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Then: Please sit by grade level
As you enter: Place a post-it on your grade-level chart to indicate which chapter you are currently teaching.
Context for Today’s Work:
Session 1 Implementation
Essentials
Session 2 Understanding the Parts of a Go Math
Lesson & ThinkCentral
Session 3 Chapter-level
Planning
Session 4 Assessment
Developing a chapter-level view of content.
Using that view to inform lesson-level
decision making.
Session Goals
As a result of this session, you will:
Develop an understanding of how models are used to support students’ conceptual understanding across the lessons of a chapter. Understand how key mathematical concepts develop over time within a grade and across grades. Be able to use your understanding of chapter goals to inform your instructional decisions and lesson-level planning.
Agenda Overview
Activity One - Taking a Chapter-Level View on Planning a) Performance Tasks
b) Teaching for Depth c) Show What You Know d) Selected problems across the chapter
Activity Two - Using Chapter-Level understanding to Plan Individual Lessons Activity Three – Practice Sharing
Furthering Your Learning:
Your level of experience: Some next places to look…
NYC Go
Math!
Portal
NYC Go Math!
eLearning
NYC Go Math!
Webinar Series
HMH
Collaboration
Attend a live
General Session…
Register at: hmhgomathgeneralsession4
.eventbrite.com
If you’re NEW to Go Math!...
If you’re familiar with Go Math!
but need more help to develop
your teaching routines or with a
specific area of practice…
If you’re proficient with Go Math
and are looking to fine-tune your
teaching and share your
experience…
Consider
joining the
Curriculum
Team and
your school
View PD
Video/
Podcasts on
ThinkCentral
Attend a live
Curriculum Team
Session…
Register at: hmhgomathcurriculumteam
session4.eventbrite.com
Give One, Get One
• Respond to each of the 4 questions on
the top half of your handout.
• Get up – move around – and GIVE a
response and GET a response for each
question, each from different people in
the room.
What • Think about a chapter with the end in mind by looking
closely at the end-of-chapter performance task
• Review the chapter “front matter” to identify what prior knowledge is presumed, what Common Core Standards are being addressed, and what research says about how students learn the content
• Work through the “Unlock the Problems”, “Investigations”, “Model and Draw”, and/or “Listen and Draw” problems from a chapter to understand the instructional models and how they develop across the chapter
• Dig into specific lessons and consider the instructional decisions that need to be made
Why
• Understanding models and connecting them to procedures is critical in Go Math!
• Models support students’ development of mathematical understandings
• Concepts and skills build within a unit and across grades in domains, so it’s important to understand where models and lessons build to
Step 1: Do the Performance Task Step 2: Review the Standards and Implementation Notes
Examining Performance Tasks Beginning with the end in mind
Step 3: Share your work with your table, and respond to the first reflection question on your Chapter Level Overview Reflection Sheet
Examining Performance Tasks Beginning with the end in mind
Examining Performance Tasks Reflection Questions
What do students need to know and be able to do to successfully complete the performance task? Additional question for consideration: What are the different ways that this task was completed by your tablemates?
Teaching for Depth
Step 1: Read “Teaching for Depth” Step 2: Respond to Reflection Question
Summarize the big ideas before digging into the chapter
Chapter Reflection Sheet Question: What important information about the chapter is shared on
the “Teaching for Depth” page?
Teaching for Depth
Step 1: Read “Teaching for Depth” Step 2: Respond to Reflection Question Step 3: Talk to Tablemates
Summarize the big ideas before digging into the chapter
Chapter Reflection Sheet Question: What important information about the chapter is shared on
the “Teaching for Depth” page?
Teaching for Depth---Share
Step 1: As a grade level team identify one important thing to share with the whole group from this page The individual closest to the door will share the table’s response with the whole
Summarize the big ideas before digging into the chapter
Show What you Know
Step 1: Review Show What you Know page Step 2: Respond to the reflection question
Understand the prerequisite skills demonstrated and be able to prioritize intervention accordingly.
Show What you Know
Chapter Reflection Sheet Question: What important skills and understandings
are checked for in the “Show What You Know”?
