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CAIM Inservice: November 15, 2014

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2 1.Focus: 2-3 topics focused on deeply in each grade. 2.Coherence: Concepts logically connected from one grade to the next and linked to other major topics within the grade. 3.Rigor: In major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.

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Rigor = Conceptual understanding + Procedural skill and fluency + Application

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Rigor requires a balance of the three discrete components of math instruction: conceptual understanding, procedural skills and fluency, and application. This is not simply a pedagogical option, but is required by the Standards. The majority of the Standards specifically call for conceptual understanding, fluency, or application, but not every standard will necessarily fit neatly into just one of these three discrete components. -For example, certain standards can be said to require procedural skill and conceptual understanding.

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6.EE.1 Write and evaluate numerical expressions involving whole‐number exponents. ▪ For example, multiply by powers of 10 and products of numbers using exponents (777 = 73).

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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 more than a set of mnemonics or discrete procedures. Conceptual understanding standards often use the terms “understand” and “recognize.”

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6.NS.5 Understand that positive and negative numbers describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real‐world contexts, explain the meaning of 0 in each situation.

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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. Fluency standards clearly state “fluently” in the standard.

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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 access and make meaning of content. Application standards typically state “apply” or “solve.”

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6.SP.4 Display numerical data in plots on a number line, including dot or line plots, histograms, and box (box and whisker) plots.

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Priorities What are the priorities we focus on in each grade?

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GradePriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K-2Addition and subtraction, measurement using whole numbers 3-5Multiplication and division of whole numbers and fractions 6Ratios and proportional relationships; early expressions and equations 7Ratios and proportional relationships; arithmetic of rational numbers 8Linear algebra 14

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Activities that give students the opportunity to demonstrate their understanding and mastery of math skills and concepts covered in class. Students Use an organized approach using one or more strategies Explain the steps and strategies used to complete the task Show evidence of checking answers for correctness and reasonableness. The tasks require analysis to explain the methods used and the reasoning behind choosing the method. 15 http://insidemathematics.org/index.php/exemplary-lessons-integrating-practice- standards

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1. Draw the next pattern in this series. In Prague some sidewalks are made of small square blocks of stone. The blocks are in different shades to make patterns that are in various sizes. National Council of Supervisors of Mathematics. http://www.mathedleadership.org/ccss/itp/sidewalk.html

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17 2. Complete the pattern below 3. What do you notice about the number of white and gray blocks? a. Fill in the blank spaces in this list 25=5 2 81=_____ 169=_____ 289=17 2 b. How many blocks will pattern 5 need? c. How many blocks will number n need? Pattern number, n1234 Number of white blocks1240 Number of gray blocks13 Total number of blocks25 National Council of Supervisors of Mathematics. http://www.mathedleadership.org/ccss/itp/sidewalk.html

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Use performance tasks Focus on Mathematical Practices Students should be challenged and struggle Guide with open ended questions Allow students to work together to solve problems

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Revolve around an interesting problem that offers several methods of solution. Addresses an essential mathematical concept outlined in the Alaska Standards. Utilizes the Mathematical Practices.

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22 Planning Model Adapted from Measured Progress Professional Development www.measuredprogress.org

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Full implementation of the new standards should be in effect for the 2014-2015 school year When creating units of instruction for classroom use, new standards will be used Shift in pedagogy Shift in assessment

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