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Learning Goals • Increase knowledge of the Standards for Mathematical Practices • Unpack the Common Core Standards using Unpacking Standards Graphic Organizer Success Criteria • Identify the Eight Mathematical Practices in a lesson • Unpack Common Core Standards using the Unpacking Document
“Good Math Students” Think about a few students who are “really good” in math. • How do they approach problems? • How do they solve problems? • How do they discuss their strategies? “Common Core will have kids thinking out loud, discussing solutions with each other, and explaining their answers.” -Stateimpact.npr.org/florida/2013
Standards for Mathematical Practice • What are they? • What do they look like in a K-5 classroom?
Do You Know The Mathematical Practices? INDIVIDUALLY: Take a moment and jot down the Mathematical Practices on the sticky note provided.
Do You Know The Mathematical Practices? WITH A PARTNER: Pair-Share: Share with your partner the list you wrote down. Compare your lists.
Do You know The Mathematical Practices? Rate Yourself What is your knowledge of the Mathematical Practices today? Place your sticky on the scale.
Do You Know The Mathematical Practices? Progression Scale Level 4- I can state all 8 Mathematical Practices and I use them daily in my classroom. Level 3- I can state all 8 Mathematical Practices and I may use them in my classroom. Level 2- I can state half of the Mathematical Practices. Level 1- I can state 2 of the Mathematical Practices. Level 0- What is a Mathematical Practice?
Standards for Mathematical Practice Mathematical Practices 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.
Standards for Mathematical Practice The Standards for Mathematical Practices describe the behaviors of mathematically proficient students.
Structure of Standards • Standards for Mathematical Practice A set of 8 standards that describe the ways in which the mathematical content standards should be approached. • Standards for Mathematical Content These standards define what students should understand and be able to do in their study of mathematics. “HOW” “What”
MP 1 - Make Sense of Problems and Persevere in Solving Them 2b, 3c • Make sense of the meaning of the task • Find an entry point or a way to start the task • Focus on concrete manipulatives before moving to pictorial representations • Develop a foundation for problem-solving strategies • Reexamine the task when they are stuck • Ask, “Does my answer make sense?”
What does MP 1 look like in a classroom? “Old” problem (little or no rigor) Tina had ten balloons. She gave seven of them away. How many balloons did Tina have then? “New” problem (with rigor) Burger Barn has one small table that can seat four people. They also have one large table that can seat double that amount. Fifteen (15) people came in at lunch time. How many people did not get a seat?
MP 2 - Reason Abstractly and Quantitatively 3c • Make sense of quantities and their relationships • Decontextualize • Contextualize • Represent symbolically (ie. Equations, expressions)
What does MP 2 look like in a classroom? I had two pencils. My mom gave me some more. Now I have five pencils. How many pencils did my mom give me? Decontextualize the problem: 2 + □ = 5
What does MP 2 look like in a classroom? 2 + □ = 5 Contextualize the problem: I had two pencils. My mom gave me some more. Now I have five pencils. How many pencils did my mom give me?
What does MP 2 look like in a classroom? How many buses are needed for 99 children to go on a field trip if each bus seats 44 students? 99÷44 Is the answer: 2r11 or 2¼ or 2.25? Recontextualize to get the answer: 3 buses
MP 3 - Construct Viable Arguments and Critique the Reasoning of Others 2a, 3b, 3c • Use mathematical terms to construct arguments • Use definitions and previously established solutions in their arguments • Engage in discussions about problem-solving strategies • Recognize and discuss reasonableness of strategies • Recognize and discuss similarities and differences between strategies
What does MP3 look like in a classroom? • I can make a plan, called a strategy, to solve the problems and discuss other students’ strategies too. http://insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/205-proportions-a-ratios-problem-3-part-d?
MP 4 - Model with Mathematics. 2e, 3c • Model with manipulatives and much more • Model with a number sentence or equation • Check to make sure the number sentence matches the context of their problem • Model with concrete manipulative representations • Model with pictorial representations • Have matching equations for their representations
What does MP 4 look like in a classroom? Model with Tools Model with Symbols 3 + □ = 7 I have three cars. My friend gives me some more cars. Now I have seven cars. How many toy cars did my friend give me? Model with Pictures Model with Words I have three cars. I get four more. Now I have seven cars.
