Download Units 1 - 13 - Nash-Rocky Mount Public Schools

Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Basic Vocabulary
Unit Number:
1
Enduring Understanding:
Students need to know the geometric vocabulary :point, line, plane, segment, ray, vertical angles, adjacent angles, supplementary & complementary angles, linear
pair, vertex, perpendicular lines, parallel lines, difference between equal & congruent, skew lines, angle bisect, midpoint & all symbols in order to make sense of
problems & persevere in solving them. Students need to attend to precision when using & discussing midpoint & distance formulas.
Students will model mathematics & attend to basic precision when doing basic constructions such as : using a compass, ruler & pencil to construct different
geometric shapes: copy a segment, bisect a segment, copy an angle & bisect an angle.
Students will attend to precision when finding the area of rectangles, squares, circles, triangles, & trapezoids.
Standard
Essential Questions
Pacing
Guideline
Key Academic
Vocabulary
5 days
G.CO.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment, based
on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
G.CO.12 Make formal geometric constructions with a
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an
angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the
perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a point
not on the line. NQ.2 Define appropriate quantities for the
purpose of descriptive modeling.NQ. 3 Choose a level of
accuracy appropriate to limitations on measurement
when reporting quantities.
G.GPE.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g.,
using the distance formula.★
What is the basic vocabulary for geometry?
How am I going to use the vocabulary correctly?
What are the symbols for geometry that I need to know?
How will I use these symbols?
How will I construct different geometric shapes, copy a
segment, bisect a segment, copy an angle & bisect an
angle?
Point
collinear points
line
plane
coplanar points
segment
endpoints
ray
initial point
opposite rays
intersect
angle
acute angle
right angle
obtuse angle
vertical angles
adjacent angles,
supplementary &
complementary angles
linear pair
vertex
perpendicular lines
parallel lines,
1
Common Core Curriculum Map 2012-2013
Common Core Math II
between equal &
congruent,
skew lines
angle bisector
midpoint
all symbols
distance & midpoint
formulas
bisects
compass
straightedge,
rectangle
square
triangle
circle
trapezoid
Unit 1 Basic Vocabulary
Suggested Resources by Unit
Location of these resources
1. Use www.classzone.com (must create free account) to assess section
quizzes & tests
2. Geometry, McDougal Littell, 2004 edition.
3. Geometry Resources, McDougal Littell, 2004 edition.
4. http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
5. http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource)
2
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name:
Postulates, Properties & Proofs
Unit Number: 2
Enduring Understanding:
Students need to know: Segment Addition Postulate, Angle Addition Postulate, Properties of Equality, Properties of Congruence in order to make
sense of problems, persevere in solving them & make use of structure.
Students need to know how to make sense of Proofs(vertical angles are congruent; when a transversal crosses parallel lines and alternate interior angles and
corresponding angles are congruent,
points on perpendicular bisector are equidistant from the segment's endpoints) in order to persevere in solving problems. Students need to know proofs to be able to
construct viable arguments & critique the reasoning of others.
Standard
Essential Questions
G.CO.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate
interior angles are congruent and corresponding angles
are congruent; points on a perpendicular bisector of a line
segment are exactly those
equidistant from the segment’s endpoints.
What are the segment & angle addition postulates?
What are the properties of equality & congruence?
How do I use the postulates & properties individually &
together?
Can I write a proof to prove: the vertical angles theorem?
Can I write a proof to prove: points on a perpendicular
bisector are equidistant from the endpoints of the segment?
Can I write a proof to prove: alternate interior angles
theorem and alternate interior angles converse?
G.CO.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment, based
on the undefined notions of point, line,
distance along a line, and distance around a circular arc.
AREI 1: Explain each step in solving a simple equation as
following from the equality of numbers asserted at the
previous step, starting from the
assumption that the original equation has a solution.
Construct a viable argument to justify a solution method.
Pacing
Guideline
8 Include day
for review &
day for test
Key Academic
Vocabulary
segment, angle
postulate, proof
equality
congruence
conjecture
counterexample, converse
theorem
two-column proof
paragraph proof
flow proof
proof
vertical angles
transversal
parallel lines
alternate interior angles
alternate exterior angles
corresponding angles
consecutive interior angles
same side interior angles
perpendicular bisector
equidistant
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Common Core Curriculum Map 2012-2013
Common Core Math II
Unit 2 Postulates, Properties & Proofs
Suggested Resources by Unit
Location of these resources
1. Use www.classzone.com (must create free account) to assess section
quizzes & tests
2. Geometry, McDougal Littell, 2004 edition.
3. Geometry Resources, McDougal Littell, 2004 edition.
4. http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
5. http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource)
4
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name:
Enduring Understanding:
Parallel & Perpendicular Lines
Unit Number: 3
Students need to attend to precision in determining the slopes of parallel & perpendicular lines, writing equations of parallel & perpendicular lines given line & point that it
passes through in order to construct viable arguments in making sense of the problems & perservering in solving them.
