Chapter 12 Resource Masters - MHSchool€¦ · lesson. Use as an additional practice or as homework for second-day teaching of the lesson. Enrichment These activities may extend the

Chapter 12Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with GlencoeCalifornia Mathematics, Grade 6. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

ISBN: 978-0-07-878307-4MHID: 0-07-878307-0 CAGR6 CRM12

Printed in the United States of America

4 5 6 7 8 9 10 MAL 14 13 12 11 10 09

Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters

booklets are available as consumable workbooks in both English and Spanish.

MHID ISBNStudy Guide and Intervention Workbook 0-07-878871-4 978-0-07-878871-0

Skills Practice Workbook 0-07-878873-0 978-0-07-878873-4

Practice Workbook 0-07-878875-7 978-0-07-878875-8

Word Problem Practice Workbook 0-07-878877-3 978-0-07-878877-2

Spanish VersionsStudy Guide and Intervention Workbook 0-07-878872-2 978-0-07-878872-7Skills Practice Workbook 0-07-878874-9 978-0-07-878874-1Practice Workbook 0-07-878876-5 978-0-07-878876-5Word Problem Practice Workbook 0-07-878878-1 978-0-07-878878-9

Answers for Workbooks The answers for Chapter 12 of these workbooks can be found in the

back of this Chapter Resource Masters booklet.

StudentWorks Plus™ This CD-ROM includes the entire Student Edition test along with the

English workbooks listed above.

TeacherWorks Plus™ All of the materials found in this booklet are included for viewing,

printing, and editing in this CD-ROM.

Spanish Assessment Masters MHID: 0-07-878879-X ISBN: 978-0-07-878879-6

These masters contain a Spanish version of Chapter 12 Test Form 2A and Form 2C.

iii

Teacher’s Guide to Using the Chapter 12 Resource Masters .........................................iv

Chapter Resources Chapter 12 Student-Built Glossary ....................1Chapter 12 Family Letter (English) ....................3Chapter 12 Family Activity (English) ..................4Chapter 12 Family Letter (Spanish) ...................5Chapter 12 Family Activity (Spanish).................6Chapter 12 Anticipation Guide (English)............7Chapter 12 Anticipation Guide (Spanish) ..........8

Lesson 12-1 Estimating SquareRootsLesson Reading Guide ......................................9Study Guide and Intervention ..........................10Skills Practice...................................................11Practice ............................................................12Word Problem Practice ....................................13Enrichment .......................................................14Scientific Calculator Activity .............................15

Lesson 12-2 The PythagoreanTheoremLesson Reading Guide ....................................16Study Guide and Intervention ..........................17Skills Practice...................................................18Practice ............................................................19Word Problem Practice ....................................20Enrichment .......................................................21

Lesson 12-3 Problem-SolvingInvestigation: Make a ModelStudy Guide and Intervention ..........................22Skills Practice...................................................23Practice ............................................................24Word Problem Practice ....................................25

Lesson 12-4 Surface Area ofRectangular PrismsLesson Reading Guide ....................................26Study Guide and Intervention ..........................27Skills Practice...................................................28Practice ............................................................29Word Problem Practice ....................................30Enrichment .......................................................31

Lesson 12-5 Surface Area ofCylindersLesson Reading Guide ....................................32Study Guide and Intervention ..........................33Skills Practice...................................................34Practice ............................................................35Word Problem Practice ....................................36Enrichment .......................................................37Scientific Calculator Activity .............................38

Chapter 12 AssessmentStudent Recording Sheet for Standardized

Test Practice ................................................39Rubric for Scoring Pre-AP................................40Chapter 12 Quizzes 1 and 2 ............................41Chapter 12 Quizzes 3 and 4 ............................42Chapter 12 Mid-Chapter Test ...........................43Chapter 12 Vocabulary Test .............................44Chapter 12 Test, Form 1 ..................................45Chapter 12 Test, Form 2A................................47Chapter 12 Test, Form 2B................................49Chapter 12 Test, Form 2C................................51Chapter 12 Test, Form 2D................................53Chapter 12 Test, Form 3 ..................................55Chapter 12 Extended-Response Test ..............57Chapter 12 Standardized Test Practice............58Unit 5 Test ........................................................61

Answers..................................................A1–A27

Contents

iv

Teacher’s Guide to Using the Chapter 12 Resource Masters

The Chapter 12 Resource Masters includes the core materials needed for Chapter 12. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing on theTeacherWorks Plus™ CD-ROM.

Chapter ResourcesStudent-Built Glossary (page 1) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 12-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.

Family Letter and Family Activity(pages 3–6) The letter informs yourstudents’ families of the mathematics theywill be learning in this chapter. The familyactivity helps them to practice problems thatare similar to those on the state test. A fullsolution for each problem is included.Spanish versions of these pages are alsoincluded. Give these to students to takehome before beginning the chapter.

Anticipation Guide (pages 7–8) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.

Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).

Study Guide and Intervention Thismaster provides vocabulary, key concepts,additional worked-out examples and CheckYour Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.

Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.

Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.

v

Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.

Enrichment These activities may extendthe concepts of the lesson, offer an historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.

Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.

Assessment OptionsThe assessment masters in the Chapter 12Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final) assessment.

Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.

Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.

Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.

Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.

Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.

Leveled Chapter Tests• Form 1 contains multiple-choice questions

and is intended for use with below gradelevel students.

• Forms 2A and 2B contain multiple-choicequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Form 3 is a free-response test for use withabove grade level students.

All of the above mentioned tests include afree-response Bonus question.

Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.

Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.

Answers• The answers for the Anticipation Guide

and Lesson Resources are provided asreduced pages with answers appearing in red.

• Full-size answer keys are provided for theassessment masters.

Chapter 12 1 Glencoe California Mathematics, Grade 6

Vocabulary TermFound

Definition/Description/Exampleon Page

hypotenuse

irrational number

leg

Pythagorean Theorem

surface area

NAME ________________________________________ DATE ______________ PERIOD _____

Student-Built Glossary

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esThis is an alphabetical list of new vocabulary terms you will learn inChapter 12. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.

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Family LetterNAME ________________________________________ DATE ______________ PERIOD _____


Dear Parent or Guardian:

We use math skills in many of the things that we do. One of

the goals of this class is to show students how things they are

learning in the classroom are relevant to the real world. For

example, understanding the Pythagorean Theorem and surface

area geography, navigation, sports, and architecture.

In Chapter 12, Extending Geometry and Measurement, your

child will learn how to find squares and square roots, use the

Pythagorean Theorem, and find surface areas of rectangular

prisms and cylinders. In the study of this chapter, your child will

complete a variety of daily classroom assignments and activities

and possibly produce a chapter project.

By signing this letter and returning it with your child, you agree

to encourage your child by getting involved. Enclosed is an

activity you can do with your child that practices how the math

in Chapter 12 might be tested. You may also wish to log on to

ca.gr6math.com for self-check quizzes and other study help.

If you have any questions or comments, feel free to contact me

at school.Sincerely,

Signature of Parent or Guardian ______________________________________ Date ________

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Family ActivityStandards Practice

NAME ________________________________________ DATE ______________ PERIOD _____


1. Andy is flying a kite as shown in thediagram.

What is the height of the kite?

A 4 feet B 8 feet C 12 feet D 16 feet

Fold here.

Solution

1. Hint: The Pythagorean Theorem statesthat the sum of the squares of the legs ofa right triangle is equal to the square ofthe hypotenuse, or a2 � b2 � c2.

The height of the kite is a leg of a righttriangle.

h2 � 62 � 102

h2 � 36 � 100h2 � 64h � 8

The answer is B.

2. Polly is painting all sides of the woodenblock shown below as the first step in anart project.

Which of the following will help hercalculate how much paint to buy?

A the volume; 720 cubic inchesB the surface area; 504 square inchesC adding the perimeter of each face;

224 inchesD the sum of the edges; 112 inches

Solution

2. The paint will cover all of the outsidesurfaces of the box. The measurementthat corresponds with the area of all ofthe faces is the surface area, which iscalculated by adding the areas of all ofthe faces.

The answer is B.

12

Fold the page along the dashed line. Work each problem on another piece of paper.Then unfold the page to check your work.

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6 ft

10 ft

Groundpoint Andy

10 in.

12 in.6 in.

Carta a la familiaNOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Capítulo 12 5 Glencoe California Mathematics, Grade 6

Estimado padre o apoderado:

Usamos destrezas matemáticas en muchas de las cosas que

hacemos. Uno de los objetivos de esta clase es demostrar a los

alumnos lo relevante que resulta para el mundo real las cosas

que estudian en el aula. Por ejemplo, comprender el teorema de

Pitágoras, la geografía del área de superficie, navegación,

deportes y arquitectura.

En el Capítulo 12, Álgebra y geometría: Extensión, su hijo(a)

aprenderá a calcular cuadrados y raíces cuadradas, a usar el teo-

rema de Pitágoras y a calcular el área de superficie de prismas y

cilindros rectangulares. En el estudio de este capítulo, su hijo(a)

completará una variedad de tareas y actividades diarias y es posi-

ble que trabaje en un proyecto del capítulo.

Al firmar esta carta y devolverla con su hijo(a), usted se com-

promete a ayudarlo(a) a participar en su aprendizaje. Junto con

esta carta, va incluida una actividad que puede realizar con

él(ella) y la cual practica lo que podrían encontrar en las prue-

bas de los conceptos matemáticos que aprenderán en el

Capítulo 12. Además, visiten ca.gr6math.com para ver

autocontroles y otras ayudas para el estudio. Si tiene cualquier

pregunta o comentario, por favor contácteme en la escuela.

Cordialmente,

Firma del padre o apoderado ________________________________________ Fecha ______

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Actividad en familiaPráctica de estándares

NOMBRE ______________________________________ FECHA ____________ PERÍODO ___


1. Andy vuela una cometa como se mues-tra en el diagrama.

¿Cuál es la altura de la cometa?

A 4 pies B 8 pies C 12 pies D 16 pies

Doblen aquí.

Solución

1. H1. Ayuda: El teorema de Pitágorasestablece que la suma de los cuadradosde los catetos de un ángulo recto esigual al cuadrado de la hipotenusa ó a2 �b2 � c2.

La altura de la cometa es un cateto deun triángulo rectángulo.

h2 � 62 � 102

h2 � 36 � 100h2 � 64h � 8

La respuesta es B.

2. Polly pinta todos los lados de un bloquede madera como primer paso de unproyecto artístico.

¿Cuál de los siguientes le ayudará acalcular cuánta pintura debe comprar?

A el volumen; 720 pulgadas cúbicasB el área de superficie; 504 pulgadas

cuadradasC sumar el perímetro de cada cara;

224 pulgadasD la suma de las aristas; 112 pulgadas

Solución

2. La pintura cubrirá toda la superficieexterna del bloque. La medida quecorresponde al área de todas las carases el área de superficie, la cual secalcula sumando las áreas de todas lascaras.

La respuesta es B.

10 pulg

12 pulg6 pulg

6 pies

10 pies

Groundpoint Andy

12

Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.

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NAME ________________________________________ DATE ______________ PERIOD _____

Anticipation GuideExtending Algebra and Geometry


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Step 2

Step 1

STEP 1 Statement STEP 2A, D, or NS A or D

1. A square root of a number is one of its two equal factors.2. You can find an estimate for the square root of 45 by finding

the square root of the perfect square closest to 45.3. All square roots are irrational numbers.4. The hypotenuse of a right triangle is the side opposite the

right angle.5. Since 102 � 62 � 82, a triangle whose sides have lengths 6,

8, and 10 will be a right triangle.6. Since a rectangular prism has six sides, the surface area

can be found by finding the area of one side and multiplying by 6.

7. If the dimensions of a rectangular prism are doubled, the surface area will also double.

8. If the dimensions of a rectangular prism are doubled, the volume will triple.

9. In finding the surface area of a cylinder, you are finding the area of two circles and a rectangle.

10. The units for surface area are always cubic units since surface area involves three-dimensional figures.

Before you begin Chapter 12

• Read each statement.

• Decide whether you Agree (A) or Disagree (D) with the statement.

• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 12

• Reread each statement and complete the last column by entering an A or a D.

• Did any of your opinions about the statements change from the first column?

• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.

12

NOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Ejercicios preparatoriosÁlgebra y geometría: Extensión


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PASO 2

Antes de comenzar el Capítulo 12

• Lee cada enunciado.

• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.

• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).

Después de completar el Capítulo 12

• Vuelve a leer cada enunciado y completa la última columna con una A o una D.

• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.

PASO 1

PASO 1 PASO 2A, D o NS

EnunciadoA o D

1. Una raíz cuadrada de un número es uno de sus dos factores iguales.

2. Puedes estimar la raíz cuadrada de 45 al extraer la raíz del cuadrado perfecto más cercano a 45.

3. Todas las raíces cuadradas son números irracionales.4. La hipotenusa de un triángulo rectángulo es el lado opuesto

al ángulo recto.5. Dado que 102 � 62 � 82, un triángulo con lados de 6, 8 y 10

será un triángulo rectángulo.6. Dado que un prisma rectangular tiene seis lados, el área de

superficie se puede hallar calculando el área de un lado y multiplicándola por 6.

7. Si se duplican las dimensiones de un prisma rectangular,también se duplicará el área de superficie.

8. Si se duplican las dimensiones de un prisma rectangular, el volumen se triplicará.

9. Al calcular el área de superficie de un cilindro, estás calculando las áreas de dos círculos y un rectángulo.

10. Las unidades para el área de superficie son siempre cúbicas,dado que el área de superficie incluye figuras tridimensionales.

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Get Ready for the LessonComplete the Mini Lab at the top of page 636 in your textbook. Writeyour answers below. Use algebra tiles to estimate the square root ofeach number to the nearest whole number.

1. 40 2. 28 3. 85 4. 62

5. Describe another method that you could use to estimate the square rootof a number.

Read the Lesson

6. Why is �4� a rational number and �2� an irrational number?

7. How do you read the statement �64� � �75� � �81�?

8. Why are �64� and �81� used in Example 1?

Remember What You Learned9. The key to estimating square roots without a calculator is to be familiar

with common perfect squares. Complete the following table of commonperfect squares then test yourself to see how many you can rememberwithout using a calculator.

