
Teach=
er: CORE
GEOMETRY 
Updat=
ed 2014 
=
; 


=
; 
=
; 

Cours=
e:
GEOMETRY 
Month=
:
All Months 













S 
Basic
Terminology 






e 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
p 
Can I=
draw and
measure two and threedimensional figures? 
Point=
s, Lines,
Planes, Space, Segments, Rays, Opposite Rays, Collinear Points, Coplanar
Points 
Read =
and write
the correct mathematical symbolism. 
Homework 

Students
will know and be able to define and identify basic terminology. 
M.09=
10.G.01Geometry
~ Identify figures using properties of sides, angles, and diagonals. Iden=
tify
the figures' type(s) of symmetry. 
t 
=
; 
Congr=
uent
Segments, Midpoint of a segment 
Draw
appropriate diagrams for stated conditions of points, lines, planes,
segments, rays, collinear points, and coplanar points. 
Quizzes 
M.09=
10.G.02Geometry
~ Draw congruent and similar figures using a compass, straightedge,
protractor, and other tools such as computer software. Make conjectures a=
bout
methods of construction. Justify the conjectures by logical arguments.&nb=
sp; 
e 
Can I
investigate and analyze properties of two and threedimensional geometric
figures? 
Types=
of angles
by measurement 
=
; 
Tests 
=
; 
m 
=
; 
Adjac=
ent
Angles, Congruent Angles, Angle Bisectors 
Inter=
pret given
information on a diagram. 
Geometers' Sketchpad L=
abs 
=
; 
b 
Am I =
able to
use technology to investigate and explore geometric properties? 
Compl=
ementary
Angles, Supplementary Angles, Vertical Angles 
Make =
proper
conclusions from a diagram. 

=
; 
e 
Can I=
make and
test conjectures? 
Types=
of Lines
â€“ Parallel, skew, perpendicular 
Apply=
the
concepts of complementary, supplementary, and vertical angles. 

=
; 
r 
Can I=
logically
communicate my mathematical reasoning in writing as well as orally? =

Ifth=
en
statements and converses 
Use A=
lgebra to
solve problems. 

=
; 

=
; 
=
; 
Deter=
mine the
hypothesis and conclusion in an ifthen statement. 

=
; 

=
; 
=
; 
State=
the
converse of an ifthen statement. 

=
; 
O 
Paral=
lel Lines 






c 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
t 
Can I=
draw and
measure two and threedimensional figures? 
Prope=
rties of
Parallel Lines â€“ corresponding angles, alternate interior, sameside
interior 
Ident=
ify pairs
of angles (corresponding angles, alternate interior, sameside interior)
formed by two lines cut by a transversal. 
Homework 

Students
will know and be able to apply properties of parallel lines. 
M.09=
10.G.02Geometry
~ Draw congruent and similar figures using a compass, straightedge,
protractor, and other tools such as computer software. Make conjectures a=
bout
methods of construction. Justify the conjectures by logical arguments.

o 
=
; 
=
; 
Apply=
the
properties of angles formed by parallel lines and a transversal. 
Quizzes 
M.09=
10.G.03Geometry
~ Recognize and solve problems involving angles formed by transversals of
coplanar lines. Identify and determine the measure of central and inscrib=
ed
angles and their associated minor and major arcs. Recognize and solve
problems associated with radii, chords, and arcs within or on the same
circle. 
b 
Am I =
able to
use technology to investigate and explore geometric properties? 
With =
the given
information determine if lines are parallel. 
=
; 
Tests 
=
; 
e 
Can I=
make and
test conjectures? 
=
; 
Use i=
nformation
about angles to conclude whether or not lines are parallel. 
Geometers' Sketchpad L=
abs 
=
; 
r 
Can I=
logically
communicate my mathematical reasoning in writing as well as orally? 
=
; 
=
; 

=
; 

=
; 
=
; 
=
; 

=
; 

Prope=
rties of
Triangles 







Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 

Can I
investigate and analyze properties of two and threedimensional geometric
figures? 
Types=
of
Triangles (Scalene, Isosceles, Equilateral, Acute, Right, Obtuse,
Equiangular) 
Disti=
nguish
between various types of triangles. 
Homework 

Students
will know and be able to identify and apply properties of various types of
triangles. 
M.09=
10.G.01Geometry
~ Identify figures using properties of sides, angles, and diagonals. Iden=
tify
the figures' type(s) of symmetry. 

