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January 2018

Across Grade Coherence and Instructional Practice in Grades 3–5. January 2018. ACROSS GRADE COHERENCE IN GRADES 3–5 Welcome Back!. ACROSS GRADE COHERENCE IN GRADES 3–5 Thank You for Your Feedback!. +. ACROSS GRADE COHERENCE IN GRADES 3–5 Norms That Support Our Learning.

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January 2018

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  1. Across Grade Coherence and Instructional Practice in Grades 3–5 January 2018

  2. ACROSS GRADE COHERENCE IN GRADES 3–5Welcome Back!

  3. ACROSS GRADE COHERENCE IN GRADES 3–5Thank You for Your Feedback! +

  4. ACROSS GRADE COHERENCE IN GRADES 3–5Norms That Support Our Learning • Take responsibility for yourself as a learner. • Honor timeframes (start, end, and activity). • Be an active and hands-on learner. • Use technology to enhance learning. • Strive for equity of voice. • Contribute to a learning environment in which it is “safe to not know.” • Identify and reframe deficit thinking and speaking.

  5. ACROSS GRADE COHERENCE IN GRADES 3–5This Week “Do the math” Equity for all Connect to our practice 5

  6. ACROSS GRADE COHERENCE IN GRADES 3–5 Today • Morning: Across Grade Coherence in Grades 3–5 • Afternoon: Instructional Practice in Grades 3–5

  7. ACROSS GRADE COHERENCE IN GRADES 3–5 Morning Objectives • Participants will understand and apply learning progressions to support students who are below grade level. • Participants will be able to identify a sequence of prerequisite standards necessary in math understanding and learning. • Participants will be able to identify onramps for teaching major work to students who are below grade level. • Participants will be able to adapt a lesson for students below grade level by adding just-in-time scaffolds based on learning progressions. • Participants will be able to explain how attending to the shift of across grade coherence is an equitable practice in Standards-aligned math instruction.

  8. ACROSS GRADE COHERENCE IN GRADES 3–5 Morning Agenda • Across Grade Coherence • Vertical Coherence Challenge • Mapping the Progressions • Tools for Understanding the Progressions • Adapting Lessons for Students Below Grade Level

  9. ACROSS GRADE COHERENCE IN GRADES 3–5 Equity Equity is engaging in practices that meet students where they are and advance their learning by giving them what they need. It’s about fairness, not sameness. Equity ensures that all children—regardless of circumstances—are receiving high-quality and Standards-aligned instruction with access to high-quality materials and resources. We want to ensure that Standards-aligned instruction is a pathway to the equitable practices needed to close the gaps caused by systemic and systematic racism, bias, and poverty. All week, we will explore our learning through an equity lens, and we will capture those moments visibly here in our room. 9

  10. ACROSS GRADE COHERENCE IN GRADES 3–5 I. Across Grade Coherence How would a student explain why is equal to ?

  11. ACROSS GRADE COHERENCE IN GRADES 3–5 What Is the Right Order? Grade 4 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Grade 3 Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Grade 5 Interpret multiplication as scaling (resizing) by…relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

  12. ACROSS GRADE COHERENCE IN GRADES 3–5 Coherence Is Key “A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. By the term coherent, the Panel means that the curriculum is marked by effective, logical progressions from earlier, less sophisticated topics into later, more sophisticated ones. Improvements like those suggested in this report promise immediate positive results with minimal additional cost.” –National Mathematics Advisory Panel

  13. ACROSS GRADE COHERENCE IN GRADES 3–5 The Progressions

  14. Across Grade Coherence: Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. 

  15. ACROSS GRADE COHERENCE IN GRADES 3–5II. Vertical Coherence Challenge • In your groups, you have 11 standards on pieces of paper. Most standards come from the Number & Operations—Fractions domains in Grades 3–5. • The standards are not labeled! • Determine which standards are prerequisites for other standards. • Bonus: Can you determine which standards belong in which grade?

  16. ACROSS GRADE COHERENCE IN GRADES 3–5 A Picture of Coherence 3.NF.A.1 2.G.A.3 D A 5.NF.A.1 4.NF.A.2 4.NF.A.1 5.NF.A.2 I E C H G 3.NF.A.3 4.NF.C.5 4.NF.B.3 B J 2.MD.B.6 3.NF.A.2 F K

  17. ACROSS GRADE COHERENCE IN GRADES 3–5Progressions of Content How does understanding the progression of content support our understanding of grade-level content?