Students will look for & make use of structure in using the properties of parallel lines cut by transversal to determine measures of angles formed.
Students will model mathematics by using appropriate tools & attending to precision in basic constructions such as construct a line parallel to a given line through a
given point, line perpendicular to a given line through a point on the line, line perpendicular to a given line through a point not on the line.
Students will reason abstractly & quantitatively in order to construct viable arguments & critique the reasoning of others to prove alternate interior angles &
corresponding angles are congruent when transversal crosses parallel lines
Standard
G.CO.12 Make formal geometric constructions with a
variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an
angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a
point not on the line. NQ.2 Define appropriate
quantities for the purpose of descriptive modeling.NQ.
3 Choose a level of accuracy appropriate to limitations
on measurement when reporting quantities.
G.CO.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when
a transversal crosses parallel lines, alternate interior
angles are congruent and corresponding angles are
congruent;points on a perpendicular bisector of a line
Essential Questions
Can I identify the transversal in a diagram of intersecting lines?
Can I find the measure of angles formed by parallel lines that
are cut by a transversal?
Can I set up and solve algebraic equations based on the
location of given information of angles formed by parallel lines
that are cut by a transversal?
Can I prove two lines are parallel using the converses of the
parallel line theorems?
Can I find the slope of two lines and determine that they are
parallel, perpendicular, or neither?
Can I write the equation of a line that is parallel or
perpendicular to a given line, through a given point?
How will I be able construct a parallel line through a given
point?
How do I construct a line perpendicular through a given point
on the line & a given point not on the line?
Can I write a proof to prove verticals congruent, alternate
interior angles & corresponding angles congruent when a
transversal crosses parallel lines?
Pacing
Guideline
8 Include day
of review &
day of test
Key Academic
Vocabulary
Transversal
intersecting lines
angle
parallel lines
converse theorem
slope
perpendicular lines;
line
point
alternate interior angles
alternate exterior angles
corresponding angles
consecutive interior angles
same side interior angles
Compass
straightedge
parallel
point
5
Common Core Curriculum Map 2012-2013
Common Core Math II
segment are exactly those equidistant from the
segment’s endpoints.
perpendicular
vertical angles
congruent
G.CO.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transformed figure
using, e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that
will carry a given figure onto another.
NQ. 2 Define appropriate quantities for the purpose of
descriptive modeling.
NQ. 3 Choose a level of accuracy appropriate to
limitations on measurement when reporting quantities.
A.CED.1 Create equations and inequalities in one
variable and use them to solve problems. Include
equations arising from linear and quadratic functions,
and simple rational and exponential functions.
A.CED.3 Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or
nonviable options in a modeling context. For example,
represent inequalities describing nutritional and cost
constraints on combinations of different foods.
G.PE.5 Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a
given point).
6
Common Core Curriculum Map 2012-2013
Common Core Math II
Unit 3 Parallel & Perpendicular Lines
Suggested Resources by Unit
Location of these resources
1. Use www.classzone.com (must create free account) to assess section
quizzes & tests
2. Geometry, McDougal Littell, 2004 edition.
3. Geometry Resources, McDougal Littell, 2004 edition.
4. http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
5. http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource)
7
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Congruent Triangles
Unit Number:
4
Enduring Understanding:
Students need to know how to write proofs about triangles concerning sum of the measures of the interior angles of a triangle is 180 degrees, exterior angles
theorem, isosceles triangles, base angles of an isosceles triangle are congruent, corresponding parts of congruent triangles, triangle congruence theorems in order
to construct viable arguments & critque the reasoning of others. Students will use this knowledge to make sense of problems & persevere in solving them.
Standard
G.CO. 6 Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid
motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motions to
decide if they are congruent.
G.CO.7 Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and
only if corresponding pairs of sides and corresponding
pairs of angles are congruent.
G.CO.8 Explain how the criteria for triangle congruence
(ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
Essential Questions
What are the properties of isosceles triangles & can I apply
them?
Can I identify corresponding parts of congruent triangles?
