Ever feel burdened by mathematics lesson planning? Your blueprint for designing Grades 6-8 math lessons that enhance state standards and address the learning needs of students is here. This indispensable handbook guides you step-by-step to plan math lessons that are purposeful, rigorous, and coherent. The effective planning process helps you

  • Clarify learning intentions and connect goals to success criteria
  • Structure lessons to fit traditional or block schedules
  • Select the formats and tasks that facilitate questioning and encourage productive struggle

Includes a lesson-planning template and examples from Grades 6-8 classrooms. Empower yourself to plan strategically, teach with intention, and build an individualized and manageable set of mathematics lesson plans.


In this book, the authors move away from the long lists of formative assessment techniques teachers have seen in the past. They have spent two years with teachers in real classrooms, boiling the practice down to five essential techniques that will move the needle in learning. These techniques are all realistic, manageable, can be built into lessons and applied every single day. They are: Observation, Interviews, "Show Me," Hinge Questions, and Exit Tasks. This book delves into each of these five techniques, offering particular tools to guide the use of each of the techniques, and suggested activities (at primary, intermediate, and middle grade levels) for their use. These activities will focus on the mathematics at each grade level and will co-reference Common Core State Standards for Mathematics and other similar standards.



Teaching turnarounds encourage productive struggle by identifying teacher and student strengths, designing strengths-based instruction, discovering students' points of power, and promoting strengths in the school community.


This reference offers practical guidance for when and how to pull together mathematics routines, resources, and teaching techniques into a coherent set of lesson plans.



Your user’s guide to the mathematics standards

In the 12 short months since the ELA versions of The Common Core Companions, Grades K-2 and 3-5, burst on the scene, they’ve already assisted tens of thousands of teachers with the day-to-day “what you do.” Teachers’ one big criticism: what about mathematics? Luckily NCTM past-president Linda Gojak and mathematics coach Ruth Harbin Miles stepped up to the task. The result? That version of the mathematics standards you wish you had.

Page by page, The Common Core Mathematics Companions clearly lay out:

  • The mathematics embedded in each standard for a deeper understanding of the content
  • Examples of what effective teaching and learning look like in the classroom  
  • Connected standards within each domain so teachers can better appreciate how they relate
  • Priorities within clusters so teachers know where to focus their time
  • The three components of rigor: conceptual understanding, procedural skills, and applications
  • Vocabulary and suggested materials for each grade-level band with explicit connections to the standards
  • Common student misconceptions around key mathematical ideas with ways to address them

Don’t spend another minute poring over the mathematics standards. Gojak and Miles have already done the heavy-lifting for you. Focus instead on how to teach them, using The Common Core Mathematics Companion as your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.


Learn effective techniques to improve students’ ability to problem solve, construct viable arguments, use tools strategically, attend to precision, and more.  

Using the Leading for Mathematical Proficiency Framework, the authors position student outcomes as the focus of all professional work and connect the Eight Mathematical Practices for students with NCTM's Eight Effective Teaching Practices to help you guide teachers toward growing mathematics proficiency in their classrooms. This hands-on resource details critical coaching and teaching actions, and offers nearly a hundred tools for shifting classroom practice in a way that leads to student math proficiency and understanding of mathematical concepts. It also hones in on key areas such as content knowledge, student engagement, questioning and discourse, analysis of student work, formative assessment, support for emergent language learners and students with special needs, and more.

Your user’s guide to the mathematics standards

In the 12 short months since the ELA versions of The Common Core Companions, Grades K-2 and 3-5, burst on the scene, they’ve already assisted tens of thousands of teachers with the day-to-day “what you do.” Teachers’ one big criticism: what about mathematics? Luckily NCTM past-president Linda Gojak and mathematics coach Ruth Harbin Miles stepped up to the task. The result? That version of the mathematics standards you wish you had.

Page by page, The Common Core Mathematics Companions clearly lay out:

  • The mathematics embedded in each standard for a deeper understanding of the content
  • Examples of what effective teaching and learning look like in the classroom  
  • Connected standards within each domain so teachers can better appreciate how they relate
  • Priorities within clusters so teachers know where to focus their time
  • The three components of rigor: conceptual understanding, procedural skills, and applications
  • Vocabulary and suggested materials for each grade-level band with explicit connections to the standards
  • Common student misconceptions around key mathematical ideas with ways to address them

Don’t spend another minute poring over the mathematics standards. Gojak and Miles have already done the heavy-lifting for you. Focus instead on how to teach them, using The Common Core Mathematics Companion as your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.


Plan K-2 math lessons that are purposeful, rigorous, and coherent, and discover your blueprint for building an exceptional foundation in math for your students. 


This expansion of the popular Common Core Mathematics Companions provides indexes for states implementing state-specific mathematics standards and shows which are the same as CCSS-M, which differ and how.

This expansion of the popular Common Core Mathematics Companions provides indexes for states implementing state-specific mathematics standards and shows which are the same as CCSS-M, which differ and how.

This expansion of the popular Common Core Mathematics Companions provides indexes for states implementing state-specific mathematics standards and shows which are the same as CCSS-M, which differ and how.

Leverage formative assessment in mathematics every single day

For fans of the bestselling book The Formative 5: Everyday Assessment Techniques for Every Math Classroom comes this updated and expanded edition for understanding and implementing highly effective, research-backed formative assessment techniques into seamless, daily practice with students in grades K-12. The Formative 5 in Action serves as an interactive guide that steers teachers toward successful implementation of the formative five techniques of observation, interviews, Show Me, hinge questions, and exit tasks. This updated guidebook offers:

  • More than 120 minutes of video examples of the five techniques in action in real K-12 classrooms, showing teachers not just what to do but how to do it
  • An engaging format with built-in reflection exercises and activities that foster both individual professional learning and promote PLC study through discussion and collaboration
  • An explicit emphasis on providing effective and timely feedback to students, while harnessing student strengths throughout teaching and learning
  • Comprehensive responses to teachers’ frequently asked questions that have surfaced since the publication of the first edition

The research is clear – the authors’ five formative assessment techniques lead to greater attention to planning and stronger instruction for teachers and better achievement for students. The Formative 5 in Action is a truly engaging resource that helps mathematics teachers and instructional leaders engage in classroom-based formative assessment with precision, intentionality, and ease.