Understand the prerequisite skills demonstrated and be able to prioritize intervention accordingly.
Step 1: Review Show What you Know page Step 2: Respond to the reflection question
Selected Problems from Lessons
To learn about the progression of mathematical ideas, use of models, and introduction of strategies over the course of this chapter, we are going to do some of the math from each lesson.
CHAPTER REFLECTION SHEET QUESTIONS: How do the models, tasks and ideas build across the chapter?
Step 1: Solve all problems in packet
Step 2: Respond to the first reflection question on the Chapter Level Overview Reflection Sheet
Selected Problems from Lessons
CHAPTER REFLECTION SHEET QUESTIONS: How do they support students in meeting the expectations of the CCLS?
Step 3: Read the CCLS that apply to this chapter
Step 4: Respond to second reflection question on the Chapter Level Overview Reflection Sheet Step 5: Talk about your responses
Selected Problems from Lessons
Reflect on the big picture of chapter
CHAPTER REFLECTION SHEET QUESTION: Identify one thing you learned (about the math or
how it is taught) as you surveyed the chapter.
Consolidate what you’ve learned about this chapter
Step 1: Respond to the reflection question on the organizer Step 2: Share with your tablemates
Reflect on the big picture of chapter
CHAPTER REFLECTION SHEET QUESTION: Identify one thing you learned (about the math or
how it is taught) as you surveyed the chapter.
Consolidate what you’ve learned about this chapter
Step 1: Respond to the reflection question on the organizer Step 2: Share with your tablemates Step 3: Room Level Share
Thinking about Grade 2, Lesson 6.1
45
This is the FIRST lesson of Chapter 6. The goal of this lesson is to reinforce the representation of 3-digit numbers with quick pictures and to use those pictures to model adding hundreds to hundreds, tens to tens, and ones to ones. It builds on the work we did representing 2-digit addition and subtraction. In this lesson, I want to make sure my students have a solid understanding of these representations.
Thinking about Grade 2, Lesson 6.1 (continued)
46
I will arrange the blocks for 46 so that the ones and tens are mixed around. I want to see if my students are holding on to the value of each block, not just counting how many blocks. When they share their quick pictures, we’ll count out loud together to check them. Tens by ten and ones by one 10, 20, 30, 40 and 1, 2, 3, 4, 5, 6.
Thinking about Grade 2, Lesson 6.1 (continued)
47
I want to reinforce how this model represents numbers into the hundreds, so I’m going to expand on the first question offered in the teacher’s edition. I’ll circle the 2 in 234, and ask “In 234, what does the 2 stand for?” 200 “So which part of my quick picture should I trace to show 200?” …I’ll continue with the 3 and the 4 in 234 and the 1, 4 and 1 in 141 The quick pictures are very close together on this page, so I will use blue to trace 234 and red to trace 141. I’ll circle the totals of hundreds, tens and ones with black.
Thinking about Grade 2, Lesson 6.1 (continued)
48
I already have a sense of who needs extra support from reviewing the Show What You Know , and I will use the Quick Check to decide who I will pull into a small group for Tier 1 RTI while the rest of the class continues with the On Your Own problems.
Thinking about Grade 3, Lesson 8.6
50
This lesson addresses an important standard in third grade. In particular, we’re focusing on expressing whole numbers as fractions and recognizing when fractions are equivalent to whole numbers. Now, I wonder if this essential question is the right one for my class and my students. I’ll come back to that question in a bit.
Thinking about Grade 3, Lesson 8.6 (continued)
51
While it’s a challenge to pace my Go Math! lessons, I know how important it is to provide periodic practice with previously learned concepts and skills. So, I’m going to do the spiral review. I’ll want to make this a quick activity—no more that 5 minutes—at the beginning of the day or right before I start my lesson.
Thinking about Grade 3, Lesson 8.6 (continued)
52
So students have used a rectangular area model with a number line. Now they’re using circular area models. I think this is going to be hard for some of my students, so I’m going to make fraction circle manipulatives available as a support.
