1. SESSION 2: Coherence Stop 2 of your instructional rounds
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Welcome!
SESSION 2: Coherence Stop 2 of your instructional rounds

2. Session 2: Coherence Goals and Purpose Participants will be able to:
Describe the coherence shift both as a logical sequencing of content across grades and important connections between standards, clusters, and domains within the grade.
1min
Here’s our objective.

3. We will study coherence to understand how:
Session 2: Coherence
We will study coherence to understand how:
the standards connect learning across grades so that students can build new understanding onto foundations built in previous years.
the standards were built and how they reinforce a major topic in a grade by utilizing supporting, complementary topics.
what it is and what it looks like.
it looks during implementation and how do we guide teacher’s growth.
1 min
The math in this session will focus on middle school standards.

4. Coherence: What and Why?
Session 2: Coherence
Coherence: What and Why?
Lena paid $18.96 for 3 pounds of coffee.
How would you teach students to graph the proportional relationship between the number of pounds of coffee and the total cost?
5 min
Ask participants how they would explain this to an 8th grader who is just beginning to relate proportional reasoning to graphing.
Responses include: teaching unit rate, teaching slope, teaching how to construct an appropriately scaled graph
Ask which one would be appropriate to teach first. (unit rate comes in 6th grade, must be a secure foundation before moving on; lines cannot be graphed before students know how to construct an appropriate scale)

5. What’s the Right Order? Session 2: Coherence Standard
Grade
Use ratio and rate reasoning to solve real-world and mathematical problems by making tables of equivalent ratios, finding missing values in tables, and plotting the pairs of values on the coordinate plane.
Graph proportional relationships, interpreting the unit rate as the slope of the graph; compare different proportional relationships in different ways.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate 6
4 min
SLIDE HAS ANIMATION
The study of mathematics rests on the idea of developing ideas from existing ones. Similarly this is how students learn; they learn mathematics based on what they already understand.
Ask participants to try to order these standards sequentially.
Share correct answer.:
A = Grade 6
B = Grade 8
C = Grade 7
Emphasize logical progression. 8 7

6. Coherence is Key Session 2: Coherence
“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.”
2 min
The idea of logical progressions of learning is an important one. This is what mathematics is: developing new ideas from existing ones.
In the Final Report of the National Mathematics Advisory Panel, this idea was highlighted.

7. The Progressions Session 2: Coherence
2 min
In fact logical progressions undergird the standards. The Progressions Documents describe the logical, gradual progression of content across grades.
These are “research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.”
Can find at achievethecore.org or any number of web sites.

8. Definition #1 – Coherence Across Grades
Session 2: Coherence
Definition #1 – Coherence Across Grades
Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. 
1 min
Coherence will have a couple of meanings for us, but one important one is about the progression of content across grades.

9. Vertical Coherence Challenge – Part 1
Session 2: Coherence
Vertical Coherence Challenge – Part 1
In your groups, you have 17 standards on pieces of paper; most come from the RP domain in grades 6-8.
They are not labeled!
Read the standards and try to determine which standards are prerequisites for other standards.
Note: There is more than one vertical strand.
Bonus: Can you determine which standards belong in which grade?
10 minutes to work with partner to get as far as you can.
10 minutes.
Can we see the vertical coherence of the standards?
Let participants know that there is more than one vertical strand. (strands are organic – a strand isn’t dictated in advance – this is basically saying there is more than one answer.)
String together standards coherently.
Share out some “pieces of the puzzle” that participants have come up with.
Link to standards doc participants will use:
See bottom of facilitator guide for “answer key.”

10. Vertical Coherence Challenge –Progression Intervention
Session 2: Coherence
Vertical Coherence Challenge –Progression Intervention
10 min
The progressions documents are an important resource to help understand the progression of learning within and across grade levels.