Number 5 6 7 8 9 10 11 12 13 14 15 16 20 25

Square 25

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideEstimating Square Roots

12-1 7NS2.4

Exercises

Example 2

Example 1

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionEstimating Square Roots


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Estimate �40� to the nearest whole number.

List some perfect squares.

1, 4, 9, 16, 25, 36, 49, …

36 � 40 � 49 40 is between the perfect squares 36 and 49.

�36� � �40� � �49� Find the square root of each number.

6 � �40� � 7 �36� � 6 and �49� � 7

So, �40� is between 6 and 7. Since 40 is closer to 36 than to 49, the best whole numberestimate is 6.

Use a calculator to find the value of �28� tothe nearest tenth.

28 5.291502622

�28� � 5.3

Check Since 52 � 25 and 25 is close to 28, the answer is reasonable.

Estimate each square root to the nearest whole number.

1. �3� 2. �8�

3. �26� 4. �41�

5. �61� 6. �94�

7. �152� 8. �850�

Use a calculator to find each square root to the nearest tenth.

9. �2� 10. �27�

11. �73� 12. �82�

13. �105� 14. �395�

15. �846� 16. �2,298�

ENTER2nd

Recall that a perfect square is a square of a rational number. In Lesson 5-8, you learned that anynumber that can be written as a fraction is a rational number. A number that cannot be written as afraction is an irrational number.

0 1 2 3 4 5 6

28

7NS2.4

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeEstimating Square Roots


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1. �5� 2. �10� 3. �21�

4. �28� 5. �78� 6. �102�

7. �179� 8. �274� 9. �303�

10. �563� 11. �592� 12. �755�

13. �981� 14. �1,356� 15. �1,688�

16. �3,287� 17. �3,985� 18. �4,125�


19. �6� 20. �19� 21. �30�

22. �77� 23. �114� 24. �125�

25. �149� 26. �182� 27. �212�

28. �436� 29. �621� 30. �853�

31. �918� 32. �1,004� 33. �1,270�

34. �5,438� 35. �4,215� 36. �5,786�

37. Order �275�, 4.91, and �23� from least to greatest.

38. Graph �42� and �62� on the same number line.

0 1 2 3 4 5 876

7NS2.4


1. �8� 2. �19� 3. �47� 4. �70�

5. �91� 6. �125� 7. �150� 8. �389�

9. �2,468� 10. �899� 11. �4,840� 12. �8,080�


13. �6� 14. �21� 15. �53� 16. �79�

17. �190� 18. �624� 19. �427� 20. �3,178�

21. �0.36� 22. �0.81� 23. �1.44� 24. �2.25�

25. ALGEBRA What whole number is closest to �a � b� if a � 24 and b � 38?

26. ALGEBRA Evaluate �x � y� to the nearest tenth if x � 10 and y � 4.5

27. QUILTING A queen-size quilt in the shape of a square has an area of 51square feet. What is the approximate length of one side of the quilt to thenearest tenth?

28. PENDULUM The formula below can be used to estimate the time it takesfor a pendulum to swing back and forth once. Use the formula to find thetime it takes for a pendulum with a length of 0.8 meter to swing back andforth once. Round to the nearest tenth.

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeEstimating Square Roots


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T � 2 � �L�• T � time (seconds)• L � length (meters)

7NS2.4

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeEstimating Square Roots


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1. GEOMETRY The diameter d of a circlewith area A is given by the formula

d � ��4�A��. What is the diameter of a

circle with an area of 56 square inches?Use 3.14 for � and round to the nearesttenth.

2. FENCING Carmen wants to buy fencingto enclose a square garden with anarea of 500 square feet. How muchfencing does Carmen need to buy?Round to the nearest tenth.

3. OCEANS The speed v in feet per secondof an ocean wave in shallow water ofdepth d in feet is given by the formulav � �32d�. What is the speed of anocean wave at a depth of 10 feet?Round to the nearest tenth.

4. LIGHTING A new flashlight has a beamwhose width w at a distance d from theflashlight is given by the formulaw � 1.2�d�. What is the width of thebeam at a distance of 30 feet? Round tothe nearest tenth.

5. SOUND The speed of sound in air c inmeters per second at a temperature Tin degrees Celsius is givenapproximately by the formula c � �402(T�� 273�)�. What is the speedof sound in air at a temperature of 25 degrees Celsius? Round to thenearest tenth.

6. PROJECTILES The muzzle velocity v infeet per second necessary for a cannonto hit a target x feet away is estimatedby the formula v � �32x�. What muzzlevelocity is required to hit a target3,000 feet away? Round to the nearesttenth.

3,000 ft

7NS2.4

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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World Series RecordsEach problem gives the name of a famous baseball player. To findwho set each record, graph the points on the number line.

1. pitched 23 strikeouts in one World Series

U at �3�, X at 3.3, K at 0.75, O at �32�, F at �6�, A at 2�

78�

2. 71 base hits in his appearances in World Series

B at �5�, R at �12�, A at 3.75, G at �1163�

, E at �52�, Y at 0.375, R at �

143�,

I at 1.6, and O at 0.7�

3. 10 runs in a single World Series

N at �60�, K at �30�, A at 4.3, S at 6.2, C at �496�, O at �45�, and J at �17�

4. batting average of 0.625 in a single World Series

E at �32�, U at 6�56�, A at �

134�, T at �55�, B at 5.3, R at �40�, H at 7.75,

B at �251�

5. 42 World Series runs in his career

E at �140�, Y at 9.6, I at 8.6, E at �90�, A at �221�, M at �70�, C at 8�

78�,

M at �100�, N at 10.7, K at 9�111�

, T at �120�, L at 11.4

0 4321

4 8765

0 4321

4 8765

8 1211109

7NS2.4

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Scientific Calculator ActivityEstimating Square Roots


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A scientific calculator can be used to estimate square roots. On the TI-34 II, the square rootfunction is used by pressing the [��] keys.

Estimate �1�5�. Round to the nearest hundredth.

Enter: [��] 15 3.872983346

So, �1�5� � 3.87.

Estimate �2�2�. Round to the nearest hundredth.

Enter: [��] 22 4.69041576

So, �2�2� � 4.69.

Estimate �1�2�5�. Round to the nearest hundredth.

Enter: [��] 125 11.18033989

So, �1�2�5� � 11.18.

Use a calculator to estimate each square root. Round to the nearest hundredth.

1. �3�5� 2. �4�2� 3. �3�1�

4. �1�2�6� 5. �1�9�0� 6. �2�

7. �3� 8. �8� 9. �1�3�

10. �5�0� 11. �6�8� 12. �5�7�

13. �3�7� 14. �9�8� 15. �4�4�

16. �8�7� 17. �1�5� 18. �1�1�

19. �1�2� 20. �1�4� 21. �2�6�

ENTER

�)2nd

ENTER

�)2nd

ENTER

�)2nd

2nd

Example 2

Example 1

Example 3

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading Guide The Pythagorean Theorem


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Get Ready for the LessonRead the introduction at the top of page 640 in your textbook. Writeyour answers below.

1. Find the area of each square.

2. How are the squares of the sides related to the areas of the squares?

3. Find the sum of the areas of the two smaller squares. How does the sumcompare to the area of the larger square?

4. Use grid paper to cut out three squares with sides 5, 12, and 13 units. Form aright triangle with these squares. Compare the sum of the areas of the twosmaller squares with the area of the larger square.

Read the Lesson5. What does the symbol �� indicate?

6. How can you find the hypotenuse of a right triangle within a rectanglewhen given only the dimensions of the rectangle?

7. In Examples 3 and 4 on page 680, how do you know which length is c?

Remember What You Learned8. Summarize what you learned in this lesson by labeling the sides of the

right triangle with the letters a, b, and c and then completing the table.

You canfind

If you knowthe lengths

a

b

c

7MG3.3

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionThe Pythagorean Theorem


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Find the missing measure of a right triangle if a � 4 inches and b � 3 inches.

c2 � a2 � b2 Pythagorean Theorem

c2 � 42 � 32 Replace a with 4 and b with 3.

c2 � 16 � 9 Evaluate 42 and 32.

c2 � 25 Add.

�c2� � �25� Take the positive square root of each side.

c � 5 Simplify.

The length of the hypotenuse is 5 inches.

Determine whether a triangle with side lengths of 6 meters,9 meters, and 12 meters is a right triangle.

c2 � a2 � b2 Pythagorean Theorem

122 � 62 � 92 Replace a with 6, b with 9, and c with 12.

144 � 36 � 81 Simplify.

144 117 Add.

The triangle is not a right triangle.

Find the missing measure of each right triangle. Round to the nearesttenth if necessary.

1. 2. 3.

Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.

4. 15 ft, 8 ft, 17 ft 5. 5 in., 13 in., 17 in. 6. 9 yd, 40 yd, 41 yd

13 cm

16 cm

a cm5 m

7.5 m

c m

9 in.

4 in.c in.

3 in.

4 in.c in.

The sides of a right triangle have special names. The sides adjacent to the right angle are the legs. The side opposite the right angle is the c2 � a2 � b2

hypotenuse. The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the lengths of the legs. In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.

b

ac

Example 1

Example 2

7MG3.3

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeThe Pythagorean Theorem


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Find the missing measure of each right triangle. Round to the nearesttenth if necessary.

1. 2.

3. 4.

5. 6.

7. 8.

9. a � 15 cm, b � 20 cm 10. a � 2 yd, b � 12 yd

11. a � 13 in., c � 16.5 in. 12. b � 8 mm, c � 17 mm

13. a � 1.3 ft, b � 4.6 ft 14. a � 14.7 m, c � 23 m

Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.

15. 10 ft, 24 ft, 26 ft 16. 5 in., 8 in., 9 in.

17. 6 cm, 9 cm, 12 cm 18. 4.5 mm, 6.0 mm, 7.5 mm

14 mmc mm

6.7 mm

11.2 m

6 m

a m

2.7 yd 3 yd

a yd

20.3 in. 32 in.

c in.

20 cm

26 cmx cm12.4 ft

a ft

15 ft

5 in.

c in.

5 in.7 m

b m

20 m

7MG3.3

Find the missing measure of each triangle. Round to the nearesttenth if necessary.

1. 2. 3.

4. a � 3.3 in., b � 5.6 in. 5. b � 2.9 mm, c � 4.4 mm 6. a � 21 yd, c � 29 yd

7. a � 2�15

� ft, c � 4�25

�ft 8. b � 7�14

� in., c � 7�34

� in. 9. a � 6�12

� yd, b � 10 yd

If a triangle has sides a, b, and c so that a2 � b2 � c2, then the triangleis a right triangle. Determine whether a triangle with the given sidelengths is a right triangle. Write yes or no.

10. 9 cm, 12 cm, 18 cm 11. 7 ft, 24 ft, 25 ft 12. 5 in., 12 in., 13 in.

Find the missing measure in each figure. Round to the nearest tenthif necessary.

13. 14.

15. SOCCER Find the width of the soccer goal.Round to the nearest tenth.

16. CONVEYOR BELT The diagram shows thehorizontal distance a conveyor belt moves a load of gravel. If the conveyor belt takes54 seconds to move gravel from the bottomof the conveyor belt to the top at a rate of 3 feet per second, how high does theconveyor belt lift the gravel? Round to the nearest tenth.

150 ft

h ft

5 ft11.2 ft

x ft

2.5 yd

x yd

1.8 yd

30 m

x m9 m

18 m

4.7 m

6.1 ma m

24 ft23.8 ft

c ft

11 cm

7 cm c cm

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeThe Pythagorean Theorem


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeThe Pythagorean Theorem


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1. ORIGAMI Chee has a piece of papermeasuring 8.5 inches by 8.5 inches. Ifshe folds the paper diagonally in half,how long is the folded side? Round tothe nearest tenth.

2. COMPUTERS In a computer catalog,a computer monitor is said to be 19 inches. This distance is the diagonaldistance across the screen. If the screenis 10 inches high, what is the width ofthe screen? Round to the nearest tenth.

3. ANTENNAS A wire 10 meters long issupporting a utility pole. The wire isanchored to the ground and is attachedto the pole 9 meters above the ground.What is the distance from the bottom ofthe pole to the point where the wire isattached to the ground? Round to thenearest tenth.

9 m10 m

x m

4. RAMPS Crystal wants to build a rampthat will rise 4 feet over a horizontaldistance of 20 feet. How long will theramp be? Round to the nearest tenth.

4 ft

20 ft

x ft

5. POOLS Salomon swims diagonallyacross his pool every day. If Salomon’spool is 4 meters wide and 16 metersdiagonally across, how long is his pool,to the nearest tenth of a meter?

6. FRAMES Rosa has a picture frame thatmeasures 12 inches by 18 inches. Whatis the diagonal distance across theframe? Round to the nearest tenth.

7MG3.3

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Pythagoras in the AirIn the diagram at the right, an airplane heads north at 180 mi/h.But, the wind is blowing towards the east at 30 mi/h. So, theairplane is really traveling east of north. The middle arrow in the diagram shows the actual direction of the airplane.

The actual speed of the plane can be found using the Pythagorean Theorem.

�302 �� 1802� � �900 �� 32,40�0�

� �33,30�0�

� 182.5

The plane’s actual speed is about 182.5 mi/h.

Find the actual speed of each airplane. Round answers to the nearesttenth. (You might wish to draw a diagram to help you solve theproblem.)

1. An airplane travels at 240 mi/h east. 2. An airplane travels at 620 mi/h west.A wind is blowing at 20 mi/h toward A wind is blowing at 35 mi/h towardthe south. the south.

3. An airplane travels at 450 mi/h south. 4. An airplane travels at 1,200 mi/h east.A wind is blowing at 40 mi/h toward A wind is blowing at 30 mi/h towardthe east. the north.

