Harvey F. Silver, president of Silver Strong & Associates and Thoughtful Education Press, was named one of the 100 most influential teachers in the country. He has conducted numerous workshops for school districts and state education departments throughout the United States. He was the principal consultant for the Georgia Critical Thinking Skills Program and the Kentucky Thoughtful Education Teacher Leadership Program. Silver is the author of several educational bestsellers, including So Each May Learn: Integrating Learning Styles and Multiple Intelligences and Teaching Styles and Strategies, both published by the Association for Supervision and Curriculum Design. With Richard Strong, Silver developed The Thoughtful Classroom—a renowned professional development program based on the commitment to “make students as important as standards.”John Brunsting is a mathematics teacher, a staff development specialist, and an author. John serves schools as a teacher and coach as well as a mathematics consultant on practical, style-based tools and strategies. He is a coordinator for Illinois Advanced Placement Institutes and cofounder of Mathematics & Technology Institutes, teacher training organizations committed to the instructional excellence of teachers. Previously an AP Calculus Exam Committee member, John coauthored Preparing for the AP Calculus Examination (2006). In 2008, John coauthored the best-selling Math Tools, Grades 3-12: 64 Ways to Differentiate Instruction and Increase Student Engagement. He has presented at national and international conferences for the National Council of Teachers of Mathematics (NCTM), National Council of Supervisors of Mathematics (NCSM), the Association for Supervision and Curriculum Development (ASCD), the Japan Association for Supervision and Curriculum Development (JASCD), Teachers Teaching with Technology (T3), and the International Conference on Computers in Education (ICCE). Terry Walsh has been a mathematics trainer and consultant for nearly 20 years. After retiring from math and administrative positions in two suburban Chicago high schools, In addition to developing Thoughtful Classroom strategies, Terry was one of the founding editor’s of the EightySomething! graphing calculator newsletter. He not only used the strategies in this book in his own classes, he has worked with teachers across the country to help them do the same. He has also incorporated ideas from Math Tools into a variety of Pre-AP Mathematics workshops that he has been leading for the College Board. Terry has led Pre-AP Math and Learning Styles workshops across the U.S as well as in Europe. He has presented at international, national, state, and local mathematics conferences sponsored by such organizations as NCTM, the Illinois and Colorado Councils of Teachers of Mathematics, Teachers Teaching with Technology (T3), and the metropolitan Math Club of Chicago (MMC). After “retirement”, Terry moved to Colorado. His commitment to educating students and his love of Mathematics brought Terry back into schools—first as the Secondary Math Instructional Coach for Fort Lupton schools and then as a Principal of a secondary charter school. Terry now actively consults with both pre-service and experienced teachers throughout the country to help them incorporate effective mathematics strategies in their classes in order to increase student learning. You can contact him at: trterryw@yahoo.com. Consulting Description Edward J. Thomas is founder and president of Dimension 2000, a professional development organization that works with teachers of mathematics. He has over 30 years of experience as a mathematics teacher at the middle school, high school, district, and undergraduate levels. Edward has authored several articles and books on mathematics instruction and has developed a number of educational games for the mathematics classroom. He was the co-chair of the Northwest Georgia P-16 Council, an initiative designed to improve teacher quality and student achievement from pre-school through the undergraduate level. Edward is an experienced mathematics consultant who has conducted workshops for schools throughout the country. He has also presented at state, regional, and national conferences for the National Council of Teachers of Mathematics (NCTM), Georgia Council of Teachers of Mathematics (GCTM), Southern Regional Education Board (SREB), Georgia Association of Educational Leaders (GAEL), Georgia Middle School Association (GMSA), and the Association for Supervision and Curriculum Development (ASCD). To learn more about Thomas’ MATHCORE 2K, an online professional development resource produced by Dimension 2000, visit http://www.mathcore2k.com/.

"I was hooked within the first 30 pages! Ideas were racing through my mind—I′m excited to blog about it and use it in the classroom. Applies to teachers of all ages—a lot of solid explanations for newbies but still full of resources that any teachers can use or modify. Any book that makes me think, and especially think about improving my practice, is definitely a worthwhile investment. Invest in yourself!"