  18. ACROSS GRADE COHERENCE IN GRADES 3–5III. Standards Mapping Protocol: • Identify 3 prerequisite standards—the standards do not have to be in 3 different grades. • Identify the aspects of rigor for each prerequisite. • Discuss with a partner: • How does each prerequisite support the standard? • Why is it important to pay attention to the rigor of the prerequisite standard? The Standards: Grade 3 – 3.OA.A.2 Grade 4 – 4.OA.A.3 Grade 5 – 5.NBT.B.7

  19. ACROSS GRADE COHERENCE IN GRADES 3–5Grade 3—3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each. 2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. 

  20. ACROSS GRADE COHERENCE IN GRADES 3–5Grade 4—4.OA.A.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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. 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 3.OA.D.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. 2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

  21. ACROSS GRADE COHERENCE IN GRADES 3–5Grade 5—5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 4.NBT.A.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. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

  22. Break

  23. ACROSS GRADE COHERENCE IN GRADES 3–5IV. Understanding the Progressions Content Guides The Progressions Documents Wiring Diagram

  24. ACROSS GRADE COHERENCE IN GRADES 3–5Understanding the Progressions How does understanding the progressions support instruction?

  25. ACROSS GRADE COHERENCE IN GRADES K-2 Leveraging the Progressions How can we leverage progressions of content to give all students access to grade-level content? 25

  26. ACROSS GRADE COHERENCE IN GRADES 3–5 V. Adapting Lessons for Students Below Grade Level Protocol: • Review Lesson 1 and identify the targeted standard. • Identify the prerequisite standards from prior grades that support the targeted standard. • What is the aspect of rigor for each prerequisite? • Discuss with a partner: • How does each prerequisite support the standard? • How could you strategically use these prerequisite standards to support students who are not on grade level? • Annotate the lesson with specific supports. • With your table: • Each pair shares out the specific adaptations you and your partner made. Explain why you made these adaptations.

  27. ACROSS GRADE COHERENCE IN GRADES 3–5Lesson Adaptations What types of adaptations could you consider at the lesson level? • Add a warm-up activity that connects to prior learning. • Add a section to the concept development portion to address prerequisite skills. • Replace one or more of the fluency activities to support understanding of prerequisites.

  28. ACROSS GRADE COHERENCE IN GRADES 3–5 Adapting Lessons for Students Below Grade Level Protocol: • 10 min: Individual work time • 15 min: Partner work • 10 min: Table share out • Goals for This Activity: • Review Lesson 1 and identify the targeted standard(s). • What are the prerequisite standards from prior grades that support this standard(s)? • What aspects of rigor are highlighted in the prerequisite standards?

  29. Transition to Partner Time! Transition to Partner Time!

  30. ACROSS GRADE COHERENCE IN GRADES 3–5 Adapting Lessons for Students Below Grade Level • Goals for This Activity: • How do these prerequisite standards support the grade-level standard(s)? • How could you strategically use these prerequisite standards to support students who are not on grade level? • Annotate the lesson with specific supports. Protocol: • 10 min: Individual work time • 15 min: Partner work • 10 min: Table share out

  31. Transition to Table Share!

  32. ACROSS GRADE COHERENCE IN GRADES 3–5 Adapting Lessons for Students Below Grade Level Protocol: • 10 min: Individual work time • 15 min: Partner work • 10 min: Table share out • Goals for This Activity: • Each pair shares out the specific adaptations made and explainswhy these adaptations were made.

  33. ACROSS GRADE COHERENCE IN GRADES 3–5 Adapting Lessons for Students Below Grade Level

  34. ACROSS GRADE COHERENCE IN GRADES 3–5 Summary • What is the shift of coherence? • How does coherence help us support students below grade level? • How does rigor help us support students below grade level?

  35. ACROSS GRADE COHERENCE IN GRADES K-2 Lunch 12:00-1:00 Lunch 12:00–1:00 35

  36. INSTRUCTIONAL PRACTICE IN GRADES 3–5Today • Morning: Across Grade Coherence in Grades 3–5 • Afternoon: Instructional Practice in Grades 3–5

  37. INSTRUCTIONAL PRACTICE IN GRADES 3–5 Afternoon Objectives • Participants will be able to use the Instructional Practice Guide (IPG) as a lesson planning tool and a coaching tool. • Participants will be able to identify where, in lessons and videos, teachers engage in Core Actions. • Participants will be able to explain the relationship between Core Actions and equitable practices in Standards-aligned math instruction.

  38. INSTRUCTIONAL PRACTICE IN GRADES 3–5 Afternoon Agenda • Intro to the Instructional Practice Guide (IPG) • Core Actions in Action! • Lesson Planning with the IPG • Connect to Practice

  39. ...effective teaching is the non-negotiable core that ensures that all students learn mathematics at high levels... –Principles to Actions: Ensuring Mathematical Success for All (NCTM) INSTRUCTIONAL PRACTICE IN GRADES K-2Instructional Practice

  40. INSTRUCTIONAL PRACTICE IN GRADES 3–5I. Instructional Practice Guide (IPG) The Instructional Practice Guide includes coaching and lesson planning tools to help teachers and those who support teachers to make the Key Shifts in instructional practice required by the State Standards.