E

N(not drawn to scale)

180 mi/h

30 mi/h

7MG3.3

Exercises

Example

When solving problems, make a model to represent the given situation in order todetermine the best plan for a solution.

GIFT WRAP Rita wants to wrap a rectangular box. The box is 12 inches by 7 inches by 3 inches high. What must be the area

of the paper so that she has a 1 inch overlap to neatly wrap the paper?

1. GARDENING Peg wants to put a stone path 3 feet wide around herrectangular garden measuring 10 feet by 15 feet. What will be theperimeter of her garden including the stone path?

2. DRAWING Dante is making a full-size drawing of his favorite cartoon character. If the figure is 1 inch by 0.5 inches and his scale is 1 inch � 10 inches, how large will the full size character be?

NAME ________________________________________ DATE ______________ PERIOD _____


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Explore You know that the box is 12 � 7 � 3 and that you need to add 1 inch tosome measures for the overlap. You also know that the wrapping paper willbe a rectangle.

Plan Draw a sketch of the box and then make a model of the box if it were cutapart and laid flat. You need the overlap going around the box.

Solve Sketch the box. Make a model of the box unfolded.

The length of the paper needed is the distance around the box plus 1 inch. So, � � 7 � 3 � 7 � 3 � 1 or 21 inches.The width of the paper would be 3 � 12 � 3 or 18 inches.The area would be 21 � 18 or 378 in2.

Check Make a box using centimeters instead of inches. Then cut a piece of paper18 centimeters by 21 centimeters to see if you can wrap the box neatly.

�

bottom

frontsi

de

sidetop

back

1 in. overlap

7 in.

12 in.

3 in.

12 in.

7 in.

3 in.

6MR2.4, 6NS2.1Study Guide and InterventionProblem-Solving Investigation: Make a Model

Make a model to solve.

1. PETS Jack’s Pet Store has 5 pets for sale. Some are birds and some aredogs. When Jack looks at the pets, he counts 18 legs. How many of eachtype of pet are there?

2. INTERIOR DESIGN JoAnn is creating a model of a living room. The room is

20 feet by 20 feet. If the scale she is using is 1 foot � �12

� inch, what are the

dimensions of her model room?

3. ART COMPETITION An art competition allows for submitted work to be nolarger than 11 inches by 14 inches. If Christene’s photograph is 8 inchesby 10 inches, what is the largest matte she can use if she wants theborder to be the same width all the way around the photo?

4. FLOORING James is laying carpet in an L-shaped room whose model isshown below. How much carpet does he need?

5. SCALE MODEL Charlotte is building a model of the Eiffel Tower. If theactual tower is 986 feet tall and Charlotte’s scale is 1 inch � 10 feet, howtall is her model?

6. SCIENCE FAIR Audrey wants to make a poster that is folded into threesections for her science fair project. The length of the poster is 36 inches.If she wants the middle section to be twice the length of the side sectionsand she wants the two side sections to be equal, what should be thelength of the middle section?

8 ft

8 ft

8 ft

12 ft

NAME ________________________________________ DATE ______________ PERIOD _____


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c.12-3 6MR2.4, 6NS2.1Skills Practice

Problem-Solving Investigation: Make a Model

Mixed Problem Solving

Select the Operation

For Exercises 1 and 2, make a model tosolve the problem.

1. ARCHITECT Mrs. Peron is designing a home for a client. The house is 45 feet by 76 feet. If she uses a scale of 1 foot � �

12

� inch, what are the dimensions of the house on the blue prints?

2. SWIMMING POOL Mr. Forrester has a swimming pool that measures 3�

13

� yards by 8 yards. If the deck around the pool is 2�

23

� yards wide, what is the outside perimeter of the deck?

Use any strategy to solve Exercises 3and 4. Some strategies are shown below.

3. BATTERIES A manufacturing plant canmake 350 batteries in 15 minutes. Howlong will it take the manufacturingplant to make 3,500 batteries?

4. SHOPPING A grocery store has five cashregisters. About 4 customers arechecked out at each register every 20minutes. How many customers arechecked out at the store each hour?

For Exercises 5 and 6, select anappropriate operation(s) to solve theproblem. Justify your selection(s) andsolve the problem.

5. TESTS Diego scored a 95 on his first testin science class. He then scored 100 onhis next 5 tests. If he scored a 91 on hisseventh test, what is his test average?

6. NEWSPAPERS Candace wants to increasethe number of newspapers she delivers.She currently delivers 58 newspapers.In fourteen weeks, she wants to bedelivering 100 newspapers. How manynewspaper deliveries must she increaseeach week to obtain her goal?

NAME ________________________________________ DATE ______________ PERIOD _____


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PROBLEM-SOLVING STRATEGIES

• Use the four-step plan.

• Draw a diagram.

• Use logical reasoning.

• Make a model.

6MR2.4, 6NS2.1PracticeProblem-Solving Investigation: Make a Model

NAME ________________________________________ DATE ______________ PERIOD _____


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1. FOOTBALL Bill, Damon and Steve arethe quarterback, center and punter onthe football team, not necessarily inthat order. The quarterback and Bill goon the bus with Damon after the game.Damon is not the punter. What positiondoes Bill play?

2. SPORTS Janelle can walk one mile in 15 minutes. How long will it take her towalk 3 miles?

3. WEATHER The Loudonville Times printsthe following chart showing thesnowfall for each day last week. Thereporter estimates that they got 10inches of snow during the past week. Isthis a reasonable estimate?

4. GARDENING The table below shows howmany tomatoes Nicholas picked eachday during the week. How many doeshe need to pick on Sunday so that hehas picked a total of 20 for the week?

5. PAINT If one gallon of paint covers 150square feet, is one gallon enough forSusie to cover a kitchen wall that is 15feet by 8 feet? Justify your answer.

6. SHOPPING Avery bought a DVD for$22.99 and got $2.01 back in change.How much did Avery give the cashier?

7. MONEY The amount in Carly’scheckbook is $750 after writing a checkfor $65 and making a deposit of $100and a deposit of $75. How much did shestart with in her checkbook?

8. VEHICLES Jim has 15 vehicles at hisgarage. Some are cars and some aremotorcycles. If he counts 58 wheels,how many of each type of vehicle doeshe have?

Day SnowfallMonday 1 inchTuesday 2 inchesWednesday 0.5 inchesThursday 1.5 inchesFriday 3.75 inchesSaturday 0 inchesSunday 0 inches

Day M T W R F S S

Number of 2 5 3 1 0 5tomatoes

Solve each problem using any strategy you have learned.

6MR2.4, 6NS2.1Word Problem PracticeProblem-Solving Investigation: Make a Model

NAME ________________________________________ DATE ______________ PERIOD _____


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Get Ready for the LessonComplete the Mini Lab at the top of page 649 in your textbook. Writeyour answers below.

1. Record the dimensions,volume, and surface area in a table.

2. Build two more prisms using all of the cubes.For each, record the dimensions, volume,and surface area.

3. Describe the prisms with the greatest and least surface areas.

Read the Lesson4. How many pairs of congruent faces are there in a rectangular prism?

Name them.

5. Tell how to find the surface area of a rectangular prism in words.

Remember What You Learned6. Work with a partner. Bring a box that is a rectangular prism to class

(any size, such as a crayon box) that you can cut apart to form a net.Label the surfaces front, back, top, bottom, side, side. Measure the facesand find the surface area. Use adhesive tape to form the net into a three-dimensional figure. Then exchange nets with your partner. Calculate thevolume of the prism. Compare the answers found from using a net and asolid.

Dimensions Volume SurfaceArea

7MG2.1Lesson Reading Guide Surface Area of Rectangular Prisms

Exercises

Example

NAME ________________________________________ DATE ______________ PERIOD _____


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Find the surface area of the rectangular prism.

You can use the net of the rectangular prism to find its surface area. There are three pairs of congruent faces in a rectangular prism:

� top and bottom� front and back� two sides

Faces Area

top and bottom (4 � 3) � (4 � 3) � 24

front and back (4 � 2) � (4 � 2) � 16

two sides (2 � 3) � (2 � 3) � 12

Sum of the areas 24 � 16 � 12 � 52

Alternatively, replace � with 4, w with 3, and h with 2 in the formula for surface area.S � 2�w � 2�h � 2wh

� 2 � 4 � 3 � 2 � 4 � 2 � 2 � 3 � 2 Follow order of operations.� 24 � 16 � 12 � 52

So, the surface area of the rectangular prism is 52 square meters.

Find the surface area of each rectangular prism.

1. 2. 3.

5 ft7 ft

9 ft

8 in.

10 in.2 in.3 cm

3 cm

7 cm

4 m

4 m

3 m

2 m

2 m

3 m

2 mback

side bottom side

front

top

4 m3 m

2 m

The sum of the areas of all the surfaces, or faces, of a three-dimensional figure is the surface area.The surface area S of a rectangular prism with length �, width w, and height h is found using the following formula.

S � 2�w � 2�h � 2wh

7MG2.1Study Guide and InterventionSurface Area of Rectangular Prisms

NAME ________________________________________ DATE ______________ PERIOD _____


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Find the surface area of each rectangular prism. Round to thenearest tenth if necessary.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. A cube has a surface area of 126 square feet. What is the area of oneface?

11. Find the surface area of a rectangular prism that has a length of 8 inches, a width of 3 inches, and a height of 6 inches.

6.4 mm

7.3 mm4.1 mm

4.5 in.

4.1 in.8.3 in.6 ft

12 ft

7 ft

4.3 in.

6 in.

3.7 in.

3 cm4 cm

8.5 cm10 mm

9 mm

9 mm

15 in.

9 in.7 in.

1 ft4 ft

7 ft

12 cm

7 cm

6 cm

7MG2.1Skills PracticeSurface Area of Rectangular Prisms

Find the surface area of each rectangular prism. Round to thenearest tenth if necessary.

1. 2. 3.

4. length � 20 cm 5. length � 31.5 in. 6. length � 5.3 mmwidth � 18 cm width � 12.2 in. width � 1.1 mmheight � 25 cm height � 24.8 in. height � 3.4 mm

7. 8.

ESTIMATION Estimate the surface area of each prism.

9. 10.

11. BIRTHDAY GIFT When wrapping a birthday gift for his mother, Kenji addsan additional 2.5 square feet of gift wrap to allow for overlap. How manysquare feet of gift wrap will Kenji use to wrap a gift 3.5 feet long,18 inches wide, and 2 feet high?

For Exercises 12 and 13, use the following information.

A company needs to package hazardous chemicals in special plastic containers that hold 80 cubic feet of chemicals.12. Find the whole number dimensions of the container that would use the

least amount of plastic.

13. If the plastic costs $0.10 per square foot, how much would it cost to make24 containers?

8.1 in.

3.8 in.

4.2 in.

8.9 mm8.9 mm

8.9 mm

x ft

7.3 ft

3 ft

4.8 ft

5 m3 m

2 m

x m

8 yd14

6 yd

12 yd

23

1.6 m

5.5 m

1.2 m

2 ft6 ft

3 ft

NAME ________________________________________ DATE ______________ PERIOD _____


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Surface Area of Rectangular Prisms

NAME ________________________________________ DATE ______________ PERIOD _____


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1. PACKAGING A packaging companyneeds to know how much cardboardwill be required to make boxes18 inches long, 12 inches wide, and10 inches high. How much cardboardwill be needed for each box if there isno overlap in the construction?

2. INSULATION Jane needs to buyinsulation for the inside of a truckcontainer. The container is arectangular prism 15 feet long, 8 feet

wide, and 7�12� feet high. How much

insulation should Jane buy if all insidesurfaces except the floor are to beinsulated?

3. ICE Suppose the length of each edge ofa cube of ice is 4 centimeters. Find thesurface area of the cube.

4 cm

4. ICE Suppose you cut the ice cube fromExercise 3 in half horizontally into twosmaller rectangular prisms. Find thesurface area of one of the two smallerprisms.

5. CONTAINERS What is the total surfacearea of the inside and outside of acontainer in the shape of a rectangularprism with length of 5 meters, width of3 meters, and height of 2.2 meters?

6. TOYS Oscar is making a play block forhis baby sister by gluing fabric over theentire surface of a foam block. Howmuch fabric will Oscar need?

6.1 in.2.3 in.

2.3 in.

7MG2.1Word Problem PracticeSurface Area of Rectangular Prisms

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Pattern Puzzles1. Make three copies of this

pattern. Fold each pattern to make a pyramid. Then, put the three pyramids together to make a cube. Draw a sketch of the completed cube.

2. Make four copies of this pattern.Fold each pattern to make a solid figure. Then, put the four solids together to make a pyramid. Make a sketch of the finished pyramid.

3. Find the surface area of the cube in Exercise 1.

7MG2.1

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading Guide Surface Area of Cylinders


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Get Ready for the LessonComplete the Mini Lab at the top of page 656 in your textbook. Writeyour answers below.

1. Make a net of the cylinder.

2. Name the shapes in the net.

3. How is the length of the rectangle related to the circles?

4. Explain how to find the surface area of the cylinder.

Read the LessonWrite the formula to use to find each of the following.

5. the area of a circle _______________

6. the circumference of a circle _______________

7. the area of a rectangle _______________

8. How would you find the surface area of a cylinder with no top? Give youranswer in words and symbols.

Remember What You Learned9. Complete the table.

Words The surface areaof a cylinder equals the area of

two bases plus the area of thecurved surface.

Symbols

7MG2.1

Example

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionSurface Area of Cylinders


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Find the surface area of the cylinder. Use 3.14

for �. Round to the nearest tenth.

S � 2�r2 � 2�rh Surface area of a cylinder.

S � 2 � 3.14(6)2 � 2 � 3.14 (6)(20) Replace � with 3.14, r with 6, and h with 20.

� 979.7 Simplify.

The surface area is about 979.7 square meters.

Find the surface area of each cylinder. Use 3.14 for �. Round to thenearest tenth.

1. 2. 3. 4.3 cm

12 cm

3 ft

24 ft

10 in.

8 in.

20 m

6 m

The diagram below shows how you can put two circles and a rectangletogether to make a cylinder.

