Math Shifts Focus Coherence Rigor These are the three shifts we need to understand for the teaching and learning of the NxGen Content Standards This section will be delivering information about focus, coherence, and rigor.

What are the Shifts? Focus: focus strongly where the standards focus Focus: The Standards call for a greater focus in mathematics. Rather than racing to cover topics in today’s mile--‐wide, inch--‐deep curriculum, teachers use the power of the eraser and significantly narrow and deepen the way time and energy is spent problems inside and outside the math classroom. conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve In the math classroom. They focus deeply on the major work of each grade so that students can gain strong foundations: solid Discussion – What do you think the advantages of focus could be?

You will watch a 2 ½ minute video You will watch a 2 ½ minute video. Jason Zimba is the math team coordinator for the common core authors. The screen shot of the video is a link to play the video. When the video starts, click on “full screen” mode. When the video ends, click “escape” to exit full screen, then close the video. Click to advance slide.

What does focus mean for our instruction? Instructional Shift: What does focus mean for our instruction? Think about this question. Make sure to read the following thoughts: Focus requires that we significantly narrow the scope of content in each grade and deepen how time and energy is spent on major topics in the classroom. Narrow the scope of content in each grade so that students more deeply experience what remains and is intended in the CCSS. Use the “Power of the Eraser” to greatly reduce the amount of material covered. The focus of the Standards in middle school are in the Domains of Ratios and Proportional Reasoning and Expressions and Equations. Many lessons in textbook curricular programs will need to be eliminated or modified to meet the shift of Focus. Lessons will need to be identified within curricular programs or created in the Focus areas.

K-2 3-5 6 7 8 GRADE FOCUS (and expectation of FLUENCY and CONCEPTUAL UNDERSTANDING) K-2 Addition and subtraction – concept, skills and problem solving 3-5 Multiplication of whole numbers and fractions – concepts, skills and problem solving 6 Ratios and proportional relationships; early expressions and equations 7 Ratios and proportional relationships; arithmetic of rational numbers 8 Linear Algebra

What are the Shifts? Focus: focus strongly where the standards focus Coherence: think across grades, and link to major topics in each grade Coherence Thinking across grades: The Standards are designed around coherent progressions from grade to grade. Principals and teachers carefully connect the learning across grades so that students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. 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 topics can serve the grade level. For example, instead of data displays as an end in themselves, they support grade--‐level word problems.

You will watch a 4 minute video. The screen shot of the video is a link to play the video. When the video starts, click on “full screen” mode. When the video ends, click “escape” to exit full screen, then close the video. Click to advance slide.

What does coherence mean for our instruction? Instructional Shift: What does coherence mean for our instruction? Coherence is about making math make sense. Mathematics is not a list of disconnected tricks or mnemonics. It is an elegant subject in which powerful knowledge results from reasoning with a small number of principles such as place value and properties of operations. The standards define progressions of learning that leverage these principles as they build knowledge over the grades. Notice how focus (reasoning with a small number of principles) plays a part in the coherence. Also, how this principle leads to the learning progressions. Connect the learning across grades so that students can build new understanding onto foundations built in previous years. Understand that the most important connections and progressions are vertical in nature: the links from one grade to the next allow students to progress in their mathematical education. Understand that each standard is not a new event but an extension of previous learning. Connections at a single grade level can be used to improve focus, by tightly linking secondary topics to the major work of the grade.

CCSS Math Content PreK K 1 2 3 4 5 6 7 8 HS Mathematical Practices Counting & Cardinality Number & Operations in Base Ten Ratios & Proportional Relationships Number & Quantity Number & Operations - Fractions The Number System Operations & Algebraic Thinking Expressions & Equations Algebra Functions Geometry Measurement & Data Statistics & Probability Notice how the content connects across grade levels (coherence) and the content is limited to fewer topics in each grade level (focus). Notice the Math practices (in pink) go across all grade levels.

What are the Shifts? Focus: focus strongly where the standards focus Coherence: think across grades, and link to major topics in each grade Rigor: in major topics, pursue with equal intensity conceptual understanding procedural skill and fluency applications Rigor: in major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity. more than a set of mnemonics or discrete procedures. Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Teachers support students’ ability to access concepts from a number of perspectives so that students are able to see math as Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single--‐digit multiplication so that students have access to more complex concepts and procedures. (at the eighth grade level procedural skill and fluency might be knowing how to “undo” a complex equation in one variable without referring to notes or previous problems Application: The Standards call for students to use math flexibly for applications. Teachers provide opportunities for students to apply math in context. Teachers in content areas outside of math, particularly science, ensure that students are using math to make meaning of and access content.

Tell participants you will watch a 2 minute video. The screen shot of the video is a link to play the video. When the video starts, click on “full screen” mode. When the video ends, click “escape” to exit full screen, then close the video. Click to advance slide.

What does rigor mean for our instruction? Instructional Shift: What does rigor mean for our instruction? Rigor involves an EQUAL INTENSITY in the pursuit of conceptual understanding, procedural skill and fluency, and in applications. To help students meet the Standards, educators will need to pursue, with equal intensity, three aspects of Rigor in the major work of each grade: conceptual understanding, procedural skill and fluency, and applications. Conceptual Understanding: Students need a conceptual understanding of key concepts. Teachers support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than just a set of mnemonics or discrete procedures. Procedural Skill and Fluency: Students need to have speed and accuracy when performing calculations. Teachers should structure class/homework time for students to practice core functions multiplication so students have access to more complex concepts and procedures. Application: Students need to be able to use math flexibly for applications. Teachers should provide opportunities for students to apply math in context.