common core state standards - mcgraw-hill education | · pdf filecommon core state standards...

SECTION 1 | Trusted Content

Common Core State StandardsCommon Core State Standards

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What is the goal of the Common Core State Standards?The mission of the Common Core State Standards is to provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that students need for success in college and careers.

W ith American students fully prepared for the future, our

communities will be best positioned to compete successfully

in the global economy. — Common Core State Standards Initiative

Who wrote the standards?The National Governors Association Center for Best Practices and the Council of Chief State School Officers worked with representatives from participating states, a wide range of educators, content experts, researchers, national organizations, and community groups.

What are the major points of the standards?The standards seek to develop both students’ mathematical understanding and their procedural skill. The Standards for Mathematical Practice describe varieties of expertise that mathematics teachers at all levels should seek to develop in their students. The Standards for Mathematical Content define what students should understand and be able to do at each level in their study of mathematics.

How do I implement the standards?The Common Core State Standards are shared goals and expectations for what knowledge and skills your students need to succeed. You as a teacher, in partnership with your colleagues, principals, superintendents, decide how the standards are to be met. Glencoe Geometry is designed to help you devise lesson plans and tailor instruction to the individual needs of the students in your classroom as you meet the Common Core State Standards.

At the high school level the Common Core State Standards are organized by conceptual category. To ease implementation four model course pathways were created: traditional, integrated, accelerated traditional and accelerated integrated. Glencoe

Algebra 1, Glencoe Geometry, and Glencoe Algebra 2 follow the traditional pathway.

v v

Unit 2 | Congruence

Self-Check Practice pp. 182, 258

Foldables pp. 172, 236

Graphing Calculator pp. 187, 294

Virtual Manipulatives pp. 206, 273

rianglesCongruent TrianglesCongruent Triangles

Get Ready for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

4-1 Classifying Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237

Explore: Geometry Lab Angles of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

4-2 Angles of Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .246

4-3 Congruent Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255

4-4 Proving Triangles Congruent—SSS, SAS . . . . . . . . . . . . . . . . . . . . . . . . . . . .264

Extend: Geometry Lab Proving Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .274

4-5 Proving Triangles Congruent—ASA, AAS . . . . . . . . . . . . . . . . . . . . . . . . . . . .275

Extend: Geometry Lab Congruence in Right Triangles . . . . . . . . . . . . . . . . . . . . . . . . . 283

4-6 Isosceles and Equilateral Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .285

Explore: Graphing Technology Lab Congruence Transformations. . . . . . . . . . . . . . . . . 294

4-7 Congruence Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .296

4-8 Triangles and Coordinate Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .315

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .316

Standardized Test Practice, Chapters 1–4 . . . . . . . . . . . . . . . . . . . . . . . . . .318

G.CO.12

G.CO.12

G.CO.10

G.CO.7, G.SRT.5

G.CO.10, G.SRT.5

G.CO.12, G.SRT.5

G.CO.10, G.SRT.5

G.SRT.5

G.CO.10, G.CO.12

G.CO.5, G.CO.6

G.CO.6, G.CO.7

G.CO.10, G.GPE.4

MathematicalContent

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Unit 2 | Congruence

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Congruent TrianglesCongruent Triangles

G.CO.12

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Lesson 1-1

5connectED.mcgraw-hill.com

Points, Lines, and Planes

1Points, Lines, and Planes Unlike the real-world objects that they model, shapes, points, lines, and planes do not have any actual size. In geometry, point, line, and

plane are considered undefined terms because they are only explained using examples and descriptions.

You are already familiar with the terms point, y

xO

point

line

plane

line, and plane from algebra. You graphed on a coordinate plane and found ordered pairs that represented points on lines. In geometry, these terms have a similar meaning.

The phrase exactly one in a statement such as, “There is exactly one line through any two points,” means that there is one and only one.

Key Concept Undefined Terms

A point is a location. It has neither shape nor size.

Named by a capital letter A

Example point A

A line is made up of points and has no thickness or width.

m

PQThere is exactly one line through any two points.

Named by the letters representing two points on the line or a lowercase script letter

Example line m, line PQ or � �� PQ , line QP or � �� QP

A plane is a flat surface made up of points that extends

C

B D

K

infinitely in all directions. There is exactly one plane through any three points not on the same line.