Can I prove & apply the triangle congruence theorems?
Can I write proofs about triangles?
Pacing
Guideline
7 Includes day
of review & day
of test
Key Academic
Vocabulary
Vertex
adjacent sides
isosceles triangle
legs
hypotenuse
base
corresponding parts
congruent
triangle
theorem
exterior angle
interior angle
base angles
vertex angle
G.CO.10 Prove theorems about triangles. Theorems
include: measures of interior angles of a triangle sum to
180°; base angles of isosceles triangles are congruent;
the segment joining midpoints of two sides of a triangle is
parallel to the third side and half the length; the medians
of a triangle meet at a point.
8
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Congruent Triangles
Suggested Resources by Unit
Unit Number: 4
Location of these resources
Use www.classzone.com (must create free account) to assess section
quizzes & tests
Geometry, McDougal Littell, 2004 edition.
Geometry Resources, McDougal Littell, 2004 edition.
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
http://secmathccss.files.wordpress.com/2011/06/9parallel_perpendicular_lines_beta_complete.pdf
Finding Equations for Parallel and Perpendicular Lines
http://ifl.lrdc.pitt.edu/cnx/Amazing%20Amanda%20--%20Task.pdf
(Discovery lesson on interior angles of a triangle)
9
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name:
Unit Number: 5
Properties of Triangles
Enduring Understanding:
Students will look for & make use of the structure of midsegments and medians of triangles, the segment joining the midpoints of two sides of a triangle is parallel to
the third side and half the length in order to make sense of the problem & persevere in solving problems.
Students will use appropriate tools & attend to precision to inscribed and circumscribed circles of a triangle & to construct equilateral triangle inscribed in a circle.
Standard
G.CO.10 Prove theorems about triangles. Theorems
include: measures of interior angles of a triangle sum
to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides
of a triangle is parallel to the third side and half the
length; the medians of a triangle meet at a point.
G.CO.13 Construct an equilateral triangle, a square,
and a regular hexagon inscribed in a circle.
G.C.3 Construct the inscribed and circumscribed
circles of a triangle, and prove properties of angles for
a quadrilateral inscribed in a circle.
Essential Questions
Can I use the properties of midsegments & medians of
triangles to determine lengths of different parts?
Can I construct the inscribed and circumscribed circles of
a triangle?
Can verify that the medians of a triangle meet at a point
and solve appropriate problems?
Can I construct a inscribed equilateral triangle in a circle?
Pacing
Guideline
6 days including
review and test
Key Academic
Vocabulary
midsegment of triangle
median of triangle
segment
triangle
parallel
inscribed circle
circumscribed circle
properties
equilateral triangle
inscribed
equilateral triangle
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Common Core Curriculum Map 2012-2013
Common Core Math II
Unit 5 Properties of Triangles
Suggested Resources by Unit
Location of these resources
http://oaklandk12public.rubiconatlas.org/Atlas/Browse/UnitMap/View/Default?UnitID=15810&Yea
rID=2013&SchoolID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=
767&
Graphic Organizer: www.ilovemath.org - "Segments of a Triangle"
Discovery Lesson - www.ilovemath.org - "Discovering Triangle Midsegments"
Use www.classzone.com (must create free account) to assess section
quizzes & tests
http://www.insidemathematics.org/pdfs/geometry/circle-and-squares/packet.pdf
(Modeling problem dealing with proportions of areas of inscribed triangles and
circles.)
http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource – “Amusement Park”)
http://www.mathsisfun.com/geometry/construct-triangleinscribe.html
(Simulation of construction of inscribed circle in a triangle.
11
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Parallelograms
Unit Number: 6
Enduring Understanding:
Students need to be able reason abstractly & quantitatively in applying the properties of parallelograms to determine measures of sides, angles & diagonals.
Students will reason abstractly & quantitatively in order to construct viable arguments & critique the reasoning of others to prove theorems of the following for
parallelograms:
opposite sides & angles are congruent, diagonals bisect each other & conversely & rectangles are parallelograms with congruent diagonals.
Students will model mathematics by using appropriate tools & attending to precision in constructing a square inscribed in a circle.Students need to be able reason
abstractly & quantitatively in applying the properties of parallelograms to determine measures of sides, angles & diagonals.
Standard
G.CO. 11 Prove theorems about parallelograms.
Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent diagonals.
G.CO.13 Construct an equilateral triangle, a square, and
a regular hexagon inscribed in a circle.
Essential Questions
Pacing
Guideline
Key Academic
Vocabulary
Can I determine the measures of the sides, angles &
diagonals of parallelograms?