• AcknowledgmentsAbout the AuthorsPreface: Math Tools: A Cure for the Common CoreIntroduction: A User′s Guide to the Second Edition1. MasteryChapter One MatrixConvergence MasteryFist Lists and SpidersGlossariesKnowledge CardsMastery ReviewMathematical ConventionsMathematical SummariesMemory BoxMental Math WarMost Valuable Point (MVP)Practice Makes PerfectProcedural NotesVocabulary Knowledge Rating (VKR)Vocabulary OrganizersWhat′s Wrong?Word Walls2. UnderstandingChapter Two MatrixAlways-Sometimes-Never(ASN)Compare & ContrastConcept AttainmentEssential Question Notes (EQN)Learning From CluesMaking NotesMath RulebookPattern FindingPrecisely SpeakingPs and QsShow MeStake Your ClaimSupport or RefuteThinking NotesThree-Way TieWhich One Doesn′t Belong?Yes, But Why?3. Self-ExpressiveChapter Three Matrix3-D Viewer: Algebraic, Graphical, and NumericalAnd the Question IsCinquainsCreate Your OwnDivergent ThinkingGroup and LabelM + M: Math and MetaphorsMaking Up Is Fun to DoMath RecipeMeaning-Full MathMetaphorical DuelsModeling With AlgebraModeling With ManipulativesPicture = 1,000 WordsVocabulary StoriesWhat If?4. InterpersonalChapter Four MatrixAttention MonitorExplaining SolutionsI Know What I KnowMath Review GamesNo Uncertain TermsPaired LearnerPeer CoachingRange FinderReal-World ConnectionsTest FeedbackWhat′s Your Favorite?Where in the World?Who′s Right?5. MosaicChapter Five MatrixAssessment MenuComprehension MenuMath Media SkillsMath NotesMATHEMATICS Writing FramesTask RotationReferencesIndex

Harvey F. Silver, president of Silver Strong & Associates and Thoughtful Education Press, was named one of the 100 most influential teachers in the country. He has conducted numerous workshops for school districts and state education departments throughout the United States. He was the principal consultant for the Georgia Critical Thinking Skills Program and the Kentucky Thoughtful Education Teacher Leadership Program. Silver is the author of several educational bestsellers, including So Each May Learn: Integrating Learning Styles and Multiple Intelligences and Teaching Styles and Strategies, both published by the Association for Supervision and Curriculum Design. With Richard Strong, Silver developed The Thoughtful Classroom—a renowned professional development program based on the commitment to “make students as important as standards.”John Brunsting is a mathematics teacher, a staff development specialist, and an author. John serves schools as a teacher and coach as well as a mathematics consultant on practical, style-based tools and strategies. He is a coordinator for Illinois Advanced Placement Institutes and cofounder of Mathematics & Technology Institutes, teacher training organizations committed to the instructional excellence of teachers. Previously an AP Calculus Exam Committee member, John coauthored Preparing for the AP Calculus Examination (2006). In 2008, John coauthored the best-selling Math Tools, Grades 3-12: 64 Ways to Differentiate Instruction and Increase Student Engagement. He has presented at national and international conferences for the National Council of Teachers of Mathematics (NCTM), National Council of Supervisors of Mathematics (NCSM), the Association for Supervision and Curriculum Development (ASCD), the Japan Association for Supervision and Curriculum Development (JASCD), Teachers Teaching with Technology (T3), and the International Conference on Computers in Education (ICCE). Terry Walsh has been a mathematics trainer and consultant for nearly 20 years. After retiring from math and administrative positions in two suburban Chicago high schools, In addition to developing Thoughtful Classroom strategies, Terry was one of the founding editor’s of the EightySomething! graphing calculator newsletter. He not only used the strategies in this book in his own classes, he has worked with teachers across the country to help them do the same. He has also incorporated ideas from Math Tools into a variety of Pre-AP Mathematics workshops that he has been leading for the College Board. Terry has led Pre-AP Math and Learning Styles workshops across the U.S as well as in Europe. He has presented at international, national, state, and local mathematics conferences sponsored by such organizations as NCTM, the Illinois and Colorado Councils of Teachers of Mathematics, Teachers Teaching with Technology (T3), and the metropolitan Math Club of Chicago (MMC). After “retirement”, Terry moved to Colorado. His commitment to educating students and his love of Mathematics brought Terry back into schools—first as the Secondary Math Instructional Coach for Fort Lupton schools and then as a Principal of a secondary charter school. Terry now actively consults with both pre-service and experienced teachers throughout the country to help them incorporate effective mathematics strategies in their classes in order to increase student learning. You can contact him at: trterryw@yahoo.com. Consulting Description Edward J. Thomas is founder and president of Dimension 2000, a professional development organization that works with teachers of mathematics. He has over 30 years of experience as a mathematics teacher at the middle school, high school, district, and undergraduate levels. Edward has authored several articles and books on mathematics instruction and has developed a number of educational games for the mathematics classroom. He was the co-chair of the Northwest Georgia P-16 Council, an initiative designed to improve teacher quality and student achievement from pre-school through the undergraduate level. Edward is an experienced mathematics consultant who has conducted workshops for schools throughout the country. He has also presented at state, regional, and national conferences for the National Council of Teachers of Mathematics (NCTM), Georgia Council of Teachers of Mathematics (GCTM), Southern Regional Education Board (SREB), Georgia Association of Educational Leaders (GAEL), Georgia Middle School Association (GMSA), and the Association for Supervision and Curriculum Development (ASCD). To learn more about Thomas’ MATHCORE 2K, an online professional development resource produced by Dimension 2000, visit http://www.mathcore2k.com/.