=
; 
=
; 
Apply=
the
concept of the sum of the angles of a triangle is 180 degrees. 
Quizzes 
M.09=
10.G.02Geometry
~ Draw congruent and similar figures using a compass, straightedge,
protractor, and other tools such as computer software. Make conjectures a=
bout
methods of construction. Justify the conjectures by logical arguments.


Am I =
able to
use technology to investigate and explore geometric properties? 
Sum o=
f the
angles of a triangle is 180 degrees. 
Apply=
the
properties of isosceles triangles. 
Tests 
M.09=
10.G.05Geometry
~ Solve simple triangle problems using the triangle angle sum property an=
d/or
the Pythagorean theorem. 

=
; 
Prope=
rties of
isosceles triangles. 
=
; 
Geometers' Sketchpad L=
abs 
M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 

Can I=
make and
test conjectures? 
=
; 
Apply=
the
concepts of triangle inequalities within a triangle. 

=
; 

=
; 
Trian=
gle
inequality. 
=
; 

=
; 

Can I=
logically
communicate my mathematical reasoning in writing as well as orally? 
=
; 
=
; 

=
; 

=
; 
=
; 
=
; 

=
; 
N 
Congr=
uent
Triangles 






o 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
v 
Can I=
draw and
measure two and threedimensional figures? 
Metho=
ds of
proving that triangles are congruent (SSS, SAS, ASA, AAS, HL). 
Demon=
strate
that two triangles are congruent by SS, SAS, ASA, AAS, and HL. 
Homework 

Students
will know and be able to use various techniques to prove triangles are
congruent. 
M.09=
10.G.04Geometry
~ Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and
properties of the figures to find missing parts of geometric figures, and
provide logical justification. 
e 
Can I=
reason by
a variety of methods? (i.e., 2 column proof, paragraph proof, indirect pr=
oof,
inductively) 
Corre=
sponding
parts of congruent triangles are congruent. 
Ident=
ify
congruent parts of congruent figures. 
Quizzes 
M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 
m 
Can I=
logically
communicate my mathematical reasoning in writing as well as orally? 
Proofs
involving isosceles triangles and triangles that are overlapping.
 =
; 
Tests 
=
; 
b 
=
; 
=
; 
Write=
a proof
(2 column, paragraph, flow chart, or, ....) for proving two triangles are
congruent and/or corresponding parts of congruent triangles are congruent=
. 
Geometers' Sketchpad L=
abs 
=
; 
e 
=
; 
=
; 
Apply=
congruent
triangle methods to triangles that are isosceles. 

=
; 
r 
=
; 
=
; 
Apply=
congruent
triangle methods to triangles that are overlapping. 

=
; 

Polyg=
ons (Nov 
Dec) 







Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 

Can I=
draw and
measure two and threedimensional figures? 
Types=
of
Polygons 
Disti=
nguish
between various types of polygons. 
Homework 

Students
will know and be able to identify, analyze, and apply angle properties of
different types of polygons. 
M.09=
10.G.01Geometry
~ Identify figures using properties of sides, angles, and diagonals. Iden=
tify
the figures' type(s) of symmetry. 

=
; 
=
; 
Find =
the
measures of interior and exterior angles of convex polygons. 
Quizzes 
M.09=
10.G.05Geometry
~ Solve simple triangle problems using the triangle angle sum property an=
d/or
the Pythagorean theorem. 