11. A Picture of Coherence Session 2: Coherence I D F K P C M A E B O H J
Grades 4 and 5
Grade 6
Grade 7
Grade 8
High School I
8.F.5 D
7.RP.1 F
6.RP.1 K
5.NF.5 P
8.F.2 C
4.NF.1 M
7.RP.2 A
8.EE.6 E
HS-BF.1 B
5.NF.3 O
6.RP.2 H
7.G.1 J
4.MD.2
4 min
Here is a picture of how these standards are organized by grade, as well as some logical connections between them. Discuss with a partner what connection you see between grades and standards (2 mins).
What is something you noticed about the coherence across grades?
Ideas to highlight:
While this exercise was centered in the RP domain, it’s impossible to stay there without tapping into other domains. This is the richness of the standards, and also the difficulty of teaching the standards.
Standards C, K, and F highlight how the NF domain is a foundation for proportional reasoning from grades 4-6
Standards O, M, H, A, and E illustrate how proportional reasoning (in grades 6 and 7) opens the door to geometry, expressions/equations, and functions in grades 8 and 9 Q
7.RP.3 L
6.RP.3a N
8.EE.8 G
5.G.2

12. CCSSM Wiring Diagram Session 2: Coherence 2 min
An extremely useful resource for understanding coherence is SAP’s “wiring diagram” that maps the coherence of the standards.
this document is helpful to show the different lead-ins to a particular standard; if a student is struggling with “getting it”, this document can help identify all the standards that lead into the one he’s struggling with. we're showing it now to let you know it exists and what it can help with.
We will use the notion of coherence heavily as we move throughout the week.

13. Definition #2 – Coherence within Grade
Session 2: Coherence
Definition #2 – Coherence within Grade
Coherence is also built into the standards in how they reinforce a major topic in a grade by utilizing supporting, complementary topics. 
1 min
Coherence has another meaning-- coherence within the grade.
Instead of a list of unrelated standards, content is connected across domains.

14. Grade Level Domain Cluster Standard
Session 2: Coherence What’s the Structure of the Standards?
Grade Level
Domain
MAFS.6.RP: Ratios & Proportional Relationships
Cluster
Cluster 1: Understand ratio concepts and use ratio reasoning to solve problems..
MAFS.6.RP.1.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
Standard
1 min
Quick review:
Quickly discuss structure of the standards.
Lessons, activities and tasks, and assessment items should roll up to the domain and cluster level.

15. Session 2: Coherence
Coherent Tasks
For the following task, name (at least) two different standards, clusters, or domains that are present.
2 min
Take a look at the following task.
(a) do the math
(b) explain which two domains are evident in the task.
What standards and/or clusters are evident in the task?

16. Grade 7 Task Session 2: Coherence 7.EE.2.3 7.EE.2.4 7.RP.2.3 7 min
7 min
THIS SLIDE HAS ANIMATION – BOTTOM STANDARDS COME IN AFTER SOLVING
Try this one.
This problem can be solved with a ratio table or by finding a unit rate, or by using expressions and /or equations.
This problem fosters proportional thinking and lends itself to a discussion of algebraic reasoning, especially if the numbers are substituted for “less clean” ones.
The problem highlights using expressions and equations (7.EE.B.3 and 7.EE.B.4) as well as proportional reasoning (7.RP.A.3).
7.EE.2.3
7.EE.2.4
7.RP.2.3

17. Coherence: The Walkthrough

18. Leading Coherent Implementation
Session 2: Coherence
Leading Coherent Implementation
Does the instruction carefully connect learning across grades so that students can build new understanding onto foundations built in previous years?
Prework:
Determine the domain of focus for the unit/module
Read the corresponding progressions document
Complete instructional rounds with standards app
What to look for:
Are the students who are getting it making connections to previous learning?
For students who are are not getting it, is the teacher leading students to make connections to previous learning?
2 min
To prepare for a walkthrough where coherence across grades is the focus, gather and complete these steps before heading into the classroom.
You will have time to do get this together before we start the video.