Named by a capital script letter or by the letters naming three points that are not all on the same line

Example plane K, plane BCD, plane CDB, plane DCB, plane DBC, plane CBD, plane BDC

Collinear points are points that lie on the same line. Noncollinear points do not lie on the same line. Coplanar points are points that lie in the same plane. Noncoplanar points do not lie in the same plane.

New Vocabularyundefined term

point

line

plane

collinear

coplanar

intersection

definition

defined term

space

Why?On a subway map, the locations of stops are represented by points. The route the train can take is modeled by a series of connected paths that look like lines. The flat surface of the map on which these points and lines lie is representative of a plane.

ThenYou used basic geometric concepts and properties to solve problems.

Now

1 Identify and model points, lines, and planes.

2 Identify intersecting lines and planes.

Bran

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Pict

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Content StandardsG.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.

Mathematical Practices4 Model with mathematics.6 Attend to precision.

Common Core State Standards

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Lesson 1-1 ResourcesResource Approaching Level AL On Level OL Beyond Level BL English Learners ELL

Teacher Edition � Differentiated Instruction, pp. 10, 11 � Differentiated Instruction, pp. 10, 11 � Differentiated Instruction, p. 10 � Differentiated Instruction, p. 10

Chapter ResourceMasters

� Study Guide and Intervention, pp. 5–6� Skills Practice, p. 7� Practice, p. 8� Word Problem Practice, p. 9� Graphing Calculator Activity, p. 11

� Study Guide and Intervention, pp. 5–6 � Skills Practice, p. 7� Practice, p. 8� Word Problem Practice, p. 9� Enrichment, p. 10� Graphing Calculator Activity, p. 11

� Practice, p. 8� Word Problem Practice, p. 9� Enrichment, p. 10� Graphing Calculator Activity, p. 11

� Study Guide and Intervention, pp. 5–6� Skills Practice, p. 7� Practice, p. 8� Word Problem Practice, p. 9� Graphing Calculator Activity, p. 11

Other� 5-Minute Check 1-1� Study Notebook� Teaching Geometry with Manipulatives

� 5-Minute Check 1-1 � Study Notebook� Teaching Geometry with Manipulatives

� 5-Minute Check 1-1 � Study Notebook

� 5-Minute Check 1-1 � Study Notebook� Teaching Geometry with Manipulatives

1 FocusVertical Alignment

Before Lesson 1-1 Use geometric concepts and properties to solve problems.

Lesson 1-1 Identify and model points, lines, and planes. Identify intersecting lines and planes.

After Lesson 1-1 Use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons.

2 TeachScaffolding QuestionsHave students read the Why? section of the lesson.

Ask:� What are some other objects that

points, lines, and planes could be used to represent? Sample response: Stars can be represented by points, lines can be used to connect the stars to form constellations, and a plane can be used to represent the sky.

� What are some other ways that combinations of points, lines, and planes are used? networks and maps

(continued on the next page)

1PoNNewVV b lVoVocabulary

22222 Identify inlines and

New Vocabulary is listed at the beginning of every lesson.

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Explore 4-2


Geometry Lab

Angles of Triangles

In this lab, you will find special relationships among the angles of a triangle.

Activity 1 Interior Angles of a Triangle

Step 1

Draw and cut out several different triangles. Label the vertices A, B, and C.

Step 2

For each triangle, fold vertex B down so that the fold line is parallel to

−− AC . Relabel as vertex B.

Step 3

Then fold vertices A and C so that they meet vertex B. Relabel as vertices A and C.

Analyze the Results 1. Angles A, B, and C are called interior angles of triangle ABC. What type of fi gure do

these three angles form when joined together in Step 3? a straight angle or straight line

2. Make a conjecture about the sum of the measures of the interior angles of a triangle.

Activity 2 Exterior Angles of a Triangle

Step 1

Unfold each triangle from Activity 1 and place each on a separate piece of paper. Extend

−− AC as shown.

Step 2

For each triangle, tear off ∠A and ∠B.

Step 3

Arrange ∠A and ∠B so that they fill the angle adjacent to ∠C as shown.