Can I
investigate and analyze properties of two and threedimensional geometric
figures? 
Sum o=
f the
interior angles and exterior angles. 
=
; 
Tests 
=
; 

=
; 
=
; 
=
; 
Geometers' Sketchpad L=
abs 
=
; 

Can I=
logically
communicate my mathematical reasoning in writing as well as orally? 
=
; 
=
; 

=
; 

=
; 
=
; 
=
; 

=
; 
D 
Prope=
rties of
Parallelograms 






e 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
c 
Can I=
draw and
measure two and threedimensional figures? 
Types=
of
quadrilaterals. 
Disti=
nguish
between various types of quadrilaterals. 
Homework 

Students
will know and be able to apply properties of quadrilaterals. 
M.09=
10.G.01Geometry
~ Identify figures using properties of sides, angles, and diagonals. Iden=
tify
the figures' type(s) of symmetry. 
e 
Can I
investigate and analyze properties of two and threedimensional geometric
figures? 
Prope=
rties of
Parallelograms 
Apply=
the
properties of parallelograms. 
Quizzes 
M.09=
10.G.02Geometry
~ Draw congruent and similar figures using a compass, straightedge,
protractor, and other tools such as computer software. Make conjectures a=
bout
methods of construction. Justify the conjectures by logical arguments.

m 
Can I=
reason by
a variety of methods? (i.e., 2 column proof, paragraph proof, indirect pr=
oof,
inductively) 
Prope=
rties of
special parallelograms (rectangle, rhombus, square). 
Apply=
the
properties of special parallelograms (rectangle, rhombus, and square).
 Tests 
M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 
b 
Am I =
able to
use technology to investigate and explore geometric properties? 
Prope=
rties of
Trapezoids and Isosceles Trapezoids. 
=
; 
Geometers' Sketchpad L=
abs 
=
; 
e 
Can I=
make and
test conjectures? 
=
; 
Apply=
the
properties of trapezoids and isosceles trapezoids. 

=
; 
r 
Can I=
logically
communicate my mathematical reasoning in writing as well as orally? 
=
; 
=
; 

=
; 

=
; 
=
; 
=
; 

=
; 
J 
Revie=
w for
Semester I Exam 






a 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
n 
Can I=
draw and
measure two and threedimensional figures? 





M.09=
10.G.01Geometry
~ Identify figures using properties of sides, angles, and diagonals. Iden=
tify
the figures' type(s) of symmetry. 
u 
=
; 
M.09=
10.G.02Geometry
~ Draw congruent and similar figures using a compass, straightedge,
protractor, and other tools such as computer software. Make conjectures a=
bout
methods of construction. Justify the conjectures by logical arguments.

a 
Can I
investigate and analyze properties of two and threedimensional geometric
figures? 
M.09=
10.G.03Geometry
~ Recognize and solve problems involving angles formed by transversals of
coplanar lines. Identify and determine the measure of central and inscrib=
ed
angles and their associated minor and major arcs. Recognize and solve
problems associated with radii, chords, and arcs within or on the same
circle. 
r 
=
; 
M.09=
10.G.04Geometry
~ Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and
properties of the figures to find missing parts of geometric figures, and
provide logical justification. 
y 
Can I=
reason by
a variety of methods? (i.e., 2 column proof, paragraph proof, indirect pr=
oof,
inductively) 
M.09=
10.G.05Geometry
~ Solve simple triangle problems using the triangle angle sum property an=
d/or
the Pythagorean theorem. 

=
; 
M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 

Can I=
work in
the coordinate plane and apply appropriate formulas to find solutions?
 =
; 

=
; 
=
; 

Do I =
use the
most effective tool to determine and calculate measurements? 
=
; 

=
; 
=
; 

Can I=
logically
communicate my mathematical reasoning in writing as well as orally? 
=
; 

=
; 
=
; 
F 
Simil=
arity and
Proportionality (Jan  Feb) 






e 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
b 
Can I=
draw and
measure two and threedimensional figures? 
Ratio=
/Proportion 
Simpl=
ify ratios
(including use of appropriate units) 
Homework 

