Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name: Basic Vocabulary / CCM1 Review Unit Number: 1
Enduring Understanding:
Students will review topics from CCM1 that will be used in CCM2. Students will be able to solve an equation for one variable and also solve and equation with the
variable on both sides. Review of midpoint and distance formulas along with Pythagorean theorem. They will also review finding the area and perimeter of triangles,
rectangles, and squares.
Students need to know the geometric vocabulary and the appropriate symbol :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.
Standard
A-CED.4
A-REI.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.
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.GPE.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g.,
using the distance formula.★
Essential Questions
A-REI.1 Can I use mathematical properties to justify my
solution?
A-CED.4. Can I solve literal equations for any given
variable?
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?
Pacing
Guideline
Key Academic
Vocabulary
5 days
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
Foundations of CCM2
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. Quizlet Flashcards- www.Quizlet.com
3. KUTA SOFTWARE for Alg 1- www.kutasoftware.com
4. Infinite Geometry- www.kutasoftware.com
5. Glencoe Geometry Concepts and Applications, Glencoe 2004
6. SAS Curriculum Pathways
7. Use www.mathisfun.com
2
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name:
Constructions and Using Formulas
Unit Number: 2
Enduring Understanding:
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. Students will also be able to solve any formula for the
missing variable. (ex- given the radius, students should be able to plug in for circumference or area. Or given the base and height, find the area of a triangle. )
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-GPE.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g.,
using the distance formula.
Essential Questions
How will I construct different geometric shapes, copy a
segment, bisect a segment, copy an angle & bisect an
angle?
G-GPE.7 Can I find the perimeter of a polygon and the
areas of triangles and rectangles?
Pacing
Guideline
Key Academic
Vocabulary
6 Include day
for review &
day for test
Bisector
Compass
Ruler
Segment
Angle
Area
Perimeter
G-GMD.1 Can I describe the parts of formulas for area and
circumference of circles, and volume of cylinders, pyramids
and cones?
G-GMD.3 Can I use the volume formulas for cylinders,
pyramids, cones and spheres?
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.
G-GMD.3 Use volume formulas for cylinders, pyramids,
cones, and spheres to solve problems.
3
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Unit 2 Constructions and Using Formulas
Suggested Resources by Unit
Location of these resources
1. Use www.classzone.com (must create free account) to assess section
quizzes & tests
2. Glencoe Geometry Concepts and Applications, Glencoe 2004
3. www.quizlet.com vocabulary flashcards
4. Geometer’s Sketchpad
5. SAS Curriculum Pathways
6. Daisy Design Construction – www. Ehow.com – step by step
4
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name:
Enduring Understanding:
Points, Lines, Planes and Segments
Unit Number: 3
Students will learn how to distinguish a point, line, ray, segment or a plane. Understand postulates that are described for lines and planes. Use a number line to
measure a segment, know what betweenness is and how to determine which point is between the other two. Students must understand the properties of equality for real
numbers. Use definition of congruent segments and midpoint to apply appropriate equality theorems. Students will use midpoint for a number line and also to find the
midpoint of a segment on the coordinate plane using the Midpoint formula.
Standard
Essential Questions
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.
Can I find the distance between two points on a number line?
G.GPE.6 Find the point on a directed line segment
between two given points that partitions the segment in
a given ratio.
How do I identify congruent segments and find the midpoints of
the segments?
G.GPE.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g.,
using the distance formula.
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.
Can I apply the properties of real numbers to the measure of
segments?
Given three points and the length of the segment, can I find
which one is between the other two?
Can I name and graph ordered pairs on a coordinate plane,
then find the length or midpoint?
Pacing
Guideline
6 Include day
of review &
day of test
Key Academic
Vocabulary
Point
Line
Plane
Ray
Segment
Postulate
Theorem
Betweenness
Congruent
Congruent segments
Midpoint
Coordinate plane
Can I find the midpoint of any given segment?
5
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Location of these resources
Suggested Resources by Unit
1. Use www.classzone.com (must create free account) to assess section
quizzes & tests
2. www.Quizlet.com (flashcards for symbols and terms)
3. Infinite Geometry- www.kutasoftware. Com
4. Glencoe Geometry Concepts and Applications, Glencoe 2004
6
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name: Angles
Unit Number: 4
Enduring Understanding
Students will define what an angle is, parts of an angle, types of angles, angle measures. Students will also use the angle addition postulate and bisect an angle.
