# PACING GUIDES FOR ENGLISH/LANGUAGE ARTS by D8S5BET

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```									                                                 PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                        14 Days                       22 Days                      10 Days

Unit Topic           Unit 1                         Unit 2                        Unit 3                       Unit 4
(Specify             Reasoning and Proof            Spatial Visual                Triangles                    2-Dimensional
skills/information
that will be
learned.)
Enduring             In proofs, deductive           Geometric figures and         The Pythagorean              Polygons are categorized
Understandings       reasoning about given          relationships can be          Theorem is essential to      by the number of sides.
(Give and/or         information is used to         represented in the            solving problems             Studying patterns can
demonstrate          reach mathematical             coordinate plane.             involving right triangles.   lead to geometric
necessary            conclusions.                    Geometric figures can        Congruent figures are        formulas and
information)          Theorems and properties       be measured in the            also similar figures, but    relationships.
exist that guarantee two       coordinate plane.             similar figures are not      Rectangles, squares, and
triangles are congruent or      The slope of a line is the   always congruent.            rhombi are
similar given certain          ratio of vertical change      Congruency and               parallelograms and
conditions.                    (rise) to horizontal          similarity have real life    belong to the set of
Relationships between         change (run).                 applications in art,         quadrilaterals.
lines, angles and figures      Slopes, distances and         architecture, and            Relationships exist
can be used to establish       midpoints can be              science.                     between sides, angles
additional mathematical        determined when a             Parallel and                 and segments in
relationships.                 segment is graphed in         perpendicular lines are      polygons.
Congruent figures are also    the coordinate plane.         used to prove triangles      By using the area
similar figures, but similar    A line’s direction and       congruent or similar.        formula of a rectangle,
figures are not always         steepness are                  30º-60º-90º and 45º-        we can derive area
congruent.                     determined by its slope.      45º-90º triangles are        formulas for other
Linear equations can be      similar triangles.           figures.
used to make
predictions.
PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:           14 Days                       14 Days                     22Days                      10 Days
Enduring              Parallel and perpendicular    A line’s slope and x- and   Special triangles have      Perimeter and
Understandings        lines are used to prove       y-intercepts have real      real world applications.    circumference are 1-
con’t       triangles congruent or        world applications.          Relationships in special   dimensional measures,
similar.                                                  right triangles can be      while area is a 2-
determined by the           dimenionsal measure.
Pythagorean Theorem.         Measurement of
geometric figures is an
essential part everyday
life.
Essential             Why write formal proofs?      Why is it important to      Why is the intersection     How can you use
Questions              Why are properties and       learn about geometric       point of special segments   patterns to find the sum
(Steps to check for   theorems about parallel       figures and relationships   in triangles important?     of the interior angles of
student               and perpendicular lines       in the coordinate plane?     What theorems              any polygon?
understanding)        useful in geometric proofs?    How do you determine       guarantee two triangles      How can you determine
How can reasoning about      information about a line    congruent?                  the measure of interior
geometric situations be       or segment graphed in        How do congruent           and exterior angles in
used to solve real life       the coordinate plane?       figures differ from         regular polygons?
problems?                      How does the Distance      similar figures?             How do you classify
If two figures are           Formula relate to the        Where are parallel and     quadrilaterals using
congruent or similar, what    Pythagorean Theorem?        perpendicular lines         special segments and
else do you know about        How do you represent        evident in everyday life?   properties?
their corresponding parts?    geometric figures in the     How are the angles          How do special
What theorems or              coordinate plane?           formed by parallel lines    segments in polygons
postulates (properties)        How do you measure         used to prove triangles     help solve everyday
guarantee two triangles       geometric figures using     congruent?                  situations?
congruent?                    the coordinate plane?
PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                        14 Days                      22 Days                    10 Days
Essential            How do congruent figures       How does slope describe      How are properties of      How can you derive the
Questions   con’t    differ from similar figures?   a line? How can you use      perpendicular lines used   various area formulas
an equation to make a        to prove congruent and     from the area of a
prediction?                  similar triangles?         rectangle?
What does the slope of        How is the Pythagorean    How can you find the
the line tell you?           Theorem related to the     areas of irregular
How do you write an         lengths of sides of        figures?
equation for a line?         special right triangles?    How does finding the
How do you write an          How does the concept of    area of the various
equation for a line if you   similarity apply to        figures apply to everyday
are given two points?        special right              situations?How are
How do you determine        triangles?How are right    perimeter,
the x- and y-intercepts      triangle relationships     circumference, and area
graphically and              used in the real world?    different from one
algebraically?                How do you find the       another?
lengths of sides of
special right triangles?