Students
will know and be able to identify and apply properties of similar figures=
. 
M.0910.G.04Geometry
~ Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and
properties of the figures to find missing parts of geometric figures, and
provide logical justification. 
r 
Can I=
reason by
a variety of methods? (i.e., 2 column proof, paragraph proof, indirect pr=
oof,
inductively) 
=
; 
Solve=
problems
using ratios and proportions. 
Quizzes 
u 
=
; 
Simil=
ar
Polygons 
Apply=
the
properties of similar polygons. 
Tests 
a 
=
; 
Simil=
ar
Triangles (AA) 
=
; 
Geometers' Sketchpad L=
abs 
r 
Can I=
logically
communicate my mathematical reasoning in writing as well as orally? 
Propo=
rtional
Lengths 
Use A=
A to
demonstrate that triangles are similar. 

y 
=
; 
=
; 
Apply=
Triangle
Proportionality and Proportion of an AngleBisector of a Triangle. <=
/td>
 
M 
Right=
Triangles
and Area (Feb  Mar) 






a 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
r 
Can I=
draw and
measure two and threedimensional figures? 
Perfe=
ct
Squares, square roots, and basic equations that require square root in
solution 
Simpl=
ify
expressions with square roots. 
Homework 

Stude=
nts will
know and be able to apply the Pythagorean Theorem and properties of Speci=
al
Right Triangles. 
M.09=
10.G.05Geometry
~ Solve simple triangle problems using the triangle angle sum property an=
d/or
the Pythagorean theorem. 
c 
Do I =
use the
most effective tool to determine and calculate measurements? 
Pytha=
gorean
Theorem 
Solve=
basic
equations that require a square root in the solution. 
Quizzes 
=
; 
M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 
h 
=
; 
=
; 
=
; 
Tests 
Stude=
nts will
know and be able to calculate the area of various geometric figures. 
M.09=
10.M.01Measurement
~ Calculate perimeter, circumference, and area of common geometric figures
such as parallelograms, trapezoids, circles, and triangles. 

Can I=
logically
communicate my mathematical reasoning in writing as well as orally? =

3060=
90,
454590 
Apply=
the
Pythagorean Theorem. 
Geometers' Sketchpad L=
abs 
=
; 
M.09=
10.M.03Measurement
~ Relate changes in the measurement of one attribute of an object to chan=
ges
in other attributes, e.g., how changing the radius or height of a cylinder
affects its surface area or volume. 

=
; 
Area =
of
Rectangles/Squares 
Deter=
mine
lengths of the sides of 306090 and 454590 triangles. 

=
; 
M.09=
10.M.04Measurement
~ Describe the effects of approximate error in measurement and rounding on
measurements and on computed values from measurements. 

=
; 
Area =
of
Parallelogram 
Use t=
he
formulas to find the areas of rectangles, parallelograms, triangles, and
trapezoids. 

=
; 
M.09=
10.N.01Number
Sense and Operations ~ Identify and use the properties of operations on r=
eal
numbers, including the associative, commutative, and distributive propert=
ies;
the existence of the identity and inverse elements for addition and
multiplication; the existence of nthroots of positive real numbers for any
positive integer n; and the inverse relationship between taking the nth r=
oot
of and the nth power of a positive real number. 

=
; 
Area =
of
Triangles and Trapezoids 
=
; 

=
; 
M.09=
10.N.03Number
Sense and Operations ~ Find the approximate value for solutions to proble=
ms
involving square roots and cube roots without the use of a calculator, e.=
g.,
Ă– 32  1 Â» 2.8. 

=
; 
=
; 
=
; 

=
; 
M.09=
10.N.04Number
Sense and Operations ~ Use estimation to judge the reasonableness of resu=
lts
of computations and of solutions to problems involving real numbers. =
; 
A 
Circl=
es 






p 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
r 
Can I=
draw and
measure two and threedimensional figures? 
Circle
Terminology 
Defin=
e and
identify the terminology related to circles. 
Homework 

Stude=
nts will
know and be able to apply properties of circles. 
M.09=
10.G.02Geometry
~ Draw congruent and similar figures using a compass, straightedge,
protractor, and other tools such as computer software. Make conjectures a=
bout
methods of construction. Justify the conjectures by logical arguments.