MP 5 - Use Appropriate Tools Strategically 2c, 2e The purpose is to move students toward a deeper understanding of these tools. • Have access to a variety of tools (counters, place value blocks, hundred boards, number lines, geometric shapes, paper/pencil, etc…) • Need to express in their own words the “what, why, and how” to help them clarify, perfect, and organize their thinking.
What does MP 5 look like in a classroom? Students have easy access to math tools. Students select their own tools.
MP 6 – Attend to Precision 2b • Communicate precisely with teachers and peers (written and verbal) • Clearly define terms • Identify the meanings of mathematical symbols and use them appropriately • Specify units of measure
What does MP 6 look like in a classroom? How might a student explain their solution to the subtraction problem shown below? 413 -168
MP 7 - Look for and Make Use of Structure 3c • Look for patterns • Recognize mathematical structures • Generalize to other problem situations • Simplify complex problems
What does MP7 look like in a classroom? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 53 + 23 = 76 53 + 23 = ? 82 - 14 = ? 82 - 14 = 68
MP 8 - Look for and Express Regularity in Repeated Reasoning 3b • Look for regularity in problem structures when solving mathematical tasks • Maintain oversight • Check for reasonableness during and after task
What does MP 8 look like in a classroom? Doubles Plus One Decompose 7 Add the double Add one more 6 + 7 = 13 6 1 12 + 1 = 13
Identify Mathematical Practices Try to identify as many examples of the mathematical practices in action as possible as you view this video of a kindergarten class.
“If the Standards for Mathematical Practice are not in place, well then, you’re not really using the Common Core.” • – Phil Daro, Common Core author - Mathematics
Do You Know The Mathematical Practices? Rate Yourself Take a moment and jot down the Mathematical Practices on the sticky note provided. Place your sticky on the scale.
Handouts • Observing Mathematical Practices in a Classroom • Questions to Develop Mathematical Thinking correlated to the SMP • SMP in Student Friendly Language • SMP Unpacked by Grade Level • Depth of Knowledge Chart • 3rd Grade Quarter 1 Placemat • Unpacking Documents
Question to Ponder • What does it mean to “really understand”? • What are indicators of knowledge without understanding? • What are concrete indicators of really understanding something? • What can the person with understanding do that the person with only knowledge cannot do?
Be able to KNOW and UNDERSTAND What we want students to know What we want students to understand Decoding Computation Communication skills – listening, speaking, writing Thinking skills – compare, confer, analyze Research – inquiry, investigate • Vocabulary • Definitions • Concepts • Key facts • Critical details • Laws, formulas
Unpacking Standards 1c • Why unpack? • Standards require a close read and analyze for meaning • Standards are rarely taught in isolation • Not all standards are equal in rigor
Your turn! • Form groups with 3-5 participants in each group. • Each group will be given five 3rd grade standards from chapter1. • Each group member should unpack at least one standard. • Share your unpacked standards with your group members. • Look for similarities and/or differences in these standards. • Groups should share their discoveries.
If you find it difficult to distinguish between the “KNOW” and the “UNDERSTAND” it is likely because, as written, the learning sequence focuses only on facts and skills. -Catherine Brighton
Model for Instructional Planning • Course Descriptions • “Chunk” the standards to identify 10 to 12 critical areas of focus or big ideas. • Integrate standards across content areas as appropriate. • Learning Goals • Define 10 to 12 major learning goals based upon the “chunks” of integrated standards from the course description. • Develop learning progression scales to describe the steps students will take to attain each learning goal as well as what success looks like at each step. • Use the learning progressions to guide lesson development; include formative assessment tasks as part of the instructional plan, identify resources in advance, and incorporate the use of technology as a tool for learning when applicable. • Use the formative assessment data to revise and/or differentiate instruction as appropriate to meet the needs of ALL students. • Lesson Plans
Content Standards MACC.4.NBT.1.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. MACC.4.NBT.1.2 : Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.MAACC.4.NBT.1:3 Use place value understanding to round multi-digit whole numbers to any place.
1c Learning Goal: Students will be able to solve problems using place value understanding to read, compare, and round multi-digit numbers by: • Recognizing a digit in one place represents ten times what it represents in the place to its right. • Reading and writing whole numbers using base-ten numerals, number names, and expanded form. • Comparing two numbers based on the meaning of the digits in each place. • Using symbols to record comparisons. • Rounding whole numbers to any place using place value understanding.