The surface area the area of the area of the of a cylinder equals two bases plus curved surface.

S � 2(�r 2) � (2�r)h

In the diagram above, the length of the rectangle is the same as the circumference of the circle. Also, the width of the rectangle is the same as the height of the cylinder.

20 m

6 m

Two congruentcircles...

...make up thetwo bases.

The rectanglemakes up thecurved surface.

C = 2�r C = 2�r

r

hh

Cr

� � � � �

7MG2.1

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeSurface Area of Cylinders


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12-5

Find the surface area of each cylinder. Use 3.14 for π.Round to the nearest tenth.

1. 2. 3.

4. 5. 6.

7. Find the surface area of a can with a radius of 4 centimeters and a heightof 11 centimeters.

8. Find the surface area of the outside of a cylindrical barrel with adiameter of 10 inches and a height of 12 inches.

9. Find the area of the curved surface of a D battery with a diameter of 3.2 centimeters and a height of 5.6 centimeters.

12.6 cm

6.5 cm

2 ft12

4 ft13

4.8 yd

7 yd

7 m

4 m

6 mm

10 mm

8 in.

24 in.

7MG2.1


1. 2. 3.

4. 5. 6.

7. diameter � 15.2 mm 8. diameter � 28.4 yd 9. radius � 50 cmheight � 9.4 mm height � 15.1 yd height � 70 cm

ESTIMATION Estimate the area of each cylinder.

10. 11. 12.

13. FUEL STORAGE A fuel storage tank needs to be painted on the inside. Ifthe height of the tank is 40 feet and the diameter is 120 feet, what is thesurface that needs to be painted? Round to the nearest hundred squarefeet.

14. PAPER TOWELS Each of the three rolls of paper towels in a package are individually wrapped in plastic. The radius of each roll is 5.6 centimeters and the height is 27.9 centimeters. How much plastic is used to individually wrap the three rolls? Round to the nearest tenth.

2.9 yd

4.1 yd

9.9 mm

7.1 mm

6.8 ft

4.2 ft

9 ft

9 ft12

4.3 cm

8 cm

6.4 m

8.1 m

5 in.3 in.1

45.5 m

4.1 m

2 ft

7 ft

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeSurface Area of Cylinders


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeSurface Area of Cylinders


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12-5

1. PACKAGING What is the area of thelabel on a box of oatmeal with a radiusof 9.3 centimeters and a height of 16.5 centimeters? Round to the nearesttenth.

2. TIRES Betty wants to know the totalsurface area of the tread on one of hertires. If the diameter of the tire is18 inches and the width of the tire is5 inches, what is the total surface areaof the tire’s tread? Round to the nearesttenth.

3. CANS A cylindrical can has a diameterof 6 inches and a height of 7.3 inches.What is the surface area of the can?Round to the nearest tenth.

4. CANS A cylindrical can has a height of14 centimeters and a radius of 4.2centimeters. Find the surface area ofthe can. Round to the nearest tenth.

5. MANUFACTURING How much sheetmetal is required to make a cylindricaltrash can with a diameter of 2 feet and

height of 4�14� feet? Round to the nearest

tenth. (Hint: Do not include the top.)

6. PLUMBING How much steel is needed tomake a hollow pipe with a radius of3 inches and a height of 15 inches?Round to the nearest tenth.

7MG2.1

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Cross SectionsIn each diagram on this page, a plane cuts through a solid figure. Theintersection of the plane with the solid figure is called a cross section.

Sketch the cross section formed in each diagram.

1. 2.

3. 4.

5. 6.

7. 8. (pyramid with atriangular base)

(pyramid with atriangular base)

(pyramid with asquare base)

7MG2.1

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Scientific Calculator ActivitySurface Area of a Cylinder


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Find the surface area of the cylinder to the nearest tenth.

A � area of bases � area of curved surface

A � 2�r2 � 2�rh

A � 2 � � � 32 � 2 � � � 3 � 12

Enter: 2 3 2 3 12 282.7433388

To the nearest tenth, the surface area of the cylinder is 282.7 cm2.

Find the surface area of each cylinder to the nearest tenth.

1. 2.

117.8 m2 1,789.2 cm2

3. 4.

56.2 m

125 m

7.9 in.

22.4 in.

25.5 cm

8.4 cm

5 m2.5 m

ENTER

�π+x 2π

3 cm

12 cm

Pre-AP

NAME ________________________________________ DATE ______________ PERIOD _____

Student Recording SheetUse this recording sheet with pages 664–665 of the Student Edition.


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Read each question. Then fill in thecorrect answer.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Record your answers for Question 12 onthe back of this paper.

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

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NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


12 Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 665 of the Student Edition.)

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General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she

arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.

Exercise 12 Rubric

Score Specific Criteria4 An accurate expression that the area of the shaded region in terms of y is 36 � y2.

An accurate expression for the area of the shaded region in terms of y if thedimensions for each region were doubled is given as 144 � (2y)2 or 144 � 4y2.

3 The expressions are written correctly; however, they are written in terms of the areaof the non-shaded region instead of the area of the shaded region.

2 One of the two expressions is incorrect and the other expression is written for thearea of the entire figure.OROne of the two expressions is incorrect and the other expression is written for thearea of the non-shaded region.

1 Only one of the two expressions is correct.

0 Response is completely incorrect.

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Estimate each square root to the nearest whole number. 1.

1. �63� 2. �150� 2.

Find the missing measure of each right triangle. Round to the nearest tenth if necessary.

3. 4. 3.

4.

5. MULTIPLE CHOICE What is the side length of a right triangle if one of the sides is 28 millimeters and the hypotenuse is 35 millimeters?

A. 12 B. 21 C. 28.8 D. 40.8 5.

48 ft

14 ftc ft

9 cm12 cm

a cm

1. BOOKS In how many ways can a bookstore arrange six different books in a row for a display? 1.

2. FRAMING A portrait 14 inches by 20 inches is bordered

by a mat that is 2 inches wide. The frame around the mat

is 1�12

� inches wide. Find the area of the portrait with the

frame and mat. 2.

3. PARKS A picnic area at a park is 90 yards long and 60 yards wide. On a diagram of the park, 1 inch � 6 yards. What are the dimensions of the picnic area on the diagram? 3.

4. DRAWINGS On a scale drawing, the scale is 4 centimeters:1 meter. What is the distance in the scale drawing for a garden 8 meters by 12 meters? 4.

5. A cafeteria vending machine contains apples, chickensandwiches, potato salad, gelatin, lettuce salad, and pudding. Without looking, an employee selects one of the items. What is the probability that a salad is selected? 5.


Chapter 12 Quiz 1(Lessons 12-1 and 12-2)

Chapter 12 Quiz 2(Lesson 12-3)

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NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

12

12

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Find the surface area of each rectangular prism.

1. 2. 1.

2.

3. length � 5 cm 4. length � 22.4 mm 3.width � 5 cm width � 24.5 mmheight � 1 cm height � 20 mm 4.

5. Find the surface area of therectangular prism. 5.

6 cm

6.6 cm

11.6 cm

14 in.

16 in.62 in.

5 in.

7 in.

2.5 in.




NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

12

12

21 cm39 cm

9 mm

8.3 mm


1. 2. 1.

2.

3. 3.

4. 4.

5. Find the surface area of a cylindrical can that has a diameter of 3.6 inches and a height of 4 inches. Roundto the nearest tenth. 5.

6 m

19 m

3 in. 26 in.

Write the letter for the correct answer in the blank at the right of each question.For Questions 1-3, estimate each square root to the nearest whole number.

1. �35�A. 5 B. 6 C. 7 D. 13 1.

2. �180�F. 12 G. 13 H. 18 J. 72 2.

3. �60�A. 3,600 B. 30 C. 8 D. 7 3.

4. Use a calculator to find �87� to the nearest tenth.F. 9 G. 9.3 H. 43.5 J. 7,569.0 4.

5. Find the missing measure for the triangle.A. 625 m C. 6 mB. 25 m D. 5 m 5.

6. REMODELING How many square feet of wallpaper are needed to cover a wall that measures 14 feet by 9 feet.F. 23 ft2 H. 126 ft2

G. 63 ft2 J. 252 ft2 6.


7. �97� 8. �106� 7.

8.

9. �224� 10. �320� 9.

10.Estimate each square root to the nearest whole number.11. �290� 12. �407� 11.

12.Find the missing measure of each right triangle. Roundto the nearest tenth if necessary. 13.

13. a � 12 cm; c � 13 cm 14. a � 11 m; c � 23 m 14.

15. SKATEBOARDING 15.A skateboarding ramp is4.5 meters long and 2.75 meters tall. To the nearesttenth, how long across the ground is the ramp?

2.75 m4.5 m

20 m

15 mc m

Chapter 12 Mid-Chapter Test(Lessons 12-1 and 12-3)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____12


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NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


12 Chapter 12 Vocabulary TestC

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Choose the correct term or number to completeeach sentence.

1. The formula for finding the surface area of a (rectangular 1.prism, cylinder) is 2�w � 2�h � 2wh.

2. An irrational number is a number that cannot be written as 2.a (decimal, fraction).

3. The diagonal of a rectangle is the (leg, hypotenuse) 3.of a right triangle.

4. A leg is one of the two sides adjacent to the right 4.(angle, side) of a right triangle.

5. The (leg, hypotenuse) is the side of a right triangle 5.that is opposite the right angle.

6. To find the surface area of a (rectangular prism, cylinder), 6.you must know the radius of the base.

7. The number �5� is (rational, irrational). 7.

8. The Pythagorean Theorem describes the relationship 8.between the length of the hypotenuse and the lengths of the legs of a(n) (isosceles, right) triangle.

9. Every positive number has (one, two) square root(s). 9.

10. A rectangular prism has (6, 8) surfaces. 10.

Define each term in your own words.

11. Pythagorean Theorem

12. surface area

hypotenuse

irrational number

leg

Pythagorean Theorem

surface area

Write the letter for the correct answer in the blank at the right of each question.

1. Use a calculator to find �78� to the nearest tenth.A. 7.8 B. 8.8 C. 9.0 D. 10.8 1.

2. Estimate �37� to the nearest whole number.F. 9 G. 8 H. 7 J. 6 2.

3. Estimate �143� to the nearest whole number.A. 10 B. 11 C. 12 D. 20,499 3.


5. Use a calculator to find �43� to the nearest tenth.A. 1,849 B. 6.6 C. 6.5 D. 3.5 5.

6. The lengths of the legs of a right triangle are 8 centimeters and6 centimeters. Which equation would you solve to find the length ofthe hypotenuse?F. 62 � x2 � 82 G. 82 � x2 � 62 H. 62 � 82 � x2 J. 82 � 62 � x2 6.

7. The length of the hypotenuse of a right triangle is 20 feet, and the lengthof one leg is 16 feet. Find the length of the other leg.A. 12 ft B. 26 ft C. 36 ft D. 72 ft 7.

8. Which could be the lengths of the sides of a right triangle?F. 30 cm, 40 cm, 50 cm H. 6 m, 8 m, 9 mG. 11 ft, 12 ft, 14 ft J. 3 cm, 4 cm, 7 cm 8.

9. ART A rectangular picture frame is 24 inches long by 18 inches wide.A diagonal brace is nailed across the back of the frame from one corner to the other. How long is the brace?A. 45 in. B. 42 in. C. 30 in. D. 21 in. 9.

10. The surface area of a cube is 150 square millimeters. What is the length of one side?F. 375 mm G. 41.7 mm H. 25 mm J. 5 mm 10.

11. Find the surface area of the rectangular prism.A. 136 mm2 C. 68 mm2

B. 80 mm2 D. 32 mm2 11.

12. CRATES Find the surface area of a crate in the shape of a rectangular

prism with a length of 5 feet, a width of 3�12� feet, and a height of 2�

12� feet.

Round to the nearest tenth.

F. 77.5 ft2 G. 44 ft2 H. 43.8 ft2 J. 22 ft2 12.

10 mm2 mm

4 mm


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12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 12 Test, Form 1C

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13. Find the surface area of the rectangular prism at the right.A. 126 cm2 C. 56 cm3

B. 90 cm2 D. 28 cm2 13.

14. Find the surface area of a cylinder with a height of 10 feet and a base with a radius of 7 feet. Round to the nearest tenth.F. 307.7 ft2 G. 747.7 ft2 H. 2,615.6 ft2 J. 2,725.5 ft2 14.

15. Find the surface area of the cylinder to the nearest tenth.A. 3,927.0 ft2 C. 471 ft2

B. 785.4 ft2 D. 157 ft2 15.

16. Find the surface area of the cylinder to the nearest tenth.F. 4,071.5 in2 H. 282.6 in2

G. 678.2 in3 J. 113.1 in2 16.

17. CANS A can of juice is 6 inches high, and its base has a radius of 2 inches. Find the surface area of the can.Round to the nearest tenth.A. 37.7 in2 B. 75.4 in2 C. 100.5 in2 D. 118.4 in2 17.

18. FRAMING A picture 12 inches by 18 inches has a frame that is 2 inches wide. Find the area of the picture with the frame.F. 216 in2 G. 252 in2 H. 280 in2 J. 432 in2 18.

19. Find the surface area of a cube with 9-centimeter edges.A. 81 cm2 B. 108 cm2 C. 324 cm2 D. 486 cm2 19.

20. Find the surface area of the cylinder. Round to the nearest tenth.

F. 1,005.3 cm2 G. 628.3 cm2 H. 408.2 cm2 J. 282.7 cm2 20.

Bonus: A cylinder has a radius of 8 centimeters and the area of its curved surface is about 351.9 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:

5 cm

8 cm

6 in

12 in

5 ft10 ft

3 cm

5 cm

6 cm

NAME ________________________________________ DATE ______________ PERIOD _____


12 Chapter 12 Test, Form 1 (continued)C

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1. Use a calculator to find �87� to the nearest tenth.

