Module 6A for Elementary Teachers Florida Standards for Mathematics: Focus on Content Standards

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    24-Dec-2015

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  • Module 6A for Elementary Teachers Florida Standards for Mathematics: Focus on Content Standards
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  • 2
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  • Professional Development Session Alignment Set 1 Governing Board School Leaders Module 6 Florida Standards Math Module 7 ELA & Data Use Teachers Math Leadership Teams Session 2 Session 2 Session 1 Session 1 ELA Data Use ELA Math Data Use 3
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  • Professional Development Session Alignment Set 2 Governing Board School Leaders Module 5 Florida Standards ELA Module 6 Florida Standards Math Module 7 ELA & Data Use Module 8 Math & Data Use Teachers Math Leadership Teams Session 4 Session 4 Session 3 Session 3 ELA Data Use Assessments Data Analysis VAM Data Analysis VAM Florida Standards Data & ELA Data & ELA Data & Math Data & Math Session 5 Session 5 Session 6 Session 6 4
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  • Module 5 ELA Module 6 Math Module 7 ELA & Data Use Module 8 Math & Data Use You Are Here Module 2 ELA Module 1 Data Use Module 4 Data Use Module 3 Math
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  • 6 8 Components of Full Florida Standards Implementation
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  • Learn more about the Practice Standards Examine the language and structure of the Florida Standards for Math Content Create and solve standards-based tasks Observe Florida Standards for Math-aligned instruction Share implementation successes and challenges and plan next steps Focus on Content Standards Outcomes 7
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  • Welcome and Introductions Pre-Assessment Sharing Implementation Experiences The Language of the Content Standards The Progression of Mathematical Concepts Lunch Meeting the Expectations of the Content Standards by Teaching with High Level Tasks Teaching the Content Standards Through Problem Solving Next Steps Post-Assessment Wrap Up Todays Agenda 8
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  • Pre-Assessment Introductory Activity 9 Guide Page 3
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  • Sharing Implementation Experiences Section 1 10
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  • Instructional Shifts for Mathematics 11 The Standards for Mathematical Content The Standards for Mathematical Practice Focus Coherence Rigor Two Areas
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  • Fewer standards allow for focusing on the major work for each grade Focus 12
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  • The Standards are designed around coherent progressions and conceptual connections. Coherence Grade 1 Grade 2Grade 3 Use place value understanding and properties of operations to add and subtract Use place value understanding and properties of operations to add and subtract fluently Use place value understanding and properties of operations to perform multi-digit arithmetic 13
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  • The Florida Standards for Math are designed around coherent progressions and conceptual connections. Coherence Math Concept Progression K-12 All Roads Lead to Algebra 14
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  • The major topics at each grade level focus equally on: Rigor CONCEPTUAL UNDERSTANDING More than getting answers Not just procedures Accessing concepts to solve problems CONCEPTUAL UNDERSTANDING More than getting answers Not just procedures Accessing concepts to solve problems PROCEDURAL SKILL AND FLUENCY Speed and accuracy Used in solving more complex problems Comes after conceptual understanding PROCEDURAL SKILL AND FLUENCY Speed and accuracy Used in solving more complex problems Comes after conceptual understanding APPLICATION OF MATHEMATICS Using math in real- world scenarios Choosing concepts without prompting APPLICATION OF MATHEMATICS Using math in real- world scenarios Choosing concepts without prompting 15
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  • The Standards for Mathematical Practice Developing Mathematical Expertise 16 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning
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  • Activity 1: Sharing Experiences Implementing Math Practice Standards 17 Sharing Implementation Experiences 1.Each participant will discuss with their table group one positive highlight, one challenge, and one lesson learned from their personal implementation of the Practice Standards thus far. 2.Each table group will then determine two positive highlights, one common challenge, and one common lesson learned that they will present to the larger group. 3.Participants will record notes and New Ideas generated from the discussion. Guide Pages 8-9 Positive Highlights Challenges Lessons Learned Guide Pages 5-6