"I was hooked within the first 30 pages! Ideas were racing through my mind—I′m excited to blog about it and use it in the classroom. Applies to teachers of all ages—a lot of solid explanations for newbies but still full of resources that any teachers can use or modify. Any book that makes me think, and especially think about improving my practice, is definitely a worthwhile investment. Invest in yourself!"

• AcknowledgmentsAbout the AuthorsPreface: Math Tools: A Cure for the Common CoreIntroduction: A User′s Guide to the Second Edition1. MasteryChapter One MatrixConvergence MasteryFist Lists and SpidersGlossariesKnowledge CardsMastery ReviewMathematical ConventionsMathematical SummariesMemory BoxMental Math WarMost Valuable Point (MVP)Practice Makes PerfectProcedural NotesVocabulary Knowledge Rating (VKR)Vocabulary OrganizersWhat′s Wrong?Word Walls2. UnderstandingChapter Two MatrixAlways-Sometimes-Never(ASN)Compare & ContrastConcept AttainmentEssential Question Notes (EQN)Learning From CluesMaking NotesMath RulebookPattern FindingPrecisely SpeakingPs and QsShow MeStake Your ClaimSupport or RefuteThinking NotesThree-Way TieWhich One Doesn′t Belong?Yes, But Why?3. Self-ExpressiveChapter Three Matrix3-D Viewer: Algebraic, Graphical, and NumericalAnd the Question IsCinquainsCreate Your OwnDivergent ThinkingGroup and LabelM + M: Math and MetaphorsMaking Up Is Fun to DoMath RecipeMeaning-Full MathMetaphorical DuelsModeling With AlgebraModeling With ManipulativesPicture = 1,000 WordsVocabulary StoriesWhat If?4. InterpersonalChapter Four MatrixAttention MonitorExplaining SolutionsI Know What I KnowMath Review GamesNo Uncertain TermsPaired LearnerPeer CoachingRange FinderReal-World ConnectionsTest FeedbackWhat′s Your Favorite?Where in the World?Who′s Right?5. MosaicChapter Five MatrixAssessment MenuComprehension MenuMath Media SkillsMath NotesMATHEMATICS Writing FramesTask RotationReferencesIndex

