1 ACROSS GRADE COHERENCE IN GRADES 35 Welcome Back 2 ACROSS GRADE COHERENCE IN GRADES 35 Thank You for Your Feedback 3 Take responsibility for yourself as a learner Honor timeframes start end and activity ID: 783531
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Slide1
July 2018
Across Grade Coherence and Instructional Practice in Grades 3–5
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Slide2ACROSS GRADE COHERENCE IN GRADES 3–5Welcome Back!
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Slide3ACROSS GRADE COHERENCE IN GRADES 3–5Thank You for Your Feedback!
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Slide4Take 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.ACROSS GRADE COHERENCE IN GRADES 3–5
Norms That Support Our Learning4
Slide5ACROSS GRADE COHERENCE IN GRADES 3–5
This WeekDayIdeas
Monday
Focus and Within Grade Coherence
Tuesday
Rigor and the
Mathematical Practices
Wednesday
Across
Grade
Coherence and Instructional Practice
Thursday
Adaptation
and
Curriculum Study
Friday
Adaptation and Practice
“Do the math”
Connect to our practice
5
Equity
for
all
Slide6ACROSS GRADE COHERENCE IN GRADES 3–5
TodayMorning: Across Grade Coherence in Grades 3–5Afternoon: Instructional Practice in Grades 3–56
Slide7ACROSS GRADE COHERENCE IN GRADES 3–5
Morning ObjectivesParticipants 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.
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Slide8ACROSS GRADE COHERENCE IN GRADES 3–5
Morning AgendaAcross Grade CoherenceVertical Coherence ChallengeMapping the ProgressionsTools for Understanding the ProgressionsAdapting Lessons for Students Below Grade Level8
Slide9ACROSS GRADE COHERENCE IN GRADES 3–5
Unpacking Equity9Equity exists when the biases derived from dominant cultural norms and values no longer predict or influence how one fares in society. Equity systematically promotes fair and impartial access to rights and opportunities. Equity may look like adding supports and scaffolds that result in fair access to opportunities or creating opportunities for all voices to be heard.
Educational Equity ensures that all children—regardless of circumstances—are receiving high-quality, grade-level, and standards-aligned instruction with access to high-quality materials and resources.We become change agents for educational equity when we acknowledge that we are part of an educational system that holds policies and practices that are inherently racist and that we have participated in this system. We now commit to ensuring that all students, regardless of how we think they come to us, leave us having grown against grade-level standards and confident in their value and abilities.
Slide10ACROSS GRADE COHERENCE IN GRADES 3–5 I. Across Grade Coherence
10How would a student explain why is equal to ?
Slide11Grade 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 3Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Grade 5Interpret 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.
ACROSS GRADE COHERENCE IN GRADES 3–5 What Is the Right Order?11
Slide12“
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 PanelACROSS GRADE COHERENCE IN GRADES 3–5 Coherence Is Key
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Slide13ACROSS GRADE COHERENCE IN GRADES 3–5
The Progressions13
Slide14Across Grade Coherence:
Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years.
Slide15In 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?ACROSS GRADE COHERENCE IN GRADES 3–5II. Vertical Coherence Challenge15
Slide16ACROSS GRADE COHERENCE IN GRADES 3–5
A Picture of Coherence
Grade 2Grade 3
Grade 4Grade 5
A
16
K
D
G
I
F
E
C
H
B
J
2.G.A.3
3.NF.A.3
5.NF.A.1
5.NF.A.2
4.NF.C.5
4.NF.A.1
4.NF.A.2
4.NF.B.3
3.NF.A.1
3.NF.A.2
2.MD.B.6
Slide17ACROSS GRADE COHERENCE IN GRADES 3–5Progressions of Content
17How does understanding the progression of content support our understanding of grade-level content?
Slide18Protocol:
Identify three prerequisite standards—the standards do not have to be in three 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?
ACROSS GRADE COHERENCE IN GRADES 3–5III. Standards Mapping18
The Standards: Grade 3 – 3.OA.A.2
Grade 4 – 4.OA.A.3 Grade 5 – 5.NBT.B.7
Slide19Interpret 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.ACROSS GRADE COHERENCE IN GRADES 3–5Grade 3—3.OA.A.2191.OA.D.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. 2.OA.C.4Use 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.3.OA.A.1Interpret products of whole numbers, e.g., interpret 5 X 7as the total number of objects in 5 groups of 7 objects each.
Slide20Solve 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.