Model and Analyze the Results 3. The angle adjacent to ∠C is called an exterior angle of triangle ABC. Make a

conjecture about the relationship among ∠A, ∠B, and the exterior angle at C.

4. Repeat the steps in Activity 2 for the exterior angles of ∠A and ∠B in each triangle.

5. Make a conjecture about the measure of an exterior angle and the sum of the measures of its nonadjacent interior angles. See margin.

The sum of the measures of the angles of any triangle is 180.

m∠A + m∠B is the measure of the exterior angle at C.

See students’ work.

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Common Core State StandardsContent StandardsG.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.).Mathematical Practices 5

CC

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3 AssessFormative AssessmentIn Exercises 1–5, students determine angle measures of the triangles used in this activity, find relationships, and make conjectures that will lead them to the Angle-Sum Theorem and the Exterior Angle Theorem.

From Concrete to AbstractStudents can further explore and conjecture about the relationships of the side and angle measures of the small triangle formed when vertex B is folded down in Activity 1. Students should see that although the side lengths are not the same, the angle measures are congruent.

1 FocusObjective Find the relationships among the measures of the interior angles of a triangle.

Materials� protractor� scissors

Teaching TipAdvise students to label the obtuse angle B when they are first working through Activity 1. They should also repeat Activity 1 using acute, right, and equilateral triangles to further verify concepts.

2 TeachWorking in Cooperative GroupsArrange students in groups of 3 or 4, mixing abilities. Then have groups complete Activity 1 and Analyze the Results 1 and 2.

Ask:� What is a commonality of all

triangles? They all have three sides and three vertices.

� When you change a triangle from an acute triangle to an obtuse triangle, how does it affect the other angle measures? the other angle measures get smaller

� When you change the angle measures, what seems to be the constant? the sum of the angles

Practice Have students complete Activity 2 and Model and Analyze the Results 3–5.

Additional Answer5. The measure of an exterior angle is

equal to the sum of the measures of the two nonadjacent interior angles.

0245_GEO_T_C04_EXP2_663930.indd 245 12-5-23 ��8:01

There are numerous tools for implementing the Common Core State Standards available throughout the program, including:� Standards at point-of-use in the Chapter Planner and in each

lesson of the Teacher Edition, � Complete standards coverage in Glencoe Geometry ensures

that you have all the content you need to teach the standards,

� Correlations that show at a glance where each standard is addressed in Glencoe Geometry.

You can also visit connectED.mcgraw-hill.com to learn more about the Common Core State Standards. There you can choose from an extensive collection of resources to use when planning instruction.

Domain

Standard

G.SRT.2

How do I decode the standards?This diagram provides clarity for decoding the standard identifiers.

Geometry LabGeometrGGGGeometry Lab

Angles of TriannnngggglAAngles of TriannggggglA gles of Tr gggggAA sA es of TriaiAngles of Triannnngggggggl

In this lab, you will find special relationships among the angles of a triangle.

A ti itActivityActivity 11 1 I t iInterio Interio A lr Anglesr Angles f Tof a Tr of a Tri liangleiangle

Geometry Lab

Angles of Triangles

Common Core State StandardsContent StandardsG.CO.12 Make formal geometric construcand methods (compass and straightedge, paper folding, dynamic geometric softwareMathematical Practices 5

CC

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Points, Lineessssss,, PPoints, Lineessssss,,

WWhhhyyyyy?y???WWhhhyyyyy???On a subwstops are rroute the tby a serieslook like lithe map o

ThenThenYou used basicgeometric concepts and properties tosolve problems.

NowNow

1 Identify and modelpoints, lines, and planes.

2 Identify intersectingplanes.2222 Identify in

s and

Points, Lines, and Planes

Content StandardsG.CO.1 Know precise definitions of angle, circleperpendicular line, paralleli d li t b

Common Core State Standards

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Conceptual CategoryG = GeometryS = Statistics and

Probability

Congruence CO

Similarity, Right Triangles, and Trigonometry

SRT

Circles C

Expressing Geometric Properties with Equations

GPE

Geometric Measurement and Dimension

GMD

Modeling with Geometry MG

Conditional Probability and the Rules of Probability

CP

Using Probability to Make Decisions MD

C CO

Domain Names Abbreviations

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(+) Advanced Mathematics Standards � Mathematical Modeling Standards


Lessons in which the standard is the primary focus are indicated in bold.