A. 8.7 B. 9.3 C. 9.8 D. 12.4 1.

2. Estimate �90� to the nearest whole number.

F. 8 G. 9 H. 10 J. 11 2.

3. Estimate �178� to the nearest whole number.

A. 12 B. 13 C. 14 D. 19 3.

4. Estimate �1,001� to the nearest whole number.

F. 33 G. 32 H. 31 J. 20 4.

5. Use a calculator to find �267� to the nearest tenth.

A. 71,289 B. 17.4 C. 16.7 D. 16.3 5.

6. The lengths of the legs of a right triangle are 22 feet and 19 feet. Whichequation would you solve to find the length of the hypotenuse?

F. 222 � x2 � 192 H. 192 � 222 � x2

G. 192 � x2 � 222 J. 192 � 222 � x2 6.

7. The length of one leg of a right triangle is 21 inches and the length ofthe hypotenuse is 35 inches. Find the length of the other leg.

A. 12 in. B. 14 in. C. 28 in. D. 1,268.5 in. 7.

8. Which could be the lengths of the sides of a right triangle?

F. 18 m, 24 m, 30 m H. 2 cm, 3 cm, 4 cmG. 19 ft, 27 ft, 39 ft J. 56 in., 112 in., 168 in. 8.

9. TELEVISION A 41-foot guy wire is used to brace an antenna. The wire isanchored 9 feet from the base of the antenna. How tall is the antenna?

A. 80 ft B. 42 ft C. 40 ft D. 22 ft 9.

10. Find the surface area of the cylinder to the nearest tenth.

F. 508.9 cm2 H. 1,130.4 cm2

G. 876.5 cm2 J. 2,799.1 cm2 10.

11. TEA CUPS A cylindrical tea cup has a height of 70 millimeters, and its base has a radius of 30 millimeters.Find the surface area of the tea cup to the nearest tenth.

A. 2,100 mm2 C. 18,840 mm2

B. 16,014 mm2 D. 461,814.1 mm2 11.

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12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 12 Test, Form 2AC

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12. Find the volume of the cylinder to the nearest tenth.F. 204.2 cm3 H. 314 cm3

G. 282.7 cm3 J. 1,256 cm3 12.

13. The surface area of a cube is 486 square feet. What is the length of one side?A. 9 ft C. 81 ftB. 27 ft D. 243 ft 13.

14. Find the surface area of the rectangular prism.F. 12,000 m2 H. 1,700 m2

G. 3,400 m2 J. 75 m2 14.

15. Find the surface area of a rectangular prism with a length of 60 feet, a width of 42 feet, and a height of 31 feet.A. 78,120 ft2 B. 11,364 ft2 C. 266 ft2 D. 134 ft2 15.

16. Find the surface area of the rectangular prism.F. 274 in2 H. 137 in2

G. 260 in2 J. 22 in2 16.

17. Find the surface area of a cylinder with a height of 7.1 meters and a base with a radius of 2.6 meters. Round to the nearest tenth.A. 359.7 m2 B. 158.4 m2 C. 137.2 m2 D. 18.5 m2 17.

18. CANS A cylindrical peach can has a height of 5.3 inches, and its base has a radius of 1.6 inches. Find the surface area of the peach can to the nearest tenth.F. 709.7 in2 G. 69.3 in2 H. 26.6 in2 J. 8.5 in2 18.

19. Find the surface area of the cylinder to the nearest tenth.A. 776.0 mm2 C. 4,737.5 mm2

B. 1,306.2 mm2 D. 6,371.1 mm2 19.

20. PAINTING All of a dresser’s outer surfaces need to be painted. The height of the dresser is 53 inches, its width is 21 inches, and its length is 43 inches.What is the surface area of the dresser?F. 47,859 in2 G. 8,590 in2 H. 6,784 in2 J. 4,295 in2 20.


26 mm

3 mm

4 in. 13 in.

5 in.

15 m

20 m

40 m

10 cm

4 cm

NAME ________________________________________ DATE ______________ PERIOD _____


12 Chapter 12 Test, Form 2A (continued)C

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1. Use a calculator to find �94� to the nearest tenth.A. 9.4 B. 9.7 C. 10.4 D. 12.4 1.


3. Estimate �102� to the nearest whole number.A. 10 B. 11 C. 12 D. 25 3.


5. Use a calculator to find �173� to the nearest tenth.A. 29,929 B. 13.2 C. 13.1 D. 5.6 5.

6. The lengths of the legs of a right triangle are 16 feet and 30 feet. Whichequation would you solve to find the length of the hypotenuse?

F. 162 � x2 � 30 H. 302 � x2 � 16G. 162 � 302 � x2 J. 302 � 162 � x2 6.

7. The length of one leg of a right triangle is 24 meters, and the length of the hypotenuse is 25 meters. Find the length of the other leg.

A. 49 m B. 35 m C. 7 m D. 1 m 7.

8. Which could be the lengths of the sides of a right triangle?

F. 7 cm, 8 cm, 10 cm H. 12 ft, 15 ft, 20 ftG. 6 cm, 8 cm, 10 cm J. 20 m, 30 m, 40 m 8.

9. TRAVEL The Garcias drove 24 miles east and then 7 miles north. Atthat point, what is the straight-line distance from their starting point?

A. 25 mi B. 31 mi C. 312.5 mi D. 625 mi 9.

10. Find the surface area of the cylinder to the nearest tenth.

F. 34,482.1 cm2 H. 4,926.0 cm2

G. 7,385.3 cm2 J. 392 cm2 10.

11. CANS A cylindrical waste can has a height of 20 inches,and its base has a radius of 10 inches. Find the surface area of the waste can to the nearest tenth.

A. 12,566.4 in2 B. 6,283.2 in2 C. 1,884 in2 D. 1,570 in2 11.

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12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 12 Test, Form 2BC

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12. Find the surface area of the cylinder to the nearest tenth.F. 1.281.8 yd2 H. 414.5 yd2

G. 565.5 yd2 J. 301.6 yd2 12.

13. The surface area of a cube is 216 square feet. What is the length of one side?A. 72 ft B. 36 ft C. 14.7 ft D. 6 ft 13.

14. Find the surface area of the rectangular prism.F. 1,250 cm2 H. 425 cm2

G. 850 cm2 J. 80 cm2 14.

15. A rectangular prism has a length of 40 inches, a width of 22 inches,and a height of 12 inches. Find the surface area of the prism.A. 10,560 in2 B. 3,248 in2 C. 1,624 in2 D. 148 in2 15.

16. Find the surface area of the rectangular prism.F. 176 cm2 H. 5,112 cm2

G. 2,556 cm2 J. 24,480 cm2 16.

17. Find the surface area of a cylinder with a height of 19 centimeters and a base with a radius of 7 centimeters. Round to the nearest tenth.A. 307.7 cm2 B. 989.6 cm2 C. 1,143.0 cm2 D. 2,924.8 cm2 17.

18. ERASERS A cylindrical eraser has a height of 15 millimeters, and its base has a radius of 9 millimeters. Find the surface area of the eraser to the nearest tenth.F. 508.7 mm2 G. 1,102.7 mm2 H. 1,356.5 mm2 J. 3,817.0 mm2 18.

19. Find the surface area of the cylinder to the nearest tenth.A. 2,010.6 in2 C. 351.7 in2

B. 502.7 in2 D. 301.6 in2 19.

20. PAINTING All of a toy box’s outer surfaces need to be painted. The height of the toy box is 26 inches, its width is 28 inches, and its length is 38 inches. What is the surface area of the toy box?F. 2,780 in2 G. 4,104 in2 H. 5,560 in2 J. 27,664 in2 20.


10 in.

8 in.

34 cm24 cm

30 cm

5 cm

25 cm10 cm

12 yd5 yd

NAME ________________________________________ DATE ______________ PERIOD _____


12 Chapter 12 Test, Form 2B (continued)C

opyright ©G

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Estimate each square root to the nearest whole number. 1.

1. �29� 2. �10� 2.

3.

3. �53� 4. �78� 4.

Use a calculator to find each square root to the 5.nearest tenth. 6.

5. �90� 6. �123� 7.7. �455� 8. �69� 8.

Find the missing measure of each right triangle.Round to the nearest tenth if necessary.

9. b � 7 cm, c � 11 cm 9.

10. a � 30 ft, c � 50 ft 10.

11. 12. 11.

12.

13. A right triangle has legs that measure 22 inches and 13 inches. Find the measure of the hypotenuse. 13.

14. MUSIC In how many ways can a music store arrange five different CDs in a row for a display? 14.

15. FRAMING A picture 15 inches by 24 inches is bordered by a mat that is 2 inches wide. The frame around the

mat is 1�12

� inches wide. Find the area of the picture

with the frame and mat. 15.

16. GARDENS A garden is 14 feet long and 8 feet wide.

On a diagram of the garden, �12

� inch � 1 foot. What

are the dimensions of the garden on the diagram? 16.

4.3 m

2 m

c m

Ass

essm

ent


12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 12 Test, Form 2CC

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a cm20 cm

17 cm

For Questions 17–24, find the surface area of each solid.Use 3.14 for π. Round to the nearest tenth if necessary.

17. 18. 17.

18.

19. 20. 19.

20.

21. 22. 21.

22.

23. 24. 23.

24.

25. STUNTS A monster truck attempted to scale a brick wall. 25.The highest point it reached on the wall was 3 meters. At that point, its rear wheels were 4.3 meters from the wall.How long is the monster truck? Round to the nearest hundredth.


4 in. 8 in.

1.2 in.

7.8 in.

4 ft1.6 ft21 mm8 mm

2 cm

4.6 cm9.8 cm

11.8 ft

5 ft16 ft

2.6 m2 m

0.8 m

5 ft4 ft

11 ft

NAME ________________________________________ DATE ______________ PERIOD _____


12 Chapter 12 Test, Form 2C (continued)C

opyright ©G

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ompanies, Inc.

Estimate each square root to the nearest whole number. 1.1. �39� 2. �5� 2.

3.

3. �84� 4. �65� 4.

Use a calculator to find each square root to the 5.

nearest tenth. 6.

5. �80� 6. �109� 7.

7. �320� 8. �74� 8.

Find the missing measure of each right triangle. Roundto the nearest tenth if necessary.

9. a � 45 m, b � 60 m 9.

10. a � 5 ft, c � 8 ft 10.

11. 12. 11.

12.

13. A right triangle has legs that measure 23 centimeters and 11 centimeters. Find the measure of the hypotenuse. 13.

14. MUSIC In how many ways can a music store arrange seven different DVDs in a row for a display? 14.

15. FRAMING A picture 18 inches by 25 inches is bordered by a mat that is 2 inches wide. The frame around the mat mat is 1�

12

� inches wide. Find the area of the picture with the frame and mat. 15.

16. GARDENS A garden is 18 feet long and 9 feet wide. On a diagram of the garden, �

12

� inch � 1 foot. What are the dimensions of the garden on the diagram? 16.

c m

14 m

14.2 m6.3 cm

x cm

10 cm

Ass

essm

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12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 12 Test, Form 2DC

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17. 18. 17.

18.

19. 20. 19.

20.

21. 22. 21.

22.

23. 24. 23.

24.

25. STUNTS A monster truck attempted to scale a brick wall. 25.The highest point it reached on the wall was 3 meters. At that point, its rear wheels were 4.3 meters from the wall.How long is the monster truck? Round to the nearest hundredth.


15.6 cm

14 cm

2 m

12.5 m35 yd

8 yd

8 mm 17.4 mm

30.4 mm9 ft

2 ft 5 ft

30 m24 m

31.1 m

6.5 in.6 in.

14 in.

NAME ________________________________________ DATE ______________ PERIOD _____


12 Chapter 12 Test, Form 2D (continued)C

opyright ©G

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ompanies, Inc.

12 in.

6 in.

Estimate each square root to the nearest whole number. 1.1. �84� 2. �29� 2.

3.

3. �141� 4. �52� 4.

Use a calculator to find each square root to the 5.

nearest tenth. 6.

5. �68� 6. �270� 7.

7. �932� 8. �509� 8.

Find the missing measure of each right triangle.Round to the nearest tenth if necessary.

9. b � 64 m, c � 80 m 9.

10. a � 11 yd, c � 18 yd 10.

11. 12. 11.

12.

13. A right triangle has a hypotenuse that measure 42.1 centimeters and a leg that measures 36.8 centimeters.Find the measure of the other leg. 13.

14. MOVIES In how many ways can a media store arrange nine different DVDs in a row for a display? 14.

15. FRAMING A picture 15�12

� inches by 28 inches is bordered

by a mat that is 2 inches wide. The frame around the mat

is 2�12

� inches wide. Find the area of the picture with the

frame and mat. 15.

16. GARDENS A garden is 3.5 meters long and 2.8 meters wide.On a diagram of the garden, 2 centimeters � 1 meter. What are the dimensions of the garden on the diagram? 16.

8.7 in.c in.

5 in.

Ass

essm

ent


12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 12 Test, Form 3C

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38.7 cm21 cm


17. 18. 17.

18.

19. 20. 19.

20.

21. 22. 21.

22.

23. 24. 23.

24.

25. GUY WIRES A vertical pole is anchored to the ground by a 29�

34

�-foot guy wire. The wire is attached to the ground

at a point 22�12

� feet from the base of the pole. How tall is

the pole? Round to the nearest tenth. 25.

Bonus: A cylinder has a diameter of 11 centimeters and the area of its curved surface is about 414.7 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:

8 mm

60 mm

33 m

12.1 m

11 ft

8.7 ft

10 cm3.6 cm

4.8 cm

11 cm

18 cm46.1 cm

2 in.12

2 in.12

2 in.12

8 yd

4 yd

6.9 yd

NAME ________________________________________ DATE ______________ PERIOD _____


12 Chapter 12 Test, Form 3 (continued)C

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8.2 mm

13.5 mm

Demonstrate your knowledge by giving a clear, concise solution to each problem.Be sure to include all relevant drawings and justify your answers. You may showyour solutions in more than one way or investigate beyond the requirements ofthe problems. If necessary, record your answers on another piece of paper.

