Teaching the Common Core Math Standards with Hands-On Activities, Grades 9-12

By Gary R. Muschla

Bring Common Core Math into high school with smart, engaging activities

Teaching Common Core Math Standards with Hands-On Activities, Grades 9-12 provides high school teachers with the kind of help they need to begin teaching the standards right away. This invaluable guide pairs each standard with one or more classroom-ready activities and suggestions for variations and extensions. Covering a range of abilities and learning styles, these activities bring the Common Core Math Standards to life as students gain fluency in math communication and develop the skillset they need to tackle successively more complex math courses in the coming years. Make math anxiety a thing of the past as you show your students how they use math every day of their lives, and give them the cognitive tools to approach any math problem with competence and confidence.

The Common Core Standards define the knowledge and skills students need to graduate high school fully prepared for college and careers. Meeting these standards positions American students more competitively in the global economy, and sets them on a track to achieve their dreams. This book shows you how to teach the math standards effectively, and facilitate a deeper understanding of math concepts and calculations.

• Help students apply their understanding of math concepts
• Teach essential abstract and critical thinking skills
• Demonstrate various problem-solving strategies
• Lay a foundation for success in higher mathematics

The rapid adoption of the Common Core Standards across the nation has left teachers scrambling for aligned lessons and activities. If you want to bring new ideas into the classroom today, look no further. Teaching Common Core Math Standards with Hands-On Activities is the high school math teacher's solution for smart, engaging Common Core math.

• Language: English
• Publisher: Wiley
• Release date: Apr 17, 2015
• ISBN: 9781119062202