Can I prove diagonals of parallelograms bisect each other &
conversely?
Can I prove the theorems about opposite sides & angles are
congruent for parallelograms?
Can I construct a inscribed square in a circle?
Can I use coordinate geometry to prove simple Geometric
theorems?
Can I construct a square inscribed in a circle?
7 days
including
review and test
quadrilateral
parallelogram
side
angle
diagonal
theorem
opposite sides
opposite angles
consecutive sides
congruent
diagonals
12
Common Core Curriculum Map 2012-2013
Common Core Math II
bisect
converse
rectangle
square
inscribed in a circle
Unit 6 Parallelograms
Suggested Resources by Unit
Give students a large copy of a parallelogram. Provide several different
parallelograms for the class. Have them use rulers and protractors to measure
the sides, the diagonals, the parts of the diagonals, and all the angles. As a
class, have them list the patterns they are seeing in their measurements. If
students do not discover all of the properties of parallelogram on their own, lead
them into the discovery.
Then give the students some parallelograms with partial information.
Using the properties they have just discovered, they should find the using parts.
Location of these resources
McDougal Littell Geometry Textbook assignments.
Practice worksheets.
Discovery Lesson: www.ilovemath.org - "Sorting Quadrilaterals"
Use www.classzone.com (must create free account) to assess section
quizzes & tests
http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource)
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
13
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Similar Triangles
Unit Number: 7
Enduring Understanding:
Students will look for & express regularity in repeated reasoning in solving proportions & in similarity theorems.
Students will write proofs about similar triangles in order construct viable arguments & critique the reasoning of others.
Reason abstractly and quantitatively in the proof writing process. As well as construct viable arguments and critique the reasoning of others as they analyze the
correctness of others proofs.
Standard
Essential Questions
Pacing Guideline
Key
Academic
Vocabulary
G.GPE.6 Find the point on a directed line segment
between two given points that partitions the segment in a
given ratio.
Can I find a point on a directed line segment between two
given points that partitions the segment in a given ratio?
Can I apply the triangle similarity theorems to determine the
measures of different parts?
Can I write proofs about triangles?
Can I apply triangle similarity theormens to the coordinate
plane and dialations?
6 days including review
and test
proportion,
extremes,
means,
geometric
mean, similar
polygons,
scale factor,
dilation,
reduction,
G.SRT.1 Verify experimentally the properties of dilations
given by a center and a scale factor:
b.The dilation of a line segment is longer or shorter in the
ratio given by the scale factor.
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Common Core Curriculum Map 2012-2013
Common Core Math II
enlargement,
theorem,
proof, triangle,
G.SRT.5 Use congruence and similarity criteria for
triangles to solve problems and to prove relationships in
geometric figures.
Unit 7 Similar Right Triangles
Suggested Resources by Unit
Location of these resources
http://oaklandk12public.rubiconatlas.org/Atlas/Browse/UnitMap/View/Default?UnitID=15810&Yea
rID=2013&SchoolID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=
767&
Use www.classzone.com (must create free account) to assess section
quizzes & tests
http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource)
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
15
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Special Right Triangles
Unit Number: 8
Enduring Understanding:
Pythagorean Theorem, similar right triangles, special right triangles, trigonometry.
Students will make sense of real world problems and persevere in solving them.
Standard
G.SRT.6 Understand that by similarity, side ratios in right triangles are
properties of the angles in the triangle, leading to definitions of trigonometric
ratios for acute angles.
G.SRT.7 Explain and use the relationship between the sine and cosine of
complementary angles.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Essential Questions
Pacing
Guideline
Key Academic
Vocabulary
Can I apply the Pythagorean Theorem?
Can I apply properties for similar right
triangles, special right triangles &
trigonometry?
8 days
including
review and test
geometric mean
Pythagorean Theorem
Pythagorean triple
special right triangles
trigonometric ratio
sine, cosine, tangent
angle of elevation
angle of depression
similarity
G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by
drawing an auxiliary line from a vertex perpendicular to the opposite side. (for
16
Common Core Curriculum Map 2012-2013
Common Core Math II
enrichment only)
G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines
to find unknown measurements in right and non-right triangles (e.g., surveying
problems, resultant forces). (for enrichment only) (for enrichment only)
A.REI.2 Solve simple rational and radical equations in one variable, and give
examples showing how extraneous solutions may arise.
N.RN.2 Rewrite expressions involving radicals and rational exponents using
the properties of exponents.