Standards            G-1.1 Demonstrate an           G-2.4 Use direct             G-3.1 Carry out a          G-2.3 Use the
understanding of the           measurement to               procedure to compute       congruence of line
axiomatic structure of         determine the length of a    the perimeter of a         segments and angles to
geometry                       segment, measure             triangle.                  solve problems.
using undefined terms,         of an angle, and distance    G-3.2 Carry out a          G-4.6 Apply congruence
definitions, postulates,       from a point to a line.      procedure to compute       and similarity between
theorems, and corollaries.     G-6.1 Use the distance       the area of a triangle.    shapes (including
formula to solve             G-3.3 Analyze how          quadrilaterals and
problems.                    changes in dimensions      polygons) to solve
affect the perimeter or    problems.
area of triangles.
PACING GUIDES FOR MATH
Grade Level: Tenth                      Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                       14 Days                       22 Days                     10 Days
Standards con’t      G-1.2 Communicate             G-6.2 Use the midpoint        G-3.4 Apply properties of   G-2.5 Carry out a
knowledge of geometric        formula to solve              isosceles and equilateral   procedure to create
relationships using           problems.                     triangles to solve          geometric constructions
mathematical                  G-2.2 Apply properties of     problems.                   (including
terminology appropriately.    parallel lines,               G-3.5 Use interior          midpoint of a line
G-1.7 Understand the          intersecting lines, and       angles, exterior angles,    segment, angle bisector,
historical development of     parallel lines cut            medians, angle bisectors,   perpendicular bisector of
geometry.                     by a transversal to solve     altitudes,                  a line segment, line
G-1.4 Formulate and test      problems.                     and perpendicular           through a given point
conjectures using a variety   G-2.5 Carry out a             bisectors to solve          that is parallel to a given
of tools such as concrete     procedure to create           problems.                   line,
models, graphing.             geometric constructions       G-3.6 Apply the Triangle    and line through a given
calculators, spreadsheets,    (including                    Sum Theorem to solve        point that is
and dynamic geometry          midpoint of a line            problems.                   perpendicular to a given
Software                      segment, angle bisector,      G-3.7 Apply the Triangle    line).
G-1.9 Demonstrate an          perpendicular bisector of     Inequality Theorem to       G-4.6 Apply congruence
understanding of how          a line segment, line          solve problems.             and similarity between
geometry applies to real      through a given point         G-3.8 Apply congruence      shapes (including
world contexts (including     that is parallel to a given   and similarity between      quadrilaterals and
architecture, construction,   line,                         triangles to solve          polygons) to solve
farming, astronomy).          and line through a given      problems.                   problems.
point that is                 G-3.9 Apply theorems to     G-2.6 Use scale factors
perpendicular to a given      prove triangles are         to solve problems
line).                        similar or congruent.       involving scale drawings
G-3.10 Use the              and
Pythagorean Theorem         models.
and its converse to solve
problems.
PACING GUIDES FOR MATH
Grade Level: Tenth                      Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                       14 Days           22 Days                     10 Days
Standards            G-1.10 Understand                               G-3.11 Use the              G-2.7 Use geometric
con’t                geometric relationships                         properties of 45-45-90      probability to solve
including constructions                         and 30-60-90 triangles      problems.
through investigations                          to solve problems.          G-4.1 Carry out a
using a variety of tools                        G-3.12 Use trigonometric    procedure to compute
such as straightedge,                           ratios (including sine,     the perimeter of
compass,                                        cosine, tangent) to solve   quadrilaterals,
paper folding, dynamic                          problems involving right    regular polygons, and
geometry software, and                          triangles.                  composite figures.
hand-held computing                                                         G-4.2 Carry out a
devices.                                                                    procedure to find the
G-1.3 Apply basic rules of                                                  area of quadrilaterals,
logic to determine the                                                      regular polygons, and
validity of the converse,                                                   composite figures.
inverse, and contrapositive                                                 G-4.3 Apply procedures
of a conditional statement                                                  to compute measures of
G-1.5 Use inductive                                                         interior and exterior
reasoning to formulate                                                      angles of polygons. area
G-1.6 Use deductive                                                         regular polygons.
reasoning to validate                                                       G-4.4 Analyze how
conjectures with formal                                                     changes in dimensions
and informal proofs, and                                                    affect the perimeter or
give counterexamples to                                                     area of quadrilaterals
disprove a statement.                                                       and regular polygons
PACING GUIDES FOR MATH
Grade Level: Tenth             Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days          14 Days               22 Days               10 Days
Standards                                                                         G-4.5 Apply
con’t                                                                             properties and
attributes of
regular polygons
and their component
parts to solve
problems.
G-2.1 Infer missing
elements of visual or
numerical geometric
patterns (including
triangular numbers,
rectangular
numbers, and
number of diagonals
in polygons).
G-2.7 Use geometric
probability to solve
problems.