Common Core State Standards, Traditional Geometry Pathway, Correlated to Glencoe Geometry, Common Core Edition

Standards Student Edition Student EditionLesson(s)

Student Edition Student EditionPage(s)

Geometry

Congruence G-CO

Experiment with transformations in the plane.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.

1-1, 1-2, 1-3, 1-4, 3-1, 3-2, 10-1

5–12, 14–21, 25–35, 36–44,173–178, 180–186, 697–705

2. Represent transformations in the plane using, e.g., transparenciesand 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 thosethat do not (e.g., translation versus horizontal stretch).

4-7, 7-6, 9-1, 9-2,Explore 9-3, 9-3,Explore 9-4, 9-4, 9-6

296–302, 511–517, 623–631,632–638, 639, 640–646, 650, 651–659, 674–681

3. Given a rectangle, parallelogram, trapezoid, or regular polygon,describe the rotations and reflections that carry it onto itself.

9-5 663–669

4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

9-1, 9-2, 9-3, Explore 9-4, 9-4

623–631, 632–638, 640–646,650, 651–659

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 thatwill carry a given figure onto another.

Explore 4-7, 9-1, 9-2, Explore 9-3, 9-3, Explore 9-4, 9-4

294–295, 623–631, 632–638,639, 640–646, 650, 651–659

Understand congruence in terms of rigid motions.6. Use geometric descriptions of rigid motions to transform figures and

to predict the effect of a given rigid motion on a given figure; giventwo figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Explore 4-7, 4-7, 9-1, 9-2,9-3, 9-4, Extend 9-6

294–295, 296–302, 623–631, 632–638, 640–646, 651–659,682–683

7. Use the definition of congruence in terms of rigid motions to showthat two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

4-3, Explore 4-7, 4-7, 9-1,9-2, 9-3, 9-4, Extend 9-6

255–263, 294–295, 296–302,623–631, 632–638, 640–646,651–659, 682–683

8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS)follow from the definition of congruence in terms of rigid motions.

4-7, Extend 9-6 296–302, 682–683

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Correlation

T13connectED.mcgraw-hill.com



Prove geometric theorems.9. Prove theorems about lines and angles.

2-7, 2-8, 3-2, 3-5, 5-1 144–150, 151–159, 180–186,207–214, 324–333

10. Prove theorems about triangles. 4-2, 4-3, 4-4, 4-5, 4-6, 4-8, 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 7-4, Explore 8-2

246–254, 255–263, 264–272,275–282, 285–293, 303–309,324–333, 335–343, 344–351,355–362, 371–380, 490–499,546

11. Prove theorems about parallelograms. 6-2, 6-3, 6-4, 6-5 403–411, 413–421, 423–429,431–438

Make geometric constructions.12. Make formal geometric constructions with a variety of tools and

methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

1-2, 1-3, 1-4, Extend 1-5, Extend 1-6, 2-7, Explore 3-2, 3-5, 3-6, 4-1, Explore 4-2, 4-4, Extend 4-4, 4-5, 4-6, Explore 5-1, Explore 5-2, Explore 5-5, Explore 6-3, 6-3, 6-4, 6-5, 7-4, 9-1,Explore 9-3, Extend 9-5, 10-3, 10-5, Extend 10-5

14–21, 25–35, 36–44, 55,65–66, 144–150, 179,207–214, 215–224, 237–244,245, 264–272, 273, 275–282,285–293, 323, 334, 363, 412,413– 421, 423–429, 430– 438,490– 499, 623–631, 639,670– 671, 715–722, 732–739, 740

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

Extend 10-5 740

Similarity, Right Triangles, and Trigonometry G-SRT

Understand similarity in terms of similarity transformations.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 thecenter unchanged.

Explore 9-6, 9-6 672– 673, 674–681

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Explore 9-6, 9-6 672– 673, 674–681

2. Given two figures, use the definition of similarity in terms ofsimilarity transformations to decide if they are similar; explain usingsimilarity transformations the meaning of similarity for triangles asthe equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

7-2, 7-3, 7-6, Extend 9-6 469– 477, 478–487, 511–517, 682– 683

3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

7-3, 7-6, Extend 9-6 478–487, 511–517, 682–683

Prove theorems involving similarity.4. Prove theorems about triangles.