Unit 8 Special Right Triangles
Suggested Resources by Unit
Location of these resources
http://oaklandk12public.rubiconatlas.org/Atlas/Browse/UnitMap/View/Default?UnitID=15810&Yea
rID=2013&SchoolID=19&TimePeriodID=14&SourceSiteID=&CurriculumMapID=
767&
Use www.classzone.com (must create free account) to assess section
quizzes & tests
Activity: www.ilovemath.org - "Around the World Pythagorean Theorem"
http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource)
http://www.insidemathematics.org/pdfs/geometry/circle-and-squares/packet.pdf
(Modeling problem dealing with proportions of areas of inscribed triangles and
circles.)
http://ifl.lrdc.pitt.edu/cnx/Squaring%20Triangles%20--%20Task.pdf
(Leads students through two different proofs of the Pythagorean Theorem)
17
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name:
Unit Number: 9
Circles
Enduring Understanding:
Identify and describe relationships among angles, radii and chords.
Prove all circles are similar.
Similarity: Length of an arc, define radian measure constant of proportion, formula for area of sector.
Relationship between central, inscribed & circumscribed angles.
Radius of circle perpendicular to tangent where radius intersects the circle.
Inscribe square, equilateral triangle, regular hexagon in a circle.
Reason abstractly and quantitatively in the the proof writing process. As well as construct viable arguments and critique the reasoning of
others as they analyze the correctness of others proofs.
Students will look for and make use of the structure of similar triangles to discover theorems concerning circles.
Standard
Essential Questions
Pacing
Key Academic
18
Common Core Curriculum Map 2012-2013
Common Core Math II
Guideline
G.C.1 Prove that all circles are similar.
G.C.2 Identify and describe relationships among inscribed
angles, radii, and chords. Include the relationship between
central, inscribed, and circumscribed angles; inscribed
angles on a diameter are right angles; the radius of a circle
is perpendicular to the tangent where the radius intersects
the circle.
G.C.5 Derive using similarity the fact that the length of the
arc intercepted by an angle is proportional to the radius, and
define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
G.GMD.1 Give an informal argument for the formulas for the
circumference of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit arguments.
Can I identify and describe relationships among angles,
radii and chords?
Can I prove all circles are similar?
Can I determine the length of an arc?
Am I able to define the radian measure of a constant
proportion?
Can I apply the formula for the area of a sector?
Can I identify & use the relationship between a central,
inscribed & circumscribed angles?
Can I determine the radius of a circle perpendicular to
tangent where the radius intersects the circle?
Can I construct a inscribed square, equilateral triangle,
regular hexagon in a circle?
6 days
Vocabulary
circle
arc
radian
measure of constant
proportion sector
central angle
inscribed angle
circumscribed angle
radius
diameter
perpendicular
tangent
square,
equilateral triangle
regular hexagon,
inscribed in circle
G.CO.13 Construct an equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
G.GPE.4 Use coordinates to prove simple geometric
theorems algebraically. For example, prove or disprove that
a figure defined by
four given points in the coordinate plane is a rectangle;
prove or disprove that the point (1, √3) lies on the circle
centered at the
origin and containing the point (0, 2).
A.REI. 10 Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a
line).
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Common Core Curriculum Map 2012-2013
Common Core Math II
Suggested Resources by Unit
Location of these resources
Geometry, McDougal Littell, 2004 edition.
Geometry Resources, McDougal Littell, 2004 edition.
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
http://www.indiana.edu/~iucme/mathmodeling/lessons.htm
(Modeling Problems Resource)
http://www.insidemathematics.org/pdfs/geometry/circle-and-squares/packet.pdf
(Modeling problem dealing with proportions of areas of inscribed triangles and
circles.)
Common Core Unit Name:
Equations of Circles and Parabolas
Unit Number: 10
Enduring Understanding:
Students will look for and make use of structure as they write the equation of a circle, given the center and radius.
Students will look for and express regularity in repeated reasoning as they complete the square to find the center and radius of a circle,
given the equation.
Students will look for and express regularity in repeated reasoning as they write the equation of parabola given the focus and directrix.
Standard
Essential Questions
G.GPE.1 Derive the equation of a circle of given center
and radius using the Pythagorean Theorem; complete the
square to find the center and radius of a circle given by
an equation.
Can I write an equation given the center & radius?
Can I complete the square to find the center & radius of a
circle given the equation?
Can I write the equation of a parabola given the focus &
directrix?
