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Question 5:
What might I see in a TK–8 mathematics lesson that supports student
achievement of the CA CCSSM?


In transitional kindergarten through grade eight (TK–8), the California Common Core State Standards for Mathematics (CA CCSSM) call for learning mathematical content in the context of real-world situations, using mathematics to solve problems, and developing “habits of mind” that foster mastery of mathematics content as well as mathematical understanding. Lessons that support student learning should reflect the three instructional shifts that are the basis of the CA CCSSM: focus, coherence, and rigor. Lessons should make connections between the Standards for Mathematical Practice (MP) to the Standards for Mathematical Content and provide students with opportunities to engage in mathematical discourse. Instruction should help students build a strong foundation in conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the mathematics they know to solve problems inside and outside the mathematics classroom.

As instructional leaders think about what they should see in a TK–8 mathematics lesson aligned to the CA CCSSM, there are several resources and tools available to consider, but the most comprehensive and widely vetted resource available to California educators is the State Board of Education-adopted Mathematics Framework. With this in mind, this section will focus on helping instructional leaders answer the question above using guidance from the framework, viewing California classroom videos featuring emerging practices, viewing a video of a local educational agency (LEA) panel discussion related to the question, and considering what all of this means for their work and local context.

Connections to the California Professional Standards for Education Leaders (CPSEL)


Education leaders facilitate the development and implementation of a shared vision of learning and growth of all students.
Element 1A: Student-Centered Vision
Leaders shape a collective vision that uses multiple measures of data and focuses on equitable access, opportunities, and outcomes for all students.
Example Indicators:
1A-1 Advance support for the academic, linguistic, cultural, social-emotional, behavioral, and physical development of each learner.
1A-2 Cultivate multiple learning opportunities and support systems that build on student assets and address student needs.
1A-3 Address achievement and opportunity disparities between student groups, with attention to those with special needs; cultural, racial, and linguistic differences; and disadvantaged socio-economic backgrounds.
1A-4 Emphasize the expectation that all students will meet content and performance standards.


Education leaders shape a collaborative culture of teaching and learning, informed by professional standards and focused on student and professional growth.
Element 2B: Curriculum and Instruction
Leaders guide and support the implementation of standards-based curriculum, instruction, and assessments that address student expectations and outcomes.
Example Indicators:
2B-1 Develop a shared understanding of adopted standards-based curriculum that reflects student content and performance expectations.
2B-2 Promote and monitor the use of state frameworks and guides that offer evidence-based instructional and support strategies to increase learning for diverse student assets and needs.
2B-3 Provide access to a variety of resources that are needed for the effective instruction and differentiated support of all students.
2B-4 Guide and monitor the alignment of curriculum, instruction, assessment, and professional practice.

Before you begin…

Prior to focusing on the question above, participants in this activity should be familiar with the following chapters of the Mathematics Framework:

The classroom videos featured on the next three pages are of specific grade levels within the TK–8 grade span. Thus, participants should review the following grade-level chapters of the Mathematics Framework to be familiar with the state-level guidance concerning math instruction in these grades:

A Note-taking Guide (DOC) is provided to help you consider the practices and perspectives shared in the videos. You may want to review it before watching the videos and print it or have it open on your desktop to have in front of you while you watch.