They will also know what adjacent angles are, linear pairs, complementary and supplementary angles, vertical angles and relationships of angles or perpendicular
lines.
Standard
Essential Questions
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.
Can I name and identify parts of an angle?
Can I measure, draw, and classify angles?
Can I find the measure of an angle and the bisector of an
angle?
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.
What are adjacent angles and linear pairs?
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 complementary and supplementary angles? How
do I find the complement or supplement of an angle?
Can I identify vertical angles, what is the relationship?
Can I construct perpendicular lines and identify the
properties?
Pacing
Guideline
9 Includes day
of review & day
of test
Key Academic
Vocabulary
Angle
Opposite rays
Straight angle
Vertex
Sides
Interior
Exterior
Protractor
Degrees
Angle bisector
Adjacent angles
Linear pair
Complementary
Supplementary
Vertical
Congruent
Perpendicular
Right angle
Obtuse angle
Acute angle
7
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name: Angles
Suggested Resources by Unit
Unit Number: 4
Location of these resources
Use www.classzone.com (must create free account) to assess section
quizzes & tests
Glencoe Geometry Concepts and Applications, Glencoe 2004
Infinite Geometry – www.kutasoftware.com
www.quizlet.com – vocabulary
SAS Curriculum pathways- www.sascurriculumpathways.com
8
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name:
Parallel/PerpendicularLines
Unit Number: 5
Enduring Understanding:
Students will be able to determine the relationship between corresponding, consecutive interior, alternate interior, alternate exterior, vertical, and consecutive interior
angles when given parallel lines that are cut by a transversal. They will be able to identify those relationships and determine angle measures accordingly. Students
will write the equation of line that is parallel or perpendicular to another line after exploring/reviewing the relationships between slopes of parallel and perpendicular
lines.
Standard
G.GMD.3 Use volume formulas for cylinders,
pyramids, cones, and spheres to solve problems.★
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.
Essential Questions
Can I describe relationships among lines, parts of lines,
and planes?
Can I identify the relationships among pairs of interior and
exterior angles formed by two parallel lines and a
transversal?
What is the relationship among corresponding angles?
Can I prove two lines are parallel or perpendicular using
the slope?
Can I write the equation of a line that is parallel or
perpendicular to a given line?
Pacing
Guideline
7 Days to include
review and test.
Key Academic
Vocabulary
Alternate interior angles
Alternate exterior angles
Consecutive interior
angles
Corresponding angles
Exterior angles
Exterior angles
Interior angles
Line
Parallel lines
Perpendicular lines
Skew lines
Transversal
Slope
Slope intercept
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.
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
9
Common Core Curriculum Map 2012-2013
Foundations of CCM2
perpendicular to a given line that passes through a
given point).
Unit 5 Parallel Lines
Suggested Resources by Unit
Location of these resources
Use www.classzone.com (must create free account) to assess section
quizzes & tests
Glencoe Geometry Concepts and Applications, Glencoe 2004
www.mathisfun.com
www.sascurriculumpathways.com
Infinite Geometry- www.kutasoftwar.com - free worksheets
10
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name: Triangles and Congruency
Unit Number: 6
Enduring Understanding:
Students will be able to classify triangles by the angles and sides and find missing angle measures. Solve for a variable or missing angle measure using algebraic
equations. Students will be able to identify types of motion in geometry: reflections, translations, and rotations. Students will understand what congruent triangles
are and use corresponding parts to write congruent statements. Use applications from theorems to prove triangle congruency by SAS, SSS, ASA, and AAS.
Standard
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.
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
Can I identify the parts of a triangle and classify by its sides
or angle measures?
Can I use the Angle Sum Theorem?
What is the difference in a rotation, reflection, or translation?
Can I identify congruent triangles by the labels?
Can I properly identify congruent triangles by SSS, SAS,
ASA, or AAS?
Pacing
Guideline
6 days
including
review and test
Key Academic
Vocabulary
Vertex
Sides
Angle
Acute
Obtuse
Right
Equilateral
Scalene
Isosceles
Legs
Base
Equilangular
Translation
Reflection
Rotation
Preimage
Image
Congruent triangle
Corresponding parts
Included angle
Included side
11
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Unit 6 Triangles and Congruency
Suggested Resources by Unit
Use www.classzone.com (must create free account) to assess section
quizzes & tests
Location of these resources
.