i 
Can I
investigate and analyze properties of two and threedimensional geometric
figures? 
Prope=
rties of
tangents, chords, and inscribed angles 
=
; 
Quizzes 
=
; 
M.09=
10.G.03Geometry
~ Recognize and solve problems involving angles formed by transversals of
coplanar lines. Identify and determine the measure of central and inscrib=
ed
angles and their associated minor and major arcs. Recognize and solve
problems associated with radii, chords, and arcs within or on the same
circle. 
l 
Am I =
able to
use technology to investigate and explore geometric properties? 
Circu=
mference
and Area of a Circle 
Apply
properties of tangents, chords, central angles, and inscribed angles. 
Tests 
Stude=
nts will
know and be able to calculate the area of various geometric figures. 
M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 

=
; 
Lengt=
h of an
arc, Area of a sector, Area of shaded regions 
Calcu=
late the
area and circumference of circles as well as the lengths of an arc, area =
of a
sector, and area of shaded regions. 
Geometers' Sketchpad L=
abs 
=
; 
M.09=
10.G.10Geometry
~ Demonstrate the ability to visualize solid objects and recognize their
projections and cross sections. 

Can I=
make and
test conjectures? 
=
; 
=
; 

=
; 
M.09=
10.M.01Measurement
~ Calculate perimeter, circumference, and area of common geometric figures
such as parallelograms, trapezoids, circles, and triangles. 

Can I=
logically
communicate my mathematical reasoning in writing as well as orally? =

=
; 
=
; 

=
; 
M.09=
10.M.03Measurement
~ Relate changes in the measurement of one attribute of an object to chan=
ges
in other attributes, e.g., how changing the radius or height of a cylinder
affects its surface area or volume. 

=
; 
=
; 
=
; 

=
; 
M.09=
10.M.04Measurement
~ Describe the effects of approximate error in measurement and rounding on
measurements and on computed values from measurements. 

Volum=
e and
Surface Area (Apr  May) 







Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 

Can I=
draw and
measure two and threedimensional figures? 
Volume
and Surface Area of Right Prisms, Right Square Pyramids, Right Cylinders,
Right Cones, Spheres 
Use
formulas to find the volume and surface area of right prisms, right square
pyramids, right cylinders, right cones, and spheres. 
Homework 

Students
will know and be able to calculate the volume and surface area of various
solids. 
M.09=
10.G.05Geometry
~ Solve simple triangle problems using the triangle angle sum property an=
d/or
the Pythagorean theorem. 

Can I
investigate and analyze properties of two and threedimensional geometric
figures? 
Quizzes 
M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 

Do I =
use the
most effective tool to determine and calculate measurements? 
Tests 
M.09=
10.G.10Geometry
~ Demonstrate the ability to visualize solid objects and recognize their
projections and cross sections. 

=
; 

M.09=
10.M.01Measurement
~ Calculate perimeter, circumference, and area of common geometric figures
such as parallelograms, trapezoids, circles, and triangles. 

Can I=
logically
communicate my mathematical reasoning in writing as well as orally? =


M.09=
10.M.02Measurement
~ Given the formula, find the lateral area, surface area, and volume of
prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of=
a
sphere with a specified surface area. 

=
; 

M.09=
10.M.03Measurement
~ Relate changes in the measurement of one attribute of an object to chan=
ges
in other attributes, e.g., how changing the radius or height of a cylinder
affects its surface area or volume. 

=
; 

M.09=
10.M.04Measurement
~ Describe the effects of approximate error in measurement and rounding on
measurements and on computed values from measurements. 
M 
MCAS
Preparation 






a 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
y 

MCAS
Preparation 




M.09=
10.D.01Data
Analysis, Statistics, and Probability ~ Select, create, and interpret an
appropriate graphical representation (e.g., scatterplot, table,
stemandleaf plots, boxandwhisker plots, circle graph, line graph, and
line plot) for a set of data and use appropriate statistics (e.g., mean,
median, range, and mode) to communicate information about the data. Use t=
hese
notions to compare different sets of data. 

