Achievethecore.org :: College- and Career-Ready Shifts in Mathematics

Focus strongly where the standards focus.

The Common Core and other college- and career-ready (CCR) standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, CCR standards require us to significantly narrow and deepen the way time and energy are spent in the math classroom. We focus deeply on the Major Work* of each grade so that students can 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.

Students should spend the large majority of their time on the major work of the grade (). Supporting work () and, where appropriate, additional work () can engage students in the major work of the grade. Emphases are given at the cluster level. Refer to the Common Core State Standards for Mathematics for the specific standards that fall within each cluster.
- Focus by Grade Level
  
  A collection of PDFs detailing the mathematical content emphasized in the Standards by grade level. These can be used as guides to inform instructional decisions regarding time and other resources.
  Access the individual grade-level focus documents here.
  
  Grades K-8 Focus Documents
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  Widely Applicable Prerequisites High School
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- Helping Teachers: Coherence and Focus
  
  William McCallum, a lead writer of the CCSS, explains how the coherence and focus of the standards were designed to help teachers succeed in the classroom. From the Hunt Institute. 2-min video.
Coherence: Think across grades, and link to major topics within grades.

Thinking across grades: College- and career-ready standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. Each standard is not a new event, but an extension of previous learning.

Linking to major topics: Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade-level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.
- Coherence Map
  
  An interactive tool that shows the connections between Common Core State Standards for Mathematics.
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- The Structure is the Standards
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- Coherence Card Activity
  
  An activity that will strengthen your understanding of Coherence. File includes directions, cards, and answer sheet. This activity is part of the Deep Dive into the Math Shifts PD.
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- The Importance of Coherence in Mathematics
  
  CCSS lead writer William McCallum explains the importance of connections within mathematics and the value of students understanding the structure and coherence of the subject. From the Hunt Institute. 5-min video.
- Progressions Documents for the Common Core State Standards for Mathematics
  
  The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.
  The progressions can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics. They would be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks.
  Access the individual progression documents here.
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Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.

Conceptual understanding: CCR standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures.
Procedural skill and fluency: CCR standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.
Application: CCR standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.
- Don’t Leave Out the Math: Phil Daro on Teaching
  
  Using a series of examples, CCSS lead writer Phil Daro stresses the value of teaching mathematics in greater depth and avoiding “clutter” in the curriculum. 5-min video.
- Building Conceptual Understanding in Mathematics
  
  A video explaining how building conceptual undertstanding can help students succeed in mathematics.

College- and Career-Ready Math Shifts at a Glance

A document explaining the biggest changes in mathematics for the CCSS and other college- and career-ready standards.
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The Common Core Shifts in Mathematics

Teachers speak about the Shifts in Mathematics required by the Common Core State Standards. 5-min video.
Professional Development for the Math Shifts

Professional Development modules that will help you understand the Shifts required by college- and career-ready standards, including the Common Core.

Focus strongly where the standards focus.

Coherence: Think across grades, and link to major topics within grades.

Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.