1. CARPENTRY A carpenter is framing a house.The front of the house measures 48 feet. The widthmeasures 36 feet. He measures diagonally across thehouse as shown. If the diagonal measurement is 62feet, are the corners of the house square (right angles)?Explain your reasoning. Use a calculator.

2. a. Compare the volumes and surface areas of the threeboxes pictured.

A B C

b. Compare the volumes and surface areas of the three containers pictured.A B C

c. Explain why you think manufacturers frequently package their products in tall boxes, bottles, or cans.

4 m

4 m

2 m

8 m

2 m

4 m

12 in.

6 in.2 in.

6 in.

6 in.4 in.

6 in.

6 in.2 in.

62 ft

48 ft

36 ft

Ass

essm

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12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 12 Extended-Response Test

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1. Evaluate |�8| � |�2|. (Lesson 2-1)

A 10 C 7B 6 D �10 1.

2. Write 49.5% as a decimal. (Lesson 4-7)

F 0.0495 H 84.095G 0.495 J 4.95 2.

3. Write 0.33% as a decimal. (Lesson 6-9)

A 0.0033 C 3.3B 0.033 D 33 3.

4. Find the percent of change from 18 to 41. Round to the nearestwhole percent. (Lesson 7-6)

F 44% H 128%G 56% J 228% 4.

5. RAFFLE In a raffle, one ticket will be drawn from a total of 200 tickets. If Maureen has 4 tickets, what is the probability that she will win? (Lesson 9-1)

A �510�

C 0.2

B 4% D �14� 5.

6. HORSES Tionna has a display that holds 8 horse figurines.If she has 17 horse figurines, how many combinations of 8 can she create? (Lesson 9-5)

F 40,320 H 2,312G 24,310 J 136 6.

7. Suppose �1 and �2 are complementary. If m�1 � 50º, findm�2. (Lesson 10 -1)

A 30º C 50ºB 40º D 130º 7.

8. Three sides of a triangle measure 6 meters, 4 meters, and5 meters. Classify the triangle by its sides. (Lesson 10-4)

F scalene H equilateralG isosceles J obtuse 8.

9. Triangle RST has vertices R(0, �7), S(�4, 2), and T(1, 9).Find the coordinates of S� after the figure is translated 5 units right and 7 units down. (Lesson 10 -9)

A (1, �5) B (�1, �5) C (�9, 9) D (�9, �5) 9. A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


12 Standardized Test Practice(Chapter 1–12)

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panies, Inc.

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

10. What is the base of a parallelogram with an area of 30 squaremiles and a height of 5 miles? (Lesson 11-1)

F 152 mi H 25 miG 35 mi J 6 mi 10.

11. Find the area of a circle with a diameter of 36 millimeters.Round to the nearest tenth. (Lesson 11-4)

A 4071.5 mm2 B 113.1 mm2

B 1017.4 mm2 D 56.5 mm2 11.

12. Find the volume of a rectangular prism with a length of 5 yards,a width of 7.5 yards, and a height of 9 yards. (Lesson 11-9)

F 21.5 yd3 H 300 yd3

G 150 yd3 J 337.5 yd3 12.

13. Estimate �75� to the nearest whole number.A 8 C 38B 9 D 80 13.

14. Find the missing measure of a right triangle with side lengths of a � 5 cm and c � 9 cm.F 56 cm H 7.5 cmG 10.3 cm J 2 cm 14.

15. CABLE A 52-foot cable reaches from the top of a pole to a point on the ground that is 48 feetfrom the base of the pole. How tall is the pole?(Lesson 12-2)

A 12 ft C 50 ftB 20 ft D 92 ft 15.

16. Find the surface area of the cylinder.Round to the nearest tenth. (Lesson 12-5)

F 301.6 in2 H 424.1 in2

G 339.1 in2 J 2,120.6 in2 16.

17. Find the area of a circle with a radius of 1.5 centimeters.Round to the nearest tenth. (Lesson 11-4)

A 4.5 cm2 C 7.1 cm2

B 4.7 cm2 D 9.4 cm2 17.

18. Find the surface area in meters of a rectangular prism that is 5 meters wide, 8.5 meters long, and 2 meters high. (Lesson 12-4)

F 15.5 m2 H 85 m2

G 44.5 m2 J 139 m2 18. F G H J

A B C D

F G H J3 in. 15 in.

A B C D

52 ft

48 ft

F G H J

A B C D

F G H J

A B C D

F G H J


Ass

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ent

12NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

(Chapter 1–12)

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19. A rectangle has a width of 3.5 inches and 19.a length of 4.25 inches. Find the perimeter of the rectangle in inches. (Lesson 3-6)

20. BAND The ratio of boys to girls in the school 20.band is 2 to 3. If there are 90 students in the band, how many of them are boys? (Lesson 6-5)

21. Use the Fundamental Counting Principle 21.to find the total number of outcomes when choosing a day in the month of September and tossing two coins. (Lesson 9-3)

22. Use the graph to tell what

22.type of translation or reflection is shown. (Lessons 10 -9, 10 -10)

23. Find the volume of the cylinder. 23.Round to the nearest tenth.(Lesson 11-10)

24. ATHLETICS A rectangular athletic field is 24.80 meters long by 60 meters wide. What is the diagonal distance across the field in meters? (Lesson 12-2)

25. WINDSTORM A strong storm blew over a billboard 27 feet tall so that it is leaning against a telephone pole 21 feet tall.(Lesson 12-2)

a. Make a drawing to represent 25a.this situation.

b. How far from the base of the telephone pole is the base of the billboard? Round to the nearest tenth if necessary. 25b.

14 in.

6 in.

y

xO

R'

P'

P

Q'

Q

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Part 2: Short Response

Instructions: Write answers to short response in the space provided.

NAME ________________________________________ DATE ______________ PERIOD _____


12 Standardized Test Practice (continued)

(Chapter 1–12)

Copyright ©

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panies, Inc.

1. INTERNET For the following table, find the number of degrees for each section of a circle graph. Then make a circle graph of the data. Round to the nearest degree.

1.

For Questions 2 and 3, draw an angle having each measurement. Then classify each angle as acute,right, obtuse, or straight.

2. 60� 2.

3. 180� 3.

4. Use the graph to describe the translation from �ABC to �A�B�C�. 4.

5. Use the graph to tell what type of reflection is shown.

5.

For Questions 6 and 7, find the best name to classify 6.each quadrilateral.

6. 7. 7.

8. Find m� A in �ABC if m�B � 73° and m�C � 48°. 8.

9. PLATES Find the the circumference of a circular plate 9.that has a diameter of 14 inches. Use 3.14 for � and round to the nearest tenth if necessary.

y

xO

S'

T'

S

U'

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y

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AC'

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Internet Use


Ass

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12NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Unit 5 Test(Chapter 11–12)

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Internet Use

Counting Number of Households online (millions)

United States 163

Japan 135

United Kingdom 122

Canada 115

Australia 11.5

10. Estimate �75� to the nearest whole number. 10.

11. Find the missing measure of a right triangle with legs 11.8 meters and 13 meters long. Round to the nearest tenth if necessary.

For Questions 12–16, find the area of each figure. Round to the nearest tenth if necessary.

12. 13. 12.

13.

14. 15. 14.

15.

16. 16.

17. Draw a top, a side, and a front view of the following figure. 17.

18. Identify the shape of the base(s) of the figure. Then classify the figure. 18.

Find the volume and surface area of each figure.Round to the nearest tenth if necessary.

19. 20. 19.

20.

19 mm

54 mm

12 cm20 cm

19.5 cm

32 mm

40 mm

10 mm 2 cm

3 in.

6 in.

4 yd

9 yd8 yd

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


12 Unit 5 Test (continued)

(Chapter 11–12)

Copyright ©

Glencoe/M

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panies, Inc.

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fin

din

g th

e A

area

of

two

circ

les

and

a re

ctan

gle.

10.

Th

e u

nit

s fo

r su

rfac

e ar

ea a

re a

lway

s cu

bic

un

its

sin

ce

Dsu

rfac

e ar

ea i

nvo

lves

th

ree-

dim

ensi

onal

fig

ure

s.

Bef

ore

you

beg

in C

ha

pte

r 12

•R

ead

each

sta

tem

ent.

•D

ecid

e w

het

her

you

Agr

ee (

A)

or D

isag

ree

(D)

wit

h t

he

stat

emen

t.

•W

rite

A o

r D

in

th

e fi

rst

colu

mn

OR

if

you

are

not

su

re w

het

her

you

agr

ee o

r di

sagr

ee,w

rite

NS

(N

ot S

ure

).

Aft

er y

ou c

omp

lete

Ch

ap

ter

12

•R

erea

d ea

ch s

tate

men

t an

d co

mpl

ete

the

last

col

um

n b

y en

teri

ng

an A

or

a D

.

•D

id a

ny

of y

our

opin

ion

s ab

out

the

stat

emen

ts c

han

ge f

rom

th

e fi

rst

colu

mn

?

•F

or t

hos

e st

atem

ents

th

at y

ou m

ark

wit

h a

D,u

se a

pie

ce o

f pa

per

to w

rite

an

ex

ampl

e of

wh

y yo

u d

isag

ree.

12

Answers (Anticipation Guide and Lesson 12-1)

Chapter 12 A1 Glencoe California Mathematics, Grade 6

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eE

stim

atin

g S

qu

are

Ro

ots

Cha

pter

12

11G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 12–1

pygp

12-1

Est

imat

e ea

ch s

qu

are

root

to

the

nea

rest

wh

ole

nu

mb

er.

1.�

5 �2

2.�

10�3

3.�

21�5

4.�

28�5

5.�

78�9

6.�

102

�10

7.�

179

�13

8.�

274

�17

9.�

303

�17

10.

�56

3�

2411

.�

592

�24

12.

�75

5�

27

13.

�98

1�

3114

.�

1,35

6�

3715

.�

1,68

8�

41

16.

�3,

287

�57

17.

�3,

985

�63

18.

�4,

125

�64

Use

a c

alcu

lato

r to

fin

d e

ach

sq

uar

e ro

ot t

o th

e n

eare

st t

enth

.

19.

�6 �

2.4

20.

�19�

4.4

21.

�30�

5.5

22.

�77�

8.8

23.

�11

4�

10.7

24.

�12

5�

11.2

25.

�14

9�

12.2

26.

�18

2�

13.5

27.

�21

2�

14.6

28.

�43

6�

20.9

29.

�62

1�

24.9

30.

�85

3�

29.2

31.

�91

8�

30.3

32.

�1,

004

�31

.733

.�

1,27

0�

35.6

34.

�5,

438

�73

.735

.�

4,21

5�

64.9

36.

�5,

786

�76

.1

37.

Ord

er �2 75 �

,4.9

1,an

d �

23�fr

om l

east

to

grea

test

.�2 75 �

,�23�

,4.9

1

38.

Gra

ph �

42�an

d �

62�on

th

e sa

me

nu

mbe

r li

ne.

01

23

45

87

64262

7NS

2.4

Exer

cise

s

Exam

ple

2

Exam

ple

1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Est

imat

ing

Sq

uar

e R

oo

ts

Cha

pter

12

10G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

12-1

Est

imat

e �

40�to

th

e n

eare

st w

hol

e n

um

ber

.

Lis

t so

me

perf

ect

squ

ares

.

1,4,

9,16

,25,

36,4

9,…

36�

40

�49

40 is

bet

wee

n th

e pe

rfec

t sq

uare

s 36

and

49.

�36�

��

40��

�49�

Fin

d th

e sq

uare

roo

t of

eac

h nu

mbe

r.

6�

�40�

�7

�36�

�6

and

�49�

�7

So,

�40�

is b

etw

een

6 a

nd

7.S

ince

40

is c

lose

r to

36

than

to

49,t

he

best

wh

ole

nu

mbe

res

tim

ate

is 6

.

Use

a c

alcu

lato

r to

fin

d t

he

valu

e of

�28 �

toth

e n

eare

st t

enth

.

285.

2915

0262

2

�28�

�5.

3

Ch

eck

Sin

ce 5

2�

25 a

nd

25 i

s cl

ose

to 2

8,th

e an

swer

is

reas

onab

le.

Est

imat

e ea

ch s

qu

are

root

to

the

nea

rest

wh

ole

nu

mb

er.

1.�

3�2

2.�

8�3

3.�

26�5

4.�

41�6

5.�

61�8

6.�

94�10

7.�

152

�12

8.�

850

�29

Use

a c

alcu

lato

r to

fin

d e

ach

sq

uar

e ro

ot t

o th

e n

eare

st t

enth

.

9.�

2�1.

410

.�

27�5.

2

11.

�73�

8.5

12.

�82�

9.1

13.

�10

5�

10.2

14.

�39

5�

19.9

15.

�84

6�

29.1

16.

�2,

298

�47

.9

ENTE

R2n

d

Rec

all t

hat

a pe

rfec

t sq

uare

is a

squ

are

of a

rat

iona

l num

ber.

In L

esso

n 5-

8, y

ou le

arne

d th

at a

nynu

mbe

r th

at c

an b

e w

ritte

n as

a f

ract

ion

is a

rat

iona

l num

ber.

A n

umbe

r th

at c

anno

t be

writ

ten

as a

frac

tion

is a

n ir

rati

on

al n

um

ber

.

01

23

45

6

28

7NS

2.4

Answers (Lesson 12-1)


An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Est

imat

ing

Sq

uar

e R

oo

ts

Cha

pter

12

13G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 12–1

pygp

12-1

1.G

EOM

ETRY

Th

e di

amet

er d

of a

cir

cle

wit

h a

rea

Ais

giv

en b

y th

e fo

rmu

la

d�

��4 �A � �.W

hat

is

the

diam

eter

of

a

circ

le w

ith

an

are

a of

56

squ

are

inch

es?

Use

3.1

4 fo

r �

and

rou

nd

to t

he

nea

rest

ten

th.

8.4

in.

2.FE

NC

ING

Car

men

wan

ts t

o bu

y fe

nci

ng

to e

ncl

ose

a sq

uar

e ga

rden

wit

h a

nar

ea o

f 50

0 sq

uar

e fe

et.H

ow m

uch

fen

cin

g do

es C

arm

en n

eed

to b

uy?