Integrations
(with other
discipline areas)

District                                                    Benchmark Exam
Assessments
(culminating
assessments)
PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          12 Days                             5 Days                           13 Days
Unit Topic           Unit 5                        Unit 6                     Unit 7
(Specify             3-Dimensional                 Transformations            Circles
skills/information
that will be
learned.)
Enduring             Three-dimensional             Transformations move or    Indirect measurement is
Understandings       figures have properties       map figures (preimages)    based on the properties
(Give and/or         similar to those of two-      onto their images.         of geometric figures.
demonstrate          dimensional figures.           Reflections, rotations,   Relationships exist
necessary                                          and translations are       among angles, segments,
information)                                       transformations that       lengths, circumference,
preserve shape and size    and area of circles.
(congruency).
Dilation is a
transformation that
preserves shape only
(similarity).

Essential            How are two-dimensional       Why do certain             How are the areas of
Questions            relationships connected       transformations preserve   polygons and circles
(Steps to check      to the properties of three-   shape and size while       related and applied?
for student          dimensional figures?          others only preserve       How are angles and
understanding)                                     shape?                     intercepted arcs of circles
How does combining        related and applied?
transformations affect
the final result?
How are the coordinates
affected by
transformations in the
PACING GUIDES FOR MATH
Grade Level: Tenth                      Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          12 Days                            5 Days                             13 Days
Essential                                         coordinate plane?
Questions                                         How are scale factors
con’t                                 used in transformations?

Standards            G-7.1 Carry out a            G-6.3 Apply                   G-5.1 Carry out a
procedure to compute         transformations               procedure to compute
the surface area of three-   (translation, reflection,     the circumference of
dimensional                  rotation, and dilation) to    circles.
objects (including cones,    figures in the coordinate     G-5.2 Carry out a
cylinders, pyramids,         plane using sketches and      procedure to compute
prisms, spheres, and         coordinates.                  the area of circles.
hemispheres).                G-6.4 Apply                   G-5.3 Analyze how a
G-7.2 Carry out a            transformations               change in radius affects
procedure to compute         (including translation        the circumference or area
the volume of three-         and dilation) to figures in   of a circle.
dimensional                  the coordinate plane          G-5.4 Carry out a
objects (including cones,    using matrices.               procedure to compute arc
cylinders, pyramids,         G-6.5 Carry out a             length or area of a sector
prisms, spheres,             procedure to represent        of a circle.
hemispheres, and             the sum of two vectors        G-5.5 Apply properties of
composite objects).          geometrically by using        component parts of a
G-7.3 Analyze how            the parallelogram             circle (including radii,
changes in dimensions        method.                       diameters, chords,
affect the volume of         G-6.6 Carry out a             sectors, arcs, and
objects (including           procedure to determine        segments) to solve
cylinders, prisms, and       the magnitude and             problems.
spheres).                    direction of the
resultant by direct
measurement using a
PACING GUIDES FOR MATH
Grade Level: Tenth                   Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          12 Days                       5 Days                      13 Days
Standards            G-7.4 Apply             scale drawing.         G-5.6 Apply
congruence and          G-6.7 Carry out a      properties of lines
similarity between      procedure to           that intersect
objects to solve        compute the            circles(including two
problems.               magnitude of the       secants, two
G-7.5 Apply a           resultant of two       tangents, or a secant
procedure to draw a     perpendicular          and a tangent) to
top-view, front-view,   vectors using the      solve problems.
and side-view of a      Pythagorean            G-5.7 Apply
three-dimensional       Theorem.               properties of central
object.                 G-6.8 Carry out a      angles, inscribed
G-7.6 Apply a           procedure to           angles, and arcs of
procedure to draw       determine the          circles to solve
an isometric view of    direction of the       problems.
a three-dimensional     resultant of two       G-2.7 Use geometric
object                  perpendicular          probability to solve
vectors using direct   problems.
measurement.

Integrations
(with other
discipline areas)

District                                                            Final Exam
Assessments
(culminating
assessments)

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