Houghton Mifflin Harcourt

Organization and Instruction

A Balanced Approach

Balanced Approach

Research shows that students benefit from a program that includes equal exposure to Discovery and Direct Instruction. By beginning each lesson with a full-class period Discovery activity, Big Ideas Math® opens the door that allows teachers to provide students with a narrower and deeper understanding of how mathematical concepts relate to the world around them. Then, the Direct Instruction provided by Big Ideas Math relates to the previous day's activity and helps to solidify understanding.

The way we learn math has changed and changed for the better! A Lifetime Network show, Balancing Act, has filmed Dr. Ron Larson as he speaks about the new directions of math. Dr. Larson is joined by Adele Atwood with the Association for Middle Level Education (AMLE) to examine students learning math at deeper levels, comprehending, using and YES, enjoying math in ways we can't imagine.

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Inductive Reasoning

"Going deeper" into the math behind the problem is at the core of the philosophy behind Big Ideas Math. When students are introduced to inductive reasoning, they begin to develop skills in logical thinking to enrich and enhance how they approach and master problems of increasing challenge levels.

Essential Questions

Questioning is a powerful tool in the mathematics classroom. The Big Ideas Math program integrates questioning throughout to encourage students to deepen their thinking about concepts and to sharpen their critical-thinking skills.

Deeper Understanding

The Big Ideas Math program promotes a deeper understanding of math concepts by use of a balanced approach of Discovery activities and Direct Instruction with examples that capture and hold students' attention.

Direct Instruction

Key Ideas

By presenting new concepts with concise words and diagrams, Big Ideas Math promotes mastery as it follows each introduction with real-life examples. Students immediately recognize how Key Ideas relate to their everyday lives, making connections that deepen and solidify their understanding.

Stepped-out Examples

When a new concept is introduced, Big Ideas Math books follow that introduction with Stepped-out Examples to lead students through solving a problem using their newly gained knowledge. This helps to solidify what a student has just learned and helps the student make the leap from discovery to understanding.

On Your Own

The On Your Own component of the Big Ideas Math program is one more way that Big Ideas Math helps students to make sense of newly learned mathematical topics. After seeing a Stepped-out Example, students can try to solve a similar problem by modeling their solution after the example.

Regular and Compacted Pathways

Regular Pathway

The Regular Pathway addresses all of the 6, 7, and 8 Grade Common Core State Standards with discovery activities and direct instruction lessons that provide students the opportunity to gain a deep understanding of the concepts. In 8 Grade students will study Linear Equations and Functions, preparing them for a full Algebra 1 course in 9 Grade.

Compacted Pathway

The Big Ideas Math Accelerated Grade 7 textbook combines all of the regular 7 and 8 Grade standards as outlined by the Common Core State Standards. In this book, you will find the same balanced approach to instruction that makes the Big Ideas Math series so successful. Students reason, construct arguments, and persevere as they work through the Essential Questions that begin each lesson. Clearly stepped-out examples, a Ron Larson hallmark, complete the lesson. The Big Ideas Math Algebra 1 book completes the compacted pathway for middle school students. Students are exposed to highly motivating and relevant problems that offer the depth and rigor needed to prepare them for Calculus and other college-level courses that will be studied during their senior year.

Record and Practice Journal

The activities that begin every Section of Big Ideas Math help students master the Mathematical Practices that accompany the Common Core State Standards. Students are able to make sense of mathematics and they learn to persevere in problem solving. As they model with mathematics in the activities, they begin to reason abstractly and construct viable arguments. As they use the manipulatives and other appropriate tools they begin to look for and make use of structure and patterns while gaining a deeper understanding of the mathematics. The Record and Practice Journal provides the students with a place to record their finding and hypothesis while they explore and discover the patterns of mathematics.

This student workbook also provides:

  • Every activity from the textbook
  • Manipulative pieces needed for the activities
  • A visual glossary for all current and supporting vocabulary
  • Practice for both prerequisite skills and the current lessons


Understanding the language of mathematics is a key to success. Big Ideas Math assists all students with vocabulary acquisition in both English and Spanish with features such as:

  • Integration of new vocabulary throughout the lessons
  • Key Vocabulary Boxes
  • Vocabulary Concept Check
  • Vocabulary Flash Cards
  • Visual glossaries in the Record and Practice Journal, which allows students to add their own notes
  • An audiovisual glossary in both English and Spanish
  • Vocabulary help from the website
  • English Language Learners (ELL) Tips
  • English/Spanish Audio feature for the e-books so students can listen to the text in English or Spanish

Different Word, Same Question


The Vocabulary and Concept Check in every Exercise Set helps to assess students' understanding and usage of mathematical terms.

Meaning of the Word

The Meaning of the Word introduces the vocabulary in context utilizing pictorial representations to aid in understanding.

Vocabulary Flashcards

Vocabulary Flash Cards

Vocabulary Flash Cards are an excellent way to help students memorize vocabulary, prepare for tests, or to reinforce what they already know.

Graphic Organizers

As students progress through the program, Big Ideas Math introduces Graphic Organizers and their use. Students learn to organize problems and find solutions with the use of information frames, note taking organizers, process diagrams, Y charts, and a variety of other aids.

Interdisciplinary Projects

It is important for students to see how math is related to other disciplines and to the world around them. Integrated into the Big Ideas Math program are interdisciplinary and job-related connections. A comprehensive study of grade-level mathematics is found in Appendix A and includes four projects. Literature, History, Art, and Science.

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