G.GPE .2 Derive the equation of a parabola given a focus
Pacing
Guideline
Key Academic
Vocabulary
8 Includes day for
test
circle
center of circle
radius
parabola
focus
20
Common Core Curriculum Map 2012-2013
Common Core Math II
and directrix.
G.CO.13 Construct an equilateral triangle, a square, and
a regular hexagon inscribed in a circle .
directrix
inscribed in a
circle
regular hexagon
A.REI.2 Solve simple rational and radical equations in
one variable, and give examples showing how
extraneous solutions may arise.
AREI.4b Solve quadratic equations by inspection (e.g.,
for x^2= 49), taking square roots, completing the square,
the quadratic formula and factoring, as appropriate to the
initial form of the equation.
A.REI. 11 Explain why the x-coordinates of the points
where the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using technology to
graph the functions, make tables of values, or find
successive approximations. Include cases where f(x)
and/or g(x)are linear, polynomial, rational, absolute value,
exponential, and logarithmic
functions.★
A.SSE.1a Interpret parts of an expression, such as terms,
factors, and coefficients.
A.SSE.2 Use the structure of an expression to identify
ways to rewrite it. For example, see x^4– y^4as (x^2)^2–
(y^2)^2, thus recognizing it as a difference of squares
that can be factored as (x^2– y^2)(x^2+ y^2).
A.SSE.3c Use the properties of exponents to transform
expressions for exponential functions. For example the
expression 1.15^tcan be rewritten as
(1.15^1/12)^12t≈ 1.012^12tto reveal the approximate
equivalent monthly interest rate if the annual rate is
15%.when the quadratic formula gives complex solutions
and write them as a ± bi for real numbers a and b.
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Common Core Curriculum Map 2012-2013
Common Core Math II
A.APR. 1 Understand that polynomials form a system
analogous to the integers, namely, they are closed under
the operations of addition, subtraction, and multiplication;
add, subtract, and multiply polynomials.
A.APR.3 Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to
construct a rough graph of the function defined by the
polynomial.
A.CED.2 Create equations in two or more variables to
represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
A.REI.7 Solve a simple system consisting of a linear
equation and a quadratic equation in two variables
algebraically and graphically. For example, find the points
of intersection between the line y = –3x and the circle
x^2+y^4= 3
A.REI. 10 Understand that the graph of an equation in
two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve(which could be a
line).
F.IF. 2 Use function notation, evaluate functions for
inputs in their domains, and interpret statements that use
function notation in terms of a context.
F. IF. 4 For a function that models a relationship between
two quantities, interpret key features of graphs and tables
in terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship.
Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end
behavior; and periodicity.★
F.IF. 5 Relate the domain of a function to its graph and,
22
Common Core Curriculum Map 2012-2013
Common Core Math II
where applicable, to the quantitative relationship it
describes. For example, if the function h(n) gives the
number of person-hours it takes to assemble n engines in
a factory, then the positive integers would be an
appropriate domain for the function.★
F.IF. 8a Use the process of factoring and completing the
square in a quadratic function to show zeros, extreme
values, and symmetry of the graph, and interpret these in
terms of a context.
F.IF. 9 Compare properties of two functions each
represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For
example, given a graph of one quadratic function and an
algebraic expression for another, say which has the
larger maximum.
F.BF.1a Determine an explicit expression, a recursive
process, or steps for calculation from a context.
F.BF.3 Identify the effect on the graph of replacing f(x) by
f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k
(both positive and negative); find the value of k given the
graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using technology.
Include recognizing even and odd functions from their
graphs and
algebraic expressions for them.
Suggested Resources by Unit
Location of these resources
1. Algebra II with Trigonometry, Prentice Hall, 1993 edition
1.Several copies available at Southern Nash High School
(Contact Ginny Etheridge, [email protected] )
2. Use www.classzone.com (must create free account) to assess section
quizzes & tests
23
Common Core Curriculum Map 2012-2013
Common Core Math II
3. Geometry, McDougal Littell, 2004 edition.
4. Geometry Resources, McDougal Littell, 2004 edition.
5. http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
Common Core Unit Name:
Unit Number: 11
Probability
Enduring Understandings:
Students will look for and express regularity in repeated reasoning as they describe subsets of a sample space to determine outcomes.
Students will look for and express regularity in repeated reasoning as they use union, intersection or complements of other events to describe outcomes of events.
Students will make sense of problems and persevere in solving them as they understand independence and conditional probability and use them to interpret data.
Students will make sense of problems and persevere in solving them as they use the rules of probability to compute probabilities of compound events in a uniform
probability model.