Book preview

Table of Contents

Title Page

Copyright

About this Book

About the Authors

Acknowledgments

Section 1: Standards and Activities for Number and Quantity

The Real Number System

N-RN.1

N-RN.2

N-RN.3

Quantities

N-Q.1

N-Q.2

N-Q.3

The Complex Number System

N-CN.1

N-CN.2

N-CN.7

Section 2: Standards and Activities for Algebra

Seeing Structure in Expressions

A-SSE.1

A-SSE.2

A-SSE.3

A-SSE.4

Arithmetic with Polynomials and Rational Expressions

A-APR.1

A-APR.2

A-APR.3

A-APR.4

A-APR.6

Creating Equations

A-CED.1

A-CED.2

A-CED.3

A-CED.4

Reasoning with Equations and Inequalities

A-REI.1

A-REI.2

A-REI.3

A-REI.4

A-REI.5

A-REI.6

A-REI.7

A-REI.10

A-REI.11

A-REI.12

Section 3: Standards and Activities for Functions

Interpreting Functions

F-IF.1

F-IF.2

F-IF.3

F-IF.4

F-IF.5

F-IF.6

F-IF.7

F-IF.8

F-IF.9

Building Functions

F-BF.1

F-BF.2

F-BF.3

F-BF.4

Linear, Quadratic, and Exponential Models

F-LE.1

F-LE.2

F-LE.3

F-LE.4

F-LE.5

Trigonometric Functions

F-TF.1

F-TF.2

F-TF.5

F-TF.8

Section 4: Standards and Activities for Geometry

Congruence

G-CO.1

G-CO.2

G-CO.3

G-CO.4

G-CO.5

G-CO.6

G-CO.7

G-CO.8

G-CO.9

G-CO.10

G-CO.11

G-CO.12

G-CO.13

Similarity, Right Triangles, and Trigonometry

G-SRT.1

G-SRT.2

G-SRT.3

G-SRT.4

G-SRT.5

G-SRT.6

G-SRT.7

G-SRT.8

Circles

G-C.1

G-C.2

G-C.3

G-C.5

Expressing Geometric Properties with Equations

G-GPE.1

G-GPE.2

G-GPE.4

G-GPE.5

G-GPE.6

G-GPE.7

Geometric Measurement and Dimension

G-GMD.1

G-GMD.3

G-GMD.4

Modeling with Geometry

G-MG.1

G-MG.2

G-MG.3

Section 5: Standards and Activities for Statistics and Probability

Interpreting Categorical and Quantitative Data

S-ID.1

S-ID.2

S-ID.3

S-ID.4

S-ID.5

S-ID.6

S-ID.7

S-ID.8

S-ID.9

Making Inferences and Justifying Conclusions

S-IC.1

S-IC.2

S-IC.3

S-IC.4

S-IC.5

S-IC.6

Conditional Probability and the Rules of Probability

S-CP.1

S-CP.2

S-CP.3

S-CP.4

S-CP.5

S-CP.6

S-CP.7

Index

End User License Agreement

Other Math Books by the Muschlas

Teaching the Common Core Math Standards with Hands-On Activities, Grades K–2

Teaching the Common Core Math Standards with Hands-On Activities, Grades 3–5

Teaching the Common Core Math Standards with Hands-On Activities, Grades 6–8

Math Starters: 5- to 10-Minute Activities Aligned with the Common Core Math Standards, Grades 6–12, 2nd Edition

Hands-On Math Projects with Real-Life Applications, Grades 3–5

Hands-On Math Projects with Real-Life Applications, Grades 6–12, 2nd Edition

Algebra Teacher's Activities Kit: 150 Ready-to-Use Activities with Real-World Applications

Geometry Teacher's Activities Kit: Ready-to-Use Lessons and Worksheets for Grades 6–12

The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills: 150 Mini-Lessons for Correcting Common Mistakes

Math Smart! Over 220 Ready-to-Use Activities to Motivate and Challenge Students, Grades 6–12

Math Games: 180 Reproducible Activities to Motivate, Excite, and Challenge Students, Grades 6–12

The Math Teacher's Book of Lists, 2nd Edition

The Math Teacher's Problem-a-Day, Grades 4–8: Over 180 Reproducible Pages of Quick Skill Builders

Math Teacher's Survival Guide: Practical Strategies, Management Techniques, and Reproducibles for New and Experienced Teachers, Grades 5–12

Teaching the Common Core Math Standards with Hands-On Activities, Grades 9-12

Judith A. Muschla

Gary Robert Muschla

Erin Muschla-Berry

Title Page

Cover Design: Wiley

Cover Art: © iStock.com/mollypix, © iStock.com/blackred, © iStock.com/kvkirillov, © iStock.com/AlexeyZel

Copyright © 2015 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla-Berry. All rights reserved.

Published by Jossey-Bass

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Library of Congress Cataloging-in-Publication Data

Muschla, Judith A.

Teaching the common core math standards with hands-on activities, grades 9-12 / Judith A. Muschla, Gary Robert Muschla, Erin Muschla-Berry.

1 online resource.

Includes index.

Description based on print version record and CIP data provided by publisher; resource not viewed.

ISBN 978-1-118-71027-2 (pdf)—ISBN 978-1-119-06220-2 (epub)—ISBN 978-1-118-71010-4 (pbk.)

1. Mathematics—Study and teaching (Middle school) 2. Mathematics—Study and teaching (Secondary)

I. Muschla, Gary Robert. II. Muschla-Berry, Erin. III. Title.

QA135.6

510.71′273—dc23

2015002888

FIRST EDITION

About this Book

The Common Core State Standards Initiative for Mathematics identifies the concepts, skills, and practices that students should understand and apply at their grade level. Mastery of these Standards at the high school level will enable students to move on to higher education and careers successfully.

Teaching the Common Core Math Standards with Hands-On Activities, Grades 9–12 offers a variety of activities that support instruction of the Standards that should be addressed in the typical high school math curriculum. (Please note that Standards designated with a + represent skills students should master to take advanced mathematics courses and lie outside the scope of this book.) The table of contents, which contains a list of the included Standards and supporting activities, is divided into five sections:

Section 1: Standards and Activities for Number and Quantity

Section 2: Standards and Activities for Algebra

Section 3: Standards and Activities for Functions

Section 4: Standards and Activities for Geometry

Section 5: Standards and Activities for Statistics and Probability

Each section is divided into two major parts: the first part contains the Standards and teacher's notes for the activities and the second part contains reproducibles that enhance the activities. The activities and reproducibles are labeled according to the numbers of the Standards.

