MATH IN FOCUS: SINGAPORE MATH BY MARSHALL CAVENDISH

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1 1. Provide an overview of the submitted product, including its intended audience, critical attributes, and distinguishing features, as well as information about product pricing. Math in Focus provides an authentic Singapore math curriculum for students in grades Kindergarten through Grade 8, highlighting problem solving as the focus of mathematical learning. This complete program teaches concepts using a concrete, pictorial, abstract learning progression to anchor learning in real-world, hands-on experiences, supported by seamless integration of technology with the use of ebooks, Interactive Whiteboard activities, online student activities, online manipulative and a bar modeling app. The reason Singapore math works is simple the program has a consistent and strong emphasis on problem solving. Other elements that contribute to the program s success include the program s focus on and support for building skills, concepts, and processes and its attention to developing students metacognition and positive attitudes towards mathematics. Students are given opportunities to reflect on their thinking, communication, and problem solving so that they can apply these skills to varied problem solving activities. How Math in Focus increases the emphasis on problem solving within its curricula is the key to its success. The program begins with a curriculum that includes fewer topics, but reaches greater depth at each level. The multi-page and multi-day lessons build students knowledge systematically and thoroughly. Hands-On activities with manipulatives and extensive skills practice also contribute to student mastery. The use of visual representations builds students skills and their conceptual understanding. To engage all students, the program uses minimal text and simple, direct visuals. As a result, all students, regardless of language skills, focus on the math lesson. To allow all students to reach high levels of conceptual understanding and use of skills, a consistent approach of concrete to pictorial to abstract pedagogy is repeatedly employed. This use of scaffolding is found throughout the program. Students are given increasingly more intricate problems for which they draw on prior knowledge as well as recently acquired concepts and skills as they combine problem solving strategies with critical thinking skills. In summary, Math in Focus is successful because the program uses a focused, coherent syllabus that integrates concepts and skills in a concrete to pictorial to abstract way, all while emphasizing problem solving. The Math in Focus Teacher s Edition provides comprehensive lesson plans, step-by-step instructional support, and embedded professional development. Core instructional materials are aligned to additional Math in Focus components to address the teacher s need to plan for transition, differentiate instruction, communicate with parents, and integrate technology. Math in Focus pricing information is available via the local HMH Account Executive.

2 2. Provide information about the research base supporting the product s methods and effectiveness. Math in Focus is published by Marshall Cavendish Education Singapore, the premier publisher of textbooks in Singapore, and distributed in the United States by Houghton Mifflin Harcourt. The program follows the pedagogical framework developed by the Singapore Ministry of Education: emphasizing concept mastery, a concrete-to-pictorial-to-abstract approach, metacognitive reasoning, and the use of model drawing to solve and justify problems. Singapore math is more than isolated strategies and model-drawing techniques. It is a carefully sequenced curriculum that has led Singapore students to international success. Math in Focus brings the authentic Singapore math pedagogy to U.S. classrooms, and is aligned with Common Core State Standards. Math in Focus is the mastery program for world-class math instruction and results in the U.S. Math in Focus introduces fewer topics in each grade, but teaches them to greater depth. Topics are taught to mastery, so they build from year to year across grade levels without repetition. Math in Focus is highly visual, following a concrete-to-pictorial-to-abstract progression. Math in Focus is sequenced in a way that measures students develop and maintain strong number sense. Students spend the majority of the first half of the year studying number. This provides the foundation necessary to move on to more complex and abstract thinking. Math in Focus utilizes model-drawing strategies that help students solve both routine and nonroutine problems. The Singapore Ministry of Education's mathematics framework emphasizes the importance of attitude and the ability to self-monitor while problem solving to achieve success in math. Math in Focus provides students with the tools they need to break down complex concepts and problems, which in turn develops positive attitudes. A comprehensive Research based report is available for Math in Focus. Please contact your local HMH Account Executive for a copy. 3. Describe how the product establishes learning goals and objectives and measures student progress towards goals and objectives. Math in Focus Chapter Openers begin with the Big Idea, an instructional objective that has been carefully selected to serve as the overarching goal of the chapter. Each lesson objective relates back to the Big Idea to build cohesiveness throughout the entire chapter and aligned to the Common Core State Standards for Mathematics. Teachers will have a chance to measure student progress towards the Chapter s Big Idea and lesson objective through multiple assessments found throughout the chapters. For example, Quick Checks can be used as a diagnostic tool to assess students level of prerequisite knowledge before they progress to the chapter. During lesson instruction, Guided Learning can be used to check students understanding of concepts thus far. At this point, teachers will have an idea whether the student needs additional support, differentiated instruction, or address any