Students will make sense of problems and persevere in solving them as they use probability to evaluate outcomes of decisions.
Standard
Essential Questions
S.CP.1 Describe events as subsets of a sample space (the set of
outcomes)using characteristics (or categories) of the outcomes, or as
unions, intersections, or complements of other events (“or,” “and,” “not”).
Can I describe a subset of a sample space to
determine outcomes?
Can I use the Addition Rule, Multiplication
Pacing
Guideline
Key Academic
Vocabulary
sample space
subset
24
Common Core Curriculum Map 2012-2013
Common Core Math II
S.CP.2 Understand that two events A and B are independent if the
probability of A and B occurring together is the product of their
probabilities, and use this characterization to determine if they are
independent.
Rule, permutations and combinations
to compute probabilities for events and
interpret the answer in terms of a model?
S.CP.3 Understand the conditional probability of A given B as P(A and
B)/P(B), and interpret independence of A and B as saying that the
conditional probability of A given B is the same as the probability of A,
and the conditional probability of B given A is the same as the probability
of B.
S.CP.4 Construct and interpret two-way frequency tables of data when
two categories are associated with each object being classified. Use the
two-way table as a sample space to decide if events are independent
and to approximate conditional probabilities. For example, collect data
from a random sample of students in your school on their favorite subject
among math, science, and English. Estimate the probability that a
randomly selected student from your school will favor science given that
the student is in tenth grade. Do the same for other subjects and
compare
the results.
union
intersection
outcome
complement
independence
probability
conditional
probability
addition rule,
multiplication rule
permutations
combinations
compound events
uniform probability
S.CP.5 Recognize and explain the concepts of conditional probability
and independence in everyday language and everyday situations. For
example, compare the chance of having lung cancer if you are a smoker
with the chance of being a smoker if you have lung cancer.
S.CP.6 Find the conditional probability of A given B as the fraction of B’s
outcomes that also belong to A, and interpret the answer in terms of the
model.
S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B),
and interpret the answer in terms of the model.
A.SSE.1b Interpret complicated expressions by viewing one or more of
their parts as a single entity. For example, interpret P(1+r)^n as the
product of P and a factor not depending on P.
Suggested Resources by Unit
Location of these resources
25
Common Core Curriculum Map 2012-2013
Common Core Math II
1. Algebra II with Trigonometry, Prentice Hall, 1993 edition
1.Several copies available at Southern Nash High School
(Contact Ginny Etheridge, [email protected] )
2. Use www.classzone.com (must create free account) to assess section
quizzes & tests
3. Geometry, McDougal Littell, 2004 edition.
4. Geometry Resources, McDougal Littell, 2004 edition.
5. http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
Common Core Unit Name:
Unit Number: 12
Volume, Area, and Surface Area
Enduring Understanding:
Students will look for and express regularity while finding the volume of cylinders, cones, pyramids & spheres.
Students will use modeling while considering the concepts of density based on area & volume.
Students will construct viable arguments and critique the reasoning of others when deriving volume formulas for cylinders, pyramids, & cones.
Students will attend to precision as they describe shapes, their measurements and properties.
Standard
G.MG. 2 Apply concepts of density based on area and
volume in modeling situations (e.g., persons per square
mile, BTUs per cubic foot).★
G-MG. 1 Use geometric shapes, their measures, and their
properties to describe objects (e.g., modeling a tree trunk or
a human torso as a cylinder).★
G.GMD.3 Use volume formulas for cylinders, pyramids,
Essential Questions
Can I apply the formulas for volume of cones,
pyramids, cylinders & spheres?
Can I model concepts of density based on area &
volume?
Can I make an informal argument for volume formulas
for cylinders, pyramids & cones?
Can I model geometric shapes, their measures &
properties?
Pacing
Guideline
3 days
Key Academic
Vocabulary
polyhedron, face, edge,
vertex, regular, convex,
cross section, Platonic
solids, tetrahedron,
octahedron,
dodecahedron,
isocahedron, prism, bases,
lateral faces, right prism,
oblique prisms, surface
26
Common Core Curriculum Map 2012-2013
Common Core Math II
area, lateral area, net,
cylinder, right cylinder,
pyramid, regular pyramid,
cone, circular cone, right
cone, volume, sphere,
center of a sphere, radius
of a sphere, chord of a
sphere, diameter, great
circle, hemisphere, similar
solids, apothem of the
polygon, center of the
polygon, radius of the
polygon, central angle of
the polygon, density,
cones, and spheres to solve problems.★
NQ.1 Use units as a way to understand problems and to
guide the solution of multi-step problems; choose and
interpret units consistently in formulas; choose and interpret
the scale and the origin in graphs and data displays.
