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First Semester
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G.1
Geometric structure. The student understands the structure of, and
relationships within, an axiomatic system. The student is expected to:
(A)
develop an awareness of the structure of a mathematical system, connecting
definitions, postulates, logical reasoning, and theorems. District:
2012 NT; 2013 NT
(B)
recognize the historical development of geometric systems and know
mathematics is developed for a variety of purposes. S District:
2012 NT; 2013 NT
(C)
compare and contrast the structures and implications of Euclidean and
non-Euclidean geometries. S District: 2012
NT; 2013
NT
G.2 Geometric structure. The student
analyzes geometric relationships in order to make and verify conjectures. The student is expected to:
(A)
use constructions to explore attributes of geometric figures and to make
conjectures about geometric relationships.
S District: 2012 51%;
2013 43%;
ACP Fall 2013 70%
(B)
make conjectures about angles, lines, polygons,
G.3 Geometric structure. The student
applies logical reasoning to justify and prove mathematical statements. The student is expected to:
(A) determine the validity of a conditional
statement, its converse, inverse, and contrapositive. S District: 2012 59%;
2013 37%
(B) construct and justify statements about
geometric figures and their properties.
S District: 2012 67%; 2013 55%
(C) use logical reasoning to prove statements
are true and find counter-examples to disprove statements that are
false. R District: 2012 50%;
2013 53%;
ACP Fall 2013 58%
(D) use inductive reasoning to formulate a
conjecture. S District: 2012
NT; 2013 40%
(E) use deductive reasoning to prove a
statement. S District: 2012
50%; 2013 41%; ACP Fall 2013 48%
G.4 Geometric structure. The
student uses a variety of representations to describe geometric relationships
and solve problems. The student is expected to select an
appropriate representation ([concrete,] pictorial, graphical, verbal, or
symbolic) in order to solve problems. S District: 2012
81%; 2013 43%
G.5 Geometric patterns. The student
uses a variety of representations to describe geometric relationships and
solve problems. The
student is expected to:
(A)
use numeric and geometric patterns to develop algebraic expressions
representing geometric properties. R District: 2012
69%; 2013 69%; ACP Fall 2013 51%
(B) use numeric and geometric patterns to make
generalizations about geometric properties, including properties of polygons,
ratios in similar figures
(C)
use properties of transformations and their compositions to make connections
between mathematics and the real world, such as tessellations. S District:
2012 89%;
2013 63%
G.7 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:
(A)
use one- and two-dimensional coordinate systems to represent points, lines,
rays, line segments, and figures.
S District: 2012 87%;
2013 29%
(B)
use slopes and equations of lines to investigate geometric relationships,
including parallel lines, perpendicular lines, and special segments of
triangles and other polygons. R District: 2012
42%; 2013 49%; ACP Fall 2013 28%
(C)
[derive and] use formulas involving length, slope, and midpoint. R
District: 2012 62%; 2013 47%; ACP Fall 2013 39%
G.9 Congruence and the geometry of
size. The student analyzes properties and describes relationships in
geometric figures. The student
is expected to:
(A)
formulate and test conjectures about the properties of parallel and
perpendicular lines based on explorations and [concrete] models. S District:
2012 55%;
2013 NT;
ACP Fall 2013 45%
(B)
formulate and test conjectures about the properties and attributes of
polygons and their component parts based on explorations and [concrete]
models. S District: 2012 NT;
2013 NT
G.10 Congruence and the geometry of
size. The student applies the concept of congruence to justify properties of
figures and solve problems. The student
is expected to:
(A)
use congruence transformations to make conjectures and justify properties of
geometric figures including figures represented on a coordinate plane. S District:
2012 63%;
2013 53%
(B)
justify and apply triangle congruence relationships. R District:
2012 59%;
2013 48%;
ACP Fall 2013 38%
G.11 Similarity and the geometry of
shape. The student applies the concepts of similarity to justify properties
of figures and solve problems. The student
is expected to:
(A)
use and extend similarity properties and transformations to explore and
justify conjectures about geometric figures.
S District: 2012 60%;
2013 57%
(B)
use ratios to solve problems involving similar figures. S District:
2012 59%;
2013 44%;
ACP Fall 2013 59%
(C)
develop, apply, and justify triangle similarity relationships,
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Second Semester
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G.1 Geometric
structure. The student understands the structure of, and relationships
within, an axiomatic system. The
student is expected to:
(A) develop an awareness of the structure of a
mathematical system, connecting definitions, postulates, logical reasoning,
and theorems. District: 2012 NT; 2013 NT
G.2 Geometric
structure. The student analyzes geometric relationships in order to make and
verify conjectures.