3 common errors students might have. The Chapters culminate with formal evaluations of student progress through the Chapter Review and Test or the Chapter Test Preps found in the Assessment resource. Remediation Options are available for students who need intervention support. These remediation options are aligned to the lesson objectives and suggest the appropriate resource for review or reteaching. 4. Describe how the product engages students with content, builds on prior learning, and develops critical thinking skills. Students love the active role they play in a Math in Focus classroom. Students explore mathematics on a daily basis, developing conceptual understanding of key mathematical topics through the use of manipulatives and the concrete-pictorial-abstract approach. Students stay engaged with active learning and rich discussion, which helps them make connections and apply the math. The curriculum is focused, covering one topic thoroughly before moving to that topic in an application or evaluative format and is coherent, so that the mathematics builds upon prior foundations and students have a true understanding. Throughout Math in Focus students are expected to engage in mathematical reasoning and to express that reasoning. It is common throughout each chapter to have a series of features that support mathematical reasoning, including: Guided Practice, which shows an example of mathematical reasoning to solve key problems. Hands-on Activities and Games, which reinforce learning and encourage the expression and peer critique of reasoning in small groups. Lets Explore, which provide students opportunities to investigate applications of concepts and consider and discuss alternate solutions. Math Journal, which requires students to reflect and express mathematical reasoning. Put on Your Thinking Cap, which specifically challenges critical thinking skills and problem-solving strategies that require mathematical reasoning. These features ensure that a significant amount of time is spent developing students capacity to develop, apply, and communicate mathematical reasoning. Challenging, non-routine situations are offered as assessment through the Put On Your Thinking Cap toward the end of each chapter. These problems ask children to draw on deep prior knowledge as well as recently acquired concepts, combining problem-solving strategies with critical thinking skills. Work problems at the end of each chapter consolidate learning and challenge students to demonstrate mastery by applying it in new ways. Teachers use ongoing diagnostic assessment resources including Checks for Understanding correlations, Common Error alerts and suggestions to use visual models and/or manipulatives to assess concrete conceptualization before moving to pictorial and abstract representations.

4 5. Describe how the product provides for differentiated instruction, inquiry-based learning, selfdirected learning, and opportunities to re-teach content. The Instructional Pathway of the Math in Focus program allows for consolidating concepts and skills for deep understanding through inquiry based practice and self-guided problem solving. Each Learn portion of the lesson is followed by opportunities to develop deeper understanding through carefully crafted skills practice in the lesson using Guided Learning and Let s Practice, real-world problems, and additional practice problems in the Extra Practice Book and advanced practice in the Enrichment book. Students can engage in inquiry-based learning trough hands-on work through the use of manipulatives, models, and technology to practice skills and communicate their reasoning. Additionally, Let s Explore! provides opportunities for students to carry out investigative activities on their own and discuss alternate solutions to open-ended questions. Extra Practice and Reteach opportunities are provided for every lesson. These can be implemented on a whole-class basis for RtI Tier 1, on a small-group basis for Tier 2, or in individual settings for Tier 3 modifications. Math in Focus Teacher's Editions provide tips for helping struggling students at point of use and reference additional Reteach and Extra Practice pages for additional support. Transition Guide: Transition Guide provides a map to help transition students into the Math in Focus program. Teachers can easily scan through the skills and concepts presented in prior years to identify background knowledge necessary for student success. English Language Learners: The concrete pictorial abstract approach is well-suited for English language learners since it is less text-heavy and has more illustrations and visuals. The Teacher's Edition provides lesson-specific suggestions for facilitating instruction for English language learners. The complete program is also available in Spanish. Reteach (Struggling Students): Reteach provides more exposure to concepts for those students who need more time to master new skills or concepts. Extra Practice (On-Level Students): Extra Practice pages correlate directly to the Workbook practices. Put On Your Thinking Cap! questions provide more practice on both non-routine and strategy-based questions. Enrichment (Advanced Students): Enrichment exercises of varying complexity provide advanced students opportunities to extend learning. 6. Describe how the product links content to real world needs, problems, and activities, as well as students lives. Math in Focus builds real-world problem solvers through frequent exposure and practice, model-drawing strategies, and challenging problems. Learn elements use models to explain computation concepts. Students become accustomed to seeing and using visual models to form mental images of mathematical ideas. Practice pages in the Workbook include both computation and problem solving sections. Each set of problem encompasses previous skills and concepts as well as word problem progress in complexity from one-step to two-step to multiple steps.

