The California Common Core State Standards for mathematics include two types of standards:
Eight Mathematical Practice Standards (identical for each grade level); and
Mathematical Content Standards (different at each grade level).
Together these standards address both “habits of mind” that students should develop to foster mathematical understanding and expertise and skills and knowledge—what students need to know and be able to do.
The mathematical content standards were built on progressions of topics across grade levels, informed by both research on children’s cognitive development and by the logical structure of mathematics.
They are:
Different at each grade level
End-of-grade-level expectations
Assessed on CAASPP
Reported by the state as Claim 1
They are:
Identical for each grade level
Assessed on CAASPP
Reported by the state as Claims 2, 3, and 4
Students should spend the large majority of their time on the major work of the grade (🟩)*. These documents from "Achieve the Core" show what is the the Major Work for each grade. Emphases are given at the cluster level.
When teachers and principals prioritize this Major Work (a.k.a., essential standards), it prepares students for the next grade level. Doing so allows students to gain strong foundations:
solid conceptual understanding,
a high degree of procedural skill and fluency, and
the ability to apply the math they know to solve problems inside and outside the math classroom.
Supporting work (🟦) and, where appropriate, additional work (🟡) can engage students in the major work of the grade.
*At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade.
Major Math Work (shown above) are aligned to the Priority Clusters assessed on CAASPP (see below)
These claims are what is reported back to schools and families from CAASPP. The overall score is based on the performance for these claims.
Claim #1 – Concepts & Procedures:
“Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”
Claim #2 – Problem Solving:
“Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”
Claim #3 – Communicating Reasoning:
“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”
Claim #4 – Modeling and Data Analysis:
“Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”
IM Certified® math curricula have earned EdReports’ highest ratings across all three review gateways: focus and coherence; rigor and mathematical practices; and usability. EdReports is a highly regarded independent nonprofit that reviews K–12 curricula for standards alignment and quality. Download the full analysis IM K–5 Math and IM 6-8 Math.