The book is designed for easy implementation. The first part of each section is organized according to Domains, followed by specific Standards and activities. The activities build on concepts and skills that you have already taught and expand the scope of your instruction through reinforcement and enrichment. Each activity includes a brief summary, special materials needed for the activity, and any special preparation that is necessary. Icons highlight activities that include cooperative learning, , or that incorporate the use of technology, . All of the activities include specific steps for implementation, and many include reproducibles.

The typical activity can be completed in one class period and focuses on application of concepts or skills, demonstration of understanding, or communication about math. Students may be required to solve problems; create mathematical models, charts, and graphs; conduct investigations with both physical and virtual manipulatives; play mathematical games; and write problems and explanations. Although many of the activities are open-ended, answer keys are provided for those that require specific answers.

Because many of the activities may be developed through various methods, we encourage you to modify them in ways that best meet the needs of your students. For example, for some activities in which we suggest that students work in pairs or groups of three, you may feel that your students will gain the most from the activity by working individually. Conversely, for some activities, rather than having students work individually, you may find it more practical to have them work with a partner. For other activities, you may prefer to divide an activity into parts and implement the parts at different times, based on your curriculum and what is best for your students. Always present each activity in a manner that satisfies your objectives and is appropriate for the capabilities of your students.

A note on modeling: modeling is an important area in mathematics and a topic of the high school Standards. Because modeling is interpreted best in relation to other Standards, many activities in this book incorporate modeling in conjunction with other skills.

To enhance your instruction of the activities, consider the following:

Use a variety of instructional tools, such as traditional boards, whiteboards, overhead projectors, computers, digital projectors, and document cameras to present material in an effective and interesting manner.

Preview every Web site and work through any exercises so that you are better able to offer guidance during the activity.

Demonstrate the use of Web sites to your students before they begin working at the site.

Place the URLs of Web sites in your browser to make the Web site easy to access.

For activities that require students to cut out cards, copy the cards on card stock and laminate them to preserve them for future use.

We hope that the activities in this resource prove to be both interesting and enjoyable for you and your students, and that the activities help your students master the concepts and skills addressed by the Standards. We extend to you our best wishes for a successful and rewarding year.

Judith A. Muschla

Gary Robert Muschla

Erin Muschla-Berry

About the Authors

Judith A. Muschla received her BA in Mathematics from Douglass College at Rutgers University and is certified to teach K–12. She taught mathematics in South River, New Jersey, for over twenty-five years at various levels at both South River High School and South River Middle School. She wrote several math curriculums and conducted mathematics workshops for teachers and parents.

Together, Judith and Gary Muschla have coauthored several math books published by Jossey-Bass: Hands-On Math Projects with Real-Life Applications, Grades 3–5 (2009); The Math Teacher's Problem-a-Day, Grades 4–8 (2008); Hands-On Math Projects with Real-Life Applications, Grades 6–12 (1996; second edition, 2006); The Math Teacher's Book of Lists (1995; second edition, 2005); Math Games: 180 Reproducible Activities to Motivate, Excite, and Challenge Students, Grades 6–12 (2004); Algebra Teacher's Activities Kit (2003); Math Smart! Over 220 Ready-to-Use Activities to Motivate and Challenge Students, Grades 6–12 (2002); Geometry Teacher's Activities Kit (2000); and Math Starters! 5- to 10-Minute Activities to Make Kids Think, Grades 6–12 (1999).

Gary Robert Muschla received his BA and MAT from Trenton State College and taught in Spotswood, New Jersey, for more than twenty-five years. In addition to math resources, he has written several resources for English and writing teachers, among them Writing Workshop Survival Kit (1993; second edition, 2005); The Writing Teacher's Book of Lists (1991; second edition, 2004); Ready-to Use Reading Proficiency Lessons and Activities, 10th Grade Level (2003); Ready-to-Use Reading Proficiency Lessons and Activities, 8th Grade Level (2002); Ready-to-Use Reading Proficiency Lessons and Activities, 4th Grade Level (2002); Reading Workshop Survival Kit (1997); and English Teacher's Great Books Activities Kit (1994), all published by Jossey-Bass.