Rou

nd

to t

he

nea

rest

ten

th.

89.4

ft

3.O

CEA

NS

Th

e sp

eed

vin

fee

t pe

r se

con

dof

an

oce

an w

ave

in s

hal

low

wat

er o

fde

pth

din

fee

t is

giv

en b

y th

e fo

rmu

lav

��

32d

�.W

hat

is

the

spee

d of

an

ocea

n w

ave

at a

dep

th o

f 10

fee

t?R

oun

d to

th

e n

eare

st t

enth

.17

.9 f

t/s

4.LI

GH

TIN

GA

new

fla

shli

ght

has

a b

eam

wh

ose

wid

th w

at a

dis

tan

ce d

from

th

efl

ash

ligh

t is

giv

en b

y th

e fo

rmu

law

�1.

2�d �.

Wh

at i

s th

e w

idth

of

the

beam

at

a di

stan

ce o

f 30

fee

t? R

oun

d to

the

nea

rest

ten

th.

6.6

ft

5.SO

UN

DT

he

spee

d of

sou

nd

in a

ir c

inm

eter

s pe

r se

con

d at

a t

empe

ratu

re T

in d

egre

es C

elsi

us

is g

iven

appr

oxim

atel

y by

th

e fo

rmu

la

c�

�40

2(T

��

273

�)�.

Wh

at i

s th

e sp

eed

of s

oun

d in

air

at

a te

mpe

ratu

re o

f 25

deg

rees

Cel

siu

s? R

oun

d to

th

en

eare

st t

enth

.34

6.1

m/s

6.PR

OJE

CTI

LES

Th

e m

uzz

le v

eloc

ity

vin

feet

per

sec

ond

nec

essa

ry f

or a

can

non

to h

it a

tar

get

xfe

et a

way

is

esti

mat

edby

th

e fo

rmu

la v

��

32x

�.W

hat

mu

zzle

velo

city

is

requ

ired

to

hit

a t

arge

t3,

000

feet

aw

ay?

Rou

nd

to t

he

nea

rest

ten

th.

309.

8 ft

/s

3,00

0 ft

7NS

2.4

Est

imat

e ea

ch s

qu

are

root

to

the

nea

rest

wh

ole

nu

mb

er.

1.�

8�3

2.�

19�4

3.�

47�7

4.�

70�8

5.�

91�10

6.�

125

�11

7.�

150

�12

8.�

389

�20

9.�

2,46

8�

5010

.�

899

�30

11.

�4,

840

�70

12.

�8,

080

�90

Use

a c

alcu

lato

r to

fin

d e

ach

sq

uar

e ro

ot t

o th

e n

eare

st t

enth

.

13.

�6�

2.4

14.

�21�

4.6

15.

�53�

7.3

16.

�79�

8.9

17.

�19

0�

13.8

18.

�62

4�

25.0

19.

�42

7�

20.7

20.

�3,

178

�56

.4

21.

�0.

36�

0.6

22.

�0.

81�

0.9

23.

�1.

44�

1.2

24.

�2.

25�

1.5

25.

ALG

EBR

AW

hat

wh

ole

nu

mbe

r is

clo

sest

to

�a

�b

�if

a�

24 a

nd

b�

38?

8

26.

ALG

EBR

AE

valu

ate

�x

�y

�to

th

e n

eare

st t

enth

if

x�

10 a

nd

y�

4.5

2.3

27.

QU

ILTI

NG

A q

uee

n-s

ize

quil

t in

th

e sh

ape

of a

squ

are

has

an

are

a of

51

squ

are

feet

.Wh

at i

s th

e ap

prox

imat

e le

ngt

h o

f on

e si

de o

f th

e qu

ilt

to t

he

nea

rest

ten

th?

7.1

ft

28.

PEN

DU

LUM

Th

e fo

rmu

la b

elow

can

be

use

d to

est

imat

e th

e ti

me

it t

akes

for

a pe

ndu

lum

to

swin

g ba

ck a

nd

fort

h o

nce

.Use

th

e fo

rmu

la t

o fi

nd

the

tim

e it

tak

es f

or a

pen

dulu

m w

ith

a l

engt

h o

f 0.

8 m

eter

to

swin

g ba

ck a

nd

fort

h o

nce

.Rou

nd

to t

he

nea

rest

ten

th.

1.8

seco

nd

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Est

imat

ing

Sq

uar

e R

oo

ts

Cha

pter

12

12G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


12-1

T�

2�

�L�

•T

�ti

me

(sec

onds

)•

L�

len

gth

(m

eter

s)

7NS

2.4



Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Scie

ntifi

c Ca

lcul

ator

Act

ivity

Est

imat

ing

Sq

uar

e R

oo

ts

Cha

pter

12

15G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 12–1

pygp

12-1

A s

cien

tifi

c ca

lcul

ator

can

be

used

to

esti

mat

e sq

uare

roo

ts.O

n th

e T

I-34

II,

the

squa

re r

oot

func

tion

is u

sed

by p

ress

ing

the

[��]

keys

.

Est

imat

e �

1 �5 �.R

ound

to

the

near

est

hund

redt

h.

Ent

er:

[��]

15

3.87

2983

346

So,

�1 �5 �

�3.

87.

Est

imat

e �

2 �2 �.R

ound

to

the

near

est

hund

redt

h.

Ent

er:

[��]

22

4.69

0415

76

So,

�2 �2 �

�4.

69.

Est

imat

e �

1 �2 �5 �.

Rou

nd t

o th

e ne

ares

t hu

ndre

dth.

Ent

er:

[��]

125

11.18

0339

89

So,

�1 �2 �

5 ��

11.1

8.

Use

a c

alcu

lato

r to

est

imat

e ea

ch s

qu

are

root

.Rou

nd

to

the

nea

rest

hu

nd

red

th.

1.�

3 �5 �2.

�4 �2 �

3.�

3 �1 �5.

926.

485.

57

4.�

1 �2 �6 �

5.�

1 �9 �0 �

6.�

2 �11

.22

13.7

81.

41

7.�

3 �8.

�8 �

9.�

1 �3 �1.

732.

833.

61

10.�

5 �0 �11

.�

6 �8 �12

.�

5 �7 �7.

078.

257.

55

13.�

3 �7 �14

.�

9 �8 �15

.�

4 �4 �6.

089.

906.

63

16.�

8 �7 �17

.�

1 �5 �18

.�

1 �1 �9.

333.

873.

31

19.�

1 �2 �20

.�

1 �4 �21

.�

2 �6 �3.

463.

745.

10

EN

TE

R

�)

2nd

EN

TE

R

�)

2nd

EN

TE

R

�)

2nd

2nd

Exam

ple

2

Exam

ple

1

Exam

ple

3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

12

14G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


12-1

Wo

rld

Ser

ies

Rec

ord

sE

ach

pro

ble

m g

ives

th

e n

ame

of a

fam

ous

bas

ebal

l p

laye

r.T

o fi

nd

wh

o se

t ea

ch r

ecor

d,g

rap

h t

he

poi

nts

on

th

e n

um

ber

lin

e.

1.p

itch

ed 2

3 st

rik

eou

ts i

n o

ne

Wor

ld S

erie

s

Uat

�3�,

Xat

3.3

,Kat

0.7

5,O

at �3 2�,

Fat

�6�,

Aat

2�7 8�

2.71

bas

e h

its

in h

is a

pp

eara

nce

s in

Wor

ld S

erie

s

Bat

�5�,

Rat

�12�

,Aat

3.7

5,G

at �1 16 3�

,Eat

�5 2�,Y

at 0

.375

,Rat

�1 43 �,

Iat

1.6

,an

d O

at 0

.7 �

3.10

ru

ns

in a

sin

gle

Wor

ld S

erie

s

Nat

�60�

,Kat

�30�

,Aat

4.3

,Sat

6.2

,Cat

�4 96 �,O

at �

45�,a

nd

Jat

�17�

4.b

atti

ng

aver

age

of 0

.625

in

a s

ingl

e W

orld

Ser

ies

Eat

�32�

,Uat

6�5 6�,

Aat

�1 34 �,T

at �

55�,B

at 5

.3,R

at �

40�,H

at 7

.75,

Bat

�2 51 �

5.42

Wor

ld S

erie

s ru

ns

in h

is c

aree

r

Eat

�14

0�

,Yat

9.6

,Iat

8.6

,Eat

�90�

,Aat

�2 21 �,M

at �

70�,C

at 8

�7 8�,

Mat

�10

0�

,Nat

10.

7,K

at 9

� 11 1�,T

at �

120

�,L

at 1

1.4

KO

UF

AX

04

32

1

48

76

5

JA

CK

SO

N

YO

GI

BE

RR

A

04

32

1

48

76

5

BA

BE

RU

HT

MK

CI

YE

MA

TN

EL

812

1110

9

7NS

2.4



An

swer

s

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

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er m

odel

roo

m?

10 in

.by

10 in

.

3.A

RT

CO

MPE

TITI

ON

An

art

com

peti

tion

all

ows

for

subm

itte

d w

ork

to b

e n

ola

rger

th

an 1

1 in

ches

by

14 i

nch

es.I

f C

hri

sten

e’s

phot

ogra

ph i

s 8

inch

esby

10

inch

es,w

hat

is

the

larg

est

mat

te s

he

can

use

if

she

wan

ts t

he

bord

er t

o be

th

e sa

me

wid

th a

ll t

he

way

aro

un

d th

e ph

oto?

1 �1 2�

in w

ide,

so t

he

ph

oto

an

d m

atte

will

be

11 in

.by

13 in

.

tog

eth

er

4.FL

OO

RIN

GJa

mes

is

layi

ng

carp

et i

n a

n L

-sh

aped

roo

m w

hos

e m

odel

is

show

n b

elow

.How

mu

ch c

arpe

t do

es h

e n

eed?

160

ft2

5.SC

ALE

MO

DEL

Ch

arlo

tte

is b

uil

din

g a

mod

el o

f th

e E

iffe

l Tow

er.I

f th

eac

tual

tow

er i

s 98

6 fe

et t

all

and

Ch

arlo

tte’

s sc

ale

is 1

in

ch�

10 f

eet,

how

tall

is

her

mod

el?

98.6

inch

es o

r 8.

2 ft

6.SC

IEN

CE

FAIR

Au

drey

wan

ts t

o m

ake

a po

ster

th

at i

s fo

lded

in

to t

hre

ese

ctio

ns

for

her

sci

ence

fai

r pr

ojec

t.T

he

len

gth

of

the

post

er i

s 36

in

ches

.If

sh

e w

ants

th

e m

iddl

e se

ctio

n t

o be

tw

ice

the

len

gth

of

the

side

sec

tion

san

d sh

e w

ants

th

e tw

o si

de s

ecti

ons

to b

e eq

ual

,wh

at s

hou

ld b

e th

ele

ngt

h o

f th

e m

iddl

e se

ctio

n?

18 in

ches

8 ft

8 ft

8 ft

12 ft

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

12

23G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

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Lesson 12–3

pygp

12-3

6MR

2.4,

6N

S2.

1Sk

ills

Prac

tice

Pro

ble

m-S

olv

ing

Inve

stig

atio

n:

Mak

e a

Mo

del

Exer

cise

s

Exam

ple

Wh

en s

olvi

ng

pro

ble

ms,

mak

e a

mod

el t

o re

pre

sen

t th

e gi

ven

sit

uat

ion

in

ord

er t

od

eter

min

e th

e b

est

pla

n f

or a

sol

uti

on.

GIF

T W

RA

PR

ita

wan

ts t

o w

rap

a r

ecta

ngu

lar

box

.Th

e b

ox i

s 12

in

ches

by

7 in

ches

by

3 in

ches

hig

h.W

hat

mu

st b

e th

e ar

ea

of t

he

pap

er s

o th

at s

he

has

a 1

in

ch o

verl

ap t

o n

eatl

y w

rap

th

e p

aper

?

1.G

AR

DEN

ING

Peg

wan

ts t

o pu

t a

ston

e pa

th 3

fee

t w

ide

arou

nd

her

rect

angu

lar

gard

en m

easu

rin

g 10

fee

t by

15

feet

.Wh

at w

ill

be t

he

peri

met

er o

f h

er g

arde

n i

ncl

udi

ng

the

ston

e pa

th?

74 f

t

2.D

RA

WIN

GD

ante

is

mak

ing

a fu

ll-s

ize

draw

ing

of h

is f

avor

ite

cart

oon

ch

arac

ter.

If t

he

figu

re i

s 1

inch

by

0.5

inch

es a

nd

his

sca

le i

s 1

inch

�10

in

ches

,how

lar

ge w

ill

the

full

siz

e ch

arac

ter

be?

10 in

.by

5 in

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

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ER

IOD

__

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Cha

pter

12

22G

lenc

oe C

alifo

rnia

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hem

atic

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rade

6


12-3

Exp

lore

You

kn

ow t

hat

th

e bo

x is

12

�7

�3

and

that

you

nee

d to

add

1 i

nch

to

som

e m

easu

res

for

the

over

lap.

You

als

o kn

ow t

hat

th

e w

rapp

ing

pape

r w

ill

be a

rec

tan

gle.

Pla

nD

raw

a s

ketc

h o

f th

e bo

x an

d th

en m

ake

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odel

of

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box

if i

t w

ere

cut

apar

t an

d la

id f

lat.

You

nee

d th

e ov

erla

p go

ing

arou

nd

the

box.

Sol

veS

ketc

h t

he

box.

Mak

e a

mod

el o

f th

e bo

x u

nfo

lded

.

Th

e le

ngt

h o

f th

e pa

per

nee

ded

is t

he

dist

ance

aro

un

d th

e bo

x pl

us

1 in

ch.S

o,�

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ches

.T

he

wid

th o

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per

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ld b

e 3

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ches

.T

he

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ld b

e 21

�18

or

378

in2 .

