of+CCM2+Guide.docx · Web viewCommon Core Curriculum Map 2012-2013 Foundations of CCM2 4 Common Core Unit Name: Basic Vocabulary / CCM1 Review Unit Number: 1 Enduring Understanding:

Common Core Curriculum Map 2012-2013Foundations of CCM2

Common Core Unit Name: Basic Vocabulary / CCM1 Review Unit Number: 1Enduring 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 Essential Questions Pacing Guideline

Key Academic Vocabulary

A-CED.4A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from theassumption 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.★

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 anangle?

5 daysPoint

collinear pointsline

plane coplanar points

segmentendpoints

ray initial point

opposite rays intersect

angle acute angle right angle

obtuse angle vertical angles

adjacent angles, supplementary &

complementary angleslinear pair

vertexperpendicular lines

parallel lines,

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between equal & congruent,skew lines

angle bisectormidpoint

all symbolsdistance & midpoint

formulasbisects

compassstraightedge,

rectanglesquaretriangle 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.com3. KUTA SOFTWARE for Alg 1- www.kutasoftware.com4. Infinite Geometry- www.kutasoftware.com5. Glencoe Geometry Concepts and Applications, Glencoe 20046. SAS Curriculum Pathways7. Use www.mathisfun.com

2

http://www.mathisfun.com/

http://www.kutasoftware.com/



Common Core Unit Name: Constructions and Using Formulas Unit Number: 2Enduring 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. )



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.

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.

How will I construct different geometric shapes, copy a segment, bisect a segment, copy an angle & bisect anangle?

G-GPE.7 Can I find the perimeter of a polygon and the areas of triangles and rectangles?

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?

6 Include day for review & day for test

BisectorCompass

RulerSegment

AngleArea

Perimeter

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Unit 2 Constructions and Using Formulas Suggested Resources by Unit Location of these resources


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

http://www.quizlet.com/


Common Core Unit Name: Points, Lines, Planes and Segments Unit Number: 3Enduring Understanding:

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.




G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

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, alternateinterior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly thoseequidistant from the segment’s endpoints.

Can I find the distance between two points on a number line?

Can I apply the properties of real numbers to the measure of segments?

How do I identify congruent segments and find the midpoints of the 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?

Can I find the midpoint of any given segment?

6 Include day of review & day of test

PointLine

PlaneRay

SegmentPostulateTheorem

BetweennessCongruent

Congruent segmentsMidpoint

Coordinate plane

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Suggested Resources by UnitLocation of these resources


2. www.Quizlet.com (flashcards for symbols and terms)

3. Infinite Geometry- www.kutasoftware. Com


6

http://www.kutasoftware/


Common Core Unit Name: Angles Unit Number: 4Enduring 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.





G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternateinterior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those

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?

What are adjacent angles and linear pairs?

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?

9 Includes day of review & day of test

AngleOpposite raysStraight angleVertexSidesInteriorExteriorProtractorDegreesAngle bisectorAdjacent anglesLinear pairComplementarySupplementaryVerticalCongruentPerpendicularRight angleObtuse angleAcute angle

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equidistant from the segment’s endpoints.

Common Core Unit Name: Angles Unit Number: 4

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

Infinite Geometry – www.kutasoftware.com

www.quizlet.com – vocabulary

SAS Curriculum pathways- www.sascurriculumpathways.com

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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.



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.

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.

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?

7 Days to include review and test.

Alternate interior anglesAlternate exterior angles

Consecutive interior angles

Corresponding anglesExterior anglesExterior anglesInterior angles

LineParallel lines

Perpendicular linesSkew linesTransversal

SlopeSlope intercept

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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).

Unit 5 Parallel LinesSuggested 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

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http://www.kutasoftwar.com/

http://www.sascurriculumpathways.com/



Common Core Unit Name: Triangles and Congruency Unit Number: 6Enduring 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.



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.

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?

