Implementing the Common Core in Mathematics: Designing, Supporting, and Monitoring High Quality Instruction

Tools for Assessing Math Instruction

Oakland Unified School District, SERP, Lawrence Hall of Science (2013). The 5x8 card. Oakland, CA: Oakland Unified School District. Available for members at this link.

This observation tool is designed to gather data about student behaviors and practices in mathematics classrooms. The front side of the card lists seven principles for student behavior in mathematics classrooms, paired with student vital actions that align to the principles. The back of the card lists the eight standards for mathematical practice identified in the Common Core State Standards in mathematics, from which the card’s seven principles derive. The student vital actions on the front provide concrete, observable student behaviors that demonstrate progress towards the eight areas of expertise and enable teachers and educators to assess development of mathematical expertise in students.

Oakland Unified School District, SERP, Lawrence Hall of Science (2012). OUSD 5x8 card compendium. Oakland, CA: Oakland Unified School District. Available for members at this link.

This guide identifies several different opportunities for educators to use the Oakland Unified School District 5x8 Card as a tool for improving mathematics instruction and examples of how to use the card in each context. In all instances, the guide focuses educators’ attention on student classroom behavior and using the 5x8 card to inform action that is both responsive to the learning needs of students and guided by the student vital actions. The guideline outlines four approaches to using the card: (1) training teachers and other educators to focus on students, (2) giving evidence-based feedback to students grounded in student vital actions, (3) helping students develop metacognitive skills to recognize and discuss student vital actions, and (4) providing feedback to teachers after observations. In all contexts, the guide recommends using the 5x8 card as a tool to improve the quality and quantity of data gathered about students.

Achieve the Core (2014). Instructional Practice Guide: Coaching K-8. New York, NY: Student Achievement Partners. Available at

This instructional practice guide is a tool to help teachers align instruction with the Common Core State Standards for mathematics (CCSSM) through planning, reflection, collaboration, and coaching that addresses the three shifts of the CCSSM: focus, coherence, and rigor. The guide breaks down the components of a lesson into three core actions: (1) ensure the work of the lesson reflects the shifts required by the CCSSM, (2) employ instructional practices that allow all students to master the content of the lesson, and (3) provide all students with opportunities to exhibit mathematical practices in connection with the content of the lesson. For each core action, the tool provides practitioners with specific indicators and opportunities to reflect on and assess how well their lesson aligns to the core actions. This guide asks teachers and/or observers to assess instructional practice according to a total of 22 indicators, 15 of which are teacher actions and seven of which assess student actions. The guide cover sheet describes it as a tool to be used for planning, reflection, collaboration and coaching by teachers and supporters of teachers through focus on an individual lesson.

Sanger Unified School District (n.d.). Sanger walkthrough tool. Sanger, CA: Author. Available for members at this link.

This iPad screen shot is a snapshot of the Sanger Walkthrough Tool used to evaluate classroom instruction. The tool is designed for coaches and evaluators to retrieve and quickly document observations of teachers on their instruction with a focus on providing constructive feedback on improving and aligning instruction to the Common Core State Standards. Its contents are adapted from the Achieve the Core Instructional Practice Guide: Coaching K-8 (referenced above in this reading list).