Infinite Geometry
www.mathisfun.com
SAS Curriculum Pathways
Infinite Geometry – www.kutasoftware.com
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
Glencoe Geometry Concepts and Applications, Glencoe 2004
12
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name: Triangles
Unit Number: 7
Enduring Understanding:
Students will be able to identify segments as medians, altitudes, perpendicular bisectors, angle bisectors, or midsegments by applying the definition of each in a
triangle. Students will be able to label the parts of isosceles and right triangles and apply the theorems for each to find angle measures or side lengths of the
appropriate triangle.
Standard
Essential Questions
Pacing Guideline
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.
Can I use the properties of median, altitude, and
midsegments to distinguish between types of segments and
find missing parts?
7 days including review
and test
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.
Can I construct a perpendicular bisector, altitude, median or
midsegment for any given triangle?
Can I verify that the medians of a triangle meet at a point in
the middle and solve appropriate problems?
Can I identify an angle bisector and use it to find angle
measures in a triangle?
Can I apply the Pythagorean theorem to find missing
measures in a right triangle?
Key
Academic
Vocabulary
Median
Centriod
Concurrent
Altitude
Perpendicular
bisector
Angle bisector
Orthocenter
Legs
Base
Hypotenuse
Pythagorean
theorem
G.CO.13 Construct an equilateral triangle, a square, and
a regular hexagon inscribed in a circle.
13
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Unit 7 Triangles
Suggested Resources by Unit
Location of these resources
Use www.classzone.com (must create free account) to assess section
quizzes & tests
SAS Curriculum Pathways
Infinite Geometry
Glencoe Geometry Concepts and Applications, Glencoe 2004
www.quizlet.com for flashcards and vocabulary quizzes
14
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name: Parallelograms
Unit Number: 8
Enduring Understanding:
Students will be able to identify the parts of a quadrilateral and find the sum of the measures of the interior angles for any given quadrilateral. They will also be able
to show and test to determine if a quadrilateral is a parallelogram. Students will be able to use properties of rectangles, rhombi, squares and trapezoids.
Standard
Essential Questions
G. CO. 3 Describe the rotations and reflections of a rectangle, parallelogram,
trapezoid, or regular polygon that maps each figure to itself.
What is a quadrilateral and how do I
name it?
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
What are the properties of a
parallelogram?
How do I determine if a quadrilateral is a
parallelogram?
What are the properties used to identify
a square, rhombus, or rectangle?
What are the parts of a trapezoid?
Pacing
Guideline
Key Academic
Vocabulary
7 days
including
review and test
Quadrilateral
Consecutive side
Nonconsecutive
Diagonal
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Base
Legs
Base angles
Median of a trapezoid
Isosceles trapezoid
Midsegment
15
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Unit 8 Parallelograms
Suggested Resources by Unit
Location of these resources
Use www.classzone.com (must create free account) to assess section
quizzes & tests
www.kutasoftware.com
www.sascurriculumpathways.com
Infinite Geometry
Glencoe Geometry Concepts and Applications, Glencoe 2004
16
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name:
Unit Number: 9
Polygons
Enduring Understanding:
Students will be able to name a polygon by determining the number of sides and angle. They will be able to find interior and exterior angles in any given polygon.
Students will also be able to find the area of triangles, trapezoids, and regular polygons. Explore ratios of perimeters and areas in similar polygons. Students will be
able to identify figures with line symmetry and rotational symmetry. Create tessellations using transformations.
Standard
Essential Questions
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.
What is a polygon? How do I name a polygon? What
makes a polygon regular?
G.GPE.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g., using
the distance formula.
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
Do I know the formulas used to find the area of a triangle,
trapezoid, or a regular polygon?
What equation do I use to find the sum of the measures
of the interior angles of any polygon?
What is the sum of the measure of all exterior angles of
any polygon?
What is the relationship between congruent polygons and
their area?
What is a line of symmetry? Can I draw lines of symmetry
if given a polygon?
Pacing
Guideline
8 days to
include test
and review
Key Academic
Vocabulary
Polygon
Regular polygon
Convex
Concave
Pentagon
Square
Hexagon
Heptagon
Octagon
Nonagon
n-gon
apothem
symmetry
line of symmetry
tessellation
rotational turn
What is a tessellation and can I create one using regular
polygons?
17
Common Core Curriculum Map 2012-2013
Foundations of CCM2
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.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.