Erin Muschla-Berry received her BS and MEd from The College of New Jersey. She is certified to teach grades K–8 with Mathematics Specialization in Grades 5–8. She currently teaches math at Monroe Township Middle School in Monroe, New Jersey, and has presented workshops for math teachers for the Association of Mathematics Teachers of New Jersey. She has coauthored seven books with Judith and Gary Muschla for Jossey-Bass: Teaching the Common Core Math Standards with Hands-On Activities, Grades K–2 (2014); Teaching the Common Core Math Standards with Hands-On Activities, Grades 3–5 (2014); Math Starters, 2nd Edition: 5- to 10-Minute Activities Aligned with the Common Core Standards, Grades 6–12 (2013); Teaching the Common Core Math Standards with Hands-On Activities, Grades 6–8 (2012); The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills (2011); The Elementary Teacher's Book of Lists (2010); and Math Teacher's Survival Guide, Grades 5–12 (2010).

Acknowledgments

We thank Chari Chanley, EdS, principal of Monroe Township Middle School; James Higgins, vice principal of Monroe Township Middle School; and Scott Sidler, vice principal of Monroe Township Middle School, for their support.

We also thank Kate Bradford, our editor at Jossey-Bass, for her guidance as we developed this book. And our thanks to Mark Karmendy, our production editor, for steering this book through the production process.

Our special thanks to Diane Turso for proofreading this book as she has done for so many of our previous books.

We appreciate the support of our many colleagues who have encouraged us in our work over the years.

And we wish to acknowledge the many students we have had the satisfaction of teaching.

Section 1

Standards and Activities for Number and Quantity

The Real Number System

The real number system consists of rational and irrational numbers. It is sometimes referred to as the continuum of real numbers.

Rational numbers are the set of numbers that can be expressed in the form of c01-math-0001 , where a and b are integers, b ≠ 0. Examples include integers, finite decimals, and repeating decimals.

Irrational numbers are the set of numbers that cannot be written as terminating or repeating decimals. Examples include c01-math-0002 , π, and e.

N-RN.1

Extend the properties of exponents to rational exponents.

1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Activity: Understanding Integer and Rational Exponents

Students will complete statements that show how the meaning of rational exponents follows from extending the properties of integer exponents.

Materials

One copy of reproducible N-RN.1, The Meaning of Rational Exponents, for each student.

Procedure

Explain that the meaning of rational exponents follows from the properties of integer exponents. Review the properties of exponents. a and b are real numbers and m and n are integers.

c01-math-0003 , c01-math-0004 , and c01-math-0005 .

c01-math-0006 , c01-math-0007 , and c01-math-0008 , a ≠ 0.

Explain that these properties can be extended to rational exponents as follows: c01-math-0009 , where a > 0 and m and n are integers, n > 0.

Explain that some expressions that have rational exponents are rational numbers. Examples include c01-math-0010 , c01-math-0011 , and c01-math-0012 . Other expressions, such as c01-math-0013 and c01-math-0014 , are irrational numbers.

Explain that the reproducible, when completed, provides an explanation of how the value of c01-math-0015 can be found using properties of exponents. Students are to complete the statements by selecting the correct expressions, which are shown at the bottom of the page. Note that the steps are sequential and each expression can be used only once.

Closure

Ask your students to summarize how they used the properties of exponents to complete the statements.

Answers

(1) c01-math-0016 (2) 2, c01-math-0017 , 16 (3) c01-math-0018 , c01-math-0019 , 8

N-RN.2

Extend the properties of exponents to rational exponents.

2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Active Activity: Finding the Values of Expressions

Working individually or in pairs, students will identify the value of expressions in simplest form.

Materials

One copy of reproducible N-RN.2, Equations and Their Values, for the class; scissors for the teacher.