Harvey F. Silver, president of Silver Strong & Associates and Thoughtful Education Press, was named one of the 100 most influential teachers in the country. He has conducted numerous workshops for school districts and state education departments throughout the United States. He was the principal consultant for the Georgia Critical Thinking Skills Program and the Kentucky Thoughtful Education Teacher Leadership Program. Silver is the author of several educational bestsellers, including So Each May Learn: Integrating Learning Styles and Multiple Intelligences and Teaching Styles and Strategies, both published by the Association for Supervision and Curriculum Design. With Richard Strong, Silver developed The Thoughtful Classroom—a renowned professional development program based on the commitment to “make students as important as standards.”John Brunsting is a mathematics teacher, a staff development specialist, and an author. John serves schools as a teacher and coach as well as a mathematics consultant on practical, style-based tools and strategies. He is a coordinator for Illinois Advanced Placement Institutes and cofounder of Mathematics & Technology Institutes, teacher training organizations committed to the instructional excellence of teachers. Previously an AP Calculus Exam Committee member, John coauthored Preparing for the AP Calculus Examination (2006). In 2008, John coauthored the best-selling Math Tools, Grades 3-12: 64 Ways to Differentiate Instruction and Increase Student Engagement. He has presented at national and international conferences for the National Council of Teachers of Mathematics (NCTM), National Council of Supervisors of Mathematics (NCSM), the Association for Supervision and Curriculum Development (ASCD), the Japan Association for Supervision and Curriculum Development (JASCD), Teachers Teaching with Technology (T3), and the International Conference on Computers in Education (ICCE). Terry Walsh has been a mathematics trainer and consultant for nearly 20 years. After retiring from math and administrative positions in two suburban Chicago high schools, In addition to developing Thoughtful Classroom strategies, Terry was one of the founding editor’s of the EightySomething! graphing calculator newsletter. He not only used the strategies in this book in his own classes, he has worked with teachers across the country to help them do the same. He has also incorporated ideas from Math Tools into a variety of Pre-AP Mathematics workshops that he has been leading for the College Board. Terry has led Pre-AP Math and Learning Styles workshops across the U.S as well as in Europe. He has presented at international, national, state, and local mathematics conferences sponsored by such organizations as NCTM, the Illinois and Colorado Councils of Teachers of Mathematics, Teachers Teaching with Technology (T3), and the metropolitan Math Club of Chicago (MMC). After “retirement”, Terry moved to Colorado. His commitment to educating students and his love of Mathematics brought Terry back into schools—first as the Secondary Math Instructional Coach for Fort Lupton schools and then as a Principal of a secondary charter school. Terry now actively consults with both pre-service and experienced teachers throughout the country to help them incorporate effective mathematics strategies in their classes in order to increase student learning. You can contact him at: trterryw@yahoo.com. Consulting Description Edward J. Thomas is founder and president of Dimension 2000, a professional development organization that works with teachers of mathematics. He has over 30 years of experience as a mathematics teacher at the middle school, high school, district, and undergraduate levels. Edward has authored several articles and books on mathematics instruction and has developed a number of educational games for the mathematics classroom. He was the co-chair of the Northwest Georgia P-16 Council, an initiative designed to improve teacher quality and student achievement from pre-school through the undergraduate level. Edward is an experienced mathematics consultant who has conducted workshops for schools throughout the country. He has also presented at state, regional, and national conferences for the National Council of Teachers of Mathematics (NCTM), Georgia Council of Teachers of Mathematics (GCTM), Southern Regional Education Board (SREB), Georgia Association of Educational Leaders (GAEL), Georgia Middle School Association (GMSA), and the Association for Supervision and Curriculum Development (ASCD). To learn more about Thomas’ MATHCORE 2K, an online professional development resource produced by Dimension 2000, visit http://www.mathcore2k.com/.

"I was hooked within the first 30 pages! Ideas were racing through my mind—I′m excited to blog about it and use it in the classroom. Applies to teachers of all ages—a lot of solid explanations for newbies but still full of resources that any teachers can use or modify. Any book that makes me think, and especially think about improving my practice, is definitely a worthwhile investment. Invest in yourself!"

• AcknowledgmentsAbout the AuthorsPreface: Math Tools: A Cure for the Common CoreIntroduction: A User′s Guide to the Second Edition1. MasteryChapter One MatrixConvergence MasteryFist Lists and SpidersGlossariesKnowledge CardsMastery ReviewMathematical ConventionsMathematical SummariesMemory BoxMental Math WarMost Valuable Point (MVP)Practice Makes PerfectProcedural NotesVocabulary Knowledge Rating (VKR)Vocabulary OrganizersWhat′s Wrong?Word Walls2. UnderstandingChapter Two MatrixAlways-Sometimes-Never(ASN)Compare & ContrastConcept AttainmentEssential Question Notes (EQN)Learning From CluesMaking NotesMath RulebookPattern FindingPrecisely SpeakingPs and QsShow MeStake Your ClaimSupport or RefuteThinking NotesThree-Way TieWhich One Doesn′t Belong?Yes, But Why?3. Self-ExpressiveChapter Three Matrix3-D Viewer: Algebraic, Graphical, and NumericalAnd the Question IsCinquainsCreate Your OwnDivergent ThinkingGroup and LabelM + M: Math and MetaphorsMaking Up Is Fun to DoMath RecipeMeaning-Full MathMetaphorical DuelsModeling With AlgebraModeling With ManipulativesPicture = 1,000 WordsVocabulary StoriesWhat If?4. InterpersonalChapter Four MatrixAttention MonitorExplaining SolutionsI Know What I KnowMath Review GamesNo Uncertain TermsPaired LearnerPeer CoachingRange FinderReal-World ConnectionsTest FeedbackWhat′s Your Favorite?Where in the World?Who′s Right?5. MosaicChapter Five MatrixAssessment MenuComprehension MenuMath Media SkillsMath NotesMATHEMATICS Writing FramesTask RotationReferencesIndex