5 Using bar models as a problem solving tool is taught explicitly in Grades 2-5. Students become familiar with the systematic way to translate complex word problems into mathematical equations, and avoid the common issue of not knowing where to start. Put On Your Thinking Cap! challenges student to solve nonroutine questions. These problems ask children to draw on deep prior experiences as well as recently acquired concepts, combining real world problem solving strategies with critical thinking skills. 7. Describe how the product provides opportunities for student-student collaboration and teacher-student interaction. Hands-On Activities and Game reinforce skills, concepts, and problem solving strategies in small group or partner settings to promote student-student collaboration. Math in Focus lets students communicate with each other, discuss their thinking, and reflect on the math they are practicing with Math Journal. The Learn element is the main feature of the lesson which is teacher led and allows for that teacher-student interaction. After instruction through the Learn element, teachers then can have their students practice along their side through the Guided Learning problems and practice. 8. Describe how the product structures assessment, including pre-assessments, benchmarks, and summative assessments. Each Chapter begins with a formative assessment in the form of a brief review of related prior knowledge and Quick Check (or Pre-Test) to inform planning and flexible grouping. An articulated sequence of instruction is designed for deep understanding through short direct instruction, scaffolded Guided Practice questions and hands-on, collaborative activities that encourage collaboration and communication and offer opportunities to assess performance. Integrated throughout each chapter are exercises of varying complexity providing opportunities for students to be creative in their strategies (problem creation, acting-out, online research, etc.). Interactive Whiteboard Lessons are available. Formative assessment is supported throughout the Teacher s Edition through Quick Checks, and Guided Practice. The Assessments book, available in print and online, provides summative assessments including pretests, chapter tests, and benchmark tests to assist in the gathering of information about student s conceptual understanding, procedural skill and fluency, and application. Assessments are designed to prepare students for the rigor the TEKS and CCSS, so both routine and non-routine problems are included. The Test Prep, or end of chapter assessment, is a summative assessment that includes three questions types (multiple choice, short answer and extended response) layered over three mathematical proficiencies (basic calculation, direct application of concepts, and l these assessments. Students are asked to justify answers, to analyze mistakes, and continue to problem solve. Digital versions of formative and summative assessments are also available through Math in Focus, the Online Assessment Generator, and the ExamView Assessment Generator.

6 9. Describe the product s tools for monitoring student progress, analyzing data, and reporting outcomes to administrators, teachers, students, and parents. Math in Focus Assessment Resources are built in to check students prior knowledge, diagnose specific areas of needs, formally assess student progress, and when necessary, identify appropriate remediation depending on student data. If a teacher uses Think Central s assessment tools, parents can access student progress through their student/parent account and reports can be run to analyze data and report outcomes. 10. Describe how the product customizes instruction for special student populations, including English language learners (ELL), special education, Response to Intervention (RtI), and gifted and talented. Please address the extent to which closed-captioning is provided in online, video- and/or audio-based content in the student and teacher materials, as well as in professional development resources. Math in Focus includes differentiation resources, available as print blackline masters and online, for teachers to customize instruction for special student populations. The clear drawings and visual aspects of Math in Focus means that the entire program is inherently accessible to English Language Learners. Additionally, the Math in Focus Teacher s Edition provides lesson specific suggestions for facilitating instruction for ELL s. Reteach pages provide more exposure to concepts for those students who need more time to master new skills or concepts. Additionally, the Math in Focus Teacher s Edition provides tips for helping struggling students at point of use. Enrichment exercises of varying complexity provide advanced students opportunities to extend the concepts, skills, and strategies they have learned in the Student book and Workbook. The Teacher s Guide to Transition and Teacher s Edition provide educators background information on important concepts in the program. The Math Background topics discuss concepts that may be new or challenging to teachers, such as strategies and models that are unique to the Singapore approach. Teachers can use the Math Background notes in the Teacher Guide to Transition to ensure they understand the strategies used to teach Singapore math before demonstrating these strategies to students who may not have used them in previous math programs. Students transitioning in Math in Focus may need extra support for concepts and skills that were missing or weak in their previous programs. The skills in each chapter s Quick Check and the Chapter Pre-Test form the Workbook help the teacher identify these weaknesses. The teacher can assign the appropriate Reteach and Extra Practice activities identified in the Instructional Pathway Charts. The online version of these charts provides direct links to the extra transitioning support that some students might need. 11. Describe the online, face-to-face, and/or virtual, publisher-provided professional development to support the ongoing product implementation. Ultimately, it is the quality of the teachers and their ability to effectively implement a proven curriculum that makes the difference in student achievement. Our Professional Development Specialists are the only Singapore math experts specifically trained on both the Singapore math

