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"In our work, we help teachers support rich, inclusive mathematical discussions among all students. For these discussions to happen, a classroom culture must be developed based on what are often new norms for mathematics class: that students should listen to each other, not just the teacher; that mistakes are OK, even welcomed, as students search for mathematical truth together. New norms take time and deliberate effort to develop."

Read more from Jennifer Knudsen, author of Mathematical Argumentation in Middle School-The What, Why, and How, on Corwin Connect.

"Debriefing is a daily exercise in most professions: business, politics, law enforcement, psychology, healthcare, law, etc. It is often seen as integral to the profession as members reflect on their learning experiences, track their progress, and name their understandings. In truth, debriefing is accepted as an everyday necessity in order for the professional to advance in his/her practice."

Read more from Margie Pearse, author of Teaching Numeracy, on Corwin Connect.

This practice activity from The Five Practices in Practice, Elementary, by Margaret “Peg” Smith, Victoria Bill, and Miriam Gamoran Sherin involves thinking about different ways students might solve the task, planning to respond to students using assessing and advancing questions, and preparing to notice key aspects of students’ thinking in the midst of instruction. 

This handy chart from The Five Practices in Practice, Elementary, by Margaret “Peg” Smith, Victoria Bill, and Miriam Gamoran Sherin identifies a set of moves that teachers can make to hold students accountable for attending to mathematics discussions and presentations.

In this introduction from Mathematize It!, Grades 3-5, the authors clearly define mathematizing and explain why it is critically important in order for students to make accurate and meaningful connections between word problems and the operations that can solve them, developing and strengthening their operation sense.

This Hinge Question Implementation Tool from The Formative 5 helps you to organize your thoughts around a single hinge question in order to better assess your students' progress and define next steps for their continued learning.

Use this observation checklist from The Formative 5 to organize your observations of your students' progress in the classroom related to a specific task. 

You want to teach mathematics to students in the middle grades—but are you ready? Early adolescents have very unique characteristics that you need to be aware of and can capitalize on to facilitate productive lessons. Here are 6 tips from Lois Williams, author of The Mathematics Lesson-Planning Handbook, Grades 6-8, for teaching mathematics in the middle grades that capitalize on middle school students’ characteristics.

Students extend their understanding of place value by bundling tens with this lesson from The Common Core Mathematics Companion, K-2. (Elementary)

Students apply and extend previous understanding of multiplication and division to multiply and divide fractions using this lesson from The Common Core Mathematics Companion, 3-5. (Elementary)

Using this lesson from The Common Core Mathematics Companion, 6-8, students analyze proportional relationships and use them to solve real-world and mathematical problems (Secondary).

Learn how to use this Matrix featured in Realizing Rigor to refine strategies and select student actions. (Secondary)