7-3, 7-4, 7-5, 8-1 478–487, 490–499, 501–508,537–545


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Common Core State Standards Common Core State Standards ContinuedContinued



5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

4-3, 4-4, Extend 4-4, 4-5, Extend 4-5, 7-3, 7-4, 7-5, 7-6, 8-1

255–263, 264–272, 273,275–282, 283–284, 478–487,490–499, 501–508, 511–517,537–545

Define trigonometric ratios and solve problems involving right triangles.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.

8-3, Explore 8-4, 8-4, Extend8-4

558–566, 567, 568–577, 578

7. Explain and use the relationship between the sine and cosine of complementary angles.

8-4 568–577

8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.�

8-2, 8-4, 8-5, 8-6 547–555, 568–577, 580–587, 588–597

Apply trigonometry to general triangles.9. (+) Derive the formula A = 1_

2ab sin (b C ) for the area of a triangle

by drawing an auxiliary line from a vertex perpendicular to theopposite side.

8-6 588–597

10. (+) Prove the Laws of Sines and Cosines and use them to solveproblems.

8-6 588–597

11. (+) Understand and apply the Law of Sines and the Law of Cosinesto find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

8-6, Extend 8-6 588–597, 598

Circles G-C

Understand and apply theorems about circles. 1. Prove that all circles are similar.

10-1 697–705

2. Identify and describe relationships among inscribed angles, radii, and chords.

10-1, 10-2, 10-3, 10-4, 10-5 697–705, 706–714, 715–722,723–730, 732–739

3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

10-4, Extend 10-5 723–730, 740

4. (+) Construct a tangent line from a point outside a given circle to the circle.

10-5 732–739

Find arc lengths and areas of sectors of circles.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 theformula for the area of a sector.

10-2, 11-3 706–714, 798–804


Correlation




Expressing Geometric Properties with Equations G-GPE

Translate between the geometric description and the equation for a conic section.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.

10-8 757–763

2. Derive the equation of a parabola given a focus and directrix. Extend 10-8 764–765

Use coordinates to prove simple geometric theorems algebraically.4. Use coordinates to prove simple geometric theorems algebraically.

4-8, 6-2, 6-3, 6-4, 6-5, 6-6, 10-8

303–309, 403–411, 413–421,423–429, 430–438, 439–448,757–763

5. Prove the slope criteria for parallel and perpendicular lines and use themto solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Explore 3-3, 3-3, 3-4, Extend 3-4, Extend 7-3

187, 188–196, 198–205, 206,488–489

6. Find the point on a directed line segment between two given pointsthat partitions the segment in a given ratio.

1-3, 7-4, 8-7, 9-6, 10-8 25–35, 490–499, 600–608, 674–681, 757–763

7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.�

1-6, 11-1 56–64, 779–786

Geometric Measurement and Dimension G-GMD

Explain volume formulas and use them to solve problems.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.

10-1, 11-3, 12-4, 12-5, 12-6 697–705, 798–804, 863–870,873–879, 880–887

3. Use volume formulas for cylinders, pyramids, cones, and spheres tosolve problems.�

1-7, 12-4, 12-5, 12-6 67–74, 863–870, 873–879,880–887

Visualize relationships between two-dimensional and three-dimensionalobjects.4. Identify the shapes of two-dimensional cross-sections of three-

dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Extend 9-3, 12-1 647–648, 839–844


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Common Core State Standards Common Core State Standards ContinuedContinued



Modeling with Geometry G-MG

Apply geometric concepts in modeling situations.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).�

Throughout the text; for example, Extend 1-1, Extend 1-7, 6-1, 11-5, 12-3

Throughout the text; for example, 13, 75–77, 393–401, 818–824, 854–862

2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).�

Extend 11-2, 12-4, 12-5 797, 863–870, 873–879

3. Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost;working with typographic grid systems based on ratios).�

2-5, 3-6, 5-1, 5-2, 5-5, 6-6, 7-1, 7-7, 8-2, 10-3, 11-2, 11-4, 12-2, 12-4, 12-6, 13-4

127–134, 215–224, 324–333,335–343, 364–370, 439–448,461–467, 518–523, 547–555,715–722, 789–796, 807–815,846–853, 863–870, 880–887,939–946

Statistics and Probability

Conditional Probability and the Rules of Probability S-CP

Understand independence and conditional probability and use them tointerpret data.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”).