  41. INSTRUCTIONAL PRACTICE IN GRADES 3–5Core Actions • Ensure the work of the lesson reflects the Shifts required by the CCSS for Mathematics. • Employ instructional practices that allow all students to learn the content of the lesson. • Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson.

  42. INSTRUCTIONAL PRACTICE IN GRADES 3–5 Core Action 1 Ensure the work of the lesson reflects the Shifts required by the CCSS for Mathematics. Indicators • The lesson focuses on the depth of grade-level cluster(s), grade-level content standard(s), or part(s) thereof. • The lesson intentionally relates new concepts to students’ prior skills and knowledge. • The lesson intentionally targets the aspect(s) of rigor (conceptual understanding, procedural skill and fluency, application) called for by the standard(s) being addressed.

  43. INSTRUCTIONAL PRACTICE IN GRADES 3–5 Core Action 2 Employ instructional practices that allow all students to learn the content of the lesson. Indicators • The teacher makes the mathematics of the lesson explicit by using explanations, representations, and/or examples. • The teacher provides opportunities for students to work with and practice grade-level problems and exercises. • The teacher strengthens all students’ understanding of the content by sharing a variety of students’ representations and solution methods. • The teacher deliberately checks for understanding throughout the lesson and adapts the lesson according to student understanding. • The teacher facilitates the summary of the mathematics with references to student work and discussion in order to reinforce the purpose of the lesson.

  44. INSTRUCTIONAL PRACTICE IN GRADES 3–5 Core Action 3 Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson. Indicators • The teacher poses high-quality questions and problems that prompt students to share their developing thinking about the content of the lesson. Students share their developing thinking about the content of the lesson. • The teacher encourages reasoning and problem solving by posing challenging problems that offer opportunities for productive struggle. Students persevere in solving problems in the face of initial difficulty. • The teacher establishes a classroom culture in which students explain their thinking. Students elaborate with a second sentence (spontaneously or prompted by the teacher or another student) to explain their thinking and connect it to their first sentence.

  45. INSTRUCTIONAL PRACTICE IN GRADES 3–5 Core Action 3—Indicators (cont’d) • The teacher creates the conditions for student conversations where students are encouraged to talk about each other’s thinking. Students talk about and ask questions about each other’s thinking, in order to clarify or improve their own mathematical understanding. • The teacher connects and develops students’ informal language to precise mathematical language appropriate to their grade. Students use precise mathematical language in their explanations and discussions. • The teacher establishes a classroom culture in which students choose and use appropriate tools when solving a problem. Students use appropriate tools strategically when solving a problem. • The teacher asks students to explain and justify work and provides feedback that helps students revise initial work. Student work includes revisions, especially revised explanations and justifications.

  46. INSTRUCTIONAL PRACTICE IN GRADES 3–5Deeper Dive with the IPG • Small Group Protocol • Read the indicators of the Core Action for your group (pp. 5–10). • Discuss the following with your small group: • How does this Core Action (including the indicators) support teachers and coaches in building understanding of Standards-aligned instruction? • What are the essential teacher practices that support the indicators? • How does this Core Action support equitable instruction for all students?

  47. INSTRUCTIONAL PRACTICE IN GRADES 3–5Deeper Dive with the IPG • Table Discussion Protocol • Turn and teach. • Discuss the following with your table group: • How does this tool support teachers and coaches in building understanding of Standards-aligned instruction? • What are essential teacher practices that support each Core Action? • Where does each of the Standards for Mathematical Practice show up in the IPG? • How does this Core Action support equitable instruction for all students?

  48. INSTRUCTIONAL PRACTICE IN GRADES 3–5Deeper Dive with the IPG Whole Group Discussion Protocol How does this tool support teachers and coaches in building understanding of Standards-aligned instruction? Where does each of the Standards for Mathematical Practice show up in the IPG? What connections did you make between the Core Actions and equitable instruction for all students?

  49. INSTRUCTIONAL PRACTICE IN GRADES 3–5 IPG Summary • Useful in both planning and coaching. • Evidence for the indicators can come from lesson materials, teacher actions, student discussion, and student work. • When using as a coaching tool, not all indicators may be evident in a single class period. • Not to be used as an evaluation instrument.

  50. INSTRUCTIONAL PRACTICE IN GRADES 3–5II. Core Actions in Action! What Core Actions are visible?

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