NQ. 2 Define appropriate quantities for the purpose of
descriptive modeling.
A.CED. 4 Rearrange formulas to highlight a quantity of
interest, using the same reasoning as in solving equations.
For example, rearrange Ohm’s law V =IR to highlight
resistance.
Unit 12 Surface Area, Area, and Volume
Suggested Resources by Unit
Location of these resources
Geometry, McDougal Littell, 2004 edition.
Geometry Resources, McDougal Littell, 2004 edition.
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
http://www.insidemathematics.org/pdfs/geometry/glasses/task.pdf
(A modeling task involving volume, includes grading rubric, reflection
questions, Common Core Standards used.)
http://www.insidemathematics.org/pdfs/geometry/triangles/packet.pdf
(A modeling problem dealing with areas of triangles and ratios.)
27
Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Transformations
Unit Number: 13
Enduring Understanding:
Students will use appropriate tools to represent transformations in the plane using software or transparencies.
Students will look for and express regularity in repeated reasoning when they describe transformations as functions that take points in the plane as inputs & give
other points as outputs.
Students will look for and make use of structure as they compare transformations that preserve distance & angle to those that do not.
Student will use modeling to describe the rotations & reflections that carry a polygon onto itself (rectangle, parallelogram, trapezoid, or regular polygon).
Students will use modeling to define rotations, reflections & translations in terms of angles, circles, perpendicular lines, parallel lines & line segments.
Students will use appropriate tools as they draw the transformed figure given rotation, reflection & translation & specify the sequence used to carry figure onto
another.
Students will reason abstractly and quantitatively as they verify experimentally the properties of dilations given by a center & a scale factor.(a.) Dilation takes a line
not passing through the center of the dilation to a parallel line & leaves line passing through the center unchanged.(b.) Dilation of line segment is longer or shorter in
the ratio given by the scale factor.
Standard
Essential Questions
Pacing
Guideline
Key Academic
Vocabulary
28
Common Core Curriculum Map 2012-2013
Common Core Math II
G.CO.2 2. Represent transformations in the plane using, e.g.,
transparencies and geometry software; describe transformations as
functions that take points in the plane as inputs and give other points as
outputs. Compare transformations that preserve distance and angle to
those that do not (e.g., translation versus horizontal stretch).
G.CO.3,3. Given a rectangle, parallelogram, trapezoid, or regular
polygon, describe the rotations and reflections that carry it onto itself.
G.CO.4 4. Develop definitions of rotations, reflections, and translations in
terms of angles, circles, perpendicular lines, parallel lines, and line
segments
Can I identify the different types of
transformations?
Can I describe how the
transformations of how a figure is
carried onto itself?
Can I compare the different
transformations?
Can I draw the different
transformations given specific
information?
Can I use the properties of dilations?
G.CO.5 5. Given a geometric figure and a rotation, reflection, or
translation, draw the transformed figure using, e.g., graph paper, tracing
paper, or geometry software. Specify a sequence of transformations that
will carry a given figure onto another.
G.SRT.1 1. Verify experimentally the properties of dilations given by a
center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a
parallel line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by
the scale factor.
image
preimage
isometry
reflection
line of symmetry
rotation
center of rotation
angle of rotation
rotational symmetry
translation
vector
initial point
terminal point
component form glide
reflection
composition
frieze pattern
reduction enlargement
translation
dilation
G.SRT.2 2. Given two figures, use the definition of similarity in terms of
similarity transformations to decide if they are similar; explain using
similarity transformations the meaning of similarity for triangles as the
equality of all corresponding pairs of angles and the proportionality of all
corresponding pairs of sides.
F.BF. 3 3. Observe using graphs and tables that a quantity increasing
exponentially eventually exceeds a quantity increasing linearly,
quadratically, or (more generally) as a polynomial function.
Suggested Resources by Unit
Location of these resources
Geometry, McDougal Littell, 2004 edition.
29
Common Core Curriculum Map 2012-2013
Common Core Math II
Geometry Resources, McDougal Littell, 2004 edition.
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
http://secmathccss.wordpress.com/secmath1/sec-math-1-year-at-aglance/sec-1-problemassessment-tasks/s1-u5-tasks/
(Culminating activity in which students design Geometric art using
transformations, circles and inscribed figures.)
30