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

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  • Module 6A for Elementary Teachers Florida Standards for Mathematics: Focus on Content Standards
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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 Progression of Mathematical Concepts Section 3 34
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  • 35 The Organization of the Standards Domain Cluster Standards
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  • Domain Distribution 36
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  • Domain Progression 37
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  • Gathering Momentum for Algebra 38 Watch Video
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  • Number and Operations in Base Ten Number and Operations in Fractions Counting and Cardinality & Operations and Algebraic Thinking Measurement and Data Geometry Exploring the Content Standards 39
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  • Activity 3 (part 1): Explore a Progression 40 Part 1 Examine your assigned domain and determine which standards focus on: Conceptual Understanding (CU) Procedural Skill and Fluency (PSF) Application (A) 2.NBT.1 Understand that three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g. 706 equals 7 hundreds, 0 tens, and 6 ones. K.NBT.1 Compose and decompose numbers from 11to19 into ten ones and some further ones e.g. by using objects, drawings, and record each composition or decomposition by a drawing or equation. 4.NBT.4 Fluently add and subtract multi-digit whole numbers to any place. Guide Page 13
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  • Activity 3 (part 2): Explore a Progression 41 Part 2 Examine your assigned domain across the K-5 grade band and record five general observations about the progression and two observations about the relationship between the Content and Practice Standards. 2.NBT.1 Understand that three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g. 706 equals 7 hundreds, 0 tens, and 6 ones. K.NBT.1 Compose and decompose numbers from 11to19 into ten ones and some further ones e.g. by using objects, drawings, and record each composition or decomposition by a drawing or equation. 1.NBT.2a Understand that numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Guide Pages 14-15 Guide Pages 13-14
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  • Activity 3 (part 3): Chunking the Standards 42 Part 3 Examine all of the Content Standards for your assigned grade level. Make connections across domains and create clusters that can be taught as part of a lesson or unit. 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Guide Page 15
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  • 1.What domains of the Florida Standards for Math do you think will be the most exciting and/or productive for you to teach to your students? 2. What domains of the Florida Standards for Math do you think will be the most challenging for your students to learn? Reflect 43 Guide Page 16
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  • 44 Lunch
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  • Meeting the Expectations of the Content Standards by Teaching with High Level Tasks Section 4 45
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  • Dont have a predictable, well-rehearsed approach or pathway to the solution. Require students to explore and understand the nature of mathematical concepts, processes, or relationships. Demand self-monitoring or self-regulation of ones own cognitive processes. Require students to access relevant knowledge and experiences and make appropriate use of them in working through the task. High Level Tasks 46 Guide Page 18
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  • Require students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions. Require considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required. Adapted from (Stein, Smith, et al (2000). Implementing Standard-Based Mathematics Instruction) High Level Tasks 47
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  • Math Class Needs a Makeover Dan Meyer 48 Watch Video
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  • Take a Look 49
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  • How can I incorporate high-level mathematics tasks that will benefit ALL of my students? The Big Question 50
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  • Open Questions Strategies for Differentiating High Level Tasks 51 Parallel Tasks
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  • An open question is framed in such as way that multiple responses and approaches can correctly answer the question. An open question allows students at varying developmental and readiness levels to equally participate in and grow from thought provoking tasks. An open question provides multiple pathways into the mathematics. 52 What are Open Questions?
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  • Question 1: To which fact family does the fact 3 x 4 = 12 belong? Question 2: Describe the picture below by using a mathematical equation. X X 53 (Small.2012, 7) Example of an Open Question
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  • An open question should be mathematically meaningful by focusing on the expectations of the content standards. An open question needs just the right amount of ambiguity. An open question is most effectively used when followed up by a whole class discussion in which the teacher strategically calls on students, conveys the message that multiple answers are welcomed, and builds connections between students answers. 54 Guidelines for Using Open Questions
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  • Turning Around a Question Asking for Similarities and Differences Replacing a Number with a Blank Creating a Sentence Using Soft Words Changing the Question 55 Guide Pages 19-21 Strategies for Writing Open Questions
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  • 56 Parallel Tasks are sets of tasks, usually two or three, that get at the same big idea and are close enough in context that they can be discussed simultaneously. (Small. 2012, 10) Parallel Tasks
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  • 57 Choice 1: Create a word problem that could be solved by multiplying two one-digit numbers. Choice 2: Create a word problem that could be solved by multiplying two numbers between 10 and 100. (Small. 2012, 10) Example of Parallel Tasks
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  • 58 Consider the following: Different developmental levels What operations students can use What size numbers students can handle Conceptual understandings that students have developed Creating Parallel Tasks
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  • 59 Things to Do: Create the parallel tasks Create parallel questions Manage task choice Hold a follow-up discussion Guide Pages 22-24 Implementing Parallel Tasks
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  • Activity 4: Teaching with High Level Tasks 60 Teaching with High Level tasks 1.Choose a grade level. 2.Choose which content and practice standards you want to work with. 3.Create Open Questions and one set of Parallel Tasks that can be used in your instruction of the Content Standards. 4.Write your final version of both the Open Questions and the Parallel Tasks on a piece of chart paper. Be prepared to present your ideas to the full group. Guide Pages 25-26
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  • Principles to Keep in Mind 61 1.All open questions must allow for correct responses at a variety of levels. 2.Parallel tasks need to be created with variations that allow struggling students to be successful and proficient students to be challenged. 3.Questions and tasks should be constructed in such a way that will allow all students to participate together in follow-up discussions.
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  • 1.How does teaching with high level tasks relate to conceptual understanding, procedural skill and fluency, and application of mathematics? 2. How does teaching with high level tasks support Floridas New Way of Work? Reflect 62 Guide Page 27
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  • Teaching the Content Standards Through Section 5 Problem Solving 63
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  • 64 Guide Pages 29-31 Watch Video
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  • 65 Guide Page 29-31 Watch Video
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  • Activity 5: A New Spin on Old Strategies 66 Center 1: Sample Lesson Plans Center 2: Math Journals Center 3: Concept Cards Center 4: Developing Fluency
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  • Next Steps Section 6 67
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  • 1.What do we think should happen at school to promote implementation of the Florida Standards for Math? 2.What can we do now in our classrooms and in the school to promote implementation of the Florida Standards for Math? 3.What are some expected challenges? 4.How can we work around the challenges? What's Your Plan? 68 Guide Page 33
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  • Closing Activities 69
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  • Learned more about the Practice Standards Examined the language and structure of the Florida Standards for Math Practice Created and solved standards-based tasks Observed Florida Standards for Math-aligned instruction Shared implementation successes and challenges and planned next steps Focus on Content Standards Outcomes 70
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  • Click to edit Master title style Where Are You Now? Assessing Your Learning 71 Post-Assessment and Session Evaluation Guide Page 35
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  • Module 2 ELA Module 1 Data Use Module 3 Math Module 4 Data Use Module 5 ELA Module 6 Math Module 7 ELA & Data Use Module 8 Math & Data Use Whats Next? Module 7 ELA & Data Use Module 4 Data Use
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