Preparation

After making one copy of the reproducible, cut out each box (each containing an I have and Who has? statement) so that you have a total of 21 slips of paper. The slips are arranged in order on the reproducible, each providing a number that is the value of the expression written on the previous slip, except for the value of the last expression, which is written on the first slip. The original reproducible will serve as your answer key.

Procedure

Mix the slips up and then distribute one slip of paper to each student or one slip to pairs of students. For a small class, you may give some students two slips. You must distribute all 21 slips.

Explain that each slip has a number in its simplest form on the left and a term that can be simplified on the right. Start the activity by asking a student to read the term that is written on the right side of his slip. You may find it helpful to write this term on the board. All students then should check the number they have on the left side of their slip to find the value of the term. Because of the way the slips are designed, only one slip will contain a correct match. The student who has the slip with the correct answer should say, I have . . ., and then provide the answer. If the student is correct, she then reads the term written on the right side of her slip. If she is incorrect, point out her error. Another student should then provide the correct answer, which is printed on the left side of his slip.

Continue this procedure until the student who read the first term has a number that is equal to the value of the last term.

Closure

Ask your students for examples of other expressions that can be simplified to the same number. For example, c01-math-0020 , and it also equals c01-math-0021 . Ask why this is so.

N-RN.3

Use properties of rational and irrational numbers.

3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Active Activity: Sums and Properties of Rational and Irrational Numbers

This is a two-day activity. Students will work in pairs or groups of three. On the first day, students will place in sequence the steps for proving that the sum of two rational numbers is rational. On the second day, they will place in sequence the steps for proving that the sum of a rational number and an irrational number is irrational. They will also draw conclusions about the difference between two rational numbers as well as the product of a nonzero rational number and an irrational number.

Materials

Scissors; reproducibles N-RN.3, Proving the Sum of Two Rational Numbers Is Rational, and N-RN.3, Proving the Sum of Rational and Irrational Numbers Is Irrational, for each pair or group of students.

Procedure

Day One

Distribute copies of reproducible N-RN.3, Proving the Sum of Two Rational Numbers Is Rational, to each pair or group of students. Explain that the table shows how to prove that the sum of two rational numbers is rational. The table has five rows, each containing a statement and an explanation. The statements and explanations are correct, but the rows are out of order.

Explain that students are to place the rows in the correct order. Suggest that they cut out each row, which will make it easier to arrange the rows correctly.

Closure

Discuss the proof. Ask your students what they can conclude about the difference of two rational numbers. (The difference of two rational numbers is a rational number.)

Answers

The sequence of some rows may vary; accept any sequence students can justify. One correct order of the rows follows: 2, 3, 5, 1, 4.

Procedure

Day two

Hand out copies of reproducible N-RN.3, Proving the Sum of Rational and Irrational Numbers Is Irrational, to each pair or group of students. Explain that the table shows how to prove that the sum of a rational number and an irrational number is irrational. This is a proof by contradiction that uses the fact that the difference of two rational numbers is rational, which was discussed during the closure on day one.

Explain that this proof assumes that the sum of a rational number and an irrational number is rational, but a contradiction makes the assumption incorrect, leading to the conclusion that the sum of a rational number and an irrational number must be irrational.

Explain that the table has seven rows; each row contains a statement and an explanation. The statements and explanations are correct, but the rows are out of order. Students are to place them in the proper order. Suggest that students cut out each row to make it easier to arrange the rows correctly.

Closure

Discuss the proof. Ask your students what they think is true about the product of a nonzero rational number and an irrational number based on their understanding of the sum of a rational number and an irrational number being irrational. (The product is an irrational number.)

Answers

The sequence of some rows may vary; accept any sequence students can justify. One correct order of the rows follows: 5, 3, 1, 4, 2, 7, 6.

Quantities

Quantities are numbers with units that involve measurement. Although in the lower grades students worked with units that addressed attributes such as length, width, height, and volume, in high school students work with other units of measurement that address a variety of problems in many different areas. Some examples include solving problems