Thinking about Grade 3, Lesson 8.6 (continued)
53
I know this is going to be really important to emphasize, so I’ll make sure to ask this question. I’m also going to ask for a volunteer to identify another whole number that can be represented as a fraction, and have students use their whiteboards to represent it with fraction circles.
Thinking about Grade 3, Lesson 8.6 (continued)
54
I’m going to capture students’ performance on these two questions on sticky labels during class. In particular, I want to know which of my students are able to rename the fraction as a whole number (#8) and which of my students are able to rename a whole number as a fraction (#11). I’ll use this assessment data in the moment and as I plan for future lessons.
Get to know one lesson in depth
Step 1: Decide who will review each of the prioritized lessons
K- 6.1, 6.2, 6.4, 6.6 1st-6.4, 6.5, 6.7, 6.8, 2nd-6.2, 6.5, 6.7, 6.10 3rd- 8.1, 8.2, 8.3, 8.4 4th- 8.1, 8.2, 8.3, 8.4 5th- 7.3, 7.5, 7.6, 7.7
To understand how models, problem structures, problem sequencing, questioning and math talk come together to further student understanding over the course of a lesson.
Goalofthelesson:
Whatistheheartofthislesson?
ModelsandRepresenta ons:
Whatmodels/representa onsareusedin
thislesson?
Howdotheysupportlearning?
DoingtheMath:
Whatproblems/exampleswouldyouwant
topriori zeinthislesson?
Whatwouldbechallengingforyourstudents?Whatstrategieswouldhelptosolvetheseproblems?
Assessment:
Whatinforma onwouldyouwantto
collecttoinformyourviewofhow
studentsaremakingsenseofthecontent?
Howwouldyoucapturethatdata?
Differen a on:Inwhatwaysmightyoudifferen atethislessonforthepar cularneedsofyourstudents?(e.g.,ELLs,SWDs,etc.)
Whatdecisionswouldyoumakeandwhatresourceswouldyouuse?
IndividualLesson-LevelReflec onSheet
Get to know one lesson in depth
Step 2: Review your lesson in the TE of your focus chapter Step 3: Respond to the questions on the Individual Lesson Level reflection sheet
To understand how models, problem structures, problem sequencing, questioning and math talk come together to further student understanding over the course of a lesson.
Goalofthelesson:
Whatistheheartofthislesson?
ModelsandRepresenta ons:
Whatmodels/representa onsareusedin
thislesson?
Howdotheysupportlearning?
DoingtheMath:
Whatproblems/exampleswouldyouwant
topriori zeinthislesson?
Whatwouldbechallengingforyourstudents?Whatstrategieswouldhelptosolvetheseproblems?
Assessment:
Whatinforma onwouldyouwantto
collecttoinformyourviewofhow
studentsaremakingsenseofthecontent?
Howwouldyoucapturethatdata?
Differen a on:Inwhatwaysmightyoudifferen atethislessonforthepar cularneedsofyourstudents?(e.g.,ELLs,SWDs,etc.)
Whatdecisionswouldyoumakeandwhatresourceswouldyouuse?
IndividualLesson-LevelReflec onSheet
Share lesson-level insights with group
Step 1: Review notes and prepare to share with your colleagues Step 2: Participants share for 5 minutes the important insights they gained and responds to questions from their tablemates Step 3: Record lesson level information on Group Reflection Sheet
To understand more of the unit deeply and to share teaching insights with colleagues focused on the same grade.
LessonNumber ThingstoRemember
GroupReflec onSheetforconnec ngmul plelessonreviews
Thisorganizerwillbeusedbyagroupofpar cipantswhoworkedondifferentlessonsfromthesamegradeleveltocapturetheir
insightsabouttheclusteroflessons.
Group
Reflection
Sheet
Each grade-level group
share one thing you are taking away from the chapter-level review
Please write one thing that you are taking away about the work at your grade level today.
Room-Level Share
Write---On your Give One Get One form: Please write one thing that you are taking away about the work at your grade level today. Aloud Share with the Room----What insights did you gain about teaching the content of this chapter?