Supporting] proof of the Pythagorean Theorem, the
sum of interior angles, base angles of
isosceles triangles, midsegments, and
medians, and apply these
relationships to solve problems;
[Supporting]
G.4A distinguish between undefined
terms, definitions, postulates,
conjectures, and theorems
[Supporting]
G.3B determine the image or preimage of a given two-dimensional
figure under a composition of rigid
transformations, a composition of
non-rigid transform-ations, and a
composition of both, including
dilations where the center can be
any point in the plane; [Readiness]
G.4B identify and determine the
validity of the converse, inverse, and
contrapositive of a conditional
statement and recognize the
connection between a biconditional
statement and a true conditional
statement with a true converse;
[Supporting]
G.3C identify the sequence of
transformations that will carry a given
pre-image onto an image on and off
the coordinate plane [Supporting]
G.4C verify that a conjecture is
false using a counterexample;
[Readiness]
G.5A investigate patterns to make
conjectures about geometric
relation-ships, including angles
formed by parallel lines cut by a
transversal, criteria required for
triangle congruence, special
segments of triangles, diagonals of
quadrilaterals, interior and exterior
angles of polygons, and special
segments and angles of circles
choosing from a variety of tools;
[Readiness]
G.1 A-G Mathematical Process
Standards. The student uses
mathematical process standards to
acquire and demonstrate
mathematical understanding
[Process]
G.4D compare geometric
relationships between Euclidean and
spherical geometries, including
parallel lines and the sum of the
angles in a triangle [Supporting]
G.12E show that the equation of a
circle with center at the origin and
radius r is x2 + y2 = r2 and determine
the equation for the graph of a circle
with radius r and center (h, k), (x - h)2
+ (y - k)2 =r2 [Supporting]
G.2B derive and use the distance,
slope, and midpoint formulas to
verify geometric relationships,
including congruence of segments
and parallelism or perpendicularity
of pairs of lines [Readiness]
G.5A investigate patterns to make
conjectures about geometric
relation-ships, including angles
formed by parallel lines cut by a
transversal, criteria required for
triangle congruence, special
segments of triangles, diagonals of
quadrilaterals, interior and exterior
angles of polygons, and special
segments and angles of circles
choosing from a variety of tools;
[Readiness]
Unit 8: Similarity and Proportional
G.6E prove a quadrilateral is a
Relationships (8 days)
parallelogram, rectangle, square, or
rhombus using opposite sides,
opposite angles, or diagonals and
apply these relationships to solve
problems. [Supporting]
G.10A identify the shapes of twodimensional cross-sections of prisms,
pyramids, cylinders, cones, and
spheres and identify three-dimensional
objects generated by rotations of twodimensional shapes [Supporting]
G.10B determine and describe
how changes in the linear
dimensions of a shape affect its
perimeter, area, surface area, or
volume, including proportional and
non-proportional dimensional
change. [Readiness]
Unit 14: Probability (10 Days)
G.1 A-G Mathematical Process
Standards. The student uses
mathematical process standards to
acquire and demonstrate
mathematical understanding
[Process]
G.11D apply the formulas for the
G.13B determine probabilities based
volume of three-dimensional
on area to solve contextual problems
figures, including prisms, pyramids,
[Supporting]
cones, cylinders, spheres, and
composite figures, to solve
problems using appropriate units
of measure. [Readiness]
G.11C apply the formulas for the
total and lateral surface area of
three-dimensional figures,
including prisms, pyramids, cones,
cylinders, spheres, and composite
figures, to solve problems using
appropriate units of measure
[Readiness]
G.1 A-G Mathematical Process
Standards. The student uses
mathematical process standards to
acquire and demonstrate
mathematical understanding
[Process]
G.13A develop strategies to use
permutations and combinations to
solve contextual problems;
[Supporting]
G.3D identify and distinguish between
G.6D verify theorems about the
reflectional and rotational symmetry in
relationships in triangles, including
a plane figure. [Supporting]
proof of the Pythagorean Theorem, the
sum of interior angles, base angles of
isosceles triangles, midsegments, and
medians, and apply these
relationships to solve problems;
[Supporting]
G.13C identify whether two events
are independent and compute the
probability of the two events
occurring together with or without
replacement; [Readiness]
G.6C apply the definition of
congruence, in terms of rigid
transformations, to identify congruent
figures and their corresponding sides
and angles; [Supporting]
G.13D apply conditional probability in
contextual problems; [Supporting]
G.7A apply the definition of similarity
in terms of a dilation to identify similar
figures and their proportional sides
and the congruent corresponding
angles [Supporting]
G.7A apply the definition of similarity
G.7B apply the Angle-Angle
in terms of a dilation to identify similar criterion to verify similar triangles
figures and their proportional sides and apply the proportionality of the
and the congruent corresponding
corresponding sides to solve
angles [Supporting]
problems. [Readiness]
G.8A prove theorems about similar
Unit 5: Triangle Classification (7 days)
triangles, including the Triangle
Proportionality theorem, and apply
these theorems to solve problems;
[Supporting]
G.1 A-G Mathematical Process
Standards. The student uses
mathematical process standards to
acquire and demonstrate
mathematical understanding
[Process]
G.5D verify the Triangle Inequality
theorem using constructions and
apply the theorem to solve problems.
[Supporting]
G.6D verify theorems about the
relationships in triangles, including
proof of the Pythagorean Theorem, the
sum of interior angles, base angles of
isosceles triangles, midsegments, and
medians, and apply these
relationships to solve problems;
[Supporting]
G.13E apply independence in
contextual problems. [Supporting]