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Differentiating Math Instruction Heather Hardin Arkansas Department of Education Professional Development Anthony Owen Arkansas Department of Education Curriculum & Instruction

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Key Shifts in Mathematics Focus - the major focus in each grade allows the emphasis on the concept to deepen Coherence - there are coherent progressions from grade to grade Rigor - with equal concentration, the three aspects of rigor must be practiced: 1. Conceptual Understanding 2. Procedural Skills and Fluency 3. Application

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FOCUS Greater focus on fewer topics: Grades K–2: Concepts, skills, and problem solving related to addition and subtraction Grades 3–5: Concepts, skills, and problem solving related to multiplication and division of whole numbers and fractions Grade 6: Ratios and proportional relationships, and early algebraic expressions and equations Grade 7: Ratios and proportional relationships, and arithmetic of rational numbers Grade 8: Linear algebra and linear functions

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COHERENCE Progression charts show coherence across grades: Where to find them: ime.math.arizona.edu/progressions/ Members on the working team: Richard Askey (reviewer), Sybilla Beckmann (writer), Douglas Clements (writer), Phil Daro (co-chair), Skip Fennell (reviewer), Brad Findell (writer), Karen Fuson (writer), Roger Howe (writer), Cathy Kessel (editor), William McCallum (chair), Bernie Madison (writer), Dick Scheaffer (writer), Denise Spangler (reviewer), Hung-Hsi Wu (writer), Jason Zimba (co-chair)

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Example from the progression document: The Number System, Grades 6-8 http://commoncoretools.me/wp-content/uploads/2013/07/ccssm_progression_NS+Number_2013-07-09.pdf

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More progression examples… https://education.ohio.gov/getattachment/Topics/Academic-Content-Standards/Mathematics/Resources-Ohio-s-New-Learning-Standards-K-12-Mathe/K-8-Standards-Progressions-2-14- 12.pdf.aspx

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RIGOR Rigor is achieving at high levels, not making things harder 3 aspects of rigor: 1. Conceptual Understanding- comprehension of mathematical understandings that use prior knowledge and new learnings 2. Procedural Skills and Fluency – skillfully and efficiently performing accurate procedures 3. Application- applying and modeling skills and concepts to unfamiliar circumstances

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How can you differentiate math instruction across grades and maintain FOCUS, COHERENCE, and RIGOR?

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The answer… THREE-ACT TASKS Let’s try one…

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ACT 1:

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How big is the killer’s shoe size? What do you notice? What questions do you have? What’s your guess? What does a wrong answer look like? What is an answer that would be way too high? Too low?

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ACT 2: What more information do you need to answer our question? How would you get it?

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Let’s compare the original guesses… Largest 1 st guess:_____ Smallest 1 st guess:_____ Difference:_____ Largest answer:_____ Smallest answer:_____ Difference:_____

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ACT 3:

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Why was your answer close but not exact? What did your model/ work not include that it should have? What did your model work include that it should not have?

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If we were going to title the lesson for today, what would a good title be? Consider these things: What math did we use? What math did we use that we already knew? What new math did we use?

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SEQUEL (optional) How big would Bigfoot’s foot look next to the dollar bill? How big would Mini me’s foot look next to the dollar bill? (Mini me from Austin Powers)

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Bone Collector Three-Act Task Standards addressed: 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

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Ratio and Proportions across grades: 6 th grade: Understand ratio concepts and use ratio reasoning to solve problems. 7 th grade: Analyze proportional relationships and use them to solve real-world and mathematical problems. 8 th grade: Understand the relationships between proportional relationships, lines, and linear equations.

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Three Act Task Act 1: Show students a video or picture that will “hook” them Pose the question for the lesson. Avoid using content “language” or vocabulary Possible questions to get students thinking: What do you notice in the video/ photograph? What’s your guess? What is a guess that is way to high? Too low? What questions do you have?

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Three-Act Task cont’d Act 2: Ask: What information do you need to answer the question? Students begin gathering information and/ or tools to answer the question Remember: Do not give students information, resources, or tools until they realize they need it and ask for it The teacher serves as a resources and supports the students thinking as they work

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Three-Act Task cont’d Act 3: Students are provided the answer Discuss answers that were too high/ too low Ask students what information they needed but did not have and what information they had but did not need Have students create a title for the lesson that relates to the math used Make sure the students know what was intended to be learned

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Three-Act Task cont’d Sequel: Pose a question for the students that extends the learning

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Other Three Act Tasks threeacts.mrmeyer.com robertkaplinsky.com/lessons/ http://mr-stadel.blogspot.com/p/3-act- catalog_17.html http://mr-stadel.blogspot.com/p/3-act- catalog_17.html http://wyrmath.wordpress.com (Would you Rather?) http://wyrmath.wordpress.com

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Arkansas Department of Education Heather Hardin Office of Professional Development Director: Kevin Beaumont 501-682-4232 Anthony Owen Office of Curriculum & Instruction Director: Stacy Smith 501-682-7442

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