13-5, 13-6 947–953, 956–963

2. Understand that two events A and A B are independent if the Bprobability of A andA B occurring together is the product of theirBprobabilities, and use this characterization to determine if they are independent.

13-5 947–953

3. Understand the conditional probability of A given A B as BP (A(( and A B )_

P (B ) ,

and interpret independence of A and A B as saying that the conditionalBprobability of A givenA B is the same as the probability of B A, and theconditional probability of B givenB A is the same as the probability of A B.

13-5 947–953

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 areindependent and to approximate conditional probabilities.

Extend 13-5 954–955

5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

13-5 947–953


Correlation




Use the rules of probability to compute probabilities of compoundevents in a uniform probability model. 6. Find the conditional probability of A given A B as the fraction ofB B ’s

outcomes that also belong to A, and interpret the answer in terms ofthe model.

13-5, Extend 13-5 947–953, 954–955

7. Apply the Addition Rule, P (A(( or A B ) = P (A(( ) AA + P (B ) - P (A(( and A B ),and interpret the answer in terms of the model.

13-6 956–963

8. (+) Apply the general Multiplication Rule in a uniform probability model, P (A(( and A B) BB = P (A(( )AA P (B |A ) = P (B )P (A(( |B ), and interpret theanswer in terms of the model.

13-5 947–953

9. (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

13-2 922–930

Using Probability to Make Decisions S-MD

Use probability to evaluate outcomes of decisions.6. (+) Use probabilities to make fair decisions (e.g., drawing by lots,

using a random number generator).

0-3, 13-4 P8–P9, 939–946

7. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end ofa game).

0-3, 13-3, 13-5 P8–P9, 931–937, 947–953


T18


Common Core State Standards for Mathematical Practice, Correlated to Glencoe Geometry, Common Core Edition


1. Make sense of problems and persevere in solving them.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: yLessons 1-5, 2-1, 3-5, 4-5, 5-4, 6-1, 7-5, 8-2, 9-5, 10-2, 11-2, 12-6, and 13-5.

2. Reason abstractly and quantitatively.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: y1-3, 2-7, 3-6, 4-2, 5-3, 6-4, 7-7, 8-4, 9-6, 10-6, 11-4, Extend 12-4, and 13-2.

3. Construct viable arguments and critique the reasoning of others.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: yLessons 1-7, 2-5, 3-5, 4-4, 5-4, 6-6, 7-4, 8-3, 9-1, 10-1, 11-5, 12-4, and 13-3.

4. Model with mathematics.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: yLessons 1-1, 2-3, 3-1, 4-7, 5-6, 6-5, 7-7, 8-7, 9-3, 10-1, 11-4, 12-3, and 13-3.

5. Use appropriate tools strategically.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: yExtend 1-6, 2-7, Explore 3-3, Explore 4-7, Explore 5-5, Extend 6-1, 7-4, Explore 8-4, Explore 9-4, Extend 10-5, Explore 11-2,and Extend 12-4.

6. Attend to precision.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: yExtend 1-2, Lessons 2-7, 3-3, 4-4, 5-1, 6-2, 7-3, 8-1, 9-2, 10-3, 11-3, 12-5, and 13-2.

7. Look for and make use of structure.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: yLessons 1-3, 2-1, 3-6, 4-1, Explore 5-5, 6-1, Extend 7-1, Explore 8-4, 9-5, 10-6, 11-4, 12-2, and 13-1.

8. Look for and express regularity in repeated reasoning.Glencoe Geometry exhibits these practices throughout the entire program. Some specific lessons for review are: yLessons 1-3, 2-1, Explore 3-3, 4-6, 5-3, 6-1, 7-1, 8-4, Explore 9-3, Extend 10-8, Extend 11-2, Explore 12-1, and 13-1.


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