Suggested Resources by Unit 9 Polygons
Location of these resources
Glencoe Geometry Concepts and Applications, Glencoe 2004
SAS Curriculum Pathways
www.mathisfun.com
www.quizlet.com
18
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name:
Circles
Unit Number: 10
Enduring Understanding:
Students will be able to identify and describe relationships among angles, radii and chords. Also, they will identify and use relationships among arcs, chords, and
diameters of a circle. Use area formula to find area or sectors of a circle.
Essential Questions
Pacing
Guideline
Key Academic
Vocabulary
7 Includes day for
test
Circle
Radius
Chord
Diameter
Central angle
Arc
Minor arc
Major arc
Semicircle
Adjacent arcs
Circumscribed
Inscribed
Circumference
Pi
Sector
Can I identify the parts of a circle?
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.
Can I distinguish between a radius, chord, and a diameter?
Can I find the radius given the diameter? What is the
relationship between all radii in a circle?
What is an arc? Central angle? How do I find the degree
measure of a minor arc? Major arc? Semicircle?
What is the arc addition postulate? How can I use it to find
missing arc lengths?
How do I show minor arcs are congruent using two chords?
What is an inscribed polygon?
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.
How do I find the circumference of a circle?
How do I find the area of a circle, or the area of a sector?
19
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Suggested Resources by Unit- Circles
Location of these resources
1. Use www.classzone.com (must create free account) to assess section
quizzes & tests
2. Glencoe Geometry Concepts and Applications, Glencoe 2004
3. Infinite Geometry- www.kutasoftware.com
20
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name: Surface Area and Volume
Unit Number: 11
Enduring Understandings:
Students will explore different solids and be able to tell likes and differences. Find the lateral area and surface areas of prisms and cylinders, along with finding the
volume. Explore regular pyramids and cones and find the lateral and surface areas. Students will find the volume of pyramids, cones, and spheres. Identify
relationships between similar solid figures.
Standard
Essential Questions
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.
How do I classify prisms and pyramids?
Pacing
Guideline
What is the difference in a cylinder and a
cone?
7 days to
include test and
review
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and
spheres to solve problems.★
G. MG. 2 Use the concept of density when referring to situations
involving area and volume models, such as persons per square mile.
Key Academic
Vocabulary
Can I identify the parts of a prism or cone to
accurately find the surface area?
Can I identify the base of a figure to find the
area?
Can I use the formula to accurately find the
volume of prism or cylinder?
Can I find the surface area of a pyramid or
cone?
What are the formulas used to find the
volume of a cone or pyramid?
What is a sphere? Can I find the surface
area or volume? Given the volume, can I find
21
Common Core Curriculum Map 2012-2013
Foundations of CCM2
the length of the radius?
What are the characteristics of similar solid
figures?
Suggested Resources by Unit- Surface area and volume
Location of these resources
1. Glencoe Geometry Concepts and Applications, Glencoe 2004
2. http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
3. www.sascurriculumpathways.com
4. www.quizlet.com
22
Common Core Curriculum Map 2012-2013
Foundations of CCM2
Common Core Unit Name:
Unit Number: 12
Types of Proofs and Writing Proofs
Enduring Understanding:
Students will learn what a proof is, the types of proofs, and how to write a two column proof. Students will use properties of equality in algebraic and geometric
proofs. Show how logic reasoning can be used to analyze and prove a geometric theorem. Students will begin to write basic proofs to prove the vertical angle
theorem, prove two triangles are congruent, and prove two segments are congruent given a figure.
Standard
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.
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.
Essential Questions
Can I write a two column proof for any given
conjecture?
What is a paragraph proof?
Can I write a proof proving the vertical angle theorem?
Given a two column proof, can I identify the reasons
for each step?
Pacing
Guideline
Key Academic
Vocabulary
6 days to
include test and
review
Paragraph proof
Two column proof
Indirect reasoning
Deductive reasoning
Negation
Statement
Inverse
Converse
contrapositive
Can I write an algebraic proof, showing how to solve
any given equation?
Given a reason, can I indentify the appropriate
statement in a two column proof?
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
23
Common Core Curriculum Map 2012-2013
Foundations of CCM2
congruent diagonals
Unit 12 Types of Proofs and Writing Proofs
Suggested Resources by Unit
Location of these resources
Glencoe Geometry Concepts and Applications, Glencoe 2004
Access for Windows- GEO unit
SAS Curriculum Pathways
24
Common Core Curriculum Map 2012-2013
Foundations of CCM2
25