7 pedagogy and the Math in Focus curriculum. Teachers learn effective pedagogy, pacing, classroom management, and both formative and summative assessment practices. This combination of Singapore math philosophy and curriculum expertise means that your teachers will gain valuable, actionable training that they can effectively translate into success for your students. Houghton Mifflin Harcourt offers on-site and online support for Math in Focus. Math in Focus Instructional Strategies This interactive workshop focuses on the big ideas of Math in Focus: Singapore Math by Marshall Cavendish. During this one-day workshop, participants gain an understanding of lesson structure, problem-solving strategies, and the Math in Focus trajectory. Special attention is paid to how students learn and the role of the teacher in Math in Focus. In addition to investigating specific grade-level content, teachers are introduced to key program components and gain an understanding of how carefully sequenced and paced instruction enhances students math achievement. Finally, teachers examine the available technology and explore ways to implement these important resources to support transition and enhance instruction. (Possible grade-level structures include K 6, K 5, K 2, 3 5, 6 8). Kindergarten and Grade 1 sessions are held separately and not presented in combination with other grade levels. Lesson Study, Effective Instruction, Examining the Mathematics This workshop provides teachers with in-depth, hands-on experiences with Math in Focus. Lesson planning, effective instruction, and mathematical content are the focus of this full-day workshop. Participants explore the big ideas introduced during instructional strategies while working to gain understanding of key grade level concepts. Special emphasis is placed on the structure of the lesson and anticipating the obstacles that might occur when teaching the Singapore pedagogy. Grade Level Courses are customized according to the time of year they are delivered fall, winter, and spring. The trainer-led sessions are designed to meet teachers where they are in the curriculum at a given time. Ideally, the Grade Level Courses are followed by Demonstration Lessons for each grade level. Grade Level Courses can be scheduled for full-day or half-day sessions for individual grades. Grade level combinations can be supported for Grades 2 3, 4 5, and 6 8 only. Math in Focus Demonstration Lessons During Year One Implementation, our Math in Focus Demonstration Lessons are best delivered in conjunction with the Grade Level Courses. After a presentation of the content, a lesson is modeled in the classroom with students. Teachers get to see questioning strategies, pacing, and implementation of the lesson structure delivered by an expert. A debriefing session follows to answer questions and ensure teachers are prepared to practice independently. Math in Focus Administrator Training Successful implementation of any instructional program requires a strong leadership team. This workshop is first presented to ensure all site-level administrators are fully aware of instructional components of Math in Focus, how to best support teachers, and what to look for in the classroom. It can be repeated later in the year for a more in-depth look into the pedagogy and just in time support for questions and answers that arise after initial implementation.

8 Math in Focus Demonstration Lesson: Guided-Lesson Design for Year Two and Three In Guided-Lesson Design Professional Development sessions, teachers will collaborate with a Math in Focus specialist to plan, teach, and refine a lesson at their grade level. Topics may include: Guided development of a lesson focusing on differentiation, questioning strategies, intentionally moving students through CPA, formative assessment, and recognizing mastery Classroom modeling of a lesson Reflection and refinement of a lesson Classroom modeling of a refined lesson ThinkCentral in the Math in Focus Classroom A wealth of just in time resources are housed on the Houghton Mifflin Harcourt ThinkCentral site for teachers to utilize in support of student learning. Electronic copies of all teacher and student materials, additional electronic planning resources, and videos of lessons for every chapter of Math in Focus are available to teachers. This seminar provides time for an in-depth teacher exploration of the resources and tips to help them accelerate their Math in Focus professional development. Bar Modeling in the Math in Focus Classroom The Math in Focus lesson sequence includes considerable utilization of the bar model approach when moving students from concrete to pictorial to abstract representations. This course focuses solely on bar modeling as it is employed in Math in Focus, with specific examples from the texts that teachers can utilize. Participants explore technology resources available for this method and tips to ensure student comprehension. Fact Fluency in the Math in Focus Classroom Computational fluency is more than a series of memorized facts. The balanced approach of Math in Focus dedicates time to teaching both the conceptual understanding of mathematical content, as well as procedures that promote efficiency. In this workshop, teachers will define and experience fact fluency as it exists in Math in Focus. Using the Fact Fluency texts as a resource, participants will look closely at content and trace the systematic strategies used to support the development of computational fluency. Math in Focus and the Struggling Learner This workshop engages participants in the process of further exploring the pedagogy, learning trajectories, and assessment systems inherent in Math in Focus to design remediation for struggling learners. Participants will leave with the tools necessary to analyze student errors, design appropriate interventions, and gather data appropriately to measure student progress. This is geared for Special Education and Intervention teachers who have previously attended the Instructional Strategies Workshop or are currently in year two or three of implementation. Every Day Counts: Calendar Math A large number of districts choose to implement Every Day Counts in conjunction with Math in Focus as a method to increase time teachers spend on the skills delineated in the TEKS and Common Core State Standards. This one- or two-day workshop can be either an overview of

9 Every Day Counts materials and processes or a more in-depth training for teachers and is best delivered in grade-level sessions. Online Professional Development Math in Focus Customized Touchpoints Many districts offer teachers the opportunity to participate in facilitated discussions according to where they are in the curriculum. Touchpoint Webinars are sequenced to the curriculum but also allow for a customized response to concerns that arise in the classrooms. The two-hour sessions are typically scheduled by grade level. Every Day Counts Touchpoints Similar to Math in Focus, this monthly series ensures that Every Day Counts teachers are supported as they progress through the curriculum. Many districts find that although not all teachers participate in every session, a community of practice focused on effective implementation often develops. Webinars are most effective when provided according to grade level. ASK (Advice-Support-Knowledge) Bar Virtual Coach Membership in the ASK Bar provides coaches and teachers with just in time and one-to-one support. As teachers grow in their mathematical competency, they need expert support and mentoring to validate their thinking, clarify their questions, and help them grow their confidence. Access to the ASK Bar is provided at the school or district level for , phone, and webinar support to help your teachers grow professionally. Phone and webinar appointments can be scheduled with a U.S.-based Singapore math coach for personal consultation. Written questions can be submitted for a comprehensive, personalized, and prompt written response and discussion. This service can be purchased for an entire school or for a single coach or administrator to serve as a contact. Math in Focus elearning Courses HMH elearning: Math in Focus is a self-paced and on-demand elearning course designed to support and compliment in-person training, providing support with implementation, pedagogy, and the philosophy behind the program. Special focus will be on lesson structure and concrete pictorial abstract pedagogy through the context of challenging chapters taught in each grade level. These elearning Courses will be complimented by student work and video. 12. Describe the technical support, including help desk access and onsite support, provided for the installation and to ensure the product s ongoing effectiveness. Include any costs associated with technical support. Please contact your designated Account Executive as the primary resource for any district support needs including installation and the product s ongoing effectiveness. We offer educational and related instructional materials support for Grades Pre-K through 8th; programs include: science, reading, language arts, mathematics, social studies, reading, math intervention, and professional development, please contact the customer support number at Teachers can tech support at techsupport@hmhpub.com. At this website there are

10 frequently asked questions that might help address your issue. From 8:00 a.m. -11:00 p.m. EST teachers can also call tech support at