19. Leading Coherent Implementation
Session 2: Coherence
Leading Coherent Implementation
Does the instruction carefully connect learning across grades so that students can build new understanding onto foundations built in previous years?
What to ask
Guiding conversations after the walk through:
If students are still not making connections:
Ask: What prerequisite knowledge is a student lacking to be able to make those connections?
Consider: Share time studying the wiring diagram, studying linking standards, with next steps being digging into curriculum for additional lessons on knowledge gaps.
3 min
After the walkthrough, here are questions to ask.

20. Leading Coherent Implementation
Session 2: Coherence
Leading Coherent Implementation
Is the instruction leveraging how the standards were built in how they reinforce a major topic in a grade by utilizing supporting, complementary topics?
How to prepare to look for within-grade coherent instruction
Complete instructional rounds with:
standards app
content emphasis in-hand
What to look for:
Are the non-major work standard(s) that are being taught supporting priority content?
5 min
To prepare for a walkthrough where coherence across grades is the focus, gather and complete these steps before heading into the classroom.
Once in the classroom, look for these cues for coherence across grades.

21. Stop 2 of your instructional rounds
Session 2: Coherence
Stop 2 of your instructional rounds
Prepare to watch the 10 min video
Prepare:
Prework
determine the domain of focus for the unit/module
(instruction in the video is addressing Standard 7.RP.1.2)
read the corresponding progressions document
Complete instructional rounds with standards app content emphasis
5 min to prepare
10 min to view video

22. Stop 2 of your instructional rounds
Session 2: Coherence
Stop 2 of your instructional rounds
Watch the 10 min video
What to look for:
Are the students who are getting it making connections to previous learning?
For students who are are not getting it, is the teacher leading students to make connections to previous learning?
10 min discussion on evidence.
Students getting it: "oh! we're supposed to set it up like a ratio?" "whoa whoa whoa! do you notice the pattern? (writes ratio)" applying knowledge of integers (grade 6)
Question 1 and 2
Students not getting it: T: if i have a third of an x and an x, how many x's do i have? (relating to fraction knowledge) S: 1 1/3x... OH! so that would be 133%!! (applying fractions and percents)

23. After the Walk Through - Questions to Ask
Session 2: Coherence
After the Walk Through - Questions to Ask
Leading the Conversation
•Are the students who are getting it making connections to previous learning?
•For students who are are not getting it, is the teacher leading students to make connections to previous learning?
If students are still not making connections:
•Ask: What prerequisite knowledge is a student lacking to be able to make those connections?
•Consider: study the wiring diagram, study linking standards, with next steps being digging into curriculum for additional lessons on knowledge gaps.
5 min
Standard 7.RP.1.2 is major work. If students are still not making connections: Consider: Share time studying the wiring diagram, studying linking standards, with next steps being digging into curriculum for additional lessons on knowledge gaps. If supporting standards are not linking to major work of the grade: What do the standards say? Same question as before: How can this chosen standard authentically lead students back to working with math content that is to emphasized in this grade? what prerequisite knowledge are students not getting it lacking to be able to make those connections? Ask: what prerequisite knowledge is a student lacking to be able to make those connections?

24. What we’re trying to avoid: blanket review
Session 2: Coherence
What we’re trying to avoid: blanket review

25. Instead, adapt in context:
Session 2: Coherence
Instead, adapt in context:
Use the progressions to add prerequisite standards to all units.
+ X.1, Y.2
+ X.1, Z.5
+ Z.2
+ X.3
+ X.1, Z.5
+ X.1, Y.5
+ X.4, Y.5, Z.6
2. Consider expanding focus on priority content where necessary.

26. Adaptation process for lessons
Session 2: Coherence
Adaptation process for lessons
(1) Adapt lessons to include prerequisite content in the context of grade-level objectives.
Two approaches:
(2) Consider adding additional lessons that address prerequisite content where necessary and appropriate. 5 1 2 3 4 5 6 7

27. Reflection: Coherence
Session 2: Coherence
Reflection: Coherence
Think about Standards implementation in your district:
What is the state of curriculum/planning around coherence in your district?
What are some preliminary steps that are needed to improve the state of coherence in your district?
5 min

28. Take a break…