6 days including review and test

VertexSidesAngleAcute

ObtuseRight

EquilateralScalene

IsoscelesLegsBase

EquilangularTranslationReflectionRotationPreimage

ImageCongruent triangle

Corresponding partsIncluded angleIncluded side

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Unit 6 Triangles and CongruencySuggested Resources by Unit Location of these resources

Use www.classzone.com (must create free account) to assess section quizzes & testsInfinite 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.)


.

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http://www.insidemathematics.org/index.php/tools-for-teachers



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 Key Academic

VocabularyG.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?

Can I verify that the medians of a triangle meet at a point in the middle and solve appropriate problems?

Can I construct a perpendicular bisector, altitude, median or midsegment for any given triangle?

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?

7 days including review and test Median

CentriodConcurrent

AltitudePerpendicular

bisectorAngle bisectorOrthocenter

LegsBase

HypotenusePythagorean

theorem

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G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Unit 7 TrianglesSuggested Resources by Unit Location of these resources



Infinite Geometry


www.quizlet.com for flashcards and vocabulary quizzes

14



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.



G. CO. 3 Describe the rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that maps each figure to itself.

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 is a quadrilateral and how do I name it?

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?

7 days including review and test

QuadrilateralConsecutive sideNonconsecutive

DiagonalParallelogram

RectangleRhombusSquare

TrapezoidBaseLegs

Base anglesMedian of a trapezoidIsosceles trapezoid

Midsegment

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Unit 8 ParallelogramsSuggested Resources by Unit Location of these resources


www.kutasoftware.com

www.sascurriculumpathways.com

Infinite Geometry


16



http://www.classzone.com/


Common Core Unit Name: Polygons Unit Number: 9

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.




G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using

What is a polygon? How do I name a polygon? What makes a polygon regular?

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?

Do I know the formulas used to find the area of a triangle, trapezoid, or a regular polygon?

8 days to include test and review

PolygonRegular polygon

ConvexConcavePentagonSquare

HexagonHeptagonOctagonNonagon

n-gonapothemsymmetry

line of symmetry17


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 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.

What is a line of symmetry? Can I draw lines of symmetry if given a polygon?

What is a tessellation and can I create one using regular polygons?

tessellationrotational turn

Suggested Resources by Unit 9 Polygons Location of these resources



www.mathisfun.com

www.quizlet.com

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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.

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.

Essential Questions

Can I identify the parts of a circle?

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?

How do I find the circumference of a circle?

Pacing Guideline

7 Includes day for test


CircleRadiusChord

DiameterCentral angle

ArcMinor arcMajor arcSemicircle

Adjacent arcsCircumscribed

InscribedCircumference

PiSector

19


How do I find the area of a circle, or the area of a sector?

Suggested Resources by Unit- Circles Location of these resources



3. Infinite Geometry- www.kutasoftware.com

20



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.

StandardA.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.

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.

Essential QuestionsHow do I classify prisms and pyramids?

What is the difference in a cylinder and a cone?

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

Pacing Guideline

7 days to include test and

review


21


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 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


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



http://www.insidemathematics.org/index.php/tools-for-teachers


Common Core Unit Name: Types of Proofs and Writing ProofsUnit Number: 12

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.



G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternateinterior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly thoseequidistant 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

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?

Can I write an algebraic proof, showing how to solve any given equation?

6 days to include test and review

Paragraph proofTwo column proofIndirect reasoning

Deductive reasoningNegation

StatementInverse

Conversecontrapositive

23


parallel to the third side and half the length; the medians of a triangle meet at a point.

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

Given a reason, can I indentify the appropriate statement in a two column proof?

Unit 12 Types of Proofs and Writing ProofsSuggested Resources by Unit Location of these resources


Access for Windows- GEO unit


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Documents

of+CCM2+Guide.docx · Web viewCommon Core Curriculum Map 2012-2013 Foundations of CCM2 4 Common Core Unit Name: Basic Vocabulary / CCM1 Review Unit Number: 1 Enduring Understanding: