Diverse Learners Use Math TrailblazersA Math Trailblazers classroom includes high-quality and interesting mathematics instruction for all learners based on the belief that all students deserve a rich and challenging math curriculum. High expectations and strong support for students and teachers allows a wide range of learners to access the rigorous mathematics in Math Trailblazers.Screen Shot 2015-03-16 at 3.20.29 PM


Math Trailblazers excels in developing students as flexible thinkers through the use of multiple strategies and representations. Instead of presenting students with one solution strategy, MTB4 lessons incorporate many strategies. Students work to choose the strategy that makes sense for them and the appropriate strategy for a given problem. Students are challenged to determine which strategies are the most efficient. In response to research, the lessons are designed to ensure that students don’t just learn and stick with one strategy. Strategy Menus give students choices and help them advance at an appropriate time. Using multiple strategies and representations for whole-number computation allows for sense-making and the development of conceptual understanding. When students are able to use a range of strategies to solve problems, they are able to access and respond to different mathematical concepts which supports a wide range of student identities and needs. Teachers are better able to differentiate to meet the needs of their students, and use the information about a student’s use of strategies to access his or her understanding of mathematical concepts. Further, a range of strategies promotes efficient, flexible, and accurate computational fluency.

Strategy Menu


The authors of Math Trailblazers know that good instruction ultimately depends on knowledgeable and flexible instructors who plan lessons carefully, and they designed a curriculum that would support both teachers and students. Incorporated into the 4th Edition are new and even more explicit strategies and tools to address diverse learning and to assist teachers with the task of differentiating their instruction. Meeting Individual Needs boxes within the lessons offer ways of dealing with misconceptions and varying student needs and differentiated practice such as games, Workshops, and kindergarten work stations are designed to re-teach, practice, and challenge in order to address the needs of all students. Some activities are specifically designed to provide students with focused intervention, or targeted practice, rather than simply more of the same practice. Assessments are regular and consistent, so individualization can be easily implemented to support each child in his or her mathematical development and learning. The program also includes tools that monitor student progress and provide useful feedback.


The curriculum allows students to develop deep insights into important concepts instead of experiencing a more cursory treatment of a broader range of topics. It avoids instruction that forces over-reliance of memorization and instead emphasizes conceptual understanding. Attention is drawn to tools within the curriculum that can assist learners to develop the needed conceptual understanding of the operations in order to gain fluency with the procedures. The lessons are intentionally designed and organized to clearly focus on the content, the process, and the products so students develop understanding of the key concepts, principles, skills, and facts of math. This intentional attention to conceptual development of mathematical concepts and careful attention to the sequence and organization of the curriculum supports all students as they learn.


The authentic tasks within Math Trailblazers lessons are challenging, and involve problem solving and reasoning that is appropriate for all learners. Helping students access math in varied ways, building on prior math knowledge, making connections across math topics, moving from concrete to representational to abstract, using multiple representations, providing many examples, offering manipulatives, attempting new strategies, and communicating solution tasks can increase accessibility for some students, and motivate and challenge all learners.


Math Trailblazers attends to increasing diversity within the classroom by incorporating most of these features daily:

  • GlossaryEngaging student materials include clear tutorials, extensive glossaries, and helpful reference sections designed to support student learning. Strategies and representations are presented with clear and explanatory visuals in helpful ways that are not distracting to students. Interactive digital components have animated diagrams and examples, step-by-step problem-solving tutorials, and enhanced Adventure Stories with “read-to-me” options.


  • Hands-on, concept-based instruction serves to provide access and motivation to all students. An engaging, problem-solving focus allows students to find alternative strategies and approaches that work best for them. Students are able to access problems differently, and use a variety of strategies for doing computation. The introduction of more than one valid procedure for each arithmetic operation offers students alternative options that align better with their learning strengths. Challenging reasoning and problem-solving tasks are solved using a range of strategies that allows more advanced thinkers to use more sophisticated strategies.


  • Adding Decimals in Grade 5Rich problems add meaningful context that helps students make sense of the mathematics, build upon their prior knowledge, and judge the reasonableness of their answers.


  • Authentic tasks develop mathematical abstract reasoning, develop metacognitive skills, and increase motivation and interest in mathematics as students do the work of real mathematicians.


  • Extensive and ongoing use of multiple representations of arithmetic operations such as manipulatives, pictures, models, and other visual representations support students by providing different entry points for understanding the operations. Students are explicitly asked to use tools and representations. They learn when and how to use them to discover what’s most efficient for them and which tools and representations work for different problems.



Using Manipulatives to Promote Understanding

  • Communication of mathematical ideas using different representations helps students understand and retain concepts when they rephrase problems in their own words, communicate their solution strategies, and summarize what others have reported. Connections to literature, problems that involve everyday life, and opportunities to read, write, and communicate about problems provide meaningful access to rigorous mathematics. Learn more about communication and discussion.


Strategies for Math Facts

  • A conceptual and systematic approach to the instruction of the math facts focuses on patterns and connections among and between facts rather than rote memorization for better retention. Students first use and develop strategies to solve the facts, and then regularly practice these facts in small groups organized by strategy with Daily Practice and Problems in Grades K–5 and Home Practice in Grades 1–5. As students become proficient with these strategies, they become fluent with the math facts. Learn more about math facts.


  • Workshops Offer Differentiated PracticeWorkshops, games, and labs incorporate a variety of strategies to address varying needs and provide another source of motivation or practice that can be used effectively with all students. Differentiated practice questions and variations of games help address a variety of students’ needs.


  • Carefully selected homework tasks with instructions to families, Letters Home, and access to online tools, reference sections, and glossaries provide support to students and families.


  • TIMS Challenge DPPsMore opportunities and time for practice within each unit include both practice connected directly to the content of the lesson and distributive practice in the form of Daily Practice and Problems in Kindergarten through 5th grade and Home Practice in Grades 1–5.


  • A balance of whole class instruction, varied small group work, and individual work combined with a supportive environment promotes understanding through discourse with props, collaborative work, and communication. Learn more about effective grouping strategies.


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