The student is expected to:
(A) use constructions to explore attributes of geometric
figures and to make conjectures about geometric relationships. S District: 2012 51%; 2013 43%
(B) 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. R District: 2012
58%; 2013 54%; ACP Spring 2013 42%
G.3 Geometric
structure. The student applies logical reasoning to justify and prove
mathematical statements. The
student is expected to:
(B) construct and
justify statements about geometric figures and their properties. S District:
2012 67%; 2013 55%
(C) use logical
reasoning to prove statements are true and find counter-examples to disprove
statements that are false. R District: 2012
50%; 2013 53%
G.4 Geometric
structure. The student uses a variety of representations to describe
geometric relationships and solve problems. The student is
expected to select an appropriate representation ([concrete,] pictorial,
graphical, verbal, or symbolic) in order to solve problems. S District:
2012 81%;
2013 43%
G.5 Geometric
patterns. The student uses a variety of representations to describe geometric
relationships and solve problems. The
student is expected to:
(A) use numeric and geometric patterns to develop
algebraic expressions representing geometric properties. R District:
2012 69%;
2013 69%
(B) use numeric and
geometric patterns to make generalizations about geometric properties,
including properties of polygons, ratios in similar figures and solids, and
angle relationships
in polygons and
circles. S District: 2012 71%; 2013 42%
(D) identify and apply patterns from right triangles to
solve meaningful problems, including special right triangles (45-45-90 and
30-60-90) and triangles whose sides are Pythagorean triples. R District:
2012 55%;
2013 51%; ACP Spring 2013 45%
G.6
Dimensionality and the geometry of location. The student analyzes the
relationship between three-dimensional geometric figures and related
two-dimensional representations and uses these representations to solve
problems. The student is
expected to:
(A) describe and draw the intersection of a given plane
with various three-dimensional geometric figures. S District: 2012 68%; 2013 42%
(B) use nets to represent and construct three-dimensional
geometric figures. S District: 2012
89%; 2013 47%; ACP Spring 2013 49%
(C) use orthographic and isometric views of
three-dimensional geometric figures to represent and construct
three-dimensional geometric figures and solve problems. S District:
2012 49%;
2013 76%
G.7
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:
(A) use one- and two-dimensional coordinate systems to
represent points, lines, rays, line segments, and figures. S District:
2012 87%;
2013 29%
(B) use slopes and equations of lines to investigate
geometric relationships, including parallel lines, perpendicular lines, and
special segments of triangles and other polygons. R District:
2012 42%;
2013 49%
(C) [derive and] use formulas involving length, slope, and
midpoint. R District: 2012
62%; 2013 47%
G.8 Congruence
and the geometry of size. The student uses tools to determine measurements of
geometric figures and extends measurement concepts to find perimeter, area,
and volume in problem situations. The student is
expected to:
(A) find areas of regular polygons, circles, and composite
figures. R District: 2012
68%; 2013 52%; ACP Spring 2013 27%
(B) find areas of sectors and arc lengths of circles using
proportional reasoning. S District: 2012
59%; 2013 47%
(C) [derive,] extend, and use the Pythagorean
Theorem. R District: 2012
59%; 2013 52%; ACP Spring 2013 38%
(D) find surface areas and volumes of prisms, pyramids,
spheres, cones, cylinders, and composites of these figures in problem
situations. R District: 2012 56%; 2013 49%; ACP Spring 2013 39%
(E) use area models to connect geometry to probability and
statistics. S District: 2012
63%; 2013 40%
(F) use conversions between measurement systems to solve
problems in real-world situations. S District: 2012
57%; 2013 NT
G.9 Congruence
and the geometry of size. The student analyzes properties and describes
relationships in geometric figures. The student is
expected to:
(B) formulate and test conjectures about the properties
and attributes of polygons and their component parts based on explorations
and [concrete] models. S District: 2012
NT;
2013 NT
(C) formulate and test conjectures about the properties
and attributes of circles and the lines that intersect them based on
explorations and [concrete] models. S District: 2012
71%; 2013 32%; ACP Spring 2013 43%
(D) analyze the characteristics of polyhedra and other
three-dimensional figures and their component parts based on explorations and
[concrete] models. S District: 2012
55%;
2013 64%
G.10 Congruence
and the geometry of size. The student applies the concept of congruence to
justify properties of figures and solve problems. The student is expected to:
(A) use congruence transformations to make conjectures and
justify properties of geometric figures including figures represented on a
coordinate plane. S District: 2012
63%;
2013 53%
G.11 Similarity
and the geometry of shape. The student applies the concepts of similarity to
justify properties of figures and solve problems. The student is expected to:
(A) use and extend similarity properties and
transformations to explore and justify conjectures about geometric
figures. S District: 2012
60%; 2013 57%
(B) use ratios to solve problems involving similar
figures. S District: 2012
59%; 2013 44%
(C) develop, apply, and justify triangle similarity
relationships, such as right triangle ratios, trigonometric ratios, and
Pythagorean triples using a variety of methods. R District: 2012 59%;
2013 40%; ACP Spring 2013 45%
(D) describe the effect on perimeter, area, and volume
when one or more dimensions of a figure are changed and apply this idea in
solving problems. R District: 2012
53%; 2013 38%;
ACP Spring 2013 36%
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