M.09=
10.D.02Data
Analysis, Statistics, and Probability ~ Approximate a line of best fit (t=
rend
line) given a set of data (e.g., scatterplot). Use technology when
appropriate. 

M.09=
10.D.03ta
Analysis, Statistics, and Probability ~ Describe and explain how the rela=
tive
sizes of a sample and the population affect the validity of predictions f=
rom
a set of data. 

M.09=
10.G.01Geometry
~ Identify figures using properties of sides, angles, and diagonals. Iden=
tify
the figures' type(s) of symmetry. 

M.09=
10.G.02Geometry
~ Draw congruent and similar figures using a compass, straightedge,
protractor, and other tools such as computer software. Make conjectures a=
bout
methods of construction. Justify the conjectures by logical arguments.


M.09=
10.G.03Geometry
~ Recognize and solve problems involving angles formed by transversals of
coplanar lines. Identify and determine the measure of central and inscrib=
ed
angles and their associated minor and major arcs. Recognize and solve
problems associated with radii, chords, and arcs within or on the same
circle. 

M.09=
10.G.04Geometry
~ Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and
properties of the figures to find missing parts of geometric figures, and
provide logical justification. 

M.09=
10.G.05Geometry
~ Solve simple triangle problems using the triangle angle sum property an=
d/or
the Pythagorean theorem. 

M.09=
10.G.06Geometry
~ Use the properties of special triangles (e.g., isosceles, equilateral,
30Â°â€“60Â°â€“90Â°, 45Â°â€“45Â°â€“90Â°) to solve problems. 

M.09=
10.G.07Geometry
~ Using rectangular coordinates, calculate midpoints of segments, slopes =
of
lines and segments, and distances between two points, and apply the resul=
ts
to the solutions of problems. 

M.09=
10.G.08Geometry
~ Find linear equations that represent lines either perpendicular or para=
llel
to a given line and through a point, e.g., by using the â€śpointslopeâ€ť
form of the equation. 

M.09=
10.G.09Geometry
~ Draw the results, and interpret transformations on figures in the
coordinate plane, e.g., translations, reflections, rotations, scale facto=
rs,
and the results of successive transformations. Apply transformations to t=
he
solutions of problems. 

M.09=
10.G.10Geometry
~ Demonstrate the ability to visualize solid objects and recognize their
projections and cross sections. 

M.09=
10.G.11Geometry
~ Use vertexedge graphs to model and solve problems. 

M.09=
10.M.01Measurement
~ Calculate perimeter, circumference, and area of common geometric figures
such as parallelograms, trapezoids, circles, and triangles. 

M.09=
10.M.02Measurement
~ Given the formula, find the lateral area, surface area, and volume of
prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of=
a
sphere with a specified surface area. 

M.09=
10.M.03Measurement
~ Relate changes in the measurement of one attribute of an object to chan=
ges
in other attributes, e.g., how changing the radius or height of a cylinder
affects its surface area or volume. 

M.09=
10.M.04Measurement
~ Describe the effects of approximate error in measurement and rounding on
measurements and on computed values from measurements. 

M.09=
10.N.01Number
Sense and Operations ~ Identify and use the properties of operations on r=
eal
numbers, including the associative, commutative, and distributive propert=
ies;
the existence of the identity and inverse elements for addition and
multiplication; the existence of nthroots of positive real numbers for any
positive integer n; and the inverse relationship between taking the nth r=
oot
of and the nth power of a positive real number. 

M.09=
10.N.02Number
Sense and Operations ~ Simplify numerical expressions, including those
involving positive integer exponents or the absolute value, e.g., 3(24â€“=
1)
=3D 45, 43 â€“ 5 + 6 =3D 14; apply such simplifications in the solution=
of
problems. 

M.09=
10.N.03Number
Sense and Operations ~ Find the approximate value for solutions to proble=
ms
involving square roots and cube roots without the use of a calculator, e.=
g.,
Ă– 32  1 Â» 2.8. 