ACROSS GRADE COHERENCE IN GRADES 3–5Grade 4—4.OA.A.3204.OA.A.2Multiply 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.8Solve 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- andtwo-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 equationswith a symbol for the unknown number to represent the problem.
Slide21Add, 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.
ACROSS GRADE COHERENCE IN GRADES 3–5Grade 5—5.NBT.B.7214.NBT.A.1Recognize 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.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.4.NBT.B.5Multiply 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.
Slide22Break
Slide23ACROSS GRADE COHERENCE IN GRADES 3–5IV. Understanding the Progressions
23The Progressions DocumentsWiring DiagramContent Guides
Slide24ACROSS GRADE COHERENCE IN GRADES 3–5Understanding the Progressions
24How does understanding the progressions support instruction?
Slide2525
ACROSS GRADE COHERENCE IN GRADES K-2 Leveraging the Progressions25
How can we leverage progressions of content to give all students access to grade-level content?
Slide26ACROSS GRADE COHERENCE IN GRADES 3–5
V. Adapting Lessons for Students Below Grade Level26Protocol: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.
Slide27ACROSS GRADE COHERENCE IN GRADES 3–5
Lesson Adaptations27What 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.
Slide28Protocol:
10 min: Individual work time15 min: Partner work10 min: Table share outACROSS GRADE COHERENCE IN GRADES 3–5 Adapting Lessons for Students Below Grade Level28Goals 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?
Slide29ACROSS GRADE COHERENCE IN GRADES 3–5
Adapting Lessons for Students Below Grade Level29Protocol: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.
Slide30Transition to Partner Time!
30Transition to Partner Time!
Slide31ACROSS GRADE COHERENCE IN GRADES 3–5
Adapting Lessons for Students Below Grade Level31Protocol: 10 min: Individual work time15 min: Partner work10 min: Table share outGoals 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.
Slide32ACROSS GRADE COHERENCE IN GRADES 3–5
Adapting Lessons for Students Below Grade Level32Protocol: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.
Slide33Transition to Table Share!
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Slide34ACROSS GRADE COHERENCE IN GRADES 3–5
Adapting Lessons for Students Below Grade Level34Protocol:10 min: Individual work time15 min: Partner work10 min: Table share outGoals for This Activity:Each pair shares out the specific adaptations made and
explains why these adaptations were made.
Slide35ACROSS GRADE COHERENCE IN GRADES 3–5
Adapting Lessons for Students Below Grade Level35Protocol: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.
Slide36ACROSS GRADE COHERENCE IN GRADES 3–5
Adapting Lessons for Students Below Grade Level36What grade-level standard does the lesson address? What is the evidence of alignment to this standard?What are the prerequisite standards from prior grades that support this standard?
Brainstorm
ways you could use these prerequisites to support students below grade level with accessing the content of this lesson.
Annotate the lesson with specific supports.
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ACROSS GRADE COHERENCE IN GRADES 3–5 SummaryWhat 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?How does this learning apply to your specific role?
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ACROSS GRADE COHERENCE IN GRADES K-2 Lunch 12:00-1:0038
Lunch 12:00–1:00
Slide39INSTRUCTIONAL PRACTICE IN GRADES 3–5
TodayMorning: Across Grade Coherence in Grades 3–5Afternoon: Instructional Practice in Grades 3–539
Slide40INSTRUCTIONAL PRACTICE IN GRADES 3–5
Afternoon ObjectivesParticipants 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.
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Slide41Intro to the Instructional Practice Guide (IPG)
Core Actions in Action!Lesson Planning with the IPGConnect to PracticeINSTRUCTIONAL PRACTICE IN GRADES 3–5 Afternoon Agenda41
Slide42INSTRUCTIONAL PRACTICE IN GRADES K-2
Instructional Practice
...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)
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Slide43INSTRUCTIONAL PRACTICE IN GRADES 3–5
I. 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.
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Slide44INSTRUCTIONAL PRACTICE IN GRADES 3–5
Core Actions
Ensure the work of the lesson reflects the Shifts required by the State Standards 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.
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Slide45INSTRUCTIONAL PRACTICE IN GRADES 3–5
Core Action 1
IndicatorsThe 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.
Ensure the work of the lesson reflects the Shifts required by
the
State Standards
for Mathematics.
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Slide46INSTRUCTIONAL PRACTICE IN GRADES 3–5
Core Action 2Employ 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.
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Slide47INSTRUCTIONAL PRACTICE IN GRADES 3–5
Core Action 3
IndicatorsThe 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.
Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson.
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Slide48The 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. INSTRUCTIONAL PRACTICE IN GRADES 3–5
Core Action 3—Indicators (cont’d)48
Slide49INSTRUCTIONAL PRACTICE IN GRADES 3–5
Deeper Dive with the IPGSmall Group ProtocolRead 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?49
Slide50INSTRUCTIONAL PRACTICE IN GRADES 3–5
Deeper Dive with the IPGTable Discussion ProtocolTurn 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?
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Slide51INSTRUCTIONAL PRACTICE IN GRADES 3–5
Deeper Dive with the IPGWhole Group Discussion ProtocolHow 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?
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Slide52Useful 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.INSTRUCTIONAL PRACTICE IN GRADES 3–5 IPG Summary
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Slide53What Core Actions are visible?
INSTRUCTIONAL PRACTICE IN GRADES 3–5
II. Core Actions in Action!
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Slide54Break
Slide55INSTRUCTIONAL PRACTICE IN GRADES 3–5
III. Lesson Planning with the IPG55How can we use the Core Actions and indicators?Planning Evaluating Reflecting
Slide56INSTRUCTIONAL PRACTICE IN GRADES 3–5
Lesson Planning
The Core Actions should be evident in planning and observable in instruction.
What parts of the lesson plan are vital
to show evidence of Core Action 1? Annotate the lesson to show these.
What are some of the things you could do to ensure alignment with the indicators for Core Actions 2 and 3
?
What to Review:
Grade 3, Module 5, Lesson 2
Grade 4, Module 5, Lesson 2
Grade 5, Module 3, Lesson 2
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Slide57INSTRUCTIONAL PRACTICE IN GRADES 3–5Example: Grade 3, Module 5, Lesson 5
The lesson emphasizes conceptual understanding, the aspect of rigor associated with 3.NF.A.1 (CA.1.C).Follow by projecting different models to check for understanding. Reteach as needed (CA.2.D).Summarize or have students summarize what it means to have equal parts (CA.2.E).57
Slide58INSTRUCTIONAL PRACTICE IN GRADES 3–5
Lesson Planning58Protocol: 15 min: Individual work time10 min: Small group collaboration15 min: Table share outGoals for This Activity:Read the lesson.Annotate the lesson for your Core Action.
What parts of the lesson plan are vital to show evidence of
Core Action 1?
What are some of the things you could do to ensure alignment with the indicators for Core Actions 2 and 3?
Slide5959
Transition to Small Group Time!59
Slide60INSTRUCTIONAL PRACTICE IN GRADES 3–5
Lesson Planning60Protocol: 15 min: Individual work time10 min: Small group collaboration15 min: Table share outGoals for This Activity:Share how you annotated the task with your group.
Slide61Transition to Table Share!
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Slide62INSTRUCTIONAL PRACTICE IN GRADES 3–5
Lesson Planning62Protocol: 15 min: Individual work time10 min: Small group collaboration15 min: Table share outGoals for This Activity:Share your annotations with the people at your table.
Discuss and record:What kinds of evidence supported the indicators for CA 1?What kinds of actions did you add to support CA 2?
What kinds of actions did you add to support CA 3?
Slide6363
Slide64INSTRUCTIONAL PRACTICE IN GRADES 3–5IV. Lesson
Planning64Protocol:Annotate your lesson for each Core Action:What is the evidence of alignment to Core Action 1? How can you improve alignment to Core Action 1?What are some of the things you could do to ensure alignment with the indicators for Core Action 2?What are some of the things you could do to ensure alignment with the indicators for
Core Action 3?
Slide65INSTRUCTIONAL PRACTICE IN GRADES 3–5Summary
65How will the Core Actions impact your work with creating and/or coaching around lesson plans, and ensuring equitable instruction for all students?How has your thinking changed about lesson planning?How have the Shifts impacted your approach to instruction?
Slide66INSTRUCTIONAL PRACTICE IN GRADES 3–5
HomeworkTo prepare for the work we will do tomorrow and Friday: Read Understanding Language- Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Located in materials for Thursday, on the Standards Institutes website: standardsinstitutes.org Think about a possible problem of practice that you are struggling with related to the content we have covered this week, that you would want to problem solve on Friday. Share this problem of practice with me today before you leave. The Problem of Practice Q&A will take place Friday afternoon. 66
Slide67Feedback
Please fill out the survey located here: www.standardsinstitutes.org.Click “Summer 2018” on the top of the page.Click “Details” on the center of the page.66
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