Ch

eck

Mak

e a

box

usi

ng

cen

tim

eter

s in

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d of

in

ches

.Th

en c

ut

a pi

ece

of p

aper

18 c

enti

met

ers

by 2

1 ce

nti

met

ers

to s

ee i

f yo

u c

an w

rap

the

box

nea

tly.

�

botto

m

front

side

side

top

back

1 in

. ove

rlap

7 in

.

12 in

.

3 in

.

12 in

.

7 in

.

3 in

.

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udy

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d In

terv

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rob

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lvin

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ake

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od

el



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

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pter

12

25G

lenc

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alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 12–3

pygp

12-3

1.FO

OTB

ALL

Bil

l,D

amon

an

d S

teve

are

the

quar

terb

ack,

cen

ter

and

pun

ter

onth

e fo

otba

ll t

eam

,not

nec

essa

rily

in

that

ord

er.T

he

quar

terb

ack

and

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l go

on t

he

bus

wit

h D

amon

aft

er t

he

gam

e.D

amon

is

not

th

e pu

nte

r.W

hat

pos

itio

ndo

es B

ill

play

?p

un

ter

2.SP

OR

TSJa

nel

le c

an w

alk

one

mil

e in

15

min

ute

s.H

ow l

ong

wil

l it

tak

e h

er t

ow

alk

3 m

iles

?45

min

ute

s

3.W

EATH

ERT

he

Lou

don

vill

e T

imes

pri

nts

the

foll

owin

g ch

art

show

ing

the

snow

fall

for

eac

h d

ay l

ast

wee

k.T

he

repo

rter

est

imat

es t

hat

th

ey g

ot 1

0in

ches

of

snow

du

rin

g th

e pa

st w

eek.

Isth

is a

rea

son

able

est

imat

e?ye

s

4.G

AR

DEN

ING

Th

e ta

ble

belo

w s

how

s h

owm

any

tom

atoe

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olas

pic

ked

each

day

duri

ng

the

wee

k.H

ow m

any

does

he

nee

d to

pic

k on

Su

nda

y so

th

at h

eh

as p

icke

d a

tota

l of

20

for

the

wee

k?4

5.PA

INT

If o

ne

gall

on o

f pa

int

cove

rs 1

50sq

uar

e fe

et,i

s on

e ga

llon

en

ough

for

Su

sie

to c

over

a k

itch

en w

all

that

is

15fe

et b

y 8

feet

? Ju

stif

y yo

ur

answ

er.

yes:

15�

8�

120

squ

are

feet

6.SH

OPP

ING

Ave

ry b

ough

t a

DV

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or$2

2.99

an

d go

t $2

.01

back

in

ch

ange

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ow m

uch

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ry g

ive

the

cash

ier?

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00

7.M

ON

EYT

he

amou

nt

in C

arly

’sch

eckb

ook

is $

750

afte

r w

riti

ng

a ch

eck

for

$65

and

mak

ing

a de

posi

t of

$10

0an

d a

depo

sit

of $

75.H

ow m

uch

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est

art

wit

h i

n h

er c

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kboo

k?$6

40

8.V

EHIC

LES

Jim

has

15

veh

icle

s at

his

gara

ge.S

ome

are

cars

an

d so

me

are

mot

orcy

cles

.If

he

cou

nts

58

wh

eels

,h

ow m

any

of e

ach

typ

e of

veh

icle

doe

sh

e h

ave?

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ars

and

1 m

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rcyc

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urs

day

1.5

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nch

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rday

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nda

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Day

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mat

oes

Sol

ve e

ach

pro

ble

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sin

g an

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rate

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ou h

ave

lear

ned

.

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ord

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lem

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olvi

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ct t

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Op

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For

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es 1

an

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,mak

e a

mod

el t

oso

lve

the

pro

ble

m.

1.A

RC

HIT

ECT

Mrs

.Per

on i

s de

sign

ing

a h

ome

for

a cl

ien

t.T

he

hou

se i

s 45

fe

et b

y 76

fee

t.If

sh

e u

ses

a sc

ale

of

1 fo

ot �

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ch,w

hat

are

th

e di

men

sion

s of

th

e h

ouse

on

th

e bl

ue

prin

ts?

22�1 2�

in.b

y 38

in.

2.SW

IMM

ING

PO

OL

Mr.

For

rest

er h

as a

sw

imm

ing

pool

th

at m

easu

res

3�1 3�

yard

s by

8 y

ards

.If

the

deck

aro

un

d th

e po

ol

is 2

�2 3�ya

rds

wid

e,w

hat

is

the

outs

ide

peri

met

er o

f th

e de

ck?

44 y

d

Use

an

y st

rate

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o so

lve

Exe

rcis

es 3

and

4.S

ome

stra

tegi

es a

re s

how

n b

elow

.

3.B

ATT

ERIE

SA

man

ufa

ctu

rin

g pl

ant

can

mak

e 35

0 ba

tter

ies

in 1

5 m

inu

tes.

How

lon

g w

ill

it t

ake

the

man

ufa

ctu

rin

gpl

ant

to m

ake

3,50

0 ba

tter

ies?

150

min

ute

s o

r 2.

5 h

ou

rs

4.SH

OPP

ING

A g

roce

ry s

tore

has

fiv

e ca

shre

gist

ers.

Abo

ut

4 cu

stom

ers

are

chec

ked

out

at e

ach

reg

iste

r ev

ery

20m

inu

tes.

How

man

y cu

stom

ers

are

chec

ked

out

at t

he

stor

e ea

ch h

our?

60 c

ust

om

ers

For

Exe

rcis

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an

d 6

,sel

ect

anap

pro

pri

ate

oper

atio

n(s

) to

sol

ve t

he

pro

ble

m.J

ust

ify

you

r se

lect

ion

(s)

and

solv

e th

e p

rob

lem

.

5.TE

STS

Die

go s

core

d a

95 o

n h

is f

irst

tes

tin

sci

ence

cla

ss.H

e th

en s

core

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nex

t 5

test

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he

scor

ed a

91

on h

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th t

est,

wh

at i

s h

is t

est

aver

age?

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ult

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atio

n,a

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itio

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div

isio

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6.N

EWSP

APE

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Can

dace

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ts t

o in

crea

seth

e n

um

ber

of n

ewsp

aper

s sh

e de

live

rs.

Sh

e cu

rren

tly

deli

vers

58

new

spap

ers.

In f

ourt

een

wee

ks,s

he

wan

ts t

o be

deli

veri

ng

100

new

spap

ers.

How

man

yn

ewsp

aper

del

iver

ies

mu

st s

he

incr

ease

each

wee

k to

obt

ain

her

goa

l?S

ub

trac

tio

n a

nd

div

isio

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100

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eek

NA

ME

____

____

____

____

____

____

____

____

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DAT

E _

____

____

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ER

IOD

__

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Cha

pter

12

24G

lenc

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Mat

hem

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6


12-3 P

RO

BL

EM

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LVIN

G S

TR

AT

EG

IES

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se t

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ur-s

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plan

.

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raw

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iagr

am.

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se lo

gica

l rea

soni

ng.

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ake

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odel

.

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ple

NA

ME

____

____

____

____

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____

____

____

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____

DAT

E _

____

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12

27G

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Mat

hem

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Lesson 12–4

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Fin

d t

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sm.

You

can

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th

e n

et o

f th

e re

ctan

gula

r pr

ism

to

fin

d it

s su

rfac

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ea.T

her

e ar

e th

ree

pair

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s in

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rect

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lar

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m:

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p an

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52

Alt

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So,

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the

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s 52

squ

are

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ers.

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d t

he

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ace

area

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each

rec

tan

gula

r p

rism

.

1.2.

3.

102

cm2

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in2

286

ft2

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7 ft

9 ft

8 in

.

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.2

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7 cm

4 m

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side

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4 m

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The

sum

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the

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, or

face

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f a

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men

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Stud

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Pri

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NA

ME

____

____

____

____

____

____

____

____

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____

DAT

E _

____

____

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ER

IOD

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12

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12-4

Get

Rea

dy

for

the

Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

649

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.R

ecor

d th

e di

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3.1,

504.

0 in

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c.Chapter 12 Assessment Answer Key

Quiz 1 (Lessons 12-1 and 12-2) Quiz 3 (Lesson 12-4) Mid-Chapter TestPage 41 Page 42 Page 43

Quiz 2 (Lesson 12-3)

Page 41

Quiz 4 (Lesson 12-5)

Page 42

1.

2.

3.

4.

5. B

7.9 cm

50 ft

12

8

1.

2.

3.

4.

5.�13

�

32 cm by 48 cm

15in. by 10 in.

567 in2

720

1.

2.

3.

4.

5. 130 in2

2,973.6 mm2

70 cm2

371.52 cm2

4,168 in2

1.

2.

3.

4.

5. 65.6 in2

361.7 mm2

7,912.8 cm2

942 m2

546.4 in2

1.

2.

3.

4.

5.

6. H

B

G

C

G

B

7.

8.

9.

10.

11.

12.

13.

14.

15. 3.6 m

20.2 m5 cm

20

17

17.9

15.0

10.3

9.8

An

swer

s

Chapter 12 Assessment Answer KeyVocabulary Test Form 1Page 44 Page 45 Page 46

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Sample answer: the sum of the areas of all the surfaces of a solid

Sample answer: a theorem that says that in a right triangle,the square of the length of thehypotenuse equals the sum of the squares of the lengths of the legs

6

two

right

irrational

cylinder

hypotenuse

angle

hypotenuse

fraction

rectangular prism

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. F

A

J

C

F

A

H

B

H

C

J

B 13.

14.

15.

16.

17.

18.

19.

20. H

D

H

C

H

C

G

A

B: 7 cm


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Form 2A Form 2BPage 47 Page 48 Page 49 Page 50

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. B

H

C

F

C

H

D

G

B

G

B 12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 4 cm

G

B

G

B

F

B

G

A

H 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. D

G

A

G

C

G

B

H

A

G

B 12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 5 cm

H

C

H

C

H

B

G

D

H


Copyright ©

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panies, Inc.Chapter 12 Assessment Answer Key

Form 2CPage 51 Page 52

1.

2.

3.

4.

5.

6.

7.8.

9.

10.

11.

12.

13.

14.

15.

16. 7 in. by 4 in.

682 in2

120

25.6 in.

10.5 cm

4.7 m

40 ft

8.5 cm

8.321.311.1

9.5

973

5 17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 8 cm

5.24 m

301.4 in2

440.9 in2

56.3 ft2

628 mm2

147.8 cm2

655.6 ft2

17.8 m2

238 ft2


An

swer

s

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Form 2DPage 53 Page 54

1.2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16. 9 in. by 4.5 in.

800 in2

5,040

25.5 m

19.9 m

7.8 cm

6.2 ft

75 m

8.6

17.910.48.9

8926 17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 9 cm

5.24 m

678.2 in2

2,899.9 cm2

182.1 m2

979.7 yd2

1,822.7 mm2

146 ft2

4,798.8 m2

428 in2


Copyright ©

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panies, Inc.Chapter 12 Assessment Answer Key

Form 3Page 55 Page 56

1.2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16. 7 cm by 5.6 cm

906.5 in2

362,880

20.4 cm

32.5 cm

10.0 in.

14.2 yd

48 m

22.6

30.516.48.2

71259 17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 12 cm

19.5 ft

633.7 mm2

3,416.3 mm2

3,427.1 m2

419.3 ft2

202.6 cm2

3,069.8 cm2

37.5 in2

229.6 yd2

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An

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s

Chapter 12 Assessment Answer Key Page 57, Extended-Response Test

Scoring Rubric

Level Specific Criteria

4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.

3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.

2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.

1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.

0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.

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Chapter 12 Assessment Answer Key Page 57, Extended-Response Test

Sample Answers

1. No; �482 �� 362� equals 60, not 62.2. a. Volume of A: 72 in3

Volume of B: 144 in3

Volume of C: 144 in3

2 � Volume A � Volume B �Volume CSurface Area of A: 120 in2

Surface Area of B: 168 in2

Surface Area of C: 216 in2

Surface Area of A � 48 � SurfaceArea of BSurface Area of B � 48 � SurfaceArea of C

b. Volume of A: 50.3 m3

Volume of B: 100.5 m3

Volume of C: 201.1 m3

4 � Volume A � 2 � Volume B �Volume CSurface Area of A: 75.4 m2

Surface Area of B: 125.7 m2

Surface Area of C: 201.1 m2

Surface Area of C � Surface Area ofB � Surface Area of A

c. An increase in height gives theappearance of a larger increase insurface area and volume than doesan increase in width, depth, orradius.

In addition to the scoring rubric found on page A23, the following sample answersmay be used as guidance in evaluating extended-response assessment items.

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An

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Chapter 12 Assessment Answer KeyStandardized Test PracticePage 58 Page 59

1.

2.

3.

4.

5.

6.

7.

8.

9. A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D 10.

11.

12.

13.

14.

15.

16.

17.

18. F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

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1

Chapter 12 Assessment Answer KeyStandardized Test PracticePage 60

19.

20.

21.

22.

23.

24.

25a.

25b. 17.0 ft

pole21 ft

board27 ft

x ft

100 m

923.2 in3

Reflection overthe x-axis

120 outcomes

36

15.5


Ass

essm

ent

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Unit 5 Test Page 61 Page 62

1.

2.

3.

4.

5.

6.

7.

8.

9. 44.0 in.

59°

rhombus

quadrilateral

reflection over y-axis

7 units right and 5 units up

straight

180˚acute

60˚

U.S., 245�; Japan, 53�;U.K, 33�; Canada, 23�;

Australia, 8�

Internet Use

UnitedStates68%

UK9%

Australia2%

Japan15%

Canada6%

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.61,211.2 mm3;8,710.4 mm2

4,680 cm3; 1,728 cm2

rectangle; rectangularpyramid

top side front

71.5 ft2

360 mm2

12.6 cm2

9 in2

32 yd2

15.3 m

9

Documents

Chapter 12 Resource Masters - MHSchool€¦ · lesson. Use as an additional practice or as homework for second-day teaching of the lesson. Enrichment These activities may extend the