M.09=
10.N.04Number
Sense and Operations ~ Use estimation to judge the reasonableness of resu=
lts
of computations and of solutions to problems involving real numbers. 

M.09=
10.P.01Patterns,
Relations and Algebra ~ Describe, complete, extend, analyze, generalize, =
and
create a wide variety of patterns, including iterative, recursive (e.g.,
Fibonacci Numbers), linear, quadratic, and exponential functional
relationships. 

M.09=
10.P.02Patterns,
Relations and Algebra ~ Demonstrate an understanding of the relationship
between various representations of a line. Determine a line's slope and x
and yintercepts from its graph or from a linear equation that represents=
the
line. Find a linear equation describing a line from a graph or a geometric
description of the line, e.g., by using the â€śpointslopeâ€ť or â€śslope
yinterceptâ€ť formulas. Explain the significance of a positive, negative,
zero, or undefined slope. 

M.09=
10.P.03Patterns,
Relations and Algebra ~ Add, subtract, and multiply polynomials. Divide
polynomials by monomials. 

M.09=
10.P.04Patterns,
Relations and Algebra ~ Demonstrate facility in symbolic manipulation of
polynomial and rational expressions by rearranging and collecting terms;
factoring (e.g., a2â€“ b2=3D (a + b)(a â€“ b), x2+ 10x + 21 =3D (x + 3)(x=
+ 7),
5x4+ 10x3â€“ 5x2=3D 5x2(x2+ 2x â€“ 1)); identifying and canceling common
factors in rational expressions; and applying the properties of positive
integer exponents. 

M.09=
10.P.05Patterns,
Relations and Algebra ~ Find solutions to quadratic equations (with real
roots) by factoring, completing the square, or using the quadratic formul=
a.
Demonstrate an understanding of the equivalence of the methods. 

M.09=
10.P.06Patterns,
Relations and Algebra ~ Solve equations and inequalities including those
involving absolute value of linear expressions (e.g., x â€“ 2 > 5) a=
nd
apply to the solution of problems. 

M.09=
10.P.07Patterns,
Relations and Algebra ~ Solve everyday problems that can be modeled using
linear, reciprocal, quadratic, or exponential functions. Apply appropriate
tabular, graphical, or symbolic methods to the solution. Include compound
interest, and direct and inverse variation problems. Use technology when
appropriate. 

M.09=
10.P.08Patterns,
Relations and Algebra ~ Solve everyday problems that can be modeled using
systems of linear equations or inequalities. Apply algebraic and graphical
methods to the solution. Use technology when appropriate. Include mixture,
rate, and work problems. 
J 
Right=
Triangle
Trigonometry 






u 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Assessments 
Lessons 
Learn=
ing
Benchmarks 
Stand=
ards 
n 
Can I=
draw and
measure two and threedimensional figures? 
Defin=
itions of
sine, cosine, and tangent of an acute angle of a right triangle. 
Ident=
ify the
sine, cosine, and tangent ratios of an acute angle of a right triangle.
 Homework 6/1/2014 

Students
will know and be able to apply trigonometric ratios to solve right triang=
les. 
M.09=
10.M.04Measurement
~ Describe the effects of approximate error in measurement and rounding on
measurements and on computed values from measurements. 
e 
Do I =
use the
most effective tool to determine and calculate measurements? 
Solve=
for sides
and angles of a right triangle. 
=
; 
Quizzes 6/1/2014 
M.09=
10.N.04Number
Sense and Operations ~ Use estimation to judge the reasonableness of resu=
lts
of computations and of solutions to problems involving real numbers. 

=
; 
Appli=
cations
including angle of elevation and angle of depression 
Solve=
right
triangle problems using the sine, cosine, and tangent ratios. 
Tests 6/1/2014 
M.11=
12.G.01Geometry
~ Define 

Can I=
logically
communicate my mathematical reasoning in writing as well as orally? =

=
; 
Use
trigonometry to solve an applied problem. 
Geometers' Sketchpad L=
abs
6/1/2014 
=
; 