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  • The Language of the Mathematical Content Standards Section 2 18
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  • Activity 2: What Do These Students Understand? Part 1 19 What Do These Students Understand? Part 1 1.Read and analyze the Who Knows Math handout on page 8 in the Participant Guide. Record your observations on what these students know and what they can do on page 9 in the Participant Guide. 2.Would you be comfortable with his/her understanding if s/he continued to approach division in his/her particular way? Explain your reasoning. Guide Pages 8-9 Guide Pages 8-9
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  • The major topics at each grade level focus equally on: Rigor CONCEPTUAL UNDERSTANDING More than getting answers Not just procedures Accessing concepts to solve problems CONCEPTUAL UNDERSTANDING More than getting answers Not just procedures Accessing concepts to solve problems PROCEDURAL SKILL AND FLUENCY Speed and accuracy Used in solving more complex problems Comes after conceptual understanding PROCEDURAL SKILL AND FLUENCY Speed and accuracy Used in solving more complex problems Comes after conceptual understanding APPLICATION OF MATHEMATICS Using math in real- world scenarios Choosing concepts without prompting APPLICATION OF MATHEMATICS Using math in real- world scenarios Choosing concepts without prompting 20
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  • 21 Guide Pages 10-11 Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. (Adding it Up: Helping Children Learn Mathematics. 2001) Conceptual Understanding
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  • 22 Example Question: What is 20 + 70? Student Response: 20 is 2 tens and 70 is 7 tens. So, 2 tens and 7 tens is 9 tens. 9 tens is the same as 90. Conceptual Understanding
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  • 23 Example Question: What is 5 + 6? Student Response: I know that 5 + 5 = 10; since 6 is 1 more than 5, then 5 + 6 much be 1 more than 10. 1 more than 10 is 11. Conceptual Understanding
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  • 24 Example Question: Why is 7 an even or odd number? Explain how you know. Student Response: 7 is odd because I cannot make pairs with all of the cubes like I can with 8 cubes. When I can make pairs with all of the cubes it is an even number. Conceptual Understanding
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  • 25 Procedural skill and fluency is demonstrated when students can perform calculations with speed and accuracy. (Achieve the Core) Fluency promotes automaticity, a critical capacity that allows students to reserve their cognitive resources for higher-level thinking. (Engage NY) Procedural Skill and Fluency
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  • Check all the equations that are true. 8 x 9 = 81 54 9 = 24 6 7 x 5 = 25 8 x 3 = 4 x 6 49 7 = 56 8 26 Mariana is learning about fractions. Show how she can divide this hexagon into 6 equal pieces. Write a fraction that shows how much of the hexagon each piece represents. Adding / subtracting with tens [Ask orally] (a) Add 10 to 17 (b) Add 10 to 367 (c) Take 10 away from 75 (d) Take 10 away from 654 Procedural Skill and Fluency
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  • 27 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. (Frieda & Parker, 2012) (Achieve the Core, 2012) Application of Mathematics
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  • 28 There are 9 cookies left in the pan. Five students want to share the cookies equally. How many cookies will each student get? (Investigations Grade 3 Unit 7, Session 1.5) Application of Mathematics Example
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  • 29 5.MD Minutes and Days What time was it 2011 minutes after the beginning of January 1, 2011? (Illustrative Mathematics) Example Application of Mathematics
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  • Activity 2: What Do These Students Understand? Part 2 30 What Do These Students Understand? Part 2 Return to the Who Knows Math handout on pages 8-9 in the Participant Guide. Which students have shown conceptual understanding, which have shown procedural skill and fluency, which have shown both, and which pieces of work would you need to know more to make the determination? Guide Pages 8-9
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  • Mathematics Fluency: A Balanced Approach 31 Watch Video
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  • How does the approach of the Florida Standards for Math Content differ from previous approaches to mathematics teaching and learning? Think About It 32
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  • Lets Take A Break 33